[www-releases] r233917 - Add llvm docs for 3.5.2

Tom Stellard thomas.stellard at amd.com
Thu Apr 2 07:06:21 PDT 2015


Added: www-releases/trunk/3.5.2/docs/tutorial/OCamlLangImpl6.html
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+  <div class="section" id="kaleidoscope-extending-the-language-user-defined-operators">
+<h1>6. Kaleidoscope: Extending the Language: User-defined Operators<a class="headerlink" href="#kaleidoscope-extending-the-language-user-defined-operators" title="Permalink to this headline">¶</a></h1>
+<div class="contents local topic" id="contents">
+<ul class="simple">
+<li><a class="reference internal" href="#chapter-6-introduction" id="id1">Chapter 6 Introduction</a></li>
+<li><a class="reference internal" href="#user-defined-operators-the-idea" id="id2">User-defined Operators: the Idea</a></li>
+<li><a class="reference internal" href="#user-defined-binary-operators" id="id3">User-defined Binary Operators</a></li>
+<li><a class="reference internal" href="#user-defined-unary-operators" id="id4">User-defined Unary Operators</a></li>
+<li><a class="reference internal" href="#kicking-the-tires" id="id5">Kicking the Tires</a></li>
+<li><a class="reference internal" href="#full-code-listing" id="id6">Full Code Listing</a></li>
+</ul>
+</div>
+<div class="section" id="chapter-6-introduction">
+<h2><a class="toc-backref" href="#id1">6.1. Chapter 6 Introduction</a><a class="headerlink" href="#chapter-6-introduction" title="Permalink to this headline">¶</a></h2>
+<p>Welcome to Chapter 6 of the “<a class="reference external" href="index.html">Implementing a language with
+LLVM</a>” tutorial. At this point in our tutorial, we now
+have a fully functional language that is fairly minimal, but also
+useful. There is still one big problem with it, however. Our language
+doesn’t have many useful operators (like division, logical negation, or
+even any comparisons besides less-than).</p>
+<p>This chapter of the tutorial takes a wild digression into adding
+user-defined operators to the simple and beautiful Kaleidoscope
+language. This digression now gives us a simple and ugly language in
+some ways, but also a powerful one at the same time. One of the great
+things about creating your own language is that you get to decide what
+is good or bad. In this tutorial we’ll assume that it is okay to use
+this as a way to show some interesting parsing techniques.</p>
+<p>At the end of this tutorial, we’ll run through an example Kaleidoscope
+application that <a class="reference external" href="#example">renders the Mandelbrot set</a>. This gives an
+example of what you can build with Kaleidoscope and its feature set.</p>
+</div>
+<div class="section" id="user-defined-operators-the-idea">
+<h2><a class="toc-backref" href="#id2">6.2. User-defined Operators: the Idea</a><a class="headerlink" href="#user-defined-operators-the-idea" title="Permalink to this headline">¶</a></h2>
+<p>The “operator overloading” that we will add to Kaleidoscope is more
+general than languages like C++. In C++, you are only allowed to
+redefine existing operators: you can’t programatically change the
+grammar, introduce new operators, change precedence levels, etc. In this
+chapter, we will add this capability to Kaleidoscope, which will let the
+user round out the set of operators that are supported.</p>
+<p>The point of going into user-defined operators in a tutorial like this
+is to show the power and flexibility of using a hand-written parser.
+Thus far, the parser we have been implementing uses recursive descent
+for most parts of the grammar and operator precedence parsing for the
+expressions. See <a class="reference external" href="OCamlLangImpl2.html">Chapter 2</a> for details. Without
+using operator precedence parsing, it would be very difficult to allow
+the programmer to introduce new operators into the grammar: the grammar
+is dynamically extensible as the JIT runs.</p>
+<p>The two specific features we’ll add are programmable unary operators
+(right now, Kaleidoscope has no unary operators at all) as well as
+binary operators. An example of this is:</p>
+<div class="highlight-python"><pre># Logical unary not.
+def unary!(v)
+  if v then
+    0
+  else
+    1;
+
+# Define > with the same precedence as <.
+def binary> 10 (LHS RHS)
+  RHS < LHS;
+
+# Binary "logical or", (note that it does not "short circuit")
+def binary| 5 (LHS RHS)
+  if LHS then
+    1
+  else if RHS then
+    1
+  else
+    0;
+
+# Define = with slightly lower precedence than relationals.
+def binary= 9 (LHS RHS)
+  !(LHS < RHS | LHS > RHS);</pre>
+</div>
+<p>Many languages aspire to being able to implement their standard runtime
+library in the language itself. In Kaleidoscope, we can implement
+significant parts of the language in the library!</p>
+<p>We will break down implementation of these features into two parts:
+implementing support for user-defined binary operators and adding unary
+operators.</p>
+</div>
+<div class="section" id="user-defined-binary-operators">
+<h2><a class="toc-backref" href="#id3">6.3. User-defined Binary Operators</a><a class="headerlink" href="#user-defined-binary-operators" title="Permalink to this headline">¶</a></h2>
+<p>Adding support for user-defined binary operators is pretty simple with
+our current framework. We’ll first add support for the unary/binary
+keywords:</p>
+<div class="highlight-ocaml"><div class="highlight"><pre><span class="k">type</span> <span class="n">token</span> <span class="o">=</span>
+  <span class="o">...</span>
+  <span class="c">(* operators *)</span>
+  <span class="o">|</span> <span class="nc">Binary</span> <span class="o">|</span> <span class="nn">Unary</span>
+
+<span class="p">...</span>
+
+<span class="n">and</span> <span class="n">lex_ident</span> <span class="n">buffer</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="o">...</span>
+      <span class="o">|</span> <span class="s2">"for"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">For</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+      <span class="o">|</span> <span class="s2">"in"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">In</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+      <span class="o">|</span> <span class="s2">"binary"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Binary</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+      <span class="o">|</span> <span class="s2">"unary"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Unary</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+</pre></div>
+</div>
+<p>This just adds lexer support for the unary and binary keywords, like we
+did in <a class="reference external" href="OCamlLangImpl5.html#iflexer">previous chapters</a>. One nice
+thing about our current AST, is that we represent binary operators with
+full generalisation by using their ASCII code as the opcode. For our
+extended operators, we’ll use this same representation, so we don’t need
+any new AST or parser support.</p>
+<p>On the other hand, we have to be able to represent the definitions of
+these new operators, in the “def binary| 5” part of the function
+definition. In our grammar so far, the “name” for the function
+definition is parsed as the “prototype” production and into the
+<tt class="docutils literal"><span class="pre">Ast.Prototype</span></tt> AST node. To represent our new user-defined operators
+as prototypes, we have to extend the <tt class="docutils literal"><span class="pre">Ast.Prototype</span></tt> AST node like
+this:</p>
+<div class="highlight-ocaml"><div class="highlight"><pre><span class="c">(* proto - This type represents the "prototype" for a function, which captures</span>
+<span class="c"> * its name, and its argument names (thus implicitly the number of arguments the</span>
+<span class="c"> * function takes). *)</span>
+<span class="k">type</span> <span class="n">proto</span> <span class="o">=</span>
+  <span class="o">|</span> <span class="nc">Prototype</span> <span class="k">of</span> <span class="kt">string</span> <span class="o">*</span> <span class="kt">string</span> <span class="kt">array</span>
+  <span class="o">|</span> <span class="nc">BinOpPrototype</span> <span class="k">of</span> <span class="kt">string</span> <span class="o">*</span> <span class="kt">string</span> <span class="kt">array</span> <span class="o">*</span> <span class="kt">int</span>
+</pre></div>
+</div>
+<p>Basically, in addition to knowing a name for the prototype, we now keep
+track of whether it was an operator, and if it was, what precedence
+level the operator is at. The precedence is only used for binary
+operators (as you’ll see below, it just doesn’t apply for unary
+operators). Now that we have a way to represent the prototype for a
+user-defined operator, we need to parse it:</p>
+<div class="highlight-ocaml"><div class="highlight"><pre><span class="c">(* prototype</span>
+<span class="c"> *   ::= id '(' id* ')'</span>
+<span class="c"> *   ::= binary LETTER number? (id, id)</span>
+<span class="c"> *   ::= unary LETTER number? (id) *)</span>
+<span class="k">let</span> <span class="n">parse_prototype</span> <span class="o">=</span>
+  <span class="k">let</span> <span class="k">rec</span> <span class="n">parse_args</span> <span class="n">accumulator</span> <span class="o">=</span> <span class="n">parser</span>
+    <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Ident</span> <span class="n">id</span><span class="o">;</span> <span class="n">e</span><span class="o">=</span><span class="n">parse_args</span> <span class="o">(</span><span class="n">id</span><span class="o">::</span><span class="n">accumulator</span><span class="o">)</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">e</span>
+    <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">accumulator</span>
+  <span class="k">in</span>
+  <span class="k">let</span> <span class="n">parse_operator</span> <span class="o">=</span> <span class="n">parser</span>
+    <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Unary</span> <span class="o">>]</span> <span class="o">-></span> <span class="s2">"unary"</span><span class="o">,</span> <span class="mi">1</span>
+    <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Binary</span> <span class="o">>]</span> <span class="o">-></span> <span class="s2">"binary"</span><span class="o">,</span> <span class="mi">2</span>
+  <span class="k">in</span>
+  <span class="k">let</span> <span class="n">parse_binary_precedence</span> <span class="o">=</span> <span class="n">parser</span>
+    <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Number</span> <span class="n">n</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">int_of_float</span> <span class="n">n</span>
+    <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span> <span class="mi">30</span>
+  <span class="k">in</span>
+  <span class="n">parser</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Ident</span> <span class="n">id</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">'('</span> <span class="o">??</span> <span class="s2">"expected '(' in prototype"</span><span class="o">;</span>
+       <span class="n">args</span><span class="o">=</span><span class="n">parse_args</span> <span class="bp">[]</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">')'</span> <span class="o">??</span> <span class="s2">"expected ')' in prototype"</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="c">(* success. *)</span>
+      <span class="nn">Ast</span><span class="p">.</span><span class="nc">Prototype</span> <span class="o">(</span><span class="n">id</span><span class="o">,</span> <span class="nn">Array</span><span class="p">.</span><span class="n">of_list</span> <span class="o">(</span><span class="nn">List</span><span class="p">.</span><span class="n">rev</span> <span class="n">args</span><span class="o">))</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="o">(</span><span class="n">prefix</span><span class="o">,</span> <span class="n">kind</span><span class="o">)=</span><span class="n">parse_operator</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="n">op</span> <span class="o">??</span> <span class="s2">"expected an operator"</span><span class="o">;</span>
+       <span class="c">(* Read the precedence if present. *)</span>
+       <span class="n">binary_precedence</span><span class="o">=</span><span class="n">parse_binary_precedence</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">'('</span> <span class="o">??</span> <span class="s2">"expected '(' in prototype"</span><span class="o">;</span>
+        <span class="n">args</span><span class="o">=</span><span class="n">parse_args</span> <span class="bp">[]</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">')'</span> <span class="o">??</span> <span class="s2">"expected ')' in prototype"</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="k">let</span> <span class="n">name</span> <span class="o">=</span> <span class="n">prefix</span> <span class="o">^</span> <span class="o">(</span><span class="nn">String</span><span class="p">.</span><span class="n">make</span> <span class="mi">1</span> <span class="n">op</span><span class="o">)</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">args</span> <span class="o">=</span> <span class="nn">Array</span><span class="p">.</span><span class="n">of_list</span> <span class="o">(</span><span class="nn">List</span><span class="p">.</span><span class="n">rev</span> <span class="n">args</span><span class="o">)</span> <span class="k">in</span>
+
+      <span class="c">(* Verify right number of arguments for operator. *)</span>
+      <span class="k">if</span> <span class="nn">Array</span><span class="p">.</span><span class="n">length</span> <span class="n">args</span> <span class="o">!=</span> <span class="n">kind</span>
+      <span class="k">then</span> <span class="k">raise</span> <span class="o">(</span><span class="nn">Stream</span><span class="p">.</span><span class="nc">Error</span> <span class="s2">"invalid number of operands for operator"</span><span class="o">)</span>
+      <span class="k">else</span>
+        <span class="k">if</span> <span class="n">kind</span> <span class="o">==</span> <span class="mi">1</span> <span class="k">then</span>
+          <span class="nn">Ast</span><span class="p">.</span><span class="nc">Prototype</span> <span class="o">(</span><span class="n">name</span><span class="o">,</span> <span class="n">args</span><span class="o">)</span>
+        <span class="k">else</span>
+          <span class="nn">Ast</span><span class="p">.</span><span class="nc">BinOpPrototype</span> <span class="o">(</span><span class="n">name</span><span class="o">,</span> <span class="n">args</span><span class="o">,</span> <span class="n">binary_precedence</span><span class="o">)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="k">raise</span> <span class="o">(</span><span class="nn">Stream</span><span class="p">.</span><span class="nc">Error</span> <span class="s2">"expected function name in prototype"</span><span class="o">)</span>
+</pre></div>
+</div>
+<p>This is all fairly straightforward parsing code, and we have already
+seen a lot of similar code in the past. One interesting part about the
+code above is the couple lines that set up <tt class="docutils literal"><span class="pre">name</span></tt> for binary
+operators. This builds names like “binary@” for a newly defined “@”
+operator. This then takes advantage of the fact that symbol names in the
+LLVM symbol table are allowed to have any character in them, including
+embedded nul characters.</p>
+<p>The next interesting thing to add, is codegen support for these binary
+operators. Given our current structure, this is a simple addition of a
+default case for our existing binary operator node:</p>
+<div class="highlight-ocaml"><div class="highlight"><pre><span class="k">let</span> <span class="n">codegen_expr</span> <span class="o">=</span> <span class="k">function</span>
+  <span class="o">...</span>
+  <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Binary</span> <span class="o">(</span><span class="n">op</span><span class="o">,</span> <span class="n">lhs</span><span class="o">,</span> <span class="n">rhs</span><span class="o">)</span> <span class="o">-></span>
+      <span class="k">let</span> <span class="n">lhs_val</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">lhs</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">rhs_val</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">rhs</span> <span class="k">in</span>
+      <span class="k">begin</span>
+        <span class="k">match</span> <span class="n">op</span> <span class="k">with</span>
+        <span class="o">|</span> <span class="sc">'+'</span> <span class="o">-></span> <span class="n">build_add</span> <span class="n">lhs_val</span> <span class="n">rhs_val</span> <span class="s2">"addtmp"</span> <span class="n">builder</span>
+        <span class="o">|</span> <span class="sc">'-'</span> <span class="o">-></span> <span class="n">build_sub</span> <span class="n">lhs_val</span> <span class="n">rhs_val</span> <span class="s2">"subtmp"</span> <span class="n">builder</span>
+        <span class="o">|</span> <span class="sc">'*'</span> <span class="o">-></span> <span class="n">build_mul</span> <span class="n">lhs_val</span> <span class="n">rhs_val</span> <span class="s2">"multmp"</span> <span class="n">builder</span>
+        <span class="o">|</span> <span class="sc">'<'</span> <span class="o">-></span>
+            <span class="c">(* Convert bool 0/1 to double 0.0 or 1.0 *)</span>
+            <span class="k">let</span> <span class="n">i</span> <span class="o">=</span> <span class="n">build_fcmp</span> <span class="nn">Fcmp</span><span class="p">.</span><span class="nc">Ult</span> <span class="n">lhs_val</span> <span class="n">rhs_val</span> <span class="s2">"cmptmp"</span> <span class="n">builder</span> <span class="k">in</span>
+            <span class="n">build_uitofp</span> <span class="n">i</span> <span class="n">double_type</span> <span class="s2">"booltmp"</span> <span class="n">builder</span>
+        <span class="o">|</span> <span class="o">_</span> <span class="o">-></span>
+            <span class="c">(* If it wasn't a builtin binary operator, it must be a user defined</span>
+<span class="c">             * one. Emit a call to it. *)</span>
+            <span class="k">let</span> <span class="n">callee</span> <span class="o">=</span> <span class="s2">"binary"</span> <span class="o">^</span> <span class="o">(</span><span class="nn">String</span><span class="p">.</span><span class="n">make</span> <span class="mi">1</span> <span class="n">op</span><span class="o">)</span> <span class="k">in</span>
+            <span class="k">let</span> <span class="n">callee</span> <span class="o">=</span>
+              <span class="k">match</span> <span class="n">lookup_function</span> <span class="n">callee</span> <span class="n">the_module</span> <span class="k">with</span>
+              <span class="o">|</span> <span class="nc">Some</span> <span class="n">callee</span> <span class="o">-></span> <span class="n">callee</span>
+              <span class="o">|</span> <span class="nc">None</span> <span class="o">-></span> <span class="k">raise</span> <span class="o">(</span><span class="nc">Error</span> <span class="s2">"binary operator not found!"</span><span class="o">)</span>
+            <span class="k">in</span>
+            <span class="n">build_call</span> <span class="n">callee</span> <span class="o">[|</span><span class="n">lhs_val</span><span class="o">;</span> <span class="n">rhs_val</span><span class="o">|]</span> <span class="s2">"binop"</span> <span class="n">builder</span>
+      <span class="k">end</span>
+</pre></div>
+</div>
+<p>As you can see above, the new code is actually really simple. It just
+does a lookup for the appropriate operator in the symbol table and
+generates a function call to it. Since user-defined operators are just
+built as normal functions (because the “prototype” boils down to a
+function with the right name) everything falls into place.</p>
+<p>The final piece of code we are missing, is a bit of top level magic:</p>
+<div class="highlight-ocaml"><div class="highlight"><pre><span class="k">let</span> <span class="n">codegen_func</span> <span class="n">the_fpm</span> <span class="o">=</span> <span class="k">function</span>
+  <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Function</span> <span class="o">(</span><span class="n">proto</span><span class="o">,</span> <span class="n">body</span><span class="o">)</span> <span class="o">-></span>
+      <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">clear</span> <span class="n">named_values</span><span class="o">;</span>
+      <span class="k">let</span> <span class="n">the_function</span> <span class="o">=</span> <span class="n">codegen_proto</span> <span class="n">proto</span> <span class="k">in</span>
+
+      <span class="c">(* If this is an operator, install it. *)</span>
+      <span class="k">begin</span> <span class="k">match</span> <span class="n">proto</span> <span class="k">with</span>
+      <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">BinOpPrototype</span> <span class="o">(</span><span class="n">name</span><span class="o">,</span> <span class="n">args</span><span class="o">,</span> <span class="n">prec</span><span class="o">)</span> <span class="o">-></span>
+          <span class="k">let</span> <span class="n">op</span> <span class="o">=</span> <span class="n">name</span><span class="o">.[</span><span class="nn">String</span><span class="p">.</span><span class="n">length</span> <span class="n">name</span> <span class="o">-</span> <span class="mi">1</span><span class="o">]</span> <span class="k">in</span>
+          <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="nn">Parser</span><span class="p">.</span><span class="n">binop_precedence</span> <span class="n">op</span> <span class="n">prec</span><span class="o">;</span>
+      <span class="o">|</span> <span class="o">_</span> <span class="o">-></span> <span class="bp">()</span>
+      <span class="k">end</span><span class="o">;</span>
+
+      <span class="c">(* Create a new basic block to start insertion into. *)</span>
+      <span class="k">let</span> <span class="n">bb</span> <span class="o">=</span> <span class="n">append_block</span> <span class="n">context</span> <span class="s2">"entry"</span> <span class="n">the_function</span> <span class="k">in</span>
+      <span class="n">position_at_end</span> <span class="n">bb</span> <span class="n">builder</span><span class="o">;</span>
+      <span class="o">...</span>
+</pre></div>
+</div>
+<p>Basically, before codegening a function, if it is a user-defined
+operator, we register it in the precedence table. This allows the binary
+operator parsing logic we already have in place to handle it. Since we
+are working on a fully-general operator precedence parser, this is all
+we need to do to “extend the grammar”.</p>
+<p>Now we have useful user-defined binary operators. This builds a lot on
+the previous framework we built for other operators. Adding unary
+operators is a bit more challenging, because we don’t have any framework
+for it yet - lets see what it takes.</p>
+</div>
+<div class="section" id="user-defined-unary-operators">
+<h2><a class="toc-backref" href="#id4">6.4. User-defined Unary Operators</a><a class="headerlink" href="#user-defined-unary-operators" title="Permalink to this headline">¶</a></h2>
+<p>Since we don’t currently support unary operators in the Kaleidoscope
+language, we’ll need to add everything to support them. Above, we added
+simple support for the ‘unary’ keyword to the lexer. In addition to
+that, we need an AST node:</p>
+<div class="highlight-ocaml"><div class="highlight"><pre><span class="k">type</span> <span class="n">expr</span> <span class="o">=</span>
+  <span class="o">...</span>
+  <span class="c">(* variant for a unary operator. *)</span>
+  <span class="o">|</span> <span class="nc">Unary</span> <span class="k">of</span> <span class="kt">char</span> <span class="o">*</span> <span class="n">expr</span>
+  <span class="o">...</span>
+</pre></div>
+</div>
+<p>This AST node is very simple and obvious by now. It directly mirrors the
+binary operator AST node, except that it only has one child. With this,
+we need to add the parsing logic. Parsing a unary operator is pretty
+simple: we’ll add a new function to do it:</p>
+<div class="highlight-ocaml"><div class="highlight"><pre><span class="c">(* unary</span>
+<span class="c"> *   ::= primary</span>
+<span class="c"> *   ::= '!' unary *)</span>
+<span class="ow">and</span> <span class="n">parse_unary</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="c">(* If this is a unary operator, read it. *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="n">op</span> <span class="k">when</span> <span class="n">op</span> <span class="o">!=</span> <span class="sc">'('</span> <span class="o">&&</span> <span class="n">op</span> <span class="o">!=</span> <span class="sc">')'</span><span class="o">;</span> <span class="n">operand</span><span class="o">=</span><span class="n">parse_expr</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="nn">Ast</span><span class="p">.</span><span class="nc">Unary</span> <span class="o">(</span><span class="n">op</span><span class="o">,</span> <span class="n">operand</span><span class="o">)</span>
+
+  <span class="c">(* If the current token is not an operator, it must be a primary expr. *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">parse_primary</span> <span class="n">stream</span>
+</pre></div>
+</div>
+<p>The grammar we add is pretty straightforward here. If we see a unary
+operator when parsing a primary operator, we eat the operator as a
+prefix and parse the remaining piece as another unary operator. This
+allows us to handle multiple unary operators (e.g. ”!!x”). Note that
+unary operators can’t have ambiguous parses like binary operators can,
+so there is no need for precedence information.</p>
+<p>The problem with this function, is that we need to call ParseUnary from
+somewhere. To do this, we change previous callers of ParsePrimary to
+call <tt class="docutils literal"><span class="pre">parse_unary</span></tt> instead:</p>
+<div class="highlight-ocaml"><div class="highlight"><pre><span class="c">(* binoprhs</span>
+<span class="c"> *   ::= ('+' primary)* *)</span>
+<span class="ow">and</span> <span class="n">parse_bin_rhs</span> <span class="n">expr_prec</span> <span class="n">lhs</span> <span class="n">stream</span> <span class="o">=</span>
+        <span class="o">...</span>
+        <span class="c">(* Parse the unary expression after the binary operator. *)</span>
+        <span class="k">let</span> <span class="n">rhs</span> <span class="o">=</span> <span class="n">parse_unary</span> <span class="n">stream</span> <span class="k">in</span>
+        <span class="o">...</span>
+
+<span class="o">...</span>
+
+<span class="c">(* expression</span>
+<span class="c"> *   ::= primary binoprhs *)</span>
+<span class="ow">and</span> <span class="n">parse_expr</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="n">lhs</span><span class="o">=</span><span class="n">parse_unary</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">parse_bin_rhs</span> <span class="mi">0</span> <span class="n">lhs</span> <span class="n">stream</span>
+</pre></div>
+</div>
+<p>With these two simple changes, we are now able to parse unary operators
+and build the AST for them. Next up, we need to add parser support for
+prototypes, to parse the unary operator prototype. We extend the binary
+operator code above with:</p>
+<div class="highlight-ocaml"><div class="highlight"><pre><span class="c">(* prototype</span>
+<span class="c"> *   ::= id '(' id* ')'</span>
+<span class="c"> *   ::= binary LETTER number? (id, id)</span>
+<span class="c"> *   ::= unary LETTER number? (id) *)</span>
+<span class="k">let</span> <span class="n">parse_prototype</span> <span class="o">=</span>
+  <span class="k">let</span> <span class="k">rec</span> <span class="n">parse_args</span> <span class="n">accumulator</span> <span class="o">=</span> <span class="n">parser</span>
+    <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Ident</span> <span class="n">id</span><span class="o">;</span> <span class="n">e</span><span class="o">=</span><span class="n">parse_args</span> <span class="o">(</span><span class="n">id</span><span class="o">::</span><span class="n">accumulator</span><span class="o">)</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">e</span>
+    <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">accumulator</span>
+  <span class="k">in</span>
+  <span class="k">let</span> <span class="n">parse_operator</span> <span class="o">=</span> <span class="n">parser</span>
+    <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Unary</span> <span class="o">>]</span> <span class="o">-></span> <span class="s2">"unary"</span><span class="o">,</span> <span class="mi">1</span>
+    <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Binary</span> <span class="o">>]</span> <span class="o">-></span> <span class="s2">"binary"</span><span class="o">,</span> <span class="mi">2</span>
+  <span class="k">in</span>
+  <span class="k">let</span> <span class="n">parse_binary_precedence</span> <span class="o">=</span> <span class="n">parser</span>
+    <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Number</span> <span class="n">n</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">int_of_float</span> <span class="n">n</span>
+    <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span> <span class="mi">30</span>
+  <span class="k">in</span>
+  <span class="n">parser</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Ident</span> <span class="n">id</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">'('</span> <span class="o">??</span> <span class="s2">"expected '(' in prototype"</span><span class="o">;</span>
+       <span class="n">args</span><span class="o">=</span><span class="n">parse_args</span> <span class="bp">[]</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">')'</span> <span class="o">??</span> <span class="s2">"expected ')' in prototype"</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="c">(* success. *)</span>
+      <span class="nn">Ast</span><span class="p">.</span><span class="nc">Prototype</span> <span class="o">(</span><span class="n">id</span><span class="o">,</span> <span class="nn">Array</span><span class="p">.</span><span class="n">of_list</span> <span class="o">(</span><span class="nn">List</span><span class="p">.</span><span class="n">rev</span> <span class="n">args</span><span class="o">))</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="o">(</span><span class="n">prefix</span><span class="o">,</span> <span class="n">kind</span><span class="o">)=</span><span class="n">parse_operator</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="n">op</span> <span class="o">??</span> <span class="s2">"expected an operator"</span><span class="o">;</span>
+       <span class="c">(* Read the precedence if present. *)</span>
+       <span class="n">binary_precedence</span><span class="o">=</span><span class="n">parse_binary_precedence</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">'('</span> <span class="o">??</span> <span class="s2">"expected '(' in prototype"</span><span class="o">;</span>
+        <span class="n">args</span><span class="o">=</span><span class="n">parse_args</span> <span class="bp">[]</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">')'</span> <span class="o">??</span> <span class="s2">"expected ')' in prototype"</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="k">let</span> <span class="n">name</span> <span class="o">=</span> <span class="n">prefix</span> <span class="o">^</span> <span class="o">(</span><span class="nn">String</span><span class="p">.</span><span class="n">make</span> <span class="mi">1</span> <span class="n">op</span><span class="o">)</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">args</span> <span class="o">=</span> <span class="nn">Array</span><span class="p">.</span><span class="n">of_list</span> <span class="o">(</span><span class="nn">List</span><span class="p">.</span><span class="n">rev</span> <span class="n">args</span><span class="o">)</span> <span class="k">in</span>
+
+      <span class="c">(* Verify right number of arguments for operator. *)</span>
+      <span class="k">if</span> <span class="nn">Array</span><span class="p">.</span><span class="n">length</span> <span class="n">args</span> <span class="o">!=</span> <span class="n">kind</span>
+      <span class="k">then</span> <span class="k">raise</span> <span class="o">(</span><span class="nn">Stream</span><span class="p">.</span><span class="nc">Error</span> <span class="s2">"invalid number of operands for operator"</span><span class="o">)</span>
+      <span class="k">else</span>
+        <span class="k">if</span> <span class="n">kind</span> <span class="o">==</span> <span class="mi">1</span> <span class="k">then</span>
+          <span class="nn">Ast</span><span class="p">.</span><span class="nc">Prototype</span> <span class="o">(</span><span class="n">name</span><span class="o">,</span> <span class="n">args</span><span class="o">)</span>
+        <span class="k">else</span>
+          <span class="nn">Ast</span><span class="p">.</span><span class="nc">BinOpPrototype</span> <span class="o">(</span><span class="n">name</span><span class="o">,</span> <span class="n">args</span><span class="o">,</span> <span class="n">binary_precedence</span><span class="o">)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="k">raise</span> <span class="o">(</span><span class="nn">Stream</span><span class="p">.</span><span class="nc">Error</span> <span class="s2">"expected function name in prototype"</span><span class="o">)</span>
+</pre></div>
+</div>
+<p>As with binary operators, we name unary operators with a name that
+includes the operator character. This assists us at code generation
+time. Speaking of, the final piece we need to add is codegen support for
+unary operators. It looks like this:</p>
+<div class="highlight-ocaml"><div class="highlight"><pre><span class="k">let</span> <span class="k">rec</span> <span class="n">codegen_expr</span> <span class="o">=</span> <span class="k">function</span>
+  <span class="o">...</span>
+  <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Unary</span> <span class="o">(</span><span class="n">op</span><span class="o">,</span> <span class="n">operand</span><span class="o">)</span> <span class="o">-></span>
+      <span class="k">let</span> <span class="n">operand</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">operand</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">callee</span> <span class="o">=</span> <span class="s2">"unary"</span> <span class="o">^</span> <span class="o">(</span><span class="nn">String</span><span class="p">.</span><span class="n">make</span> <span class="mi">1</span> <span class="n">op</span><span class="o">)</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">callee</span> <span class="o">=</span>
+        <span class="k">match</span> <span class="n">lookup_function</span> <span class="n">callee</span> <span class="n">the_module</span> <span class="k">with</span>
+        <span class="o">|</span> <span class="nc">Some</span> <span class="n">callee</span> <span class="o">-></span> <span class="n">callee</span>
+        <span class="o">|</span> <span class="nc">None</span> <span class="o">-></span> <span class="k">raise</span> <span class="o">(</span><span class="nc">Error</span> <span class="s2">"unknown unary operator"</span><span class="o">)</span>
+      <span class="k">in</span>
+      <span class="n">build_call</span> <span class="n">callee</span> <span class="o">[|</span><span class="n">operand</span><span class="o">|]</span> <span class="s2">"unop"</span> <span class="n">builder</span>
+</pre></div>
+</div>
+<p>This code is similar to, but simpler than, the code for binary
+operators. It is simpler primarily because it doesn’t need to handle any
+predefined operators.</p>
+</div>
+<div class="section" id="kicking-the-tires">
+<h2><a class="toc-backref" href="#id5">6.5. Kicking the Tires</a><a class="headerlink" href="#kicking-the-tires" title="Permalink to this headline">¶</a></h2>
+<p>It is somewhat hard to believe, but with a few simple extensions we’ve
+covered in the last chapters, we have grown a real-ish language. With
+this, we can do a lot of interesting things, including I/O, math, and a
+bunch of other things. For example, we can now add a nice sequencing
+operator (printd is defined to print out the specified value and a
+newline):</p>
+<div class="highlight-python"><pre>ready> extern printd(x);
+Read extern: declare double @printd(double)
+ready> def binary : 1 (x y) 0;  # Low-precedence operator that ignores operands.
+..
+ready> printd(123) : printd(456) : printd(789);
+123.000000
+456.000000
+789.000000
+Evaluated to 0.000000</pre>
+</div>
+<p>We can also define a bunch of other “primitive” operations, such as:</p>
+<div class="highlight-python"><pre># Logical unary not.
+def unary!(v)
+  if v then
+    0
+  else
+    1;
+
+# Unary negate.
+def unary-(v)
+  0-v;
+
+# Define > with the same precedence as <.
+def binary> 10 (LHS RHS)
+  RHS < LHS;
+
+# Binary logical or, which does not short circuit.
+def binary| 5 (LHS RHS)
+  if LHS then
+    1
+  else if RHS then
+    1
+  else
+    0;
+
+# Binary logical and, which does not short circuit.
+def binary& 6 (LHS RHS)
+  if !LHS then
+    0
+  else
+    !!RHS;
+
+# Define = with slightly lower precedence than relationals.
+def binary = 9 (LHS RHS)
+  !(LHS < RHS | LHS > RHS);</pre>
+</div>
+<p>Given the previous if/then/else support, we can also define interesting
+functions for I/O. For example, the following prints out a character
+whose “density” reflects the value passed in: the lower the value, the
+denser the character:</p>
+<div class="highlight-python"><pre>ready>
+
+extern putchard(char)
+def printdensity(d)
+  if d > 8 then
+    putchard(32)  # ' '
+  else if d > 4 then
+    putchard(46)  # '.'
+  else if d > 2 then
+    putchard(43)  # '+'
+  else
+    putchard(42); # '*'
+...
+ready> printdensity(1): printdensity(2): printdensity(3) :
+          printdensity(4): printdensity(5): printdensity(9): putchard(10);
+*++..
+Evaluated to 0.000000</pre>
+</div>
+<p>Based on these simple primitive operations, we can start to define more
+interesting things. For example, here’s a little function that solves
+for the number of iterations it takes a function in the complex plane to
+converge:</p>
+<div class="highlight-python"><pre># determine whether the specific location diverges.
+# Solve for z = z^2 + c in the complex plane.
+def mandleconverger(real imag iters creal cimag)
+  if iters > 255 | (real*real + imag*imag > 4) then
+    iters
+  else
+    mandleconverger(real*real - imag*imag + creal,
+                    2*real*imag + cimag,
+                    iters+1, creal, cimag);
+
+# return the number of iterations required for the iteration to escape
+def mandleconverge(real imag)
+  mandleconverger(real, imag, 0, real, imag);</pre>
+</div>
+<p>This “z = z<sup>2</sup> + c” function is a beautiful little creature
+that is the basis for computation of the <a class="reference external" href="http://en.wikipedia.org/wiki/Mandelbrot_set">Mandelbrot
+Set</a>. Our
+<tt class="docutils literal"><span class="pre">mandelconverge</span></tt> function returns the number of iterations that it
+takes for a complex orbit to escape, saturating to 255. This is not a
+very useful function by itself, but if you plot its value over a
+two-dimensional plane, you can see the Mandelbrot set. Given that we are
+limited to using putchard here, our amazing graphical output is limited,
+but we can whip together something using the density plotter above:</p>
+<div class="highlight-python"><pre># compute and plot the mandlebrot set with the specified 2 dimensional range
+# info.
+def mandelhelp(xmin xmax xstep   ymin ymax ystep)
+  for y = ymin, y < ymax, ystep in (
+    (for x = xmin, x < xmax, xstep in
+       printdensity(mandleconverge(x,y)))
+    : putchard(10)
+  )
+
+# mandel - This is a convenient helper function for plotting the mandelbrot set
+# from the specified position with the specified Magnification.
+def mandel(realstart imagstart realmag imagmag)
+  mandelhelp(realstart, realstart+realmag*78, realmag,
+             imagstart, imagstart+imagmag*40, imagmag);</pre>
+</div>
+<p>Given this, we can try plotting out the mandlebrot set! Lets try it out:</p>
+<div class="highlight-python"><pre>ready> mandel(-2.3, -1.3, 0.05, 0.07);
+*******************************+++++++++++*************************************
+*************************+++++++++++++++++++++++*******************************
+**********************+++++++++++++++++++++++++++++****************************
+*******************+++++++++++++++++++++.. ...++++++++*************************
+*****************++++++++++++++++++++++.... ...+++++++++***********************
+***************+++++++++++++++++++++++.....   ...+++++++++*********************
+**************+++++++++++++++++++++++....     ....+++++++++********************
+*************++++++++++++++++++++++......      .....++++++++*******************
+************+++++++++++++++++++++.......       .......+++++++******************
+***********+++++++++++++++++++....                ... .+++++++*****************
+**********+++++++++++++++++.......                     .+++++++****************
+*********++++++++++++++...........                    ...+++++++***************
+********++++++++++++............                      ...++++++++**************
+********++++++++++... ..........                        .++++++++**************
+*******+++++++++.....                                   .+++++++++*************
+*******++++++++......                                  ..+++++++++*************
+*******++++++.......                                   ..+++++++++*************
+*******+++++......                                     ..+++++++++*************
+*******.... ....                                      ...+++++++++*************
+*******.... .                                         ...+++++++++*************
+*******+++++......                                    ...+++++++++*************
+*******++++++.......                                   ..+++++++++*************
+*******++++++++......                                   .+++++++++*************
+*******+++++++++.....                                  ..+++++++++*************
+********++++++++++... ..........                        .++++++++**************
+********++++++++++++............                      ...++++++++**************
+*********++++++++++++++..........                     ...+++++++***************
+**********++++++++++++++++........                     .+++++++****************
+**********++++++++++++++++++++....                ... ..+++++++****************
+***********++++++++++++++++++++++.......       .......++++++++*****************
+************+++++++++++++++++++++++......      ......++++++++******************
+**************+++++++++++++++++++++++....      ....++++++++********************
+***************+++++++++++++++++++++++.....   ...+++++++++*********************
+*****************++++++++++++++++++++++....  ...++++++++***********************
+*******************+++++++++++++++++++++......++++++++*************************
+*********************++++++++++++++++++++++.++++++++***************************
+*************************+++++++++++++++++++++++*******************************
+******************************+++++++++++++************************************
+*******************************************************************************
+*******************************************************************************
+*******************************************************************************
+Evaluated to 0.000000
+ready> mandel(-2, -1, 0.02, 0.04);
+**************************+++++++++++++++++++++++++++++++++++++++++++++++++++++
+***********************++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+*********************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++.
+*******************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++...
+*****************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++.....
+***************++++++++++++++++++++++++++++++++++++++++++++++++++++++++........
+**************++++++++++++++++++++++++++++++++++++++++++++++++++++++...........
+************+++++++++++++++++++++++++++++++++++++++++++++++++++++..............
+***********++++++++++++++++++++++++++++++++++++++++++++++++++........        .
+**********++++++++++++++++++++++++++++++++++++++++++++++.............
+********+++++++++++++++++++++++++++++++++++++++++++..................
+*******+++++++++++++++++++++++++++++++++++++++.......................
+******+++++++++++++++++++++++++++++++++++...........................
+*****++++++++++++++++++++++++++++++++............................
+*****++++++++++++++++++++++++++++...............................
+****++++++++++++++++++++++++++......   .........................
+***++++++++++++++++++++++++.........     ......    ...........
+***++++++++++++++++++++++............
+**+++++++++++++++++++++..............
+**+++++++++++++++++++................
+*++++++++++++++++++.................
+*++++++++++++++++............ ...
+*++++++++++++++..............
+*+++....++++................
+*..........  ...........
+*
+*..........  ...........
+*+++....++++................
+*++++++++++++++..............
+*++++++++++++++++............ ...
+*++++++++++++++++++.................
+**+++++++++++++++++++................
+**+++++++++++++++++++++..............
+***++++++++++++++++++++++............
+***++++++++++++++++++++++++.........     ......    ...........
+****++++++++++++++++++++++++++......   .........................
+*****++++++++++++++++++++++++++++...............................
+*****++++++++++++++++++++++++++++++++............................
+******+++++++++++++++++++++++++++++++++++...........................
+*******+++++++++++++++++++++++++++++++++++++++.......................
+********+++++++++++++++++++++++++++++++++++++++++++..................
+Evaluated to 0.000000
+ready> mandel(-0.9, -1.4, 0.02, 0.03);
+*******************************************************************************
+*******************************************************************************
+*******************************************************************************
+**********+++++++++++++++++++++************************************************
+*+++++++++++++++++++++++++++++++++++++++***************************************
++++++++++++++++++++++++++++++++++++++++++++++**********************************
+++++++++++++++++++++++++++++++++++++++++++++++++++*****************************
+++++++++++++++++++++++++++++++++++++++++++++++++++++++*************************
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++**********************
++++++++++++++++++++++++++++++++++.........++++++++++++++++++*******************
++++++++++++++++++++++++++++++++....   ......+++++++++++++++++++****************
++++++++++++++++++++++++++++++.......  ........+++++++++++++++++++**************
+++++++++++++++++++++++++++++........   ........++++++++++++++++++++************
++++++++++++++++++++++++++++.........     ..  ...+++++++++++++++++++++**********
+++++++++++++++++++++++++++...........        ....++++++++++++++++++++++********
+++++++++++++++++++++++++.............       .......++++++++++++++++++++++******
++++++++++++++++++++++++.............        ........+++++++++++++++++++++++****
+++++++++++++++++++++++...........           ..........++++++++++++++++++++++***
+++++++++++++++++++++...........                .........++++++++++++++++++++++*
+++++++++++++++++++............                  ...........++++++++++++++++++++
+++++++++++++++++...............                 .............++++++++++++++++++
+++++++++++++++.................                 ...............++++++++++++++++
+++++++++++++..................                  .................++++++++++++++
++++++++++..................                      .................+++++++++++++
+++++++........        .                               .........  ..++++++++++++
+++............                                         ......    ....++++++++++
+..............                                                    ...++++++++++
+..............                                                    ....+++++++++
+..............                                                    .....++++++++
+.............                                                    ......++++++++
+...........                                                     .......++++++++
+.........                                                       ........+++++++
+.........                                                       ........+++++++
+.........                                                           ....+++++++
+........                                                             ...+++++++
+.......                                                              ...+++++++
+                                                                    ....+++++++
+                                                                   .....+++++++
+                                                                    ....+++++++
+                                                                    ....+++++++
+                                                                    ....+++++++
+Evaluated to 0.000000
+ready> ^D</pre>
+</div>
+<p>At this point, you may be starting to realize that Kaleidoscope is a
+real and powerful language. It may not be self-similar :), but it can be
+used to plot things that are!</p>
+<p>With this, we conclude the “adding user-defined operators” chapter of
+the tutorial. We have successfully augmented our language, adding the
+ability to extend the language in the library, and we have shown how
+this can be used to build a simple but interesting end-user application
+in Kaleidoscope. At this point, Kaleidoscope can build a variety of
+applications that are functional and can call functions with
+side-effects, but it can’t actually define and mutate a variable itself.</p>
+<p>Strikingly, variable mutation is an important feature of some languages,
+and it is not at all obvious how to <a class="reference external" href="OCamlLangImpl7.html">add support for mutable
+variables</a> without having to add an “SSA
+construction” phase to your front-end. In the next chapter, we will
+describe how you can add variable mutation without building SSA in your
+front-end.</p>
+</div>
+<div class="section" id="full-code-listing">
+<h2><a class="toc-backref" href="#id6">6.6. Full Code Listing</a><a class="headerlink" href="#full-code-listing" title="Permalink to this headline">¶</a></h2>
+<p>Here is the complete code listing for our running example, enhanced with
+the if/then/else and for expressions.. To build this example, use:</p>
+<div class="highlight-bash"><div class="highlight"><pre><span class="c"># Compile</span>
+ocamlbuild toy.byte
+<span class="c"># Run</span>
+./toy.byte
+</pre></div>
+</div>
+<p>Here is the code:</p>
+<dl class="docutils">
+<dt>_tags:</dt>
+<dd><div class="first last highlight-python"><pre><{lexer,parser}.ml>: use_camlp4, pp(camlp4of)
+<*.{byte,native}>: g++, use_llvm, use_llvm_analysis
+<*.{byte,native}>: use_llvm_executionengine, use_llvm_target
+<*.{byte,native}>: use_llvm_scalar_opts, use_bindings</pre>
+</div>
+</dd>
+<dt>myocamlbuild.ml:</dt>
+<dd><div class="first last highlight-ocaml"><div class="highlight"><pre><span class="k">open</span> <span class="nc">Ocamlbuild_plugin</span><span class="o">;;</span>
+
+<span class="n">ocaml_lib</span> <span class="o">~</span><span class="n">extern</span><span class="o">:</span><span class="bp">true</span> <span class="s2">"llvm"</span><span class="o">;;</span>
+<span class="n">ocaml_lib</span> <span class="o">~</span><span class="n">extern</span><span class="o">:</span><span class="bp">true</span> <span class="s2">"llvm_analysis"</span><span class="o">;;</span>
+<span class="n">ocaml_lib</span> <span class="o">~</span><span class="n">extern</span><span class="o">:</span><span class="bp">true</span> <span class="s2">"llvm_executionengine"</span><span class="o">;;</span>
+<span class="n">ocaml_lib</span> <span class="o">~</span><span class="n">extern</span><span class="o">:</span><span class="bp">true</span> <span class="s2">"llvm_target"</span><span class="o">;;</span>
+<span class="n">ocaml_lib</span> <span class="o">~</span><span class="n">extern</span><span class="o">:</span><span class="bp">true</span> <span class="s2">"llvm_scalar_opts"</span><span class="o">;;</span>
+
+<span class="n">flag</span> <span class="o">[</span><span class="s2">"link"</span><span class="o">;</span> <span class="s2">"ocaml"</span><span class="o">;</span> <span class="s2">"g++"</span><span class="o">]</span> <span class="o">(</span><span class="nc">S</span><span class="o">[</span><span class="nc">A</span><span class="s2">"-cc"</span><span class="o">;</span> <span class="nc">A</span><span class="s2">"g++"</span><span class="o">;</span> <span class="nc">A</span><span class="s2">"-cclib"</span><span class="o">;</span> <span class="nc">A</span><span class="s2">"-rdynamic"</span><span class="o">]);;</span>
+<span class="n">dep</span> <span class="o">[</span><span class="s2">"link"</span><span class="o">;</span> <span class="s2">"ocaml"</span><span class="o">;</span> <span class="s2">"use_bindings"</span><span class="o">]</span> <span class="o">[</span><span class="s2">"bindings.o"</span><span class="o">];;</span>
+</pre></div>
+</div>
+</dd>
+<dt>token.ml:</dt>
+<dd><div class="first last highlight-ocaml"><div class="highlight"><pre><span class="c">(*===----------------------------------------------------------------------===</span>
+<span class="c"> * Lexer Tokens</span>
+<span class="c"> *===----------------------------------------------------------------------===*)</span>
+
+<span class="c">(* The lexer returns these 'Kwd' if it is an unknown character, otherwise one of</span>
+<span class="c"> * these others for known things. *)</span>
+<span class="k">type</span> <span class="n">token</span> <span class="o">=</span>
+  <span class="c">(* commands *)</span>
+  <span class="o">|</span> <span class="nc">Def</span> <span class="o">|</span> <span class="nc">Extern</span>
+
+  <span class="c">(* primary *)</span>
+  <span class="o">|</span> <span class="nc">Ident</span> <span class="k">of</span> <span class="kt">string</span> <span class="o">|</span> <span class="nc">Number</span> <span class="k">of</span> <span class="kt">float</span>
+
+  <span class="c">(* unknown *)</span>
+  <span class="o">|</span> <span class="nc">Kwd</span> <span class="k">of</span> <span class="kt">char</span>
+
+  <span class="c">(* control *)</span>
+  <span class="o">|</span> <span class="nc">If</span> <span class="o">|</span> <span class="nc">Then</span> <span class="o">|</span> <span class="nc">Else</span>
+  <span class="o">|</span> <span class="nc">For</span> <span class="o">|</span> <span class="nc">In</span>
+
+  <span class="c">(* operators *)</span>
+  <span class="o">|</span> <span class="nc">Binary</span> <span class="o">|</span> <span class="nc">Unary</span>
+</pre></div>
+</div>
+</dd>
+<dt>lexer.ml:</dt>
+<dd><div class="first last highlight-ocaml"><div class="highlight"><pre><span class="c">(*===----------------------------------------------------------------------===</span>
+<span class="c"> * Lexer</span>
+<span class="c"> *===----------------------------------------------------------------------===*)</span>
+
+<span class="k">let</span> <span class="k">rec</span> <span class="n">lex</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="c">(* Skip any whitespace. *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span> <span class="o">(</span><span class="sc">' '</span> <span class="o">|</span> <span class="sc">'\n'</span> <span class="o">|</span> <span class="sc">'\r'</span> <span class="o">|</span> <span class="sc">'\t'</span><span class="o">);</span> <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">lex</span> <span class="n">stream</span>
+
+  <span class="c">(* identifier: [a-zA-Z][a-zA-Z0-9] *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span> <span class="o">(</span><span class="sc">'A'</span> <span class="o">..</span> <span class="sc">'Z'</span> <span class="o">|</span> <span class="sc">'a'</span> <span class="o">..</span> <span class="sc">'z'</span> <span class="k">as</span> <span class="n">c</span><span class="o">);</span> <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="k">let</span> <span class="n">buffer</span> <span class="o">=</span> <span class="nn">Buffer</span><span class="p">.</span><span class="n">create</span> <span class="mi">1</span> <span class="k">in</span>
+      <span class="nn">Buffer</span><span class="p">.</span><span class="n">add_char</span> <span class="n">buffer</span> <span class="n">c</span><span class="o">;</span>
+      <span class="n">lex_ident</span> <span class="n">buffer</span> <span class="n">stream</span>
+
+  <span class="c">(* number: [0-9.]+ *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span> <span class="o">(</span><span class="sc">'0'</span> <span class="o">..</span> <span class="sc">'9'</span> <span class="k">as</span> <span class="n">c</span><span class="o">);</span> <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="k">let</span> <span class="n">buffer</span> <span class="o">=</span> <span class="nn">Buffer</span><span class="p">.</span><span class="n">create</span> <span class="mi">1</span> <span class="k">in</span>
+      <span class="nn">Buffer</span><span class="p">.</span><span class="n">add_char</span> <span class="n">buffer</span> <span class="n">c</span><span class="o">;</span>
+      <span class="n">lex_number</span> <span class="n">buffer</span> <span class="n">stream</span>
+
+  <span class="c">(* Comment until end of line. *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span> <span class="o">(</span><span class="sc">'#'</span><span class="o">);</span> <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="n">lex_comment</span> <span class="n">stream</span>
+
+  <span class="c">(* Otherwise, just return the character as its ascii value. *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="n">c</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="n">c</span><span class="o">;</span> <span class="n">lex</span> <span class="n">stream</span> <span class="o">>]</span>
+
+  <span class="c">(* end of stream. *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span> <span class="o">[<</span> <span class="o">>]</span>
+
+<span class="ow">and</span> <span class="n">lex_number</span> <span class="n">buffer</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span> <span class="o">(</span><span class="sc">'0'</span> <span class="o">..</span> <span class="sc">'9'</span> <span class="o">|</span> <span class="sc">'.'</span> <span class="k">as</span> <span class="n">c</span><span class="o">);</span> <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="nn">Buffer</span><span class="p">.</span><span class="n">add_char</span> <span class="n">buffer</span> <span class="n">c</span><span class="o">;</span>
+      <span class="n">lex_number</span> <span class="n">buffer</span> <span class="n">stream</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="n">stream</span><span class="o">=</span><span class="n">lex</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Number</span> <span class="o">(</span><span class="n">float_of_string</span> <span class="o">(</span><span class="nn">Buffer</span><span class="p">.</span><span class="n">contents</span> <span class="n">buffer</span><span class="o">));</span> <span class="n">stream</span> <span class="o">>]</span>
+
+<span class="ow">and</span> <span class="n">lex_ident</span> <span class="n">buffer</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span> <span class="o">(</span><span class="sc">'A'</span> <span class="o">..</span> <span class="sc">'Z'</span> <span class="o">|</span> <span class="sc">'a'</span> <span class="o">..</span> <span class="sc">'z'</span> <span class="o">|</span> <span class="sc">'0'</span> <span class="o">..</span> <span class="sc">'9'</span> <span class="k">as</span> <span class="n">c</span><span class="o">);</span> <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="nn">Buffer</span><span class="p">.</span><span class="n">add_char</span> <span class="n">buffer</span> <span class="n">c</span><span class="o">;</span>
+      <span class="n">lex_ident</span> <span class="n">buffer</span> <span class="n">stream</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="n">stream</span><span class="o">=</span><span class="n">lex</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="k">match</span> <span class="nn">Buffer</span><span class="p">.</span><span class="n">contents</span> <span class="n">buffer</span> <span class="k">with</span>
+      <span class="o">|</span> <span class="s2">"def"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Def</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+      <span class="o">|</span> <span class="s2">"extern"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Extern</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+      <span class="o">|</span> <span class="s2">"if"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">If</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+      <span class="o">|</span> <span class="s2">"then"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Then</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+      <span class="o">|</span> <span class="s2">"else"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Else</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+      <span class="o">|</span> <span class="s2">"for"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">For</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+      <span class="o">|</span> <span class="s2">"in"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">In</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+      <span class="o">|</span> <span class="s2">"binary"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Binary</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+      <span class="o">|</span> <span class="s2">"unary"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Unary</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+      <span class="o">|</span> <span class="n">id</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Ident</span> <span class="n">id</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+
+<span class="ow">and</span> <span class="n">lex_comment</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span> <span class="o">(</span><span class="sc">'\n'</span><span class="o">);</span> <span class="n">stream</span><span class="o">=</span><span class="n">lex</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">stream</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="n">c</span><span class="o">;</span> <span class="n">e</span><span class="o">=</span><span class="n">lex_comment</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">e</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span> <span class="o">[<</span> <span class="o">>]</span>
+</pre></div>
+</div>
+</dd>
+<dt>ast.ml:</dt>
+<dd><div class="first last highlight-ocaml"><div class="highlight"><pre><span class="c">(*===----------------------------------------------------------------------===</span>
+<span class="c"> * Abstract Syntax Tree (aka Parse Tree)</span>
+<span class="c"> *===----------------------------------------------------------------------===*)</span>
+
+<span class="c">(* expr - Base type for all expression nodes. *)</span>
+<span class="k">type</span> <span class="n">expr</span> <span class="o">=</span>
+  <span class="c">(* variant for numeric literals like "1.0". *)</span>
+  <span class="o">|</span> <span class="nc">Number</span> <span class="k">of</span> <span class="kt">float</span>
+
+  <span class="c">(* variant for referencing a variable, like "a". *)</span>
+  <span class="o">|</span> <span class="nc">Variable</span> <span class="k">of</span> <span class="kt">string</span>
+
+  <span class="c">(* variant for a unary operator. *)</span>
+  <span class="o">|</span> <span class="nc">Unary</span> <span class="k">of</span> <span class="kt">char</span> <span class="o">*</span> <span class="n">expr</span>
+
+  <span class="c">(* variant for a binary operator. *)</span>
+  <span class="o">|</span> <span class="nc">Binary</span> <span class="k">of</span> <span class="kt">char</span> <span class="o">*</span> <span class="n">expr</span> <span class="o">*</span> <span class="n">expr</span>
+
+  <span class="c">(* variant for function calls. *)</span>
+  <span class="o">|</span> <span class="nc">Call</span> <span class="k">of</span> <span class="kt">string</span> <span class="o">*</span> <span class="n">expr</span> <span class="kt">array</span>
+
+  <span class="c">(* variant for if/then/else. *)</span>
+  <span class="o">|</span> <span class="nc">If</span> <span class="k">of</span> <span class="n">expr</span> <span class="o">*</span> <span class="n">expr</span> <span class="o">*</span> <span class="n">expr</span>
+
+  <span class="c">(* variant for for/in. *)</span>
+  <span class="o">|</span> <span class="nc">For</span> <span class="k">of</span> <span class="kt">string</span> <span class="o">*</span> <span class="n">expr</span> <span class="o">*</span> <span class="n">expr</span> <span class="o">*</span> <span class="n">expr</span> <span class="n">option</span> <span class="o">*</span> <span class="n">expr</span>
+
+<span class="c">(* proto - This type represents the "prototype" for a function, which captures</span>
+<span class="c"> * its name, and its argument names (thus implicitly the number of arguments the</span>
+<span class="c"> * function takes). *)</span>
+<span class="k">type</span> <span class="n">proto</span> <span class="o">=</span>
+  <span class="o">|</span> <span class="nc">Prototype</span> <span class="k">of</span> <span class="kt">string</span> <span class="o">*</span> <span class="kt">string</span> <span class="kt">array</span>
+  <span class="o">|</span> <span class="nc">BinOpPrototype</span> <span class="k">of</span> <span class="kt">string</span> <span class="o">*</span> <span class="kt">string</span> <span class="kt">array</span> <span class="o">*</span> <span class="kt">int</span>
+
+<span class="c">(* func - This type represents a function definition itself. *)</span>
+<span class="k">type</span> <span class="n">func</span> <span class="o">=</span> <span class="nc">Function</span> <span class="k">of</span> <span class="n">proto</span> <span class="o">*</span> <span class="n">expr</span>
+</pre></div>
+</div>
+</dd>
+<dt>parser.ml:</dt>
+<dd><div class="first last highlight-ocaml"><div class="highlight"><pre><span class="c">(*===---------------------------------------------------------------------===</span>
+<span class="c"> * Parser</span>
+<span class="c"> *===---------------------------------------------------------------------===*)</span>
+
+<span class="c">(* binop_precedence - This holds the precedence for each binary operator that is</span>
+<span class="c"> * defined *)</span>
+<span class="k">let</span> <span class="n">binop_precedence</span><span class="o">:(</span><span class="kt">char</span><span class="o">,</span> <span class="kt">int</span><span class="o">)</span> <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">t</span> <span class="o">=</span> <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">create</span> <span class="mi">10</span>
+
+<span class="c">(* precedence - Get the precedence of the pending binary operator token. *)</span>
+<span class="k">let</span> <span class="n">precedence</span> <span class="n">c</span> <span class="o">=</span> <span class="k">try</span> <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">find</span> <span class="n">binop_precedence</span> <span class="n">c</span> <span class="k">with</span> <span class="nc">Not_found</span> <span class="o">-></span> <span class="o">-</span><span class="mi">1</span>
+
+<span class="c">(* primary</span>
+<span class="c"> *   ::= identifier</span>
+<span class="c"> *   ::= numberexpr</span>
+<span class="c"> *   ::= parenexpr</span>
+<span class="c"> *   ::= ifexpr</span>
+<span class="c"> *   ::= forexpr *)</span>
+<span class="k">let</span> <span class="k">rec</span> <span class="n">parse_primary</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="c">(* numberexpr ::= number *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Number</span> <span class="n">n</span> <span class="o">>]</span> <span class="o">-></span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Number</span> <span class="n">n</span>
+
+  <span class="c">(* parenexpr ::= '(' expression ')' *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">'('</span><span class="o">;</span> <span class="n">e</span><span class="o">=</span><span class="n">parse_expr</span><span class="o">;</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">')'</span> <span class="o">??</span> <span class="s2">"expected ')'"</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">e</span>
+
+  <span class="c">(* identifierexpr</span>
+<span class="c">   *   ::= identifier</span>
+<span class="c">   *   ::= identifier '(' argumentexpr ')' *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Ident</span> <span class="n">id</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="k">let</span> <span class="k">rec</span> <span class="n">parse_args</span> <span class="n">accumulator</span> <span class="o">=</span> <span class="n">parser</span>
+        <span class="o">|</span> <span class="o">[<</span> <span class="n">e</span><span class="o">=</span><span class="n">parse_expr</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span>
+            <span class="k">begin</span> <span class="n">parser</span>
+              <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">','</span><span class="o">;</span> <span class="n">e</span><span class="o">=</span><span class="n">parse_args</span> <span class="o">(</span><span class="n">e</span> <span class="o">::</span> <span class="n">accumulator</span><span class="o">)</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">e</span>
+              <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">e</span> <span class="o">::</span> <span class="n">accumulator</span>
+            <span class="k">end</span> <span class="n">stream</span>
+        <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">accumulator</span>
+      <span class="k">in</span>
+      <span class="k">let</span> <span class="k">rec</span> <span class="n">parse_ident</span> <span class="n">id</span> <span class="o">=</span> <span class="n">parser</span>
+        <span class="c">(* Call. *)</span>
+        <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">'('</span><span class="o">;</span>
+             <span class="n">args</span><span class="o">=</span><span class="n">parse_args</span> <span class="bp">[]</span><span class="o">;</span>
+             <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">')'</span> <span class="o">??</span> <span class="s2">"expected ')'"</span><span class="o">>]</span> <span class="o">-></span>
+            <span class="nn">Ast</span><span class="p">.</span><span class="nc">Call</span> <span class="o">(</span><span class="n">id</span><span class="o">,</span> <span class="nn">Array</span><span class="p">.</span><span class="n">of_list</span> <span class="o">(</span><span class="nn">List</span><span class="p">.</span><span class="n">rev</span> <span class="n">args</span><span class="o">))</span>
+
+        <span class="c">(* Simple variable ref. *)</span>
+        <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Variable</span> <span class="n">id</span>
+      <span class="k">in</span>
+      <span class="n">parse_ident</span> <span class="n">id</span> <span class="n">stream</span>
+
+  <span class="c">(* ifexpr ::= 'if' expr 'then' expr 'else' expr *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">If</span><span class="o">;</span> <span class="n">c</span><span class="o">=</span><span class="n">parse_expr</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Then</span> <span class="o">??</span> <span class="s2">"expected 'then'"</span><span class="o">;</span> <span class="n">t</span><span class="o">=</span><span class="n">parse_expr</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Else</span> <span class="o">??</span> <span class="s2">"expected 'else'"</span><span class="o">;</span> <span class="n">e</span><span class="o">=</span><span class="n">parse_expr</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="nn">Ast</span><span class="p">.</span><span class="nc">If</span> <span class="o">(</span><span class="n">c</span><span class="o">,</span> <span class="n">t</span><span class="o">,</span> <span class="n">e</span><span class="o">)</span>
+
+  <span class="c">(* forexpr</span>
+<span class="c">        ::= 'for' identifier '=' expr ',' expr (',' expr)? 'in' expression *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">For</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Ident</span> <span class="n">id</span> <span class="o">??</span> <span class="s2">"expected identifier after for"</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">'='</span> <span class="o">??</span> <span class="s2">"expected '=' after for"</span><span class="o">;</span>
+       <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="k">begin</span> <span class="n">parser</span>
+        <span class="o">|</span> <span class="o">[<</span>
+             <span class="n">start</span><span class="o">=</span><span class="n">parse_expr</span><span class="o">;</span>
+             <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">','</span> <span class="o">??</span> <span class="s2">"expected ',' after for"</span><span class="o">;</span>
+             <span class="n">end_</span><span class="o">=</span><span class="n">parse_expr</span><span class="o">;</span>
+             <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span>
+            <span class="k">let</span> <span class="n">step</span> <span class="o">=</span>
+              <span class="k">begin</span> <span class="n">parser</span>
+              <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">','</span><span class="o">;</span> <span class="n">step</span><span class="o">=</span><span class="n">parse_expr</span> <span class="o">>]</span> <span class="o">-></span> <span class="nc">Some</span> <span class="n">step</span>
+              <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span> <span class="nc">None</span>
+              <span class="k">end</span> <span class="n">stream</span>
+            <span class="k">in</span>
+            <span class="k">begin</span> <span class="n">parser</span>
+            <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">In</span><span class="o">;</span> <span class="n">body</span><span class="o">=</span><span class="n">parse_expr</span> <span class="o">>]</span> <span class="o">-></span>
+                <span class="nn">Ast</span><span class="p">.</span><span class="nc">For</span> <span class="o">(</span><span class="n">id</span><span class="o">,</span> <span class="n">start</span><span class="o">,</span> <span class="n">end_</span><span class="o">,</span> <span class="n">step</span><span class="o">,</span> <span class="n">body</span><span class="o">)</span>
+            <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span>
+                <span class="k">raise</span> <span class="o">(</span><span class="nn">Stream</span><span class="p">.</span><span class="nc">Error</span> <span class="s2">"expected 'in' after for"</span><span class="o">)</span>
+            <span class="k">end</span> <span class="n">stream</span>
+        <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span>
+            <span class="k">raise</span> <span class="o">(</span><span class="nn">Stream</span><span class="p">.</span><span class="nc">Error</span> <span class="s2">"expected '=' after for"</span><span class="o">)</span>
+      <span class="k">end</span> <span class="n">stream</span>
+
+  <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span> <span class="k">raise</span> <span class="o">(</span><span class="nn">Stream</span><span class="p">.</span><span class="nc">Error</span> <span class="s2">"unknown token when expecting an expression."</span><span class="o">)</span>
+
+<span class="c">(* unary</span>
+<span class="c"> *   ::= primary</span>
+<span class="c"> *   ::= '!' unary *)</span>
+<span class="ow">and</span> <span class="n">parse_unary</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="c">(* If this is a unary operator, read it. *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="n">op</span> <span class="k">when</span> <span class="n">op</span> <span class="o">!=</span> <span class="sc">'('</span> <span class="o">&&</span> <span class="n">op</span> <span class="o">!=</span> <span class="sc">')'</span><span class="o">;</span> <span class="n">operand</span><span class="o">=</span><span class="n">parse_expr</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="nn">Ast</span><span class="p">.</span><span class="nc">Unary</span> <span class="o">(</span><span class="n">op</span><span class="o">,</span> <span class="n">operand</span><span class="o">)</span>
+
+  <span class="c">(* If the current token is not an operator, it must be a primary expr. *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">parse_primary</span> <span class="n">stream</span>
+
+<span class="c">(* binoprhs</span>
+<span class="c"> *   ::= ('+' primary)* *)</span>
+<span class="ow">and</span> <span class="n">parse_bin_rhs</span> <span class="n">expr_prec</span> <span class="n">lhs</span> <span class="n">stream</span> <span class="o">=</span>
+  <span class="k">match</span> <span class="nn">Stream</span><span class="p">.</span><span class="n">peek</span> <span class="n">stream</span> <span class="k">with</span>
+  <span class="c">(* If this is a binop, find its precedence. *)</span>
+  <span class="o">|</span> <span class="nc">Some</span> <span class="o">(</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="n">c</span><span class="o">)</span> <span class="k">when</span> <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">mem</span> <span class="n">binop_precedence</span> <span class="n">c</span> <span class="o">-></span>
+      <span class="k">let</span> <span class="n">token_prec</span> <span class="o">=</span> <span class="n">precedence</span> <span class="n">c</span> <span class="k">in</span>
+
+      <span class="c">(* If this is a binop that binds at least as tightly as the current binop,</span>
+<span class="c">       * consume it, otherwise we are done. *)</span>
+      <span class="k">if</span> <span class="n">token_prec</span> <span class="o"><</span> <span class="n">expr_prec</span> <span class="k">then</span> <span class="n">lhs</span> <span class="k">else</span> <span class="k">begin</span>
+        <span class="c">(* Eat the binop. *)</span>
+        <span class="nn">Stream</span><span class="p">.</span><span class="n">junk</span> <span class="n">stream</span><span class="o">;</span>
+
+        <span class="c">(* Parse the unary expression after the binary operator. *)</span>
+        <span class="k">let</span> <span class="n">rhs</span> <span class="o">=</span> <span class="n">parse_unary</span> <span class="n">stream</span> <span class="k">in</span>
+
+        <span class="c">(* Okay, we know this is a binop. *)</span>
+        <span class="k">let</span> <span class="n">rhs</span> <span class="o">=</span>
+          <span class="k">match</span> <span class="nn">Stream</span><span class="p">.</span><span class="n">peek</span> <span class="n">stream</span> <span class="k">with</span>
+          <span class="o">|</span> <span class="nc">Some</span> <span class="o">(</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="n">c2</span><span class="o">)</span> <span class="o">-></span>
+              <span class="c">(* If BinOp binds less tightly with rhs than the operator after</span>
+<span class="c">               * rhs, let the pending operator take rhs as its lhs. *)</span>
+              <span class="k">let</span> <span class="n">next_prec</span> <span class="o">=</span> <span class="n">precedence</span> <span class="n">c2</span> <span class="k">in</span>
+              <span class="k">if</span> <span class="n">token_prec</span> <span class="o"><</span> <span class="n">next_prec</span>
+              <span class="k">then</span> <span class="n">parse_bin_rhs</span> <span class="o">(</span><span class="n">token_prec</span> <span class="o">+</span> <span class="mi">1</span><span class="o">)</span> <span class="n">rhs</span> <span class="n">stream</span>
+              <span class="k">else</span> <span class="n">rhs</span>
+          <span class="o">|</span> <span class="o">_</span> <span class="o">-></span> <span class="n">rhs</span>
+        <span class="k">in</span>
+
+        <span class="c">(* Merge lhs/rhs. *)</span>
+        <span class="k">let</span> <span class="n">lhs</span> <span class="o">=</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Binary</span> <span class="o">(</span><span class="n">c</span><span class="o">,</span> <span class="n">lhs</span><span class="o">,</span> <span class="n">rhs</span><span class="o">)</span> <span class="k">in</span>
+        <span class="n">parse_bin_rhs</span> <span class="n">expr_prec</span> <span class="n">lhs</span> <span class="n">stream</span>
+      <span class="k">end</span>
+  <span class="o">|</span> <span class="o">_</span> <span class="o">-></span> <span class="n">lhs</span>
+
+<span class="c">(* expression</span>
+<span class="c"> *   ::= primary binoprhs *)</span>
+<span class="ow">and</span> <span class="n">parse_expr</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="n">lhs</span><span class="o">=</span><span class="n">parse_unary</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">parse_bin_rhs</span> <span class="mi">0</span> <span class="n">lhs</span> <span class="n">stream</span>
+
+<span class="c">(* prototype</span>
+<span class="c"> *   ::= id '(' id* ')'</span>
+<span class="c"> *   ::= binary LETTER number? (id, id)</span>
+<span class="c"> *   ::= unary LETTER number? (id) *)</span>
+<span class="k">let</span> <span class="n">parse_prototype</span> <span class="o">=</span>
+  <span class="k">let</span> <span class="k">rec</span> <span class="n">parse_args</span> <span class="n">accumulator</span> <span class="o">=</span> <span class="n">parser</span>
+    <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Ident</span> <span class="n">id</span><span class="o">;</span> <span class="n">e</span><span class="o">=</span><span class="n">parse_args</span> <span class="o">(</span><span class="n">id</span><span class="o">::</span><span class="n">accumulator</span><span class="o">)</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">e</span>
+    <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">accumulator</span>
+  <span class="k">in</span>
+  <span class="k">let</span> <span class="n">parse_operator</span> <span class="o">=</span> <span class="n">parser</span>
+    <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Unary</span> <span class="o">>]</span> <span class="o">-></span> <span class="s2">"unary"</span><span class="o">,</span> <span class="mi">1</span>
+    <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Binary</span> <span class="o">>]</span> <span class="o">-></span> <span class="s2">"binary"</span><span class="o">,</span> <span class="mi">2</span>
+  <span class="k">in</span>
+  <span class="k">let</span> <span class="n">parse_binary_precedence</span> <span class="o">=</span> <span class="n">parser</span>
+    <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Number</span> <span class="n">n</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">int_of_float</span> <span class="n">n</span>
+    <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span> <span class="mi">30</span>
+  <span class="k">in</span>
+  <span class="n">parser</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Ident</span> <span class="n">id</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">'('</span> <span class="o">??</span> <span class="s2">"expected '(' in prototype"</span><span class="o">;</span>
+       <span class="n">args</span><span class="o">=</span><span class="n">parse_args</span> <span class="bp">[]</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">')'</span> <span class="o">??</span> <span class="s2">"expected ')' in prototype"</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="c">(* success. *)</span>
+      <span class="nn">Ast</span><span class="p">.</span><span class="nc">Prototype</span> <span class="o">(</span><span class="n">id</span><span class="o">,</span> <span class="nn">Array</span><span class="p">.</span><span class="n">of_list</span> <span class="o">(</span><span class="nn">List</span><span class="p">.</span><span class="n">rev</span> <span class="n">args</span><span class="o">))</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="o">(</span><span class="n">prefix</span><span class="o">,</span> <span class="n">kind</span><span class="o">)=</span><span class="n">parse_operator</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="n">op</span> <span class="o">??</span> <span class="s2">"expected an operator"</span><span class="o">;</span>
+       <span class="c">(* Read the precedence if present. *)</span>
+       <span class="n">binary_precedence</span><span class="o">=</span><span class="n">parse_binary_precedence</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">'('</span> <span class="o">??</span> <span class="s2">"expected '(' in prototype"</span><span class="o">;</span>
+        <span class="n">args</span><span class="o">=</span><span class="n">parse_args</span> <span class="bp">[]</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">')'</span> <span class="o">??</span> <span class="s2">"expected ')' in prototype"</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="k">let</span> <span class="n">name</span> <span class="o">=</span> <span class="n">prefix</span> <span class="o">^</span> <span class="o">(</span><span class="nn">String</span><span class="p">.</span><span class="n">make</span> <span class="mi">1</span> <span class="n">op</span><span class="o">)</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">args</span> <span class="o">=</span> <span class="nn">Array</span><span class="p">.</span><span class="n">of_list</span> <span class="o">(</span><span class="nn">List</span><span class="p">.</span><span class="n">rev</span> <span class="n">args</span><span class="o">)</span> <span class="k">in</span>
+
+      <span class="c">(* Verify right number of arguments for operator. *)</span>
+      <span class="k">if</span> <span class="nn">Array</span><span class="p">.</span><span class="n">length</span> <span class="n">args</span> <span class="o">!=</span> <span class="n">kind</span>
+      <span class="k">then</span> <span class="k">raise</span> <span class="o">(</span><span class="nn">Stream</span><span class="p">.</span><span class="nc">Error</span> <span class="s2">"invalid number of operands for operator"</span><span class="o">)</span>
+      <span class="k">else</span>
+        <span class="k">if</span> <span class="n">kind</span> <span class="o">==</span> <span class="mi">1</span> <span class="k">then</span>
+          <span class="nn">Ast</span><span class="p">.</span><span class="nc">Prototype</span> <span class="o">(</span><span class="n">name</span><span class="o">,</span> <span class="n">args</span><span class="o">)</span>
+        <span class="k">else</span>
+          <span class="nn">Ast</span><span class="p">.</span><span class="nc">BinOpPrototype</span> <span class="o">(</span><span class="n">name</span><span class="o">,</span> <span class="n">args</span><span class="o">,</span> <span class="n">binary_precedence</span><span class="o">)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="k">raise</span> <span class="o">(</span><span class="nn">Stream</span><span class="p">.</span><span class="nc">Error</span> <span class="s2">"expected function name in prototype"</span><span class="o">)</span>
+
+<span class="c">(* definition ::= 'def' prototype expression *)</span>
+<span class="k">let</span> <span class="n">parse_definition</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Def</span><span class="o">;</span> <span class="n">p</span><span class="o">=</span><span class="n">parse_prototype</span><span class="o">;</span> <span class="n">e</span><span class="o">=</span><span class="n">parse_expr</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="nn">Ast</span><span class="p">.</span><span class="nc">Function</span> <span class="o">(</span><span class="n">p</span><span class="o">,</span> <span class="n">e</span><span class="o">)</span>
+
+<span class="c">(* toplevelexpr ::= expression *)</span>
+<span class="k">let</span> <span class="n">parse_toplevel</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="n">e</span><span class="o">=</span><span class="n">parse_expr</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="c">(* Make an anonymous proto. *)</span>
+      <span class="nn">Ast</span><span class="p">.</span><span class="nc">Function</span> <span class="o">(</span><span class="nn">Ast</span><span class="p">.</span><span class="nc">Prototype</span> <span class="o">(</span><span class="s2">""</span><span class="o">,</span> <span class="o">[||]),</span> <span class="n">e</span><span class="o">)</span>
+
+<span class="c">(*  external ::= 'extern' prototype *)</span>
+<span class="k">let</span> <span class="n">parse_extern</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Extern</span><span class="o">;</span> <span class="n">e</span><span class="o">=</span><span class="n">parse_prototype</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">e</span>
+</pre></div>
+</div>
+</dd>
+<dt>codegen.ml:</dt>
+<dd><div class="first last highlight-ocaml"><div class="highlight"><pre><span class="c">(*===----------------------------------------------------------------------===</span>
+<span class="c"> * Code Generation</span>
+<span class="c"> *===----------------------------------------------------------------------===*)</span>
+
+<span class="k">open</span> <span class="nc">Llvm</span>
+
+<span class="k">exception</span> <span class="nc">Error</span> <span class="k">of</span> <span class="kt">string</span>
+
+<span class="k">let</span> <span class="n">context</span> <span class="o">=</span> <span class="n">global_context</span> <span class="bp">()</span>
+<span class="k">let</span> <span class="n">the_module</span> <span class="o">=</span> <span class="n">create_module</span> <span class="n">context</span> <span class="s2">"my cool jit"</span>
+<span class="k">let</span> <span class="n">builder</span> <span class="o">=</span> <span class="n">builder</span> <span class="n">context</span>
+<span class="k">let</span> <span class="n">named_values</span><span class="o">:(</span><span class="kt">string</span><span class="o">,</span> <span class="n">llvalue</span><span class="o">)</span> <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">t</span> <span class="o">=</span> <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">create</span> <span class="mi">10</span>
+<span class="k">let</span> <span class="n">double_type</span> <span class="o">=</span> <span class="n">double_type</span> <span class="n">context</span>
+
+<span class="k">let</span> <span class="k">rec</span> <span class="n">codegen_expr</span> <span class="o">=</span> <span class="k">function</span>
+  <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Number</span> <span class="n">n</span> <span class="o">-></span> <span class="n">const_float</span> <span class="n">double_type</span> <span class="n">n</span>
+  <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Variable</span> <span class="n">name</span> <span class="o">-></span>
+      <span class="o">(</span><span class="k">try</span> <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">find</span> <span class="n">named_values</span> <span class="n">name</span> <span class="k">with</span>
+        <span class="o">|</span> <span class="nc">Not_found</span> <span class="o">-></span> <span class="k">raise</span> <span class="o">(</span><span class="nc">Error</span> <span class="s2">"unknown variable name"</span><span class="o">))</span>
+  <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Unary</span> <span class="o">(</span><span class="n">op</span><span class="o">,</span> <span class="n">operand</span><span class="o">)</span> <span class="o">-></span>
+      <span class="k">let</span> <span class="n">operand</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">operand</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">callee</span> <span class="o">=</span> <span class="s2">"unary"</span> <span class="o">^</span> <span class="o">(</span><span class="nn">String</span><span class="p">.</span><span class="n">make</span> <span class="mi">1</span> <span class="n">op</span><span class="o">)</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">callee</span> <span class="o">=</span>
+        <span class="k">match</span> <span class="n">lookup_function</span> <span class="n">callee</span> <span class="n">the_module</span> <span class="k">with</span>
+        <span class="o">|</span> <span class="nc">Some</span> <span class="n">callee</span> <span class="o">-></span> <span class="n">callee</span>
+        <span class="o">|</span> <span class="nc">None</span> <span class="o">-></span> <span class="k">raise</span> <span class="o">(</span><span class="nc">Error</span> <span class="s2">"unknown unary operator"</span><span class="o">)</span>
+      <span class="k">in</span>
+      <span class="n">build_call</span> <span class="n">callee</span> <span class="o">[|</span><span class="n">operand</span><span class="o">|]</span> <span class="s2">"unop"</span> <span class="n">builder</span>
+  <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Binary</span> <span class="o">(</span><span class="n">op</span><span class="o">,</span> <span class="n">lhs</span><span class="o">,</span> <span class="n">rhs</span><span class="o">)</span> <span class="o">-></span>
+      <span class="k">let</span> <span class="n">lhs_val</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">lhs</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">rhs_val</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">rhs</span> <span class="k">in</span>
+      <span class="k">begin</span>
+        <span class="k">match</span> <span class="n">op</span> <span class="k">with</span>
+        <span class="o">|</span> <span class="sc">'+'</span> <span class="o">-></span> <span class="n">build_add</span> <span class="n">lhs_val</span> <span class="n">rhs_val</span> <span class="s2">"addtmp"</span> <span class="n">builder</span>
+        <span class="o">|</span> <span class="sc">'-'</span> <span class="o">-></span> <span class="n">build_sub</span> <span class="n">lhs_val</span> <span class="n">rhs_val</span> <span class="s2">"subtmp"</span> <span class="n">builder</span>
+        <span class="o">|</span> <span class="sc">'*'</span> <span class="o">-></span> <span class="n">build_mul</span> <span class="n">lhs_val</span> <span class="n">rhs_val</span> <span class="s2">"multmp"</span> <span class="n">builder</span>
+        <span class="o">|</span> <span class="sc">'<'</span> <span class="o">-></span>
+            <span class="c">(* Convert bool 0/1 to double 0.0 or 1.0 *)</span>
+            <span class="k">let</span> <span class="n">i</span> <span class="o">=</span> <span class="n">build_fcmp</span> <span class="nn">Fcmp</span><span class="p">.</span><span class="nc">Ult</span> <span class="n">lhs_val</span> <span class="n">rhs_val</span> <span class="s2">"cmptmp"</span> <span class="n">builder</span> <span class="k">in</span>
+            <span class="n">build_uitofp</span> <span class="n">i</span> <span class="n">double_type</span> <span class="s2">"booltmp"</span> <span class="n">builder</span>
+        <span class="o">|</span> <span class="o">_</span> <span class="o">-></span>
+            <span class="c">(* If it wasn't a builtin binary operator, it must be a user defined</span>
+<span class="c">             * one. Emit a call to it. *)</span>
+            <span class="k">let</span> <span class="n">callee</span> <span class="o">=</span> <span class="s2">"binary"</span> <span class="o">^</span> <span class="o">(</span><span class="nn">String</span><span class="p">.</span><span class="n">make</span> <span class="mi">1</span> <span class="n">op</span><span class="o">)</span> <span class="k">in</span>
+            <span class="k">let</span> <span class="n">callee</span> <span class="o">=</span>
+              <span class="k">match</span> <span class="n">lookup_function</span> <span class="n">callee</span> <span class="n">the_module</span> <span class="k">with</span>
+              <span class="o">|</span> <span class="nc">Some</span> <span class="n">callee</span> <span class="o">-></span> <span class="n">callee</span>
+              <span class="o">|</span> <span class="nc">None</span> <span class="o">-></span> <span class="k">raise</span> <span class="o">(</span><span class="nc">Error</span> <span class="s2">"binary operator not found!"</span><span class="o">)</span>
+            <span class="k">in</span>
+            <span class="n">build_call</span> <span class="n">callee</span> <span class="o">[|</span><span class="n">lhs_val</span><span class="o">;</span> <span class="n">rhs_val</span><span class="o">|]</span> <span class="s2">"binop"</span> <span class="n">builder</span>
+      <span class="k">end</span>
+  <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Call</span> <span class="o">(</span><span class="n">callee</span><span class="o">,</span> <span class="n">args</span><span class="o">)</span> <span class="o">-></span>
+      <span class="c">(* Look up the name in the module table. *)</span>
+      <span class="k">let</span> <span class="n">callee</span> <span class="o">=</span>
+        <span class="k">match</span> <span class="n">lookup_function</span> <span class="n">callee</span> <span class="n">the_module</span> <span class="k">with</span>
+        <span class="o">|</span> <span class="nc">Some</span> <span class="n">callee</span> <span class="o">-></span> <span class="n">callee</span>
+        <span class="o">|</span> <span class="nc">None</span> <span class="o">-></span> <span class="k">raise</span> <span class="o">(</span><span class="nc">Error</span> <span class="s2">"unknown function referenced"</span><span class="o">)</span>
+      <span class="k">in</span>
+      <span class="k">let</span> <span class="n">params</span> <span class="o">=</span> <span class="n">params</span> <span class="n">callee</span> <span class="k">in</span>
+
+      <span class="c">(* If argument mismatch error. *)</span>
+      <span class="k">if</span> <span class="nn">Array</span><span class="p">.</span><span class="n">length</span> <span class="n">params</span> <span class="o">==</span> <span class="nn">Array</span><span class="p">.</span><span class="n">length</span> <span class="n">args</span> <span class="k">then</span> <span class="bp">()</span> <span class="k">else</span>
+        <span class="k">raise</span> <span class="o">(</span><span class="nc">Error</span> <span class="s2">"incorrect # arguments passed"</span><span class="o">);</span>
+      <span class="k">let</span> <span class="n">args</span> <span class="o">=</span> <span class="nn">Array</span><span class="p">.</span><span class="n">map</span> <span class="n">codegen_expr</span> <span class="n">args</span> <span class="k">in</span>
+      <span class="n">build_call</span> <span class="n">callee</span> <span class="n">args</span> <span class="s2">"calltmp"</span> <span class="n">builder</span>
+  <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">If</span> <span class="o">(</span><span class="n">cond</span><span class="o">,</span> <span class="n">then_</span><span class="o">,</span> <span class="n">else_</span><span class="o">)</span> <span class="o">-></span>
+      <span class="k">let</span> <span class="n">cond</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">cond</span> <span class="k">in</span>
+
+      <span class="c">(* Convert condition to a bool by comparing equal to 0.0 *)</span>
+      <span class="k">let</span> <span class="n">zero</span> <span class="o">=</span> <span class="n">const_float</span> <span class="n">double_type</span> <span class="mi">0</span><span class="o">.</span><span class="mi">0</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">cond_val</span> <span class="o">=</span> <span class="n">build_fcmp</span> <span class="nn">Fcmp</span><span class="p">.</span><span class="nc">One</span> <span class="n">cond</span> <span class="n">zero</span> <span class="s2">"ifcond"</span> <span class="n">builder</span> <span class="k">in</span>
+
+      <span class="c">(* Grab the first block so that we might later add the conditional branch</span>
+<span class="c">       * to it at the end of the function. *)</span>
+      <span class="k">let</span> <span class="n">start_bb</span> <span class="o">=</span> <span class="n">insertion_block</span> <span class="n">builder</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">the_function</span> <span class="o">=</span> <span class="n">block_parent</span> <span class="n">start_bb</span> <span class="k">in</span>
+
+      <span class="k">let</span> <span class="n">then_bb</span> <span class="o">=</span> <span class="n">append_block</span> <span class="n">context</span> <span class="s2">"then"</span> <span class="n">the_function</span> <span class="k">in</span>
+
+      <span class="c">(* Emit 'then' value. *)</span>
+      <span class="n">position_at_end</span> <span class="n">then_bb</span> <span class="n">builder</span><span class="o">;</span>
+      <span class="k">let</span> <span class="n">then_val</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">then_</span> <span class="k">in</span>
+
+      <span class="c">(* Codegen of 'then' can change the current block, update then_bb for the</span>
+<span class="c">       * phi. We create a new name because one is used for the phi node, and the</span>
+<span class="c">       * other is used for the conditional branch. *)</span>
+      <span class="k">let</span> <span class="n">new_then_bb</span> <span class="o">=</span> <span class="n">insertion_block</span> <span class="n">builder</span> <span class="k">in</span>
+
+      <span class="c">(* Emit 'else' value. *)</span>
+      <span class="k">let</span> <span class="n">else_bb</span> <span class="o">=</span> <span class="n">append_block</span> <span class="n">context</span> <span class="s2">"else"</span> <span class="n">the_function</span> <span class="k">in</span>
+      <span class="n">position_at_end</span> <span class="n">else_bb</span> <span class="n">builder</span><span class="o">;</span>
+      <span class="k">let</span> <span class="n">else_val</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">else_</span> <span class="k">in</span>
+
+      <span class="c">(* Codegen of 'else' can change the current block, update else_bb for the</span>
+<span class="c">       * phi. *)</span>
+      <span class="k">let</span> <span class="n">new_else_bb</span> <span class="o">=</span> <span class="n">insertion_block</span> <span class="n">builder</span> <span class="k">in</span>
+
+      <span class="c">(* Emit merge block. *)</span>
+      <span class="k">let</span> <span class="n">merge_bb</span> <span class="o">=</span> <span class="n">append_block</span> <span class="n">context</span> <span class="s2">"ifcont"</span> <span class="n">the_function</span> <span class="k">in</span>
+      <span class="n">position_at_end</span> <span class="n">merge_bb</span> <span class="n">builder</span><span class="o">;</span>
+      <span class="k">let</span> <span class="n">incoming</span> <span class="o">=</span> <span class="o">[(</span><span class="n">then_val</span><span class="o">,</span> <span class="n">new_then_bb</span><span class="o">);</span> <span class="o">(</span><span class="n">else_val</span><span class="o">,</span> <span class="n">new_else_bb</span><span class="o">)]</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">phi</span> <span class="o">=</span> <span class="n">build_phi</span> <span class="n">incoming</span> <span class="s2">"iftmp"</span> <span class="n">builder</span> <span class="k">in</span>
+
+      <span class="c">(* Return to the start block to add the conditional branch. *)</span>
+      <span class="n">position_at_end</span> <span class="n">start_bb</span> <span class="n">builder</span><span class="o">;</span>
+      <span class="n">ignore</span> <span class="o">(</span><span class="n">build_cond_br</span> <span class="n">cond_val</span> <span class="n">then_bb</span> <span class="n">else_bb</span> <span class="n">builder</span><span class="o">);</span>
+
+      <span class="c">(* Set a unconditional branch at the end of the 'then' block and the</span>
+<span class="c">       * 'else' block to the 'merge' block. *)</span>
+      <span class="n">position_at_end</span> <span class="n">new_then_bb</span> <span class="n">builder</span><span class="o">;</span> <span class="n">ignore</span> <span class="o">(</span><span class="n">build_br</span> <span class="n">merge_bb</span> <span class="n">builder</span><span class="o">);</span>
+      <span class="n">position_at_end</span> <span class="n">new_else_bb</span> <span class="n">builder</span><span class="o">;</span> <span class="n">ignore</span> <span class="o">(</span><span class="n">build_br</span> <span class="n">merge_bb</span> <span class="n">builder</span><span class="o">);</span>
+
+      <span class="c">(* Finally, set the builder to the end of the merge block. *)</span>
+      <span class="n">position_at_end</span> <span class="n">merge_bb</span> <span class="n">builder</span><span class="o">;</span>
+
+      <span class="n">phi</span>
+  <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">For</span> <span class="o">(</span><span class="n">var_name</span><span class="o">,</span> <span class="n">start</span><span class="o">,</span> <span class="n">end_</span><span class="o">,</span> <span class="n">step</span><span class="o">,</span> <span class="n">body</span><span class="o">)</span> <span class="o">-></span>
+      <span class="c">(* Emit the start code first, without 'variable' in scope. *)</span>
+      <span class="k">let</span> <span class="n">start_val</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">start</span> <span class="k">in</span>
+
+      <span class="c">(* Make the new basic block for the loop header, inserting after current</span>
+<span class="c">       * block. *)</span>
+      <span class="k">let</span> <span class="n">preheader_bb</span> <span class="o">=</span> <span class="n">insertion_block</span> <span class="n">builder</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">the_function</span> <span class="o">=</span> <span class="n">block_parent</span> <span class="n">preheader_bb</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">loop_bb</span> <span class="o">=</span> <span class="n">append_block</span> <span class="n">context</span> <span class="s2">"loop"</span> <span class="n">the_function</span> <span class="k">in</span>
+
+      <span class="c">(* Insert an explicit fall through from the current block to the</span>
+<span class="c">       * loop_bb. *)</span>
+      <span class="n">ignore</span> <span class="o">(</span><span class="n">build_br</span> <span class="n">loop_bb</span> <span class="n">builder</span><span class="o">);</span>
+
+      <span class="c">(* Start insertion in loop_bb. *)</span>
+      <span class="n">position_at_end</span> <span class="n">loop_bb</span> <span class="n">builder</span><span class="o">;</span>
+
+      <span class="c">(* Start the PHI node with an entry for start. *)</span>
+      <span class="k">let</span> <span class="n">variable</span> <span class="o">=</span> <span class="n">build_phi</span> <span class="o">[(</span><span class="n">start_val</span><span class="o">,</span> <span class="n">preheader_bb</span><span class="o">)]</span> <span class="n">var_name</span> <span class="n">builder</span> <span class="k">in</span>
+
+      <span class="c">(* Within the loop, the variable is defined equal to the PHI node. If it</span>
+<span class="c">       * shadows an existing variable, we have to restore it, so save it</span>
+<span class="c">       * now. *)</span>
+      <span class="k">let</span> <span class="n">old_val</span> <span class="o">=</span>
+        <span class="k">try</span> <span class="nc">Some</span> <span class="o">(</span><span class="nn">Hashtbl</span><span class="p">.</span><span class="n">find</span> <span class="n">named_values</span> <span class="n">var_name</span><span class="o">)</span> <span class="k">with</span> <span class="nc">Not_found</span> <span class="o">-></span> <span class="nc">None</span>
+      <span class="k">in</span>
+      <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="n">named_values</span> <span class="n">var_name</span> <span class="n">variable</span><span class="o">;</span>
+
+      <span class="c">(* Emit the body of the loop.  This, like any other expr, can change the</span>
+<span class="c">       * current BB.  Note that we ignore the value computed by the body, but</span>
+<span class="c">       * don't allow an error *)</span>
+      <span class="n">ignore</span> <span class="o">(</span><span class="n">codegen_expr</span> <span class="n">body</span><span class="o">);</span>
+
+      <span class="c">(* Emit the step value. *)</span>
+      <span class="k">let</span> <span class="n">step_val</span> <span class="o">=</span>
+        <span class="k">match</span> <span class="n">step</span> <span class="k">with</span>
+        <span class="o">|</span> <span class="nc">Some</span> <span class="n">step</span> <span class="o">-></span> <span class="n">codegen_expr</span> <span class="n">step</span>
+        <span class="c">(* If not specified, use 1.0. *)</span>
+        <span class="o">|</span> <span class="nc">None</span> <span class="o">-></span> <span class="n">const_float</span> <span class="n">double_type</span> <span class="mi">1</span><span class="o">.</span><span class="mi">0</span>
+      <span class="k">in</span>
+
+      <span class="k">let</span> <span class="n">next_var</span> <span class="o">=</span> <span class="n">build_add</span> <span class="n">variable</span> <span class="n">step_val</span> <span class="s2">"nextvar"</span> <span class="n">builder</span> <span class="k">in</span>
+
+      <span class="c">(* Compute the end condition. *)</span>
+      <span class="k">let</span> <span class="n">end_cond</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">end_</span> <span class="k">in</span>
+
+      <span class="c">(* Convert condition to a bool by comparing equal to 0.0. *)</span>
+      <span class="k">let</span> <span class="n">zero</span> <span class="o">=</span> <span class="n">const_float</span> <span class="n">double_type</span> <span class="mi">0</span><span class="o">.</span><span class="mi">0</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">end_cond</span> <span class="o">=</span> <span class="n">build_fcmp</span> <span class="nn">Fcmp</span><span class="p">.</span><span class="nc">One</span> <span class="n">end_cond</span> <span class="n">zero</span> <span class="s2">"loopcond"</span> <span class="n">builder</span> <span class="k">in</span>
+
+      <span class="c">(* Create the "after loop" block and insert it. *)</span>
+      <span class="k">let</span> <span class="n">loop_end_bb</span> <span class="o">=</span> <span class="n">insertion_block</span> <span class="n">builder</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">after_bb</span> <span class="o">=</span> <span class="n">append_block</span> <span class="n">context</span> <span class="s2">"afterloop"</span> <span class="n">the_function</span> <span class="k">in</span>
+
+      <span class="c">(* Insert the conditional branch into the end of loop_end_bb. *)</span>
+      <span class="n">ignore</span> <span class="o">(</span><span class="n">build_cond_br</span> <span class="n">end_cond</span> <span class="n">loop_bb</span> <span class="n">after_bb</span> <span class="n">builder</span><span class="o">);</span>
+
+      <span class="c">(* Any new code will be inserted in after_bb. *)</span>
+      <span class="n">position_at_end</span> <span class="n">after_bb</span> <span class="n">builder</span><span class="o">;</span>
+
+      <span class="c">(* Add a new entry to the PHI node for the backedge. *)</span>
+      <span class="n">add_incoming</span> <span class="o">(</span><span class="n">next_var</span><span class="o">,</span> <span class="n">loop_end_bb</span><span class="o">)</span> <span class="n">variable</span><span class="o">;</span>
+
+      <span class="c">(* Restore the unshadowed variable. *)</span>
+      <span class="k">begin</span> <span class="k">match</span> <span class="n">old_val</span> <span class="k">with</span>
+      <span class="o">|</span> <span class="nc">Some</span> <span class="n">old_val</span> <span class="o">-></span> <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="n">named_values</span> <span class="n">var_name</span> <span class="n">old_val</span>
+      <span class="o">|</span> <span class="nc">None</span> <span class="o">-></span> <span class="bp">()</span>
+      <span class="k">end</span><span class="o">;</span>
+
+      <span class="c">(* for expr always returns 0.0. *)</span>
+      <span class="n">const_null</span> <span class="n">double_type</span>
+
+<span class="k">let</span> <span class="n">codegen_proto</span> <span class="o">=</span> <span class="k">function</span>
+  <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Prototype</span> <span class="o">(</span><span class="n">name</span><span class="o">,</span> <span class="n">args</span><span class="o">)</span> <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">BinOpPrototype</span> <span class="o">(</span><span class="n">name</span><span class="o">,</span> <span class="n">args</span><span class="o">,</span> <span class="o">_)</span> <span class="o">-></span>
+      <span class="c">(* Make the function type: double(double,double) etc. *)</span>
+      <span class="k">let</span> <span class="n">doubles</span> <span class="o">=</span> <span class="nn">Array</span><span class="p">.</span><span class="n">make</span> <span class="o">(</span><span class="nn">Array</span><span class="p">.</span><span class="n">length</span> <span class="n">args</span><span class="o">)</span> <span class="n">double_type</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">ft</span> <span class="o">=</span> <span class="n">function_type</span> <span class="n">double_type</span> <span class="n">doubles</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">f</span> <span class="o">=</span>
+        <span class="k">match</span> <span class="n">lookup_function</span> <span class="n">name</span> <span class="n">the_module</span> <span class="k">with</span>
+        <span class="o">|</span> <span class="nc">None</span> <span class="o">-></span> <span class="n">declare_function</span> <span class="n">name</span> <span class="n">ft</span> <span class="n">the_module</span>
+
+        <span class="c">(* If 'f' conflicted, there was already something named 'name'. If it</span>
+<span class="c">         * has a body, don't allow redefinition or reextern. *)</span>
+        <span class="o">|</span> <span class="nc">Some</span> <span class="n">f</span> <span class="o">-></span>
+            <span class="c">(* If 'f' already has a body, reject this. *)</span>
+            <span class="k">if</span> <span class="n">block_begin</span> <span class="n">f</span> <span class="o"><></span> <span class="nc">At_end</span> <span class="n">f</span> <span class="k">then</span>
+              <span class="k">raise</span> <span class="o">(</span><span class="nc">Error</span> <span class="s2">"redefinition of function"</span><span class="o">);</span>
+
+            <span class="c">(* If 'f' took a different number of arguments, reject. *)</span>
+            <span class="k">if</span> <span class="n">element_type</span> <span class="o">(</span><span class="n">type_of</span> <span class="n">f</span><span class="o">)</span> <span class="o"><></span> <span class="n">ft</span> <span class="k">then</span>
+              <span class="k">raise</span> <span class="o">(</span><span class="nc">Error</span> <span class="s2">"redefinition of function with different # args"</span><span class="o">);</span>
+            <span class="n">f</span>
+      <span class="k">in</span>
+
+      <span class="c">(* Set names for all arguments. *)</span>
+      <span class="nn">Array</span><span class="p">.</span><span class="n">iteri</span> <span class="o">(</span><span class="k">fun</span> <span class="n">i</span> <span class="n">a</span> <span class="o">-></span>
+        <span class="k">let</span> <span class="n">n</span> <span class="o">=</span> <span class="n">args</span><span class="o">.(</span><span class="n">i</span><span class="o">)</span> <span class="k">in</span>
+        <span class="n">set_value_name</span> <span class="n">n</span> <span class="n">a</span><span class="o">;</span>
+        <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="n">named_values</span> <span class="n">n</span> <span class="n">a</span><span class="o">;</span>
+      <span class="o">)</span> <span class="o">(</span><span class="n">params</span> <span class="n">f</span><span class="o">);</span>
+      <span class="n">f</span>
+
+<span class="k">let</span> <span class="n">codegen_func</span> <span class="n">the_fpm</span> <span class="o">=</span> <span class="k">function</span>
+  <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Function</span> <span class="o">(</span><span class="n">proto</span><span class="o">,</span> <span class="n">body</span><span class="o">)</span> <span class="o">-></span>
+      <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">clear</span> <span class="n">named_values</span><span class="o">;</span>
+      <span class="k">let</span> <span class="n">the_function</span> <span class="o">=</span> <span class="n">codegen_proto</span> <span class="n">proto</span> <span class="k">in</span>
+
+      <span class="c">(* If this is an operator, install it. *)</span>
+      <span class="k">begin</span> <span class="k">match</span> <span class="n">proto</span> <span class="k">with</span>
+      <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">BinOpPrototype</span> <span class="o">(</span><span class="n">name</span><span class="o">,</span> <span class="n">args</span><span class="o">,</span> <span class="n">prec</span><span class="o">)</span> <span class="o">-></span>
+          <span class="k">let</span> <span class="n">op</span> <span class="o">=</span> <span class="n">name</span><span class="o">.[</span><span class="nn">String</span><span class="p">.</span><span class="n">length</span> <span class="n">name</span> <span class="o">-</span> <span class="mi">1</span><span class="o">]</span> <span class="k">in</span>
+          <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="nn">Parser</span><span class="p">.</span><span class="n">binop_precedence</span> <span class="n">op</span> <span class="n">prec</span><span class="o">;</span>
+      <span class="o">|</span> <span class="o">_</span> <span class="o">-></span> <span class="bp">()</span>
+      <span class="k">end</span><span class="o">;</span>
+
+      <span class="c">(* Create a new basic block to start insertion into. *)</span>
+      <span class="k">let</span> <span class="n">bb</span> <span class="o">=</span> <span class="n">append_block</span> <span class="n">context</span> <span class="s2">"entry"</span> <span class="n">the_function</span> <span class="k">in</span>
+      <span class="n">position_at_end</span> <span class="n">bb</span> <span class="n">builder</span><span class="o">;</span>
+
+      <span class="k">try</span>
+        <span class="k">let</span> <span class="n">ret_val</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">body</span> <span class="k">in</span>
+
+        <span class="c">(* Finish off the function. *)</span>
+        <span class="k">let</span> <span class="o">_</span> <span class="o">=</span> <span class="n">build_ret</span> <span class="n">ret_val</span> <span class="n">builder</span> <span class="k">in</span>
+
+        <span class="c">(* Validate the generated code, checking for consistency. *)</span>
+        <span class="nn">Llvm_analysis</span><span class="p">.</span><span class="n">assert_valid_function</span> <span class="n">the_function</span><span class="o">;</span>
+
+        <span class="c">(* Optimize the function. *)</span>
+        <span class="k">let</span> <span class="o">_</span> <span class="o">=</span> <span class="nn">PassManager</span><span class="p">.</span><span class="n">run_function</span> <span class="n">the_function</span> <span class="n">the_fpm</span> <span class="k">in</span>
+
+        <span class="n">the_function</span>
+      <span class="k">with</span> <span class="n">e</span> <span class="o">-></span>
+        <span class="n">delete_function</span> <span class="n">the_function</span><span class="o">;</span>
+        <span class="k">raise</span> <span class="n">e</span>
+</pre></div>
+</div>
+</dd>
+<dt>toplevel.ml:</dt>
+<dd><div class="first last highlight-ocaml"><div class="highlight"><pre><span class="c">(*===----------------------------------------------------------------------===</span>
+<span class="c"> * Top-Level parsing and JIT Driver</span>
+<span class="c"> *===----------------------------------------------------------------------===*)</span>
+
+<span class="k">open</span> <span class="nc">Llvm</span>
+<span class="k">open</span> <span class="nc">Llvm_executionengine</span>
+
+<span class="c">(* top ::= definition | external | expression | ';' *)</span>
+<span class="k">let</span> <span class="k">rec</span> <span class="n">main_loop</span> <span class="n">the_fpm</span> <span class="n">the_execution_engine</span> <span class="n">stream</span> <span class="o">=</span>
+  <span class="k">match</span> <span class="nn">Stream</span><span class="p">.</span><span class="n">peek</span> <span class="n">stream</span> <span class="k">with</span>
+  <span class="o">|</span> <span class="nc">None</span> <span class="o">-></span> <span class="bp">()</span>
+
+  <span class="c">(* ignore top-level semicolons. *)</span>
+  <span class="o">|</span> <span class="nc">Some</span> <span class="o">(</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">';'</span><span class="o">)</span> <span class="o">-></span>
+      <span class="nn">Stream</span><span class="p">.</span><span class="n">junk</span> <span class="n">stream</span><span class="o">;</span>
+      <span class="n">main_loop</span> <span class="n">the_fpm</span> <span class="n">the_execution_engine</span> <span class="n">stream</span>
+
+  <span class="o">|</span> <span class="nc">Some</span> <span class="n">token</span> <span class="o">-></span>
+      <span class="k">begin</span>
+        <span class="k">try</span> <span class="k">match</span> <span class="n">token</span> <span class="k">with</span>
+        <span class="o">|</span> <span class="nn">Token</span><span class="p">.</span><span class="nc">Def</span> <span class="o">-></span>
+            <span class="k">let</span> <span class="n">e</span> <span class="o">=</span> <span class="nn">Parser</span><span class="p">.</span><span class="n">parse_definition</span> <span class="n">stream</span> <span class="k">in</span>
+            <span class="n">print_endline</span> <span class="s2">"parsed a function definition."</span><span class="o">;</span>
+            <span class="n">dump_value</span> <span class="o">(</span><span class="nn">Codegen</span><span class="p">.</span><span class="n">codegen_func</span> <span class="n">the_fpm</span> <span class="n">e</span><span class="o">);</span>
+        <span class="o">|</span> <span class="nn">Token</span><span class="p">.</span><span class="nc">Extern</span> <span class="o">-></span>
+            <span class="k">let</span> <span class="n">e</span> <span class="o">=</span> <span class="nn">Parser</span><span class="p">.</span><span class="n">parse_extern</span> <span class="n">stream</span> <span class="k">in</span>
+            <span class="n">print_endline</span> <span class="s2">"parsed an extern."</span><span class="o">;</span>
+            <span class="n">dump_value</span> <span class="o">(</span><span class="nn">Codegen</span><span class="p">.</span><span class="n">codegen_proto</span> <span class="n">e</span><span class="o">);</span>
+        <span class="o">|</span> <span class="o">_</span> <span class="o">-></span>
+            <span class="c">(* Evaluate a top-level expression into an anonymous function. *)</span>
+            <span class="k">let</span> <span class="n">e</span> <span class="o">=</span> <span class="nn">Parser</span><span class="p">.</span><span class="n">parse_toplevel</span> <span class="n">stream</span> <span class="k">in</span>
+            <span class="n">print_endline</span> <span class="s2">"parsed a top-level expr"</span><span class="o">;</span>
+            <span class="k">let</span> <span class="n">the_function</span> <span class="o">=</span> <span class="nn">Codegen</span><span class="p">.</span><span class="n">codegen_func</span> <span class="n">the_fpm</span> <span class="n">e</span> <span class="k">in</span>
+            <span class="n">dump_value</span> <span class="n">the_function</span><span class="o">;</span>
+
+            <span class="c">(* JIT the function, returning a function pointer. *)</span>
+            <span class="k">let</span> <span class="n">result</span> <span class="o">=</span> <span class="nn">ExecutionEngine</span><span class="p">.</span><span class="n">run_function</span> <span class="n">the_function</span> <span class="o">[||]</span>
+              <span class="n">the_execution_engine</span> <span class="k">in</span>
+
+            <span class="n">print_string</span> <span class="s2">"Evaluated to "</span><span class="o">;</span>
+            <span class="n">print_float</span> <span class="o">(</span><span class="nn">GenericValue</span><span class="p">.</span><span class="n">as_float</span> <span class="nn">Codegen</span><span class="p">.</span><span class="n">double_type</span> <span class="n">result</span><span class="o">);</span>
+            <span class="n">print_newline</span> <span class="bp">()</span><span class="o">;</span>
+        <span class="k">with</span> <span class="nn">Stream</span><span class="p">.</span><span class="nc">Error</span> <span class="n">s</span> <span class="o">|</span> <span class="nn">Codegen</span><span class="p">.</span><span class="nc">Error</span> <span class="n">s</span> <span class="o">-></span>
+          <span class="c">(* Skip token for error recovery. *)</span>
+          <span class="nn">Stream</span><span class="p">.</span><span class="n">junk</span> <span class="n">stream</span><span class="o">;</span>
+          <span class="n">print_endline</span> <span class="n">s</span><span class="o">;</span>
+      <span class="k">end</span><span class="o">;</span>
+      <span class="n">print_string</span> <span class="s2">"ready> "</span><span class="o">;</span> <span class="n">flush</span> <span class="n">stdout</span><span class="o">;</span>
+      <span class="n">main_loop</span> <span class="n">the_fpm</span> <span class="n">the_execution_engine</span> <span class="n">stream</span>
+</pre></div>
+</div>
+</dd>
+<dt>toy.ml:</dt>
+<dd><div class="first last highlight-ocaml"><div class="highlight"><pre><span class="c">(*===----------------------------------------------------------------------===</span>
+<span class="c"> * Main driver code.</span>
+<span class="c"> *===----------------------------------------------------------------------===*)</span>
+
+<span class="k">open</span> <span class="nc">Llvm</span>
+<span class="k">open</span> <span class="nc">Llvm_executionengine</span>
+<span class="k">open</span> <span class="nc">Llvm_target</span>
+<span class="k">open</span> <span class="nc">Llvm_scalar_opts</span>
+
+<span class="k">let</span> <span class="n">main</span> <span class="bp">()</span> <span class="o">=</span>
+  <span class="n">ignore</span> <span class="o">(</span><span class="n">initialize_native_target</span> <span class="bp">()</span><span class="o">);</span>
+
+  <span class="c">(* Install standard binary operators.</span>
+<span class="c">   * 1 is the lowest precedence. *)</span>
+  <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="nn">Parser</span><span class="p">.</span><span class="n">binop_precedence</span> <span class="sc">'<'</span> <span class="mi">10</span><span class="o">;</span>
+  <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="nn">Parser</span><span class="p">.</span><span class="n">binop_precedence</span> <span class="sc">'+'</span> <span class="mi">20</span><span class="o">;</span>
+  <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="nn">Parser</span><span class="p">.</span><span class="n">binop_precedence</span> <span class="sc">'-'</span> <span class="mi">20</span><span class="o">;</span>
+  <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="nn">Parser</span><span class="p">.</span><span class="n">binop_precedence</span> <span class="sc">'*'</span> <span class="mi">40</span><span class="o">;</span>    <span class="c">(* highest. *)</span>
+
+  <span class="c">(* Prime the first token. *)</span>
+  <span class="n">print_string</span> <span class="s2">"ready> "</span><span class="o">;</span> <span class="n">flush</span> <span class="n">stdout</span><span class="o">;</span>
+  <span class="k">let</span> <span class="n">stream</span> <span class="o">=</span> <span class="nn">Lexer</span><span class="p">.</span><span class="n">lex</span> <span class="o">(</span><span class="nn">Stream</span><span class="p">.</span><span class="n">of_channel</span> <span class="n">stdin</span><span class="o">)</span> <span class="k">in</span>
+
+  <span class="c">(* Create the JIT. *)</span>
+  <span class="k">let</span> <span class="n">the_execution_engine</span> <span class="o">=</span> <span class="nn">ExecutionEngine</span><span class="p">.</span><span class="n">create</span> <span class="nn">Codegen</span><span class="p">.</span><span class="n">the_module</span> <span class="k">in</span>
+  <span class="k">let</span> <span class="n">the_fpm</span> <span class="o">=</span> <span class="nn">PassManager</span><span class="p">.</span><span class="n">create_function</span> <span class="nn">Codegen</span><span class="p">.</span><span class="n">the_module</span> <span class="k">in</span>
+
+  <span class="c">(* Set up the optimizer pipeline.  Start with registering info about how the</span>
+<span class="c">   * target lays out data structures. *)</span>
+  <span class="nn">DataLayout</span><span class="p">.</span><span class="n">add</span> <span class="o">(</span><span class="nn">ExecutionEngine</span><span class="p">.</span><span class="n">target_data</span> <span class="n">the_execution_engine</span><span class="o">)</span> <span class="n">the_fpm</span><span class="o">;</span>
+
+  <span class="c">(* Do simple "peephole" optimizations and bit-twiddling optzn. *)</span>
+  <span class="n">add_instruction_combination</span> <span class="n">the_fpm</span><span class="o">;</span>
+
+  <span class="c">(* reassociate expressions. *)</span>
+  <span class="n">add_reassociation</span> <span class="n">the_fpm</span><span class="o">;</span>
+
+  <span class="c">(* Eliminate Common SubExpressions. *)</span>
+  <span class="n">add_gvn</span> <span class="n">the_fpm</span><span class="o">;</span>
+
+  <span class="c">(* Simplify the control flow graph (deleting unreachable blocks, etc). *)</span>
+  <span class="n">add_cfg_simplification</span> <span class="n">the_fpm</span><span class="o">;</span>
+
+  <span class="n">ignore</span> <span class="o">(</span><span class="nn">PassManager</span><span class="p">.</span><span class="n">initialize</span> <span class="n">the_fpm</span><span class="o">);</span>
+
+  <span class="c">(* Run the main "interpreter loop" now. *)</span>
+  <span class="nn">Toplevel</span><span class="p">.</span><span class="n">main_loop</span> <span class="n">the_fpm</span> <span class="n">the_execution_engine</span> <span class="n">stream</span><span class="o">;</span>
+
+  <span class="c">(* Print out all the generated code. *)</span>
+  <span class="n">dump_module</span> <span class="nn">Codegen</span><span class="p">.</span><span class="n">the_module</span>
+<span class="o">;;</span>
+
+<span class="n">main</span> <span class="bp">()</span>
+</pre></div>
+</div>
+</dd>
+<dt>bindings.c</dt>
+<dd><div class="first last highlight-c"><div class="highlight"><pre><span class="cp">#include <stdio.h></span>
+
+<span class="cm">/* putchard - putchar that takes a double and returns 0. */</span>
+<span class="k">extern</span> <span class="kt">double</span> <span class="nf">putchard</span><span class="p">(</span><span class="kt">double</span> <span class="n">X</span><span class="p">)</span> <span class="p">{</span>
+  <span class="n">putchar</span><span class="p">((</span><span class="kt">char</span><span class="p">)</span><span class="n">X</span><span class="p">);</span>
+  <span class="k">return</span> <span class="mi">0</span><span class="p">;</span>
+<span class="p">}</span>
+
+<span class="cm">/* printd - printf that takes a double prints it as "%f\n", returning 0. */</span>
+<span class="k">extern</span> <span class="kt">double</span> <span class="nf">printd</span><span class="p">(</span><span class="kt">double</span> <span class="n">X</span><span class="p">)</span> <span class="p">{</span>
+  <span class="n">printf</span><span class="p">(</span><span class="s">"%f</span><span class="se">\n</span><span class="s">"</span><span class="p">,</span> <span class="n">X</span><span class="p">);</span>
+  <span class="k">return</span> <span class="mi">0</span><span class="p">;</span>
+<span class="p">}</span>
+</pre></div>
+</div>
+</dd>
+</dl>
+<p><a class="reference external" href="OCamlLangImpl7.html">Next: Extending the language: mutable variables / SSA
+construction</a></p>
+</div>
+</div>
+
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+  <div class="section" id="kaleidoscope-extending-the-language-mutable-variables">
+<h1>7. Kaleidoscope: Extending the Language: Mutable Variables<a class="headerlink" href="#kaleidoscope-extending-the-language-mutable-variables" title="Permalink to this headline">¶</a></h1>
+<div class="contents local topic" id="contents">
+<ul class="simple">
+<li><a class="reference internal" href="#chapter-7-introduction" id="id2">Chapter 7 Introduction</a></li>
+<li><a class="reference internal" href="#why-is-this-a-hard-problem" id="id3">Why is this a hard problem?</a></li>
+<li><a class="reference internal" href="#memory-in-llvm" id="id4">Memory in LLVM</a></li>
+<li><a class="reference internal" href="#mutable-variables-in-kaleidoscope" id="id5">Mutable Variables in Kaleidoscope</a></li>
+<li><a class="reference internal" href="#adjusting-existing-variables-for-mutation" id="id6">Adjusting Existing Variables for Mutation</a></li>
+<li><a class="reference internal" href="#new-assignment-operator" id="id7">New Assignment Operator</a></li>
+<li><a class="reference internal" href="#user-defined-local-variables" id="id8">User-defined Local Variables</a></li>
+<li><a class="reference internal" href="#id1" id="id9">Full Code Listing</a></li>
+</ul>
+</div>
+<div class="section" id="chapter-7-introduction">
+<h2><a class="toc-backref" href="#id2">7.1. Chapter 7 Introduction</a><a class="headerlink" href="#chapter-7-introduction" title="Permalink to this headline">¶</a></h2>
+<p>Welcome to Chapter 7 of the “<a class="reference external" href="index.html">Implementing a language with
+LLVM</a>” tutorial. In chapters 1 through 6, we’ve built a
+very respectable, albeit simple, <a class="reference external" href="http://en.wikipedia.org/wiki/Functional_programming">functional programming
+language</a>. In our
+journey, we learned some parsing techniques, how to build and represent
+an AST, how to build LLVM IR, and how to optimize the resultant code as
+well as JIT compile it.</p>
+<p>While Kaleidoscope is interesting as a functional language, the fact
+that it is functional makes it “too easy” to generate LLVM IR for it. In
+particular, a functional language makes it very easy to build LLVM IR
+directly in <a class="reference external" href="http://en.wikipedia.org/wiki/Static_single_assignment_form">SSA
+form</a>.
+Since LLVM requires that the input code be in SSA form, this is a very
+nice property and it is often unclear to newcomers how to generate code
+for an imperative language with mutable variables.</p>
+<p>The short (and happy) summary of this chapter is that there is no need
+for your front-end to build SSA form: LLVM provides highly tuned and
+well tested support for this, though the way it works is a bit
+unexpected for some.</p>
+</div>
+<div class="section" id="why-is-this-a-hard-problem">
+<h2><a class="toc-backref" href="#id3">7.2. Why is this a hard problem?</a><a class="headerlink" href="#why-is-this-a-hard-problem" title="Permalink to this headline">¶</a></h2>
+<p>To understand why mutable variables cause complexities in SSA
+construction, consider this extremely simple C example:</p>
+<div class="highlight-c"><div class="highlight"><pre><span class="kt">int</span> <span class="n">G</span><span class="p">,</span> <span class="n">H</span><span class="p">;</span>
+<span class="kt">int</span> <span class="nf">test</span><span class="p">(</span><span class="kt">_Bool</span> <span class="n">Condition</span><span class="p">)</span> <span class="p">{</span>
+  <span class="kt">int</span> <span class="n">X</span><span class="p">;</span>
+  <span class="k">if</span> <span class="p">(</span><span class="n">Condition</span><span class="p">)</span>
+    <span class="n">X</span> <span class="o">=</span> <span class="n">G</span><span class="p">;</span>
+  <span class="k">else</span>
+    <span class="n">X</span> <span class="o">=</span> <span class="n">H</span><span class="p">;</span>
+  <span class="k">return</span> <span class="n">X</span><span class="p">;</span>
+<span class="p">}</span>
+</pre></div>
+</div>
+<p>In this case, we have the variable “X”, whose value depends on the path
+executed in the program. Because there are two different possible values
+for X before the return instruction, a PHI node is inserted to merge the
+two values. The LLVM IR that we want for this example looks like this:</p>
+<div class="highlight-llvm"><div class="highlight"><pre><span class="vg">@G</span> <span class="p">=</span> <span class="k">weak</span> <span class="k">global</span> <span class="k">i32</span> <span class="m">0</span>   <span class="c">; type of @G is i32*</span>
+<span class="vg">@H</span> <span class="p">=</span> <span class="k">weak</span> <span class="k">global</span> <span class="k">i32</span> <span class="m">0</span>   <span class="c">; type of @H is i32*</span>
+
+<span class="k">define</span> <span class="k">i32</span> <span class="vg">@test</span><span class="p">(</span><span class="k">i1</span> <span class="nv">%Condition</span><span class="p">)</span> <span class="p">{</span>
+<span class="nl">entry:</span>
+  <span class="k">br</span> <span class="k">i1</span> <span class="nv">%Condition</span><span class="p">,</span> <span class="kt">label</span> <span class="nv">%cond_true</span><span class="p">,</span> <span class="kt">label</span> <span class="nv">%cond_false</span>
+
+<span class="nl">cond_true:</span>
+  <span class="nv">%X.0</span> <span class="p">=</span> <span class="k">load</span> <span class="k">i32</span><span class="p">*</span> <span class="vg">@G</span>
+  <span class="k">br</span> <span class="kt">label</span> <span class="nv">%cond_next</span>
+
+<span class="nl">cond_false:</span>
+  <span class="nv">%X.1</span> <span class="p">=</span> <span class="k">load</span> <span class="k">i32</span><span class="p">*</span> <span class="vg">@H</span>
+  <span class="k">br</span> <span class="kt">label</span> <span class="nv">%cond_next</span>
+
+<span class="nl">cond_next:</span>
+  <span class="nv">%X.2</span> <span class="p">=</span> <span class="k">phi</span> <span class="k">i32</span> <span class="p">[</span> <span class="nv">%X.1</span><span class="p">,</span> <span class="nv">%cond_false</span> <span class="p">],</span> <span class="p">[</span> <span class="nv">%X.0</span><span class="p">,</span> <span class="nv">%cond_true</span> <span class="p">]</span>
+  <span class="k">ret</span> <span class="k">i32</span> <span class="nv">%X.2</span>
+<span class="p">}</span>
+</pre></div>
+</div>
+<p>In this example, the loads from the G and H global variables are
+explicit in the LLVM IR, and they live in the then/else branches of the
+if statement (cond_true/cond_false). In order to merge the incoming
+values, the X.2 phi node in the cond_next block selects the right value
+to use based on where control flow is coming from: if control flow comes
+from the cond_false block, X.2 gets the value of X.1. Alternatively, if
+control flow comes from cond_true, it gets the value of X.0. The intent
+of this chapter is not to explain the details of SSA form. For more
+information, see one of the many <a class="reference external" href="http://en.wikipedia.org/wiki/Static_single_assignment_form">online
+references</a>.</p>
+<p>The question for this article is “who places the phi nodes when lowering
+assignments to mutable variables?”. The issue here is that LLVM
+<em>requires</em> that its IR be in SSA form: there is no “non-ssa” mode for
+it. However, SSA construction requires non-trivial algorithms and data
+structures, so it is inconvenient and wasteful for every front-end to
+have to reproduce this logic.</p>
+</div>
+<div class="section" id="memory-in-llvm">
+<h2><a class="toc-backref" href="#id4">7.3. Memory in LLVM</a><a class="headerlink" href="#memory-in-llvm" title="Permalink to this headline">¶</a></h2>
+<p>The ‘trick’ here is that while LLVM does require all register values to
+be in SSA form, it does not require (or permit) memory objects to be in
+SSA form. In the example above, note that the loads from G and H are
+direct accesses to G and H: they are not renamed or versioned. This
+differs from some other compiler systems, which do try to version memory
+objects. In LLVM, instead of encoding dataflow analysis of memory into
+the LLVM IR, it is handled with <a class="reference external" href="../WritingAnLLVMPass.html">Analysis
+Passes</a> which are computed on demand.</p>
+<p>With this in mind, the high-level idea is that we want to make a stack
+variable (which lives in memory, because it is on the stack) for each
+mutable object in a function. To take advantage of this trick, we need
+to talk about how LLVM represents stack variables.</p>
+<p>In LLVM, all memory accesses are explicit with load/store instructions,
+and it is carefully designed not to have (or need) an “address-of”
+operator. Notice how the type of the @G/@H global variables is actually
+“i32*” even though the variable is defined as “i32”. What this means is
+that @G defines <em>space</em> for an i32 in the global data area, but its
+<em>name</em> actually refers to the address for that space. Stack variables
+work the same way, except that instead of being declared with global
+variable definitions, they are declared with the <a class="reference external" href="../LangRef.html#i_alloca">LLVM alloca
+instruction</a>:</p>
+<div class="highlight-llvm"><div class="highlight"><pre><span class="k">define</span> <span class="k">i32</span> <span class="vg">@example</span><span class="p">()</span> <span class="p">{</span>
+<span class="nl">entry:</span>
+  <span class="nv">%X</span> <span class="p">=</span> <span class="k">alloca</span> <span class="k">i32</span>           <span class="c">; type of %X is i32*.</span>
+  <span class="p">...</span>
+  <span class="nv">%tmp</span> <span class="p">=</span> <span class="k">load</span> <span class="k">i32</span><span class="p">*</span> <span class="nv">%X</span>       <span class="c">; load the stack value %X from the stack.</span>
+  <span class="nv">%tmp2</span> <span class="p">=</span> <span class="k">add</span> <span class="k">i32</span> <span class="nv">%tmp</span><span class="p">,</span> <span class="m">1</span>   <span class="c">; increment it</span>
+  <span class="k">store</span> <span class="k">i32</span> <span class="nv">%tmp2</span><span class="p">,</span> <span class="k">i32</span><span class="p">*</span> <span class="nv">%X</span>  <span class="c">; store it back</span>
+  <span class="p">...</span>
+</pre></div>
+</div>
+<p>This code shows an example of how you can declare and manipulate a stack
+variable in the LLVM IR. Stack memory allocated with the alloca
+instruction is fully general: you can pass the address of the stack slot
+to functions, you can store it in other variables, etc. In our example
+above, we could rewrite the example to use the alloca technique to avoid
+using a PHI node:</p>
+<div class="highlight-llvm"><div class="highlight"><pre><span class="vg">@G</span> <span class="p">=</span> <span class="k">weak</span> <span class="k">global</span> <span class="k">i32</span> <span class="m">0</span>   <span class="c">; type of @G is i32*</span>
+<span class="vg">@H</span> <span class="p">=</span> <span class="k">weak</span> <span class="k">global</span> <span class="k">i32</span> <span class="m">0</span>   <span class="c">; type of @H is i32*</span>
+
+<span class="k">define</span> <span class="k">i32</span> <span class="vg">@test</span><span class="p">(</span><span class="k">i1</span> <span class="nv">%Condition</span><span class="p">)</span> <span class="p">{</span>
+<span class="nl">entry:</span>
+  <span class="nv">%X</span> <span class="p">=</span> <span class="k">alloca</span> <span class="k">i32</span>           <span class="c">; type of %X is i32*.</span>
+  <span class="k">br</span> <span class="k">i1</span> <span class="nv">%Condition</span><span class="p">,</span> <span class="kt">label</span> <span class="nv">%cond_true</span><span class="p">,</span> <span class="kt">label</span> <span class="nv">%cond_false</span>
+
+<span class="nl">cond_true:</span>
+  <span class="nv">%X.0</span> <span class="p">=</span> <span class="k">load</span> <span class="k">i32</span><span class="p">*</span> <span class="vg">@G</span>
+        <span class="k">store</span> <span class="k">i32</span> <span class="nv">%X.0</span><span class="p">,</span> <span class="k">i32</span><span class="p">*</span> <span class="nv">%X</span>   <span class="c">; Update X</span>
+  <span class="k">br</span> <span class="kt">label</span> <span class="nv">%cond_next</span>
+
+<span class="nl">cond_false:</span>
+  <span class="nv">%X.1</span> <span class="p">=</span> <span class="k">load</span> <span class="k">i32</span><span class="p">*</span> <span class="vg">@H</span>
+        <span class="k">store</span> <span class="k">i32</span> <span class="nv">%X.1</span><span class="p">,</span> <span class="k">i32</span><span class="p">*</span> <span class="nv">%X</span>   <span class="c">; Update X</span>
+  <span class="k">br</span> <span class="kt">label</span> <span class="nv">%cond_next</span>
+
+<span class="nl">cond_next:</span>
+  <span class="nv">%X.2</span> <span class="p">=</span> <span class="k">load</span> <span class="k">i32</span><span class="p">*</span> <span class="nv">%X</span>       <span class="c">; Read X</span>
+  <span class="k">ret</span> <span class="k">i32</span> <span class="nv">%X.2</span>
+<span class="p">}</span>
+</pre></div>
+</div>
+<p>With this, we have discovered a way to handle arbitrary mutable
+variables without the need to create Phi nodes at all:</p>
+<ol class="arabic simple">
+<li>Each mutable variable becomes a stack allocation.</li>
+<li>Each read of the variable becomes a load from the stack.</li>
+<li>Each update of the variable becomes a store to the stack.</li>
+<li>Taking the address of a variable just uses the stack address
+directly.</li>
+</ol>
+<p>While this solution has solved our immediate problem, it introduced
+another one: we have now apparently introduced a lot of stack traffic
+for very simple and common operations, a major performance problem.
+Fortunately for us, the LLVM optimizer has a highly-tuned optimization
+pass named “mem2reg” that handles this case, promoting allocas like this
+into SSA registers, inserting Phi nodes as appropriate. If you run this
+example through the pass, for example, you’ll get:</p>
+<div class="highlight-bash"><div class="highlight"><pre><span class="nv">$ </span>llvm-as < example.ll | opt -mem2reg | llvm-dis
+ at G <span class="o">=</span> weak global i32 0
+ at H <span class="o">=</span> weak global i32 0
+
+define i32 @test<span class="o">(</span>i1 %Condition<span class="o">)</span> <span class="o">{</span>
+entry:
+  br i1 %Condition, label %cond_true, label %cond_false
+
+cond_true:
+  %X.0 <span class="o">=</span> load i32* @G
+  br label %cond_next
+
+cond_false:
+  %X.1 <span class="o">=</span> load i32* @H
+  br label %cond_next
+
+cond_next:
+  %X.01 <span class="o">=</span> phi i32 <span class="o">[</span> %X.1, %cond_false <span class="o">]</span>, <span class="o">[</span> %X.0, %cond_true <span class="o">]</span>
+  ret i32 %X.01
+<span class="o">}</span>
+</pre></div>
+</div>
+<p>The mem2reg pass implements the standard “iterated dominance frontier”
+algorithm for constructing SSA form and has a number of optimizations
+that speed up (very common) degenerate cases. The mem2reg optimization
+pass is the answer to dealing with mutable variables, and we highly
+recommend that you depend on it. Note that mem2reg only works on
+variables in certain circumstances:</p>
+<ol class="arabic simple">
+<li>mem2reg is alloca-driven: it looks for allocas and if it can handle
+them, it promotes them. It does not apply to global variables or heap
+allocations.</li>
+<li>mem2reg only looks for alloca instructions in the entry block of the
+function. Being in the entry block guarantees that the alloca is only
+executed once, which makes analysis simpler.</li>
+<li>mem2reg only promotes allocas whose uses are direct loads and stores.
+If the address of the stack object is passed to a function, or if any
+funny pointer arithmetic is involved, the alloca will not be
+promoted.</li>
+<li>mem2reg only works on allocas of <a class="reference external" href="../LangRef.html#t_classifications">first
+class</a> values (such as pointers,
+scalars and vectors), and only if the array size of the allocation is
+1 (or missing in the .ll file). mem2reg is not capable of promoting
+structs or arrays to registers. Note that the “scalarrepl” pass is
+more powerful and can promote structs, “unions”, and arrays in many
+cases.</li>
+</ol>
+<p>All of these properties are easy to satisfy for most imperative
+languages, and we’ll illustrate it below with Kaleidoscope. The final
+question you may be asking is: should I bother with this nonsense for my
+front-end? Wouldn’t it be better if I just did SSA construction
+directly, avoiding use of the mem2reg optimization pass? In short, we
+strongly recommend that you use this technique for building SSA form,
+unless there is an extremely good reason not to. Using this technique
+is:</p>
+<ul class="simple">
+<li>Proven and well tested: clang uses this technique
+for local mutable variables. As such, the most common clients of LLVM
+are using this to handle a bulk of their variables. You can be sure
+that bugs are found fast and fixed early.</li>
+<li>Extremely Fast: mem2reg has a number of special cases that make it
+fast in common cases as well as fully general. For example, it has
+fast-paths for variables that are only used in a single block,
+variables that only have one assignment point, good heuristics to
+avoid insertion of unneeded phi nodes, etc.</li>
+<li>Needed for debug info generation: <a class="reference external" href="../SourceLevelDebugging.html">Debug information in
+LLVM</a> relies on having the address of
+the variable exposed so that debug info can be attached to it. This
+technique dovetails very naturally with this style of debug info.</li>
+</ul>
+<p>If nothing else, this makes it much easier to get your front-end up and
+running, and is very simple to implement. Lets extend Kaleidoscope with
+mutable variables now!</p>
+</div>
+<div class="section" id="mutable-variables-in-kaleidoscope">
+<h2><a class="toc-backref" href="#id5">7.4. Mutable Variables in Kaleidoscope</a><a class="headerlink" href="#mutable-variables-in-kaleidoscope" title="Permalink to this headline">¶</a></h2>
+<p>Now that we know the sort of problem we want to tackle, lets see what
+this looks like in the context of our little Kaleidoscope language.
+We’re going to add two features:</p>
+<ol class="arabic simple">
+<li>The ability to mutate variables with the ‘=’ operator.</li>
+<li>The ability to define new variables.</li>
+</ol>
+<p>While the first item is really what this is about, we only have
+variables for incoming arguments as well as for induction variables, and
+redefining those only goes so far :). Also, the ability to define new
+variables is a useful thing regardless of whether you will be mutating
+them. Here’s a motivating example that shows how we could use these:</p>
+<div class="highlight-python"><pre># Define ':' for sequencing: as a low-precedence operator that ignores operands
+# and just returns the RHS.
+def binary : 1 (x y) y;
+
+# Recursive fib, we could do this before.
+def fib(x)
+  if (x < 3) then
+    1
+  else
+    fib(x-1)+fib(x-2);
+
+# Iterative fib.
+def fibi(x)
+  var a = 1, b = 1, c in
+  (for i = 3, i < x in
+     c = a + b :
+     a = b :
+     b = c) :
+  b;
+
+# Call it.
+fibi(10);</pre>
+</div>
+<p>In order to mutate variables, we have to change our existing variables
+to use the “alloca trick”. Once we have that, we’ll add our new
+operator, then extend Kaleidoscope to support new variable definitions.</p>
+</div>
+<div class="section" id="adjusting-existing-variables-for-mutation">
+<h2><a class="toc-backref" href="#id6">7.5. Adjusting Existing Variables for Mutation</a><a class="headerlink" href="#adjusting-existing-variables-for-mutation" title="Permalink to this headline">¶</a></h2>
+<p>The symbol table in Kaleidoscope is managed at code generation time by
+the ‘<tt class="docutils literal"><span class="pre">named_values</span></tt>‘ map. This map currently keeps track of the LLVM
+“Value*” that holds the double value for the named variable. In order
+to support mutation, we need to change this slightly, so that it
+<tt class="docutils literal"><span class="pre">named_values</span></tt> holds the <em>memory location</em> of the variable in
+question. Note that this change is a refactoring: it changes the
+structure of the code, but does not (by itself) change the behavior of
+the compiler. All of these changes are isolated in the Kaleidoscope code
+generator.</p>
+<p>At this point in Kaleidoscope’s development, it only supports variables
+for two things: incoming arguments to functions and the induction
+variable of ‘for’ loops. For consistency, we’ll allow mutation of these
+variables in addition to other user-defined variables. This means that
+these will both need memory locations.</p>
+<p>To start our transformation of Kaleidoscope, we’ll change the
+<tt class="docutils literal"><span class="pre">named_values</span></tt> map so that it maps to AllocaInst* instead of Value*.
+Once we do this, the C++ compiler will tell us what parts of the code we
+need to update:</p>
+<p><strong>Note:</strong> the ocaml bindings currently model both <tt class="docutils literal"><span class="pre">Value*</span></tt>‘s and
+<tt class="docutils literal"><span class="pre">AllocInst*</span></tt>‘s as <tt class="docutils literal"><span class="pre">Llvm.llvalue</span></tt>‘s, but this may change in the future
+to be more type safe.</p>
+<div class="highlight-ocaml"><div class="highlight"><pre><span class="k">let</span> <span class="n">named_values</span><span class="o">:(</span><span class="kt">string</span><span class="o">,</span> <span class="n">llvalue</span><span class="o">)</span> <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">t</span> <span class="o">=</span> <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">create</span> <span class="mi">10</span>
+</pre></div>
+</div>
+<p>Also, since we will need to create these alloca’s, we’ll use a helper
+function that ensures that the allocas are created in the entry block of
+the function:</p>
+<div class="highlight-ocaml"><div class="highlight"><pre><span class="c">(* Create an alloca instruction in the entry block of the function. This</span>
+<span class="c"> * is used for mutable variables etc. *)</span>
+<span class="k">let</span> <span class="n">create_entry_block_alloca</span> <span class="n">the_function</span> <span class="n">var_name</span> <span class="o">=</span>
+  <span class="k">let</span> <span class="n">builder</span> <span class="o">=</span> <span class="n">builder_at</span> <span class="o">(</span><span class="n">instr_begin</span> <span class="o">(</span><span class="n">entry_block</span> <span class="n">the_function</span><span class="o">))</span> <span class="k">in</span>
+  <span class="n">build_alloca</span> <span class="n">double_type</span> <span class="n">var_name</span> <span class="n">builder</span>
+</pre></div>
+</div>
+<p>This funny looking code creates an <tt class="docutils literal"><span class="pre">Llvm.llbuilder</span></tt> object that is
+pointing at the first instruction of the entry block. It then creates an
+alloca with the expected name and returns it. Because all values in
+Kaleidoscope are doubles, there is no need to pass in a type to use.</p>
+<p>With this in place, the first functionality change we want to make is to
+variable references. In our new scheme, variables live on the stack, so
+code generating a reference to them actually needs to produce a load
+from the stack slot:</p>
+<div class="highlight-ocaml"><div class="highlight"><pre><span class="k">let</span> <span class="k">rec</span> <span class="n">codegen_expr</span> <span class="o">=</span> <span class="k">function</span>
+  <span class="o">...</span>
+  <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Variable</span> <span class="n">name</span> <span class="o">-></span>
+      <span class="k">let</span> <span class="n">v</span> <span class="o">=</span> <span class="k">try</span> <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">find</span> <span class="n">named_values</span> <span class="n">name</span> <span class="k">with</span>
+        <span class="o">|</span> <span class="nc">Not_found</span> <span class="o">-></span> <span class="k">raise</span> <span class="o">(</span><span class="nc">Error</span> <span class="s2">"unknown variable name"</span><span class="o">)</span>
+      <span class="k">in</span>
+      <span class="c">(* Load the value. *)</span>
+      <span class="n">build_load</span> <span class="n">v</span> <span class="n">name</span> <span class="n">builder</span>
+</pre></div>
+</div>
+<p>As you can see, this is pretty straightforward. Now we need to update
+the things that define the variables to set up the alloca. We’ll start
+with <tt class="docutils literal"><span class="pre">codegen_expr</span> <span class="pre">Ast.For</span> <span class="pre">...</span></tt> (see the <a class="reference external" href="#code">full code listing</a>
+for the unabridged code):</p>
+<div class="highlight-ocaml"><div class="highlight"><pre><span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">For</span> <span class="o">(</span><span class="n">var_name</span><span class="o">,</span> <span class="n">start</span><span class="o">,</span> <span class="n">end_</span><span class="o">,</span> <span class="n">step</span><span class="o">,</span> <span class="n">body</span><span class="o">)</span> <span class="o">-></span>
+    <span class="k">let</span> <span class="n">the_function</span> <span class="o">=</span> <span class="n">block_parent</span> <span class="o">(</span><span class="n">insertion_block</span> <span class="n">builder</span><span class="o">)</span> <span class="k">in</span>
+
+    <span class="c">(* Create an alloca for the variable in the entry block. *)</span>
+    <span class="k">let</span> <span class="n">alloca</span> <span class="o">=</span> <span class="n">create_entry_block_alloca</span> <span class="n">the_function</span> <span class="n">var_name</span> <span class="k">in</span>
+
+    <span class="c">(* Emit the start code first, without 'variable' in scope. *)</span>
+    <span class="k">let</span> <span class="n">start_val</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">start</span> <span class="k">in</span>
+
+    <span class="c">(* Store the value into the alloca. *)</span>
+    <span class="n">ignore</span><span class="o">(</span><span class="n">build_store</span> <span class="n">start_val</span> <span class="n">alloca</span> <span class="n">builder</span><span class="o">);</span>
+
+    <span class="o">...</span>
+
+    <span class="c">(* Within the loop, the variable is defined equal to the PHI node. If it</span>
+<span class="c">     * shadows an existing variable, we have to restore it, so save it</span>
+<span class="c">     * now. *)</span>
+    <span class="k">let</span> <span class="n">old_val</span> <span class="o">=</span>
+      <span class="k">try</span> <span class="nc">Some</span> <span class="o">(</span><span class="nn">Hashtbl</span><span class="p">.</span><span class="n">find</span> <span class="n">named_values</span> <span class="n">var_name</span><span class="o">)</span> <span class="k">with</span> <span class="nc">Not_found</span> <span class="o">-></span> <span class="nc">None</span>
+    <span class="k">in</span>
+    <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="n">named_values</span> <span class="n">var_name</span> <span class="n">alloca</span><span class="o">;</span>
+
+    <span class="o">...</span>
+
+    <span class="c">(* Compute the end condition. *)</span>
+    <span class="k">let</span> <span class="n">end_cond</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">end_</span> <span class="k">in</span>
+
+    <span class="c">(* Reload, increment, and restore the alloca. This handles the case where</span>
+<span class="c">     * the body of the loop mutates the variable. *)</span>
+    <span class="k">let</span> <span class="n">cur_var</span> <span class="o">=</span> <span class="n">build_load</span> <span class="n">alloca</span> <span class="n">var_name</span> <span class="n">builder</span> <span class="k">in</span>
+    <span class="k">let</span> <span class="n">next_var</span> <span class="o">=</span> <span class="n">build_add</span> <span class="n">cur_var</span> <span class="n">step_val</span> <span class="s2">"nextvar"</span> <span class="n">builder</span> <span class="k">in</span>
+    <span class="n">ignore</span><span class="o">(</span><span class="n">build_store</span> <span class="n">next_var</span> <span class="n">alloca</span> <span class="n">builder</span><span class="o">);</span>
+    <span class="o">...</span>
+</pre></div>
+</div>
+<p>This code is virtually identical to the code <a class="reference external" href="OCamlLangImpl5.html#forcodegen">before we allowed mutable
+variables</a>. The big difference is that
+we no longer have to construct a PHI node, and we use load/store to
+access the variable as needed.</p>
+<p>To support mutable argument variables, we need to also make allocas for
+them. The code for this is also pretty simple:</p>
+<div class="highlight-ocaml"><div class="highlight"><pre><span class="c">(* Create an alloca for each argument and register the argument in the symbol</span>
+<span class="c"> * table so that references to it will succeed. *)</span>
+<span class="k">let</span> <span class="n">create_argument_allocas</span> <span class="n">the_function</span> <span class="n">proto</span> <span class="o">=</span>
+  <span class="k">let</span> <span class="n">args</span> <span class="o">=</span> <span class="k">match</span> <span class="n">proto</span> <span class="k">with</span>
+    <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Prototype</span> <span class="o">(_,</span> <span class="n">args</span><span class="o">)</span> <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">BinOpPrototype</span> <span class="o">(_,</span> <span class="n">args</span><span class="o">,</span> <span class="o">_)</span> <span class="o">-></span> <span class="n">args</span>
+  <span class="k">in</span>
+  <span class="nn">Array</span><span class="p">.</span><span class="n">iteri</span> <span class="o">(</span><span class="k">fun</span> <span class="n">i</span> <span class="n">ai</span> <span class="o">-></span>
+    <span class="k">let</span> <span class="n">var_name</span> <span class="o">=</span> <span class="n">args</span><span class="o">.(</span><span class="n">i</span><span class="o">)</span> <span class="k">in</span>
+    <span class="c">(* Create an alloca for this variable. *)</span>
+    <span class="k">let</span> <span class="n">alloca</span> <span class="o">=</span> <span class="n">create_entry_block_alloca</span> <span class="n">the_function</span> <span class="n">var_name</span> <span class="k">in</span>
+
+    <span class="c">(* Store the initial value into the alloca. *)</span>
+    <span class="n">ignore</span><span class="o">(</span><span class="n">build_store</span> <span class="n">ai</span> <span class="n">alloca</span> <span class="n">builder</span><span class="o">);</span>
+
+    <span class="c">(* Add arguments to variable symbol table. *)</span>
+    <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="n">named_values</span> <span class="n">var_name</span> <span class="n">alloca</span><span class="o">;</span>
+  <span class="o">)</span> <span class="o">(</span><span class="n">params</span> <span class="n">the_function</span><span class="o">)</span>
+</pre></div>
+</div>
+<p>For each argument, we make an alloca, store the input value to the
+function into the alloca, and register the alloca as the memory location
+for the argument. This method gets invoked by <tt class="docutils literal"><span class="pre">Codegen.codegen_func</span></tt>
+right after it sets up the entry block for the function.</p>
+<p>The final missing piece is adding the mem2reg pass, which allows us to
+get good codegen once again:</p>
+<div class="highlight-ocaml"><div class="highlight"><pre><span class="k">let</span> <span class="n">main</span> <span class="bp">()</span> <span class="o">=</span>
+  <span class="o">...</span>
+  <span class="k">let</span> <span class="n">the_fpm</span> <span class="o">=</span> <span class="nn">PassManager</span><span class="p">.</span><span class="n">create_function</span> <span class="nn">Codegen</span><span class="p">.</span><span class="n">the_module</span> <span class="k">in</span>
+
+  <span class="c">(* Set up the optimizer pipeline.  Start with registering info about how the</span>
+<span class="c">   * target lays out data structures. *)</span>
+  <span class="nn">DataLayout</span><span class="p">.</span><span class="n">add</span> <span class="o">(</span><span class="nn">ExecutionEngine</span><span class="p">.</span><span class="n">target_data</span> <span class="n">the_execution_engine</span><span class="o">)</span> <span class="n">the_fpm</span><span class="o">;</span>
+
+  <span class="c">(* Promote allocas to registers. *)</span>
+  <span class="n">add_memory_to_register_promotion</span> <span class="n">the_fpm</span><span class="o">;</span>
+
+  <span class="c">(* Do simple "peephole" optimizations and bit-twiddling optzn. *)</span>
+  <span class="n">add_instruction_combining</span> <span class="n">the_fpm</span><span class="o">;</span>
+
+  <span class="c">(* reassociate expressions. *)</span>
+  <span class="n">add_reassociation</span> <span class="n">the_fpm</span><span class="o">;</span>
+</pre></div>
+</div>
+<p>It is interesting to see what the code looks like before and after the
+mem2reg optimization runs. For example, this is the before/after code
+for our recursive fib function. Before the optimization:</p>
+<div class="highlight-llvm"><div class="highlight"><pre><span class="k">define</span> <span class="kt">double</span> <span class="vg">@fib</span><span class="p">(</span><span class="kt">double</span> <span class="nv">%x</span><span class="p">)</span> <span class="p">{</span>
+<span class="nl">entry:</span>
+  <span class="nv">%x1</span> <span class="p">=</span> <span class="k">alloca</span> <span class="kt">double</span>
+  <span class="k">store</span> <span class="kt">double</span> <span class="nv">%x</span><span class="p">,</span> <span class="kt">double</span><span class="p">*</span> <span class="nv">%x1</span>
+  <span class="nv">%x2</span> <span class="p">=</span> <span class="k">load</span> <span class="kt">double</span><span class="p">*</span> <span class="nv">%x1</span>
+  <span class="nv">%cmptmp</span> <span class="p">=</span> <span class="k">fcmp</span> <span class="k">ult</span> <span class="kt">double</span> <span class="nv">%x2</span><span class="p">,</span> <span class="m">3.000000e+00</span>
+  <span class="nv">%booltmp</span> <span class="p">=</span> <span class="k">uitofp</span> <span class="k">i1</span> <span class="nv">%cmptmp</span> <span class="k">to</span> <span class="kt">double</span>
+  <span class="nv">%ifcond</span> <span class="p">=</span> <span class="k">fcmp</span> <span class="k">one</span> <span class="kt">double</span> <span class="nv">%booltmp</span><span class="p">,</span> <span class="m">0.000000e+00</span>
+  <span class="k">br</span> <span class="k">i1</span> <span class="nv">%ifcond</span><span class="p">,</span> <span class="kt">label</span> <span class="nv">%then</span><span class="p">,</span> <span class="kt">label</span> <span class="nv">%else</span>
+
+<span class="nl">then:</span>    <span class="c">; preds = %entry</span>
+  <span class="k">br</span> <span class="kt">label</span> <span class="nv">%ifcont</span>
+
+<span class="nl">else:</span>    <span class="c">; preds = %entry</span>
+  <span class="nv">%x3</span> <span class="p">=</span> <span class="k">load</span> <span class="kt">double</span><span class="p">*</span> <span class="nv">%x1</span>
+  <span class="nv">%subtmp</span> <span class="p">=</span> <span class="k">fsub</span> <span class="kt">double</span> <span class="nv">%x3</span><span class="p">,</span> <span class="m">1.000000e+00</span>
+  <span class="nv">%calltmp</span> <span class="p">=</span> <span class="k">call</span> <span class="kt">double</span> <span class="vg">@fib</span><span class="p">(</span><span class="kt">double</span> <span class="nv">%subtmp</span><span class="p">)</span>
+  <span class="nv">%x4</span> <span class="p">=</span> <span class="k">load</span> <span class="kt">double</span><span class="p">*</span> <span class="nv">%x1</span>
+  <span class="nv">%subtmp5</span> <span class="p">=</span> <span class="k">fsub</span> <span class="kt">double</span> <span class="nv">%x4</span><span class="p">,</span> <span class="m">2.000000e+00</span>
+  <span class="nv">%calltmp6</span> <span class="p">=</span> <span class="k">call</span> <span class="kt">double</span> <span class="vg">@fib</span><span class="p">(</span><span class="kt">double</span> <span class="nv">%subtmp5</span><span class="p">)</span>
+  <span class="nv">%addtmp</span> <span class="p">=</span> <span class="k">fadd</span> <span class="kt">double</span> <span class="nv">%calltmp</span><span class="p">,</span> <span class="nv">%calltmp6</span>
+  <span class="k">br</span> <span class="kt">label</span> <span class="nv">%ifcont</span>
+
+<span class="nl">ifcont:</span>    <span class="c">; preds = %else, %then</span>
+  <span class="nv">%iftmp</span> <span class="p">=</span> <span class="k">phi</span> <span class="kt">double</span> <span class="p">[</span> <span class="m">1.000000e+00</span><span class="p">,</span> <span class="nv">%then</span> <span class="p">],</span> <span class="p">[</span> <span class="nv">%addtmp</span><span class="p">,</span> <span class="nv">%else</span> <span class="p">]</span>
+  <span class="k">ret</span> <span class="kt">double</span> <span class="nv">%iftmp</span>
+<span class="p">}</span>
+</pre></div>
+</div>
+<p>Here there is only one variable (x, the input argument) but you can
+still see the extremely simple-minded code generation strategy we are
+using. In the entry block, an alloca is created, and the initial input
+value is stored into it. Each reference to the variable does a reload
+from the stack. Also, note that we didn’t modify the if/then/else
+expression, so it still inserts a PHI node. While we could make an
+alloca for it, it is actually easier to create a PHI node for it, so we
+still just make the PHI.</p>
+<p>Here is the code after the mem2reg pass runs:</p>
+<div class="highlight-llvm"><div class="highlight"><pre><span class="k">define</span> <span class="kt">double</span> <span class="vg">@fib</span><span class="p">(</span><span class="kt">double</span> <span class="nv">%x</span><span class="p">)</span> <span class="p">{</span>
+<span class="nl">entry:</span>
+  <span class="nv">%cmptmp</span> <span class="p">=</span> <span class="k">fcmp</span> <span class="k">ult</span> <span class="kt">double</span> <span class="nv">%x</span><span class="p">,</span> <span class="m">3.000000e+00</span>
+  <span class="nv">%booltmp</span> <span class="p">=</span> <span class="k">uitofp</span> <span class="k">i1</span> <span class="nv">%cmptmp</span> <span class="k">to</span> <span class="kt">double</span>
+  <span class="nv">%ifcond</span> <span class="p">=</span> <span class="k">fcmp</span> <span class="k">one</span> <span class="kt">double</span> <span class="nv">%booltmp</span><span class="p">,</span> <span class="m">0.000000e+00</span>
+  <span class="k">br</span> <span class="k">i1</span> <span class="nv">%ifcond</span><span class="p">,</span> <span class="kt">label</span> <span class="nv">%then</span><span class="p">,</span> <span class="kt">label</span> <span class="nv">%else</span>
+
+<span class="nl">then:</span>
+  <span class="k">br</span> <span class="kt">label</span> <span class="nv">%ifcont</span>
+
+<span class="nl">else:</span>
+  <span class="nv">%subtmp</span> <span class="p">=</span> <span class="k">fsub</span> <span class="kt">double</span> <span class="nv">%x</span><span class="p">,</span> <span class="m">1.000000e+00</span>
+  <span class="nv">%calltmp</span> <span class="p">=</span> <span class="k">call</span> <span class="kt">double</span> <span class="vg">@fib</span><span class="p">(</span><span class="kt">double</span> <span class="nv">%subtmp</span><span class="p">)</span>
+  <span class="nv">%subtmp5</span> <span class="p">=</span> <span class="k">fsub</span> <span class="kt">double</span> <span class="nv">%x</span><span class="p">,</span> <span class="m">2.000000e+00</span>
+  <span class="nv">%calltmp6</span> <span class="p">=</span> <span class="k">call</span> <span class="kt">double</span> <span class="vg">@fib</span><span class="p">(</span><span class="kt">double</span> <span class="nv">%subtmp5</span><span class="p">)</span>
+  <span class="nv">%addtmp</span> <span class="p">=</span> <span class="k">fadd</span> <span class="kt">double</span> <span class="nv">%calltmp</span><span class="p">,</span> <span class="nv">%calltmp6</span>
+  <span class="k">br</span> <span class="kt">label</span> <span class="nv">%ifcont</span>
+
+<span class="nl">ifcont:</span>    <span class="c">; preds = %else, %then</span>
+  <span class="nv">%iftmp</span> <span class="p">=</span> <span class="k">phi</span> <span class="kt">double</span> <span class="p">[</span> <span class="m">1.000000e+00</span><span class="p">,</span> <span class="nv">%then</span> <span class="p">],</span> <span class="p">[</span> <span class="nv">%addtmp</span><span class="p">,</span> <span class="nv">%else</span> <span class="p">]</span>
+  <span class="k">ret</span> <span class="kt">double</span> <span class="nv">%iftmp</span>
+<span class="p">}</span>
+</pre></div>
+</div>
+<p>This is a trivial case for mem2reg, since there are no redefinitions of
+the variable. The point of showing this is to calm your tension about
+inserting such blatent inefficiencies :).</p>
+<p>After the rest of the optimizers run, we get:</p>
+<div class="highlight-llvm"><div class="highlight"><pre><span class="k">define</span> <span class="kt">double</span> <span class="vg">@fib</span><span class="p">(</span><span class="kt">double</span> <span class="nv">%x</span><span class="p">)</span> <span class="p">{</span>
+<span class="nl">entry:</span>
+  <span class="nv">%cmptmp</span> <span class="p">=</span> <span class="k">fcmp</span> <span class="k">ult</span> <span class="kt">double</span> <span class="nv">%x</span><span class="p">,</span> <span class="m">3.000000e+00</span>
+  <span class="nv">%booltmp</span> <span class="p">=</span> <span class="k">uitofp</span> <span class="k">i1</span> <span class="nv">%cmptmp</span> <span class="k">to</span> <span class="kt">double</span>
+  <span class="nv">%ifcond</span> <span class="p">=</span> <span class="k">fcmp</span> <span class="k">ueq</span> <span class="kt">double</span> <span class="nv">%booltmp</span><span class="p">,</span> <span class="m">0.000000e+00</span>
+  <span class="k">br</span> <span class="k">i1</span> <span class="nv">%ifcond</span><span class="p">,</span> <span class="kt">label</span> <span class="nv">%else</span><span class="p">,</span> <span class="kt">label</span> <span class="nv">%ifcont</span>
+
+<span class="nl">else:</span>
+  <span class="nv">%subtmp</span> <span class="p">=</span> <span class="k">fsub</span> <span class="kt">double</span> <span class="nv">%x</span><span class="p">,</span> <span class="m">1.000000e+00</span>
+  <span class="nv">%calltmp</span> <span class="p">=</span> <span class="k">call</span> <span class="kt">double</span> <span class="vg">@fib</span><span class="p">(</span><span class="kt">double</span> <span class="nv">%subtmp</span><span class="p">)</span>
+  <span class="nv">%subtmp5</span> <span class="p">=</span> <span class="k">fsub</span> <span class="kt">double</span> <span class="nv">%x</span><span class="p">,</span> <span class="m">2.000000e+00</span>
+  <span class="nv">%calltmp6</span> <span class="p">=</span> <span class="k">call</span> <span class="kt">double</span> <span class="vg">@fib</span><span class="p">(</span><span class="kt">double</span> <span class="nv">%subtmp5</span><span class="p">)</span>
+  <span class="nv">%addtmp</span> <span class="p">=</span> <span class="k">fadd</span> <span class="kt">double</span> <span class="nv">%calltmp</span><span class="p">,</span> <span class="nv">%calltmp6</span>
+  <span class="k">ret</span> <span class="kt">double</span> <span class="nv">%addtmp</span>
+
+<span class="nl">ifcont:</span>
+  <span class="k">ret</span> <span class="kt">double</span> <span class="m">1.000000e+00</span>
+<span class="p">}</span>
+</pre></div>
+</div>
+<p>Here we see that the simplifycfg pass decided to clone the return
+instruction into the end of the ‘else’ block. This allowed it to
+eliminate some branches and the PHI node.</p>
+<p>Now that all symbol table references are updated to use stack variables,
+we’ll add the assignment operator.</p>
+</div>
+<div class="section" id="new-assignment-operator">
+<h2><a class="toc-backref" href="#id7">7.6. New Assignment Operator</a><a class="headerlink" href="#new-assignment-operator" title="Permalink to this headline">¶</a></h2>
+<p>With our current framework, adding a new assignment operator is really
+simple. We will parse it just like any other binary operator, but handle
+it internally (instead of allowing the user to define it). The first
+step is to set a precedence:</p>
+<div class="highlight-ocaml"><div class="highlight"><pre><span class="k">let</span> <span class="n">main</span> <span class="bp">()</span> <span class="o">=</span>
+  <span class="c">(* Install standard binary operators.</span>
+<span class="c">   * 1 is the lowest precedence. *)</span>
+  <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="nn">Parser</span><span class="p">.</span><span class="n">binop_precedence</span> <span class="sc">'='</span> <span class="mi">2</span><span class="o">;</span>
+  <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="nn">Parser</span><span class="p">.</span><span class="n">binop_precedence</span> <span class="sc">'<'</span> <span class="mi">10</span><span class="o">;</span>
+  <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="nn">Parser</span><span class="p">.</span><span class="n">binop_precedence</span> <span class="sc">'+'</span> <span class="mi">20</span><span class="o">;</span>
+  <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="nn">Parser</span><span class="p">.</span><span class="n">binop_precedence</span> <span class="sc">'-'</span> <span class="mi">20</span><span class="o">;</span>
+  <span class="o">...</span>
+</pre></div>
+</div>
+<p>Now that the parser knows the precedence of the binary operator, it
+takes care of all the parsing and AST generation. We just need to
+implement codegen for the assignment operator. This looks like:</p>
+<div class="highlight-ocaml"><div class="highlight"><pre><span class="k">let</span> <span class="k">rec</span> <span class="n">codegen_expr</span> <span class="o">=</span> <span class="k">function</span>
+      <span class="k">begin</span> <span class="k">match</span> <span class="n">op</span> <span class="k">with</span>
+      <span class="o">|</span> <span class="sc">'='</span> <span class="o">-></span>
+          <span class="c">(* Special case '=' because we don't want to emit the LHS as an</span>
+<span class="c">           * expression. *)</span>
+          <span class="k">let</span> <span class="n">name</span> <span class="o">=</span>
+            <span class="k">match</span> <span class="n">lhs</span> <span class="k">with</span>
+            <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Variable</span> <span class="n">name</span> <span class="o">-></span> <span class="n">name</span>
+            <span class="o">|</span> <span class="o">_</span> <span class="o">-></span> <span class="k">raise</span> <span class="o">(</span><span class="nc">Error</span> <span class="s2">"destination of '=' must be a variable"</span><span class="o">)</span>
+          <span class="k">in</span>
+</pre></div>
+</div>
+<p>Unlike the rest of the binary operators, our assignment operator doesn’t
+follow the “emit LHS, emit RHS, do computation” model. As such, it is
+handled as a special case before the other binary operators are handled.
+The other strange thing is that it requires the LHS to be a variable. It
+is invalid to have “(x+1) = expr” - only things like “x = expr” are
+allowed.</p>
+<div class="highlight-ocaml"><div class="highlight"><pre>    <span class="c">(* Codegen the rhs. *)</span>
+    <span class="k">let</span> <span class="n">val_</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">rhs</span> <span class="k">in</span>
+
+    <span class="c">(* Lookup the name. *)</span>
+    <span class="k">let</span> <span class="n">variable</span> <span class="o">=</span> <span class="k">try</span> <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">find</span> <span class="n">named_values</span> <span class="n">name</span> <span class="k">with</span>
+    <span class="o">|</span> <span class="nc">Not_found</span> <span class="o">-></span> <span class="k">raise</span> <span class="o">(</span><span class="nc">Error</span> <span class="s2">"unknown variable name"</span><span class="o">)</span>
+    <span class="k">in</span>
+    <span class="n">ignore</span><span class="o">(</span><span class="n">build_store</span> <span class="n">val_</span> <span class="n">variable</span> <span class="n">builder</span><span class="o">);</span>
+    <span class="n">val_</span>
+<span class="o">|</span> <span class="o">_</span> <span class="o">-></span>
+      <span class="o">...</span>
+</pre></div>
+</div>
+<p>Once we have the variable, codegen’ing the assignment is
+straightforward: we emit the RHS of the assignment, create a store, and
+return the computed value. Returning a value allows for chained
+assignments like “X = (Y = Z)”.</p>
+<p>Now that we have an assignment operator, we can mutate loop variables
+and arguments. For example, we can now run code like this:</p>
+<div class="highlight-python"><pre># Function to print a double.
+extern printd(x);
+
+# Define ':' for sequencing: as a low-precedence operator that ignores operands
+# and just returns the RHS.
+def binary : 1 (x y) y;
+
+def test(x)
+  printd(x) :
+  x = 4 :
+  printd(x);
+
+test(123);</pre>
+</div>
+<p>When run, this example prints “123” and then “4”, showing that we did
+actually mutate the value! Okay, we have now officially implemented our
+goal: getting this to work requires SSA construction in the general
+case. However, to be really useful, we want the ability to define our
+own local variables, lets add this next!</p>
+</div>
+<div class="section" id="user-defined-local-variables">
+<h2><a class="toc-backref" href="#id8">7.7. User-defined Local Variables</a><a class="headerlink" href="#user-defined-local-variables" title="Permalink to this headline">¶</a></h2>
+<p>Adding var/in is just like any other other extensions we made to
+Kaleidoscope: we extend the lexer, the parser, the AST and the code
+generator. The first step for adding our new ‘var/in’ construct is to
+extend the lexer. As before, this is pretty trivial, the code looks like
+this:</p>
+<div class="highlight-ocaml"><div class="highlight"><pre><span class="k">type</span> <span class="n">token</span> <span class="o">=</span>
+  <span class="o">...</span>
+  <span class="c">(* var definition *)</span>
+  <span class="o">|</span> <span class="nn">Var</span>
+
+<span class="p">...</span>
+
+<span class="n">and</span> <span class="n">lex_ident</span> <span class="n">buffer</span> <span class="o">=</span> <span class="n">parser</span>
+      <span class="o">...</span>
+      <span class="o">|</span> <span class="s2">"in"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">In</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+      <span class="o">|</span> <span class="s2">"binary"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Binary</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+      <span class="o">|</span> <span class="s2">"unary"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Unary</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+      <span class="o">|</span> <span class="s2">"var"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Var</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+      <span class="o">...</span>
+</pre></div>
+</div>
+<p>The next step is to define the AST node that we will construct. For
+var/in, it looks like this:</p>
+<div class="highlight-ocaml"><div class="highlight"><pre><span class="k">type</span> <span class="n">expr</span> <span class="o">=</span>
+  <span class="o">...</span>
+  <span class="c">(* variant for var/in. *)</span>
+  <span class="o">|</span> <span class="nc">Var</span> <span class="k">of</span> <span class="o">(</span><span class="kt">string</span> <span class="o">*</span> <span class="n">expr</span> <span class="n">option</span><span class="o">)</span> <span class="kt">array</span> <span class="o">*</span> <span class="n">expr</span>
+  <span class="o">...</span>
+</pre></div>
+</div>
+<p>var/in allows a list of names to be defined all at once, and each name
+can optionally have an initializer value. As such, we capture this
+information in the VarNames vector. Also, var/in has a body, this body
+is allowed to access the variables defined by the var/in.</p>
+<p>With this in place, we can define the parser pieces. The first thing we
+do is add it as a primary expression:</p>
+<div class="highlight-ocaml"><div class="highlight"><pre><span class="c">(* primary</span>
+<span class="c"> *   ::= identifier</span>
+<span class="c"> *   ::= numberexpr</span>
+<span class="c"> *   ::= parenexpr</span>
+<span class="c"> *   ::= ifexpr</span>
+<span class="c"> *   ::= forexpr</span>
+<span class="c"> *   ::= varexpr *)</span>
+<span class="k">let</span> <span class="k">rec</span> <span class="n">parse_primary</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="o">...</span>
+  <span class="c">(* varexpr</span>
+<span class="c">   *   ::= 'var' identifier ('=' expression?</span>
+<span class="c">   *             (',' identifier ('=' expression)?)* 'in' expression *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Var</span><span class="o">;</span>
+       <span class="c">(* At least one variable name is required. *)</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Ident</span> <span class="n">id</span> <span class="o">??</span> <span class="s2">"expected identifier after var"</span><span class="o">;</span>
+       <span class="n">init</span><span class="o">=</span><span class="n">parse_var_init</span><span class="o">;</span>
+       <span class="n">var_names</span><span class="o">=</span><span class="n">parse_var_names</span> <span class="o">[(</span><span class="n">id</span><span class="o">,</span> <span class="n">init</span><span class="o">)];</span>
+       <span class="c">(* At this point, we have to have 'in'. *)</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">In</span> <span class="o">??</span> <span class="s2">"expected 'in' keyword after 'var'"</span><span class="o">;</span>
+       <span class="n">body</span><span class="o">=</span><span class="n">parse_expr</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="nn">Ast</span><span class="p">.</span><span class="nc">Var</span> <span class="o">(</span><span class="nn">Array</span><span class="p">.</span><span class="n">of_list</span> <span class="o">(</span><span class="nn">List</span><span class="p">.</span><span class="n">rev</span> <span class="n">var_names</span><span class="o">),</span> <span class="n">body</span><span class="o">)</span>
+
+<span class="o">...</span>
+
+<span class="ow">and</span> <span class="n">parse_var_init</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="c">(* read in the optional initializer. *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">'='</span><span class="o">;</span> <span class="n">e</span><span class="o">=</span><span class="n">parse_expr</span> <span class="o">>]</span> <span class="o">-></span> <span class="nc">Some</span> <span class="n">e</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span> <span class="nc">None</span>
+
+<span class="ow">and</span> <span class="n">parse_var_names</span> <span class="n">accumulator</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">','</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Ident</span> <span class="n">id</span> <span class="o">??</span> <span class="s2">"expected identifier list after var"</span><span class="o">;</span>
+       <span class="n">init</span><span class="o">=</span><span class="n">parse_var_init</span><span class="o">;</span>
+       <span class="n">e</span><span class="o">=</span><span class="n">parse_var_names</span> <span class="o">((</span><span class="n">id</span><span class="o">,</span> <span class="n">init</span><span class="o">)</span> <span class="o">::</span> <span class="n">accumulator</span><span class="o">)</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">e</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">accumulator</span>
+</pre></div>
+</div>
+<p>Now that we can parse and represent the code, we need to support
+emission of LLVM IR for it. This code starts out with:</p>
+<div class="highlight-ocaml"><div class="highlight"><pre><span class="k">let</span> <span class="k">rec</span> <span class="n">codegen_expr</span> <span class="o">=</span> <span class="k">function</span>
+  <span class="o">...</span>
+  <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Var</span> <span class="o">(</span><span class="n">var_names</span><span class="o">,</span> <span class="n">body</span><span class="o">)</span>
+      <span class="k">let</span> <span class="n">old_bindings</span> <span class="o">=</span> <span class="n">ref</span> <span class="bp">[]</span> <span class="k">in</span>
+
+      <span class="k">let</span> <span class="n">the_function</span> <span class="o">=</span> <span class="n">block_parent</span> <span class="o">(</span><span class="n">insertion_block</span> <span class="n">builder</span><span class="o">)</span> <span class="k">in</span>
+
+      <span class="c">(* Register all variables and emit their initializer. *)</span>
+      <span class="nn">Array</span><span class="p">.</span><span class="n">iter</span> <span class="o">(</span><span class="k">fun</span> <span class="o">(</span><span class="n">var_name</span><span class="o">,</span> <span class="n">init</span><span class="o">)</span> <span class="o">-></span>
+</pre></div>
+</div>
+<p>Basically it loops over all the variables, installing them one at a
+time. For each variable we put into the symbol table, we remember the
+previous value that we replace in OldBindings.</p>
+<div class="highlight-ocaml"><div class="highlight"><pre>  <span class="c">(* Emit the initializer before adding the variable to scope, this</span>
+<span class="c">   * prevents the initializer from referencing the variable itself, and</span>
+<span class="c">   * permits stuff like this:</span>
+<span class="c">   *   var a = 1 in</span>
+<span class="c">   *     var a = a in ...   # refers to outer 'a'. *)</span>
+  <span class="k">let</span> <span class="n">init_val</span> <span class="o">=</span>
+    <span class="k">match</span> <span class="n">init</span> <span class="k">with</span>
+    <span class="o">|</span> <span class="nc">Some</span> <span class="n">init</span> <span class="o">-></span> <span class="n">codegen_expr</span> <span class="n">init</span>
+    <span class="c">(* If not specified, use 0.0. *)</span>
+    <span class="o">|</span> <span class="nc">None</span> <span class="o">-></span> <span class="n">const_float</span> <span class="n">double_type</span> <span class="mi">0</span><span class="o">.</span><span class="mi">0</span>
+  <span class="k">in</span>
+
+  <span class="k">let</span> <span class="n">alloca</span> <span class="o">=</span> <span class="n">create_entry_block_alloca</span> <span class="n">the_function</span> <span class="n">var_name</span> <span class="k">in</span>
+  <span class="n">ignore</span><span class="o">(</span><span class="n">build_store</span> <span class="n">init_val</span> <span class="n">alloca</span> <span class="n">builder</span><span class="o">);</span>
+
+  <span class="c">(* Remember the old variable binding so that we can restore the binding</span>
+<span class="c">   * when we unrecurse. *)</span>
+
+  <span class="k">begin</span>
+    <span class="k">try</span>
+      <span class="k">let</span> <span class="n">old_value</span> <span class="o">=</span> <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">find</span> <span class="n">named_values</span> <span class="n">var_name</span> <span class="k">in</span>
+      <span class="n">old_bindings</span> <span class="o">:=</span> <span class="o">(</span><span class="n">var_name</span><span class="o">,</span> <span class="n">old_value</span><span class="o">)</span> <span class="o">::</span> <span class="o">!</span><span class="n">old_bindings</span><span class="o">;</span>
+    <span class="k">with</span> <span class="nc">Not_found</span> <span class="o">></span> <span class="bp">()</span>
+  <span class="k">end</span><span class="o">;</span>
+
+  <span class="c">(* Remember this binding. *)</span>
+  <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="n">named_values</span> <span class="n">var_name</span> <span class="n">alloca</span><span class="o">;</span>
+<span class="o">)</span> <span class="n">var_names</span><span class="o">;</span>
+</pre></div>
+</div>
+<p>There are more comments here than code. The basic idea is that we emit
+the initializer, create the alloca, then update the symbol table to
+point to it. Once all the variables are installed in the symbol table,
+we evaluate the body of the var/in expression:</p>
+<div class="highlight-ocaml"><div class="highlight"><pre><span class="c">(* Codegen the body, now that all vars are in scope. *)</span>
+<span class="k">let</span> <span class="n">body_val</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">body</span> <span class="k">in</span>
+</pre></div>
+</div>
+<p>Finally, before returning, we restore the previous variable bindings:</p>
+<div class="highlight-ocaml"><div class="highlight"><pre><span class="c">(* Pop all our variables from scope. *)</span>
+<span class="nn">List</span><span class="p">.</span><span class="n">iter</span> <span class="o">(</span><span class="k">fun</span> <span class="o">(</span><span class="n">var_name</span><span class="o">,</span> <span class="n">old_value</span><span class="o">)</span> <span class="o">-></span>
+  <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="n">named_values</span> <span class="n">var_name</span> <span class="n">old_value</span>
+<span class="o">)</span> <span class="o">!</span><span class="n">old_bindings</span><span class="o">;</span>
+
+<span class="c">(* Return the body computation. *)</span>
+<span class="n">body_val</span>
+</pre></div>
+</div>
+<p>The end result of all of this is that we get properly scoped variable
+definitions, and we even (trivially) allow mutation of them :).</p>
+<p>With this, we completed what we set out to do. Our nice iterative fib
+example from the intro compiles and runs just fine. The mem2reg pass
+optimizes all of our stack variables into SSA registers, inserting PHI
+nodes where needed, and our front-end remains simple: no “iterated
+dominance frontier” computation anywhere in sight.</p>
+</div>
+<div class="section" id="id1">
+<h2><a class="toc-backref" href="#id9">7.8. Full Code Listing</a><a class="headerlink" href="#id1" title="Permalink to this headline">¶</a></h2>
+<p>Here is the complete code listing for our running example, enhanced with
+mutable variables and var/in support. To build this example, use:</p>
+<div class="highlight-bash"><div class="highlight"><pre><span class="c"># Compile</span>
+ocamlbuild toy.byte
+<span class="c"># Run</span>
+./toy.byte
+</pre></div>
+</div>
+<p>Here is the code:</p>
+<dl class="docutils">
+<dt>_tags:</dt>
+<dd><div class="first last highlight-python"><pre><{lexer,parser}.ml>: use_camlp4, pp(camlp4of)
+<*.{byte,native}>: g++, use_llvm, use_llvm_analysis
+<*.{byte,native}>: use_llvm_executionengine, use_llvm_target
+<*.{byte,native}>: use_llvm_scalar_opts, use_bindings</pre>
+</div>
+</dd>
+<dt>myocamlbuild.ml:</dt>
+<dd><div class="first last highlight-ocaml"><div class="highlight"><pre><span class="k">open</span> <span class="nc">Ocamlbuild_plugin</span><span class="o">;;</span>
+
+<span class="n">ocaml_lib</span> <span class="o">~</span><span class="n">extern</span><span class="o">:</span><span class="bp">true</span> <span class="s2">"llvm"</span><span class="o">;;</span>
+<span class="n">ocaml_lib</span> <span class="o">~</span><span class="n">extern</span><span class="o">:</span><span class="bp">true</span> <span class="s2">"llvm_analysis"</span><span class="o">;;</span>
+<span class="n">ocaml_lib</span> <span class="o">~</span><span class="n">extern</span><span class="o">:</span><span class="bp">true</span> <span class="s2">"llvm_executionengine"</span><span class="o">;;</span>
+<span class="n">ocaml_lib</span> <span class="o">~</span><span class="n">extern</span><span class="o">:</span><span class="bp">true</span> <span class="s2">"llvm_target"</span><span class="o">;;</span>
+<span class="n">ocaml_lib</span> <span class="o">~</span><span class="n">extern</span><span class="o">:</span><span class="bp">true</span> <span class="s2">"llvm_scalar_opts"</span><span class="o">;;</span>
+
+<span class="n">flag</span> <span class="o">[</span><span class="s2">"link"</span><span class="o">;</span> <span class="s2">"ocaml"</span><span class="o">;</span> <span class="s2">"g++"</span><span class="o">]</span> <span class="o">(</span><span class="nc">S</span><span class="o">[</span><span class="nc">A</span><span class="s2">"-cc"</span><span class="o">;</span> <span class="nc">A</span><span class="s2">"g++"</span><span class="o">;</span> <span class="nc">A</span><span class="s2">"-cclib"</span><span class="o">;</span> <span class="nc">A</span><span class="s2">"-rdynamic"</span><span class="o">]);;</span>
+<span class="n">dep</span> <span class="o">[</span><span class="s2">"link"</span><span class="o">;</span> <span class="s2">"ocaml"</span><span class="o">;</span> <span class="s2">"use_bindings"</span><span class="o">]</span> <span class="o">[</span><span class="s2">"bindings.o"</span><span class="o">];;</span>
+</pre></div>
+</div>
+</dd>
+<dt>token.ml:</dt>
+<dd><div class="first last highlight-ocaml"><div class="highlight"><pre><span class="c">(*===----------------------------------------------------------------------===</span>
+<span class="c"> * Lexer Tokens</span>
+<span class="c"> *===----------------------------------------------------------------------===*)</span>
+
+<span class="c">(* The lexer returns these 'Kwd' if it is an unknown character, otherwise one of</span>
+<span class="c"> * these others for known things. *)</span>
+<span class="k">type</span> <span class="n">token</span> <span class="o">=</span>
+  <span class="c">(* commands *)</span>
+  <span class="o">|</span> <span class="nc">Def</span> <span class="o">|</span> <span class="nc">Extern</span>
+
+  <span class="c">(* primary *)</span>
+  <span class="o">|</span> <span class="nc">Ident</span> <span class="k">of</span> <span class="kt">string</span> <span class="o">|</span> <span class="nc">Number</span> <span class="k">of</span> <span class="kt">float</span>
+
+  <span class="c">(* unknown *)</span>
+  <span class="o">|</span> <span class="nc">Kwd</span> <span class="k">of</span> <span class="kt">char</span>
+
+  <span class="c">(* control *)</span>
+  <span class="o">|</span> <span class="nc">If</span> <span class="o">|</span> <span class="nc">Then</span> <span class="o">|</span> <span class="nc">Else</span>
+  <span class="o">|</span> <span class="nc">For</span> <span class="o">|</span> <span class="nc">In</span>
+
+  <span class="c">(* operators *)</span>
+  <span class="o">|</span> <span class="nc">Binary</span> <span class="o">|</span> <span class="nc">Unary</span>
+
+  <span class="c">(* var definition *)</span>
+  <span class="o">|</span> <span class="nc">Var</span>
+</pre></div>
+</div>
+</dd>
+<dt>lexer.ml:</dt>
+<dd><div class="first last highlight-ocaml"><div class="highlight"><pre><span class="c">(*===----------------------------------------------------------------------===</span>
+<span class="c"> * Lexer</span>
+<span class="c"> *===----------------------------------------------------------------------===*)</span>
+
+<span class="k">let</span> <span class="k">rec</span> <span class="n">lex</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="c">(* Skip any whitespace. *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span> <span class="o">(</span><span class="sc">' '</span> <span class="o">|</span> <span class="sc">'\n'</span> <span class="o">|</span> <span class="sc">'\r'</span> <span class="o">|</span> <span class="sc">'\t'</span><span class="o">);</span> <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">lex</span> <span class="n">stream</span>
+
+  <span class="c">(* identifier: [a-zA-Z][a-zA-Z0-9] *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span> <span class="o">(</span><span class="sc">'A'</span> <span class="o">..</span> <span class="sc">'Z'</span> <span class="o">|</span> <span class="sc">'a'</span> <span class="o">..</span> <span class="sc">'z'</span> <span class="k">as</span> <span class="n">c</span><span class="o">);</span> <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="k">let</span> <span class="n">buffer</span> <span class="o">=</span> <span class="nn">Buffer</span><span class="p">.</span><span class="n">create</span> <span class="mi">1</span> <span class="k">in</span>
+      <span class="nn">Buffer</span><span class="p">.</span><span class="n">add_char</span> <span class="n">buffer</span> <span class="n">c</span><span class="o">;</span>
+      <span class="n">lex_ident</span> <span class="n">buffer</span> <span class="n">stream</span>
+
+  <span class="c">(* number: [0-9.]+ *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span> <span class="o">(</span><span class="sc">'0'</span> <span class="o">..</span> <span class="sc">'9'</span> <span class="k">as</span> <span class="n">c</span><span class="o">);</span> <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="k">let</span> <span class="n">buffer</span> <span class="o">=</span> <span class="nn">Buffer</span><span class="p">.</span><span class="n">create</span> <span class="mi">1</span> <span class="k">in</span>
+      <span class="nn">Buffer</span><span class="p">.</span><span class="n">add_char</span> <span class="n">buffer</span> <span class="n">c</span><span class="o">;</span>
+      <span class="n">lex_number</span> <span class="n">buffer</span> <span class="n">stream</span>
+
+  <span class="c">(* Comment until end of line. *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span> <span class="o">(</span><span class="sc">'#'</span><span class="o">);</span> <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="n">lex_comment</span> <span class="n">stream</span>
+
+  <span class="c">(* Otherwise, just return the character as its ascii value. *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="n">c</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="n">c</span><span class="o">;</span> <span class="n">lex</span> <span class="n">stream</span> <span class="o">>]</span>
+
+  <span class="c">(* end of stream. *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span> <span class="o">[<</span> <span class="o">>]</span>
+
+<span class="ow">and</span> <span class="n">lex_number</span> <span class="n">buffer</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span> <span class="o">(</span><span class="sc">'0'</span> <span class="o">..</span> <span class="sc">'9'</span> <span class="o">|</span> <span class="sc">'.'</span> <span class="k">as</span> <span class="n">c</span><span class="o">);</span> <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="nn">Buffer</span><span class="p">.</span><span class="n">add_char</span> <span class="n">buffer</span> <span class="n">c</span><span class="o">;</span>
+      <span class="n">lex_number</span> <span class="n">buffer</span> <span class="n">stream</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="n">stream</span><span class="o">=</span><span class="n">lex</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Number</span> <span class="o">(</span><span class="n">float_of_string</span> <span class="o">(</span><span class="nn">Buffer</span><span class="p">.</span><span class="n">contents</span> <span class="n">buffer</span><span class="o">));</span> <span class="n">stream</span> <span class="o">>]</span>
+
+<span class="ow">and</span> <span class="n">lex_ident</span> <span class="n">buffer</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span> <span class="o">(</span><span class="sc">'A'</span> <span class="o">..</span> <span class="sc">'Z'</span> <span class="o">|</span> <span class="sc">'a'</span> <span class="o">..</span> <span class="sc">'z'</span> <span class="o">|</span> <span class="sc">'0'</span> <span class="o">..</span> <span class="sc">'9'</span> <span class="k">as</span> <span class="n">c</span><span class="o">);</span> <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="nn">Buffer</span><span class="p">.</span><span class="n">add_char</span> <span class="n">buffer</span> <span class="n">c</span><span class="o">;</span>
+      <span class="n">lex_ident</span> <span class="n">buffer</span> <span class="n">stream</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="n">stream</span><span class="o">=</span><span class="n">lex</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="k">match</span> <span class="nn">Buffer</span><span class="p">.</span><span class="n">contents</span> <span class="n">buffer</span> <span class="k">with</span>
+      <span class="o">|</span> <span class="s2">"def"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Def</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+      <span class="o">|</span> <span class="s2">"extern"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Extern</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+      <span class="o">|</span> <span class="s2">"if"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">If</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+      <span class="o">|</span> <span class="s2">"then"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Then</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+      <span class="o">|</span> <span class="s2">"else"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Else</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+      <span class="o">|</span> <span class="s2">"for"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">For</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+      <span class="o">|</span> <span class="s2">"in"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">In</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+      <span class="o">|</span> <span class="s2">"binary"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Binary</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+      <span class="o">|</span> <span class="s2">"unary"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Unary</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+      <span class="o">|</span> <span class="s2">"var"</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Var</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+      <span class="o">|</span> <span class="n">id</span> <span class="o">-></span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Ident</span> <span class="n">id</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span>
+
+<span class="ow">and</span> <span class="n">lex_comment</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span> <span class="o">(</span><span class="sc">'\n'</span><span class="o">);</span> <span class="n">stream</span><span class="o">=</span><span class="n">lex</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">stream</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="n">c</span><span class="o">;</span> <span class="n">e</span><span class="o">=</span><span class="n">lex_comment</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">e</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span> <span class="o">[<</span> <span class="o">>]</span>
+</pre></div>
+</div>
+</dd>
+<dt>ast.ml:</dt>
+<dd><div class="first last highlight-ocaml"><div class="highlight"><pre><span class="c">(*===----------------------------------------------------------------------===</span>
+<span class="c"> * Abstract Syntax Tree (aka Parse Tree)</span>
+<span class="c"> *===----------------------------------------------------------------------===*)</span>
+
+<span class="c">(* expr - Base type for all expression nodes. *)</span>
+<span class="k">type</span> <span class="n">expr</span> <span class="o">=</span>
+  <span class="c">(* variant for numeric literals like "1.0". *)</span>
+  <span class="o">|</span> <span class="nc">Number</span> <span class="k">of</span> <span class="kt">float</span>
+
+  <span class="c">(* variant for referencing a variable, like "a". *)</span>
+  <span class="o">|</span> <span class="nc">Variable</span> <span class="k">of</span> <span class="kt">string</span>
+
+  <span class="c">(* variant for a unary operator. *)</span>
+  <span class="o">|</span> <span class="nc">Unary</span> <span class="k">of</span> <span class="kt">char</span> <span class="o">*</span> <span class="n">expr</span>
+
+  <span class="c">(* variant for a binary operator. *)</span>
+  <span class="o">|</span> <span class="nc">Binary</span> <span class="k">of</span> <span class="kt">char</span> <span class="o">*</span> <span class="n">expr</span> <span class="o">*</span> <span class="n">expr</span>
+
+  <span class="c">(* variant for function calls. *)</span>
+  <span class="o">|</span> <span class="nc">Call</span> <span class="k">of</span> <span class="kt">string</span> <span class="o">*</span> <span class="n">expr</span> <span class="kt">array</span>
+
+  <span class="c">(* variant for if/then/else. *)</span>
+  <span class="o">|</span> <span class="nc">If</span> <span class="k">of</span> <span class="n">expr</span> <span class="o">*</span> <span class="n">expr</span> <span class="o">*</span> <span class="n">expr</span>
+
+  <span class="c">(* variant for for/in. *)</span>
+  <span class="o">|</span> <span class="nc">For</span> <span class="k">of</span> <span class="kt">string</span> <span class="o">*</span> <span class="n">expr</span> <span class="o">*</span> <span class="n">expr</span> <span class="o">*</span> <span class="n">expr</span> <span class="n">option</span> <span class="o">*</span> <span class="n">expr</span>
+
+  <span class="c">(* variant for var/in. *)</span>
+  <span class="o">|</span> <span class="nc">Var</span> <span class="k">of</span> <span class="o">(</span><span class="kt">string</span> <span class="o">*</span> <span class="n">expr</span> <span class="n">option</span><span class="o">)</span> <span class="kt">array</span> <span class="o">*</span> <span class="n">expr</span>
+
+<span class="c">(* proto - This type represents the "prototype" for a function, which captures</span>
+<span class="c"> * its name, and its argument names (thus implicitly the number of arguments the</span>
+<span class="c"> * function takes). *)</span>
+<span class="k">type</span> <span class="n">proto</span> <span class="o">=</span>
+  <span class="o">|</span> <span class="nc">Prototype</span> <span class="k">of</span> <span class="kt">string</span> <span class="o">*</span> <span class="kt">string</span> <span class="kt">array</span>
+  <span class="o">|</span> <span class="nc">BinOpPrototype</span> <span class="k">of</span> <span class="kt">string</span> <span class="o">*</span> <span class="kt">string</span> <span class="kt">array</span> <span class="o">*</span> <span class="kt">int</span>
+
+<span class="c">(* func - This type represents a function definition itself. *)</span>
+<span class="k">type</span> <span class="n">func</span> <span class="o">=</span> <span class="nc">Function</span> <span class="k">of</span> <span class="n">proto</span> <span class="o">*</span> <span class="n">expr</span>
+</pre></div>
+</div>
+</dd>
+<dt>parser.ml:</dt>
+<dd><div class="first last highlight-ocaml"><div class="highlight"><pre><span class="c">(*===---------------------------------------------------------------------===</span>
+<span class="c"> * Parser</span>
+<span class="c"> *===---------------------------------------------------------------------===*)</span>
+
+<span class="c">(* binop_precedence - This holds the precedence for each binary operator that is</span>
+<span class="c"> * defined *)</span>
+<span class="k">let</span> <span class="n">binop_precedence</span><span class="o">:(</span><span class="kt">char</span><span class="o">,</span> <span class="kt">int</span><span class="o">)</span> <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">t</span> <span class="o">=</span> <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">create</span> <span class="mi">10</span>
+
+<span class="c">(* precedence - Get the precedence of the pending binary operator token. *)</span>
+<span class="k">let</span> <span class="n">precedence</span> <span class="n">c</span> <span class="o">=</span> <span class="k">try</span> <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">find</span> <span class="n">binop_precedence</span> <span class="n">c</span> <span class="k">with</span> <span class="nc">Not_found</span> <span class="o">-></span> <span class="o">-</span><span class="mi">1</span>
+
+<span class="c">(* primary</span>
+<span class="c"> *   ::= identifier</span>
+<span class="c"> *   ::= numberexpr</span>
+<span class="c"> *   ::= parenexpr</span>
+<span class="c"> *   ::= ifexpr</span>
+<span class="c"> *   ::= forexpr</span>
+<span class="c"> *   ::= varexpr *)</span>
+<span class="k">let</span> <span class="k">rec</span> <span class="n">parse_primary</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="c">(* numberexpr ::= number *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Number</span> <span class="n">n</span> <span class="o">>]</span> <span class="o">-></span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Number</span> <span class="n">n</span>
+
+  <span class="c">(* parenexpr ::= '(' expression ')' *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">'('</span><span class="o">;</span> <span class="n">e</span><span class="o">=</span><span class="n">parse_expr</span><span class="o">;</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">')'</span> <span class="o">??</span> <span class="s2">"expected ')'"</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">e</span>
+
+  <span class="c">(* identifierexpr</span>
+<span class="c">   *   ::= identifier</span>
+<span class="c">   *   ::= identifier '(' argumentexpr ')' *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Ident</span> <span class="n">id</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="k">let</span> <span class="k">rec</span> <span class="n">parse_args</span> <span class="n">accumulator</span> <span class="o">=</span> <span class="n">parser</span>
+        <span class="o">|</span> <span class="o">[<</span> <span class="n">e</span><span class="o">=</span><span class="n">parse_expr</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span>
+            <span class="k">begin</span> <span class="n">parser</span>
+              <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">','</span><span class="o">;</span> <span class="n">e</span><span class="o">=</span><span class="n">parse_args</span> <span class="o">(</span><span class="n">e</span> <span class="o">::</span> <span class="n">accumulator</span><span class="o">)</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">e</span>
+              <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">e</span> <span class="o">::</span> <span class="n">accumulator</span>
+            <span class="k">end</span> <span class="n">stream</span>
+        <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">accumulator</span>
+      <span class="k">in</span>
+      <span class="k">let</span> <span class="k">rec</span> <span class="n">parse_ident</span> <span class="n">id</span> <span class="o">=</span> <span class="n">parser</span>
+        <span class="c">(* Call. *)</span>
+        <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">'('</span><span class="o">;</span>
+             <span class="n">args</span><span class="o">=</span><span class="n">parse_args</span> <span class="bp">[]</span><span class="o">;</span>
+             <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">')'</span> <span class="o">??</span> <span class="s2">"expected ')'"</span><span class="o">>]</span> <span class="o">-></span>
+            <span class="nn">Ast</span><span class="p">.</span><span class="nc">Call</span> <span class="o">(</span><span class="n">id</span><span class="o">,</span> <span class="nn">Array</span><span class="p">.</span><span class="n">of_list</span> <span class="o">(</span><span class="nn">List</span><span class="p">.</span><span class="n">rev</span> <span class="n">args</span><span class="o">))</span>
+
+        <span class="c">(* Simple variable ref. *)</span>
+        <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Variable</span> <span class="n">id</span>
+      <span class="k">in</span>
+      <span class="n">parse_ident</span> <span class="n">id</span> <span class="n">stream</span>
+
+  <span class="c">(* ifexpr ::= 'if' expr 'then' expr 'else' expr *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">If</span><span class="o">;</span> <span class="n">c</span><span class="o">=</span><span class="n">parse_expr</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Then</span> <span class="o">??</span> <span class="s2">"expected 'then'"</span><span class="o">;</span> <span class="n">t</span><span class="o">=</span><span class="n">parse_expr</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Else</span> <span class="o">??</span> <span class="s2">"expected 'else'"</span><span class="o">;</span> <span class="n">e</span><span class="o">=</span><span class="n">parse_expr</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="nn">Ast</span><span class="p">.</span><span class="nc">If</span> <span class="o">(</span><span class="n">c</span><span class="o">,</span> <span class="n">t</span><span class="o">,</span> <span class="n">e</span><span class="o">)</span>
+
+  <span class="c">(* forexpr</span>
+<span class="c">        ::= 'for' identifier '=' expr ',' expr (',' expr)? 'in' expression *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">For</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Ident</span> <span class="n">id</span> <span class="o">??</span> <span class="s2">"expected identifier after for"</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">'='</span> <span class="o">??</span> <span class="s2">"expected '=' after for"</span><span class="o">;</span>
+       <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="k">begin</span> <span class="n">parser</span>
+        <span class="o">|</span> <span class="o">[<</span>
+             <span class="n">start</span><span class="o">=</span><span class="n">parse_expr</span><span class="o">;</span>
+             <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">','</span> <span class="o">??</span> <span class="s2">"expected ',' after for"</span><span class="o">;</span>
+             <span class="n">end_</span><span class="o">=</span><span class="n">parse_expr</span><span class="o">;</span>
+             <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span>
+            <span class="k">let</span> <span class="n">step</span> <span class="o">=</span>
+              <span class="k">begin</span> <span class="n">parser</span>
+              <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">','</span><span class="o">;</span> <span class="n">step</span><span class="o">=</span><span class="n">parse_expr</span> <span class="o">>]</span> <span class="o">-></span> <span class="nc">Some</span> <span class="n">step</span>
+              <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span> <span class="nc">None</span>
+              <span class="k">end</span> <span class="n">stream</span>
+            <span class="k">in</span>
+            <span class="k">begin</span> <span class="n">parser</span>
+            <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">In</span><span class="o">;</span> <span class="n">body</span><span class="o">=</span><span class="n">parse_expr</span> <span class="o">>]</span> <span class="o">-></span>
+                <span class="nn">Ast</span><span class="p">.</span><span class="nc">For</span> <span class="o">(</span><span class="n">id</span><span class="o">,</span> <span class="n">start</span><span class="o">,</span> <span class="n">end_</span><span class="o">,</span> <span class="n">step</span><span class="o">,</span> <span class="n">body</span><span class="o">)</span>
+            <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span>
+                <span class="k">raise</span> <span class="o">(</span><span class="nn">Stream</span><span class="p">.</span><span class="nc">Error</span> <span class="s2">"expected 'in' after for"</span><span class="o">)</span>
+            <span class="k">end</span> <span class="n">stream</span>
+        <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span>
+            <span class="k">raise</span> <span class="o">(</span><span class="nn">Stream</span><span class="p">.</span><span class="nc">Error</span> <span class="s2">"expected '=' after for"</span><span class="o">)</span>
+      <span class="k">end</span> <span class="n">stream</span>
+
+  <span class="c">(* varexpr</span>
+<span class="c">   *   ::= 'var' identifier ('=' expression?</span>
+<span class="c">   *             (',' identifier ('=' expression)?)* 'in' expression *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Var</span><span class="o">;</span>
+       <span class="c">(* At least one variable name is required. *)</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Ident</span> <span class="n">id</span> <span class="o">??</span> <span class="s2">"expected identifier after var"</span><span class="o">;</span>
+       <span class="n">init</span><span class="o">=</span><span class="n">parse_var_init</span><span class="o">;</span>
+       <span class="n">var_names</span><span class="o">=</span><span class="n">parse_var_names</span> <span class="o">[(</span><span class="n">id</span><span class="o">,</span> <span class="n">init</span><span class="o">)];</span>
+       <span class="c">(* At this point, we have to have 'in'. *)</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">In</span> <span class="o">??</span> <span class="s2">"expected 'in' keyword after 'var'"</span><span class="o">;</span>
+       <span class="n">body</span><span class="o">=</span><span class="n">parse_expr</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="nn">Ast</span><span class="p">.</span><span class="nc">Var</span> <span class="o">(</span><span class="nn">Array</span><span class="p">.</span><span class="n">of_list</span> <span class="o">(</span><span class="nn">List</span><span class="p">.</span><span class="n">rev</span> <span class="n">var_names</span><span class="o">),</span> <span class="n">body</span><span class="o">)</span>
+
+  <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span> <span class="k">raise</span> <span class="o">(</span><span class="nn">Stream</span><span class="p">.</span><span class="nc">Error</span> <span class="s2">"unknown token when expecting an expression."</span><span class="o">)</span>
+
+<span class="c">(* unary</span>
+<span class="c"> *   ::= primary</span>
+<span class="c"> *   ::= '!' unary *)</span>
+<span class="ow">and</span> <span class="n">parse_unary</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="c">(* If this is a unary operator, read it. *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="n">op</span> <span class="k">when</span> <span class="n">op</span> <span class="o">!=</span> <span class="sc">'('</span> <span class="o">&&</span> <span class="n">op</span> <span class="o">!=</span> <span class="sc">')'</span><span class="o">;</span> <span class="n">operand</span><span class="o">=</span><span class="n">parse_expr</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="nn">Ast</span><span class="p">.</span><span class="nc">Unary</span> <span class="o">(</span><span class="n">op</span><span class="o">,</span> <span class="n">operand</span><span class="o">)</span>
+
+  <span class="c">(* If the current token is not an operator, it must be a primary expr. *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">parse_primary</span> <span class="n">stream</span>
+
+<span class="c">(* binoprhs</span>
+<span class="c"> *   ::= ('+' primary)* *)</span>
+<span class="ow">and</span> <span class="n">parse_bin_rhs</span> <span class="n">expr_prec</span> <span class="n">lhs</span> <span class="n">stream</span> <span class="o">=</span>
+  <span class="k">match</span> <span class="nn">Stream</span><span class="p">.</span><span class="n">peek</span> <span class="n">stream</span> <span class="k">with</span>
+  <span class="c">(* If this is a binop, find its precedence. *)</span>
+  <span class="o">|</span> <span class="nc">Some</span> <span class="o">(</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="n">c</span><span class="o">)</span> <span class="k">when</span> <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">mem</span> <span class="n">binop_precedence</span> <span class="n">c</span> <span class="o">-></span>
+      <span class="k">let</span> <span class="n">token_prec</span> <span class="o">=</span> <span class="n">precedence</span> <span class="n">c</span> <span class="k">in</span>
+
+      <span class="c">(* If this is a binop that binds at least as tightly as the current binop,</span>
+<span class="c">       * consume it, otherwise we are done. *)</span>
+      <span class="k">if</span> <span class="n">token_prec</span> <span class="o"><</span> <span class="n">expr_prec</span> <span class="k">then</span> <span class="n">lhs</span> <span class="k">else</span> <span class="k">begin</span>
+        <span class="c">(* Eat the binop. *)</span>
+        <span class="nn">Stream</span><span class="p">.</span><span class="n">junk</span> <span class="n">stream</span><span class="o">;</span>
+
+        <span class="c">(* Parse the primary expression after the binary operator. *)</span>
+        <span class="k">let</span> <span class="n">rhs</span> <span class="o">=</span> <span class="n">parse_unary</span> <span class="n">stream</span> <span class="k">in</span>
+
+        <span class="c">(* Okay, we know this is a binop. *)</span>
+        <span class="k">let</span> <span class="n">rhs</span> <span class="o">=</span>
+          <span class="k">match</span> <span class="nn">Stream</span><span class="p">.</span><span class="n">peek</span> <span class="n">stream</span> <span class="k">with</span>
+          <span class="o">|</span> <span class="nc">Some</span> <span class="o">(</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="n">c2</span><span class="o">)</span> <span class="o">-></span>
+              <span class="c">(* If BinOp binds less tightly with rhs than the operator after</span>
+<span class="c">               * rhs, let the pending operator take rhs as its lhs. *)</span>
+              <span class="k">let</span> <span class="n">next_prec</span> <span class="o">=</span> <span class="n">precedence</span> <span class="n">c2</span> <span class="k">in</span>
+              <span class="k">if</span> <span class="n">token_prec</span> <span class="o"><</span> <span class="n">next_prec</span>
+              <span class="k">then</span> <span class="n">parse_bin_rhs</span> <span class="o">(</span><span class="n">token_prec</span> <span class="o">+</span> <span class="mi">1</span><span class="o">)</span> <span class="n">rhs</span> <span class="n">stream</span>
+              <span class="k">else</span> <span class="n">rhs</span>
+          <span class="o">|</span> <span class="o">_</span> <span class="o">-></span> <span class="n">rhs</span>
+        <span class="k">in</span>
+
+        <span class="c">(* Merge lhs/rhs. *)</span>
+        <span class="k">let</span> <span class="n">lhs</span> <span class="o">=</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Binary</span> <span class="o">(</span><span class="n">c</span><span class="o">,</span> <span class="n">lhs</span><span class="o">,</span> <span class="n">rhs</span><span class="o">)</span> <span class="k">in</span>
+        <span class="n">parse_bin_rhs</span> <span class="n">expr_prec</span> <span class="n">lhs</span> <span class="n">stream</span>
+      <span class="k">end</span>
+  <span class="o">|</span> <span class="o">_</span> <span class="o">-></span> <span class="n">lhs</span>
+
+<span class="ow">and</span> <span class="n">parse_var_init</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="c">(* read in the optional initializer. *)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">'='</span><span class="o">;</span> <span class="n">e</span><span class="o">=</span><span class="n">parse_expr</span> <span class="o">>]</span> <span class="o">-></span> <span class="nc">Some</span> <span class="n">e</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span> <span class="nc">None</span>
+
+<span class="ow">and</span> <span class="n">parse_var_names</span> <span class="n">accumulator</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">','</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Ident</span> <span class="n">id</span> <span class="o">??</span> <span class="s2">"expected identifier list after var"</span><span class="o">;</span>
+       <span class="n">init</span><span class="o">=</span><span class="n">parse_var_init</span><span class="o">;</span>
+       <span class="n">e</span><span class="o">=</span><span class="n">parse_var_names</span> <span class="o">((</span><span class="n">id</span><span class="o">,</span> <span class="n">init</span><span class="o">)</span> <span class="o">::</span> <span class="n">accumulator</span><span class="o">)</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">e</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">accumulator</span>
+
+<span class="c">(* expression</span>
+<span class="c"> *   ::= primary binoprhs *)</span>
+<span class="ow">and</span> <span class="n">parse_expr</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="n">lhs</span><span class="o">=</span><span class="n">parse_unary</span><span class="o">;</span> <span class="n">stream</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">parse_bin_rhs</span> <span class="mi">0</span> <span class="n">lhs</span> <span class="n">stream</span>
+
+<span class="c">(* prototype</span>
+<span class="c"> *   ::= id '(' id* ')'</span>
+<span class="c"> *   ::= binary LETTER number? (id, id)</span>
+<span class="c"> *   ::= unary LETTER number? (id) *)</span>
+<span class="k">let</span> <span class="n">parse_prototype</span> <span class="o">=</span>
+  <span class="k">let</span> <span class="k">rec</span> <span class="n">parse_args</span> <span class="n">accumulator</span> <span class="o">=</span> <span class="n">parser</span>
+    <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Ident</span> <span class="n">id</span><span class="o">;</span> <span class="n">e</span><span class="o">=</span><span class="n">parse_args</span> <span class="o">(</span><span class="n">id</span><span class="o">::</span><span class="n">accumulator</span><span class="o">)</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">e</span>
+    <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">accumulator</span>
+  <span class="k">in</span>
+  <span class="k">let</span> <span class="n">parse_operator</span> <span class="o">=</span> <span class="n">parser</span>
+    <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Unary</span> <span class="o">>]</span> <span class="o">-></span> <span class="s2">"unary"</span><span class="o">,</span> <span class="mi">1</span>
+    <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Binary</span> <span class="o">>]</span> <span class="o">-></span> <span class="s2">"binary"</span><span class="o">,</span> <span class="mi">2</span>
+  <span class="k">in</span>
+  <span class="k">let</span> <span class="n">parse_binary_precedence</span> <span class="o">=</span> <span class="n">parser</span>
+    <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Number</span> <span class="n">n</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">int_of_float</span> <span class="n">n</span>
+    <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span> <span class="mi">30</span>
+  <span class="k">in</span>
+  <span class="n">parser</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Ident</span> <span class="n">id</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">'('</span> <span class="o">??</span> <span class="s2">"expected '(' in prototype"</span><span class="o">;</span>
+       <span class="n">args</span><span class="o">=</span><span class="n">parse_args</span> <span class="bp">[]</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">')'</span> <span class="o">??</span> <span class="s2">"expected ')' in prototype"</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="c">(* success. *)</span>
+      <span class="nn">Ast</span><span class="p">.</span><span class="nc">Prototype</span> <span class="o">(</span><span class="n">id</span><span class="o">,</span> <span class="nn">Array</span><span class="p">.</span><span class="n">of_list</span> <span class="o">(</span><span class="nn">List</span><span class="p">.</span><span class="n">rev</span> <span class="n">args</span><span class="o">))</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="o">(</span><span class="n">prefix</span><span class="o">,</span> <span class="n">kind</span><span class="o">)=</span><span class="n">parse_operator</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="n">op</span> <span class="o">??</span> <span class="s2">"expected an operator"</span><span class="o">;</span>
+       <span class="c">(* Read the precedence if present. *)</span>
+       <span class="n">binary_precedence</span><span class="o">=</span><span class="n">parse_binary_precedence</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">'('</span> <span class="o">??</span> <span class="s2">"expected '(' in prototype"</span><span class="o">;</span>
+        <span class="n">args</span><span class="o">=</span><span class="n">parse_args</span> <span class="bp">[]</span><span class="o">;</span>
+       <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">')'</span> <span class="o">??</span> <span class="s2">"expected ')' in prototype"</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="k">let</span> <span class="n">name</span> <span class="o">=</span> <span class="n">prefix</span> <span class="o">^</span> <span class="o">(</span><span class="nn">String</span><span class="p">.</span><span class="n">make</span> <span class="mi">1</span> <span class="n">op</span><span class="o">)</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">args</span> <span class="o">=</span> <span class="nn">Array</span><span class="p">.</span><span class="n">of_list</span> <span class="o">(</span><span class="nn">List</span><span class="p">.</span><span class="n">rev</span> <span class="n">args</span><span class="o">)</span> <span class="k">in</span>
+
+      <span class="c">(* Verify right number of arguments for operator. *)</span>
+      <span class="k">if</span> <span class="nn">Array</span><span class="p">.</span><span class="n">length</span> <span class="n">args</span> <span class="o">!=</span> <span class="n">kind</span>
+      <span class="k">then</span> <span class="k">raise</span> <span class="o">(</span><span class="nn">Stream</span><span class="p">.</span><span class="nc">Error</span> <span class="s2">"invalid number of operands for operator"</span><span class="o">)</span>
+      <span class="k">else</span>
+        <span class="k">if</span> <span class="n">kind</span> <span class="o">==</span> <span class="mi">1</span> <span class="k">then</span>
+          <span class="nn">Ast</span><span class="p">.</span><span class="nc">Prototype</span> <span class="o">(</span><span class="n">name</span><span class="o">,</span> <span class="n">args</span><span class="o">)</span>
+        <span class="k">else</span>
+          <span class="nn">Ast</span><span class="p">.</span><span class="nc">BinOpPrototype</span> <span class="o">(</span><span class="n">name</span><span class="o">,</span> <span class="n">args</span><span class="o">,</span> <span class="n">binary_precedence</span><span class="o">)</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="k">raise</span> <span class="o">(</span><span class="nn">Stream</span><span class="p">.</span><span class="nc">Error</span> <span class="s2">"expected function name in prototype"</span><span class="o">)</span>
+
+<span class="c">(* definition ::= 'def' prototype expression *)</span>
+<span class="k">let</span> <span class="n">parse_definition</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Def</span><span class="o">;</span> <span class="n">p</span><span class="o">=</span><span class="n">parse_prototype</span><span class="o">;</span> <span class="n">e</span><span class="o">=</span><span class="n">parse_expr</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="nn">Ast</span><span class="p">.</span><span class="nc">Function</span> <span class="o">(</span><span class="n">p</span><span class="o">,</span> <span class="n">e</span><span class="o">)</span>
+
+<span class="c">(* toplevelexpr ::= expression *)</span>
+<span class="k">let</span> <span class="n">parse_toplevel</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="n">e</span><span class="o">=</span><span class="n">parse_expr</span> <span class="o">>]</span> <span class="o">-></span>
+      <span class="c">(* Make an anonymous proto. *)</span>
+      <span class="nn">Ast</span><span class="p">.</span><span class="nc">Function</span> <span class="o">(</span><span class="nn">Ast</span><span class="p">.</span><span class="nc">Prototype</span> <span class="o">(</span><span class="s2">""</span><span class="o">,</span> <span class="o">[||]),</span> <span class="n">e</span><span class="o">)</span>
+
+<span class="c">(*  external ::= 'extern' prototype *)</span>
+<span class="k">let</span> <span class="n">parse_extern</span> <span class="o">=</span> <span class="n">parser</span>
+  <span class="o">|</span> <span class="o">[<</span> <span class="k">'</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Extern</span><span class="o">;</span> <span class="n">e</span><span class="o">=</span><span class="n">parse_prototype</span> <span class="o">>]</span> <span class="o">-></span> <span class="n">e</span>
+</pre></div>
+</div>
+</dd>
+<dt>codegen.ml:</dt>
+<dd><div class="first last highlight-ocaml"><div class="highlight"><pre><span class="c">(*===----------------------------------------------------------------------===</span>
+<span class="c"> * Code Generation</span>
+<span class="c"> *===----------------------------------------------------------------------===*)</span>
+
+<span class="k">open</span> <span class="nc">Llvm</span>
+
+<span class="k">exception</span> <span class="nc">Error</span> <span class="k">of</span> <span class="kt">string</span>
+
+<span class="k">let</span> <span class="n">context</span> <span class="o">=</span> <span class="n">global_context</span> <span class="bp">()</span>
+<span class="k">let</span> <span class="n">the_module</span> <span class="o">=</span> <span class="n">create_module</span> <span class="n">context</span> <span class="s2">"my cool jit"</span>
+<span class="k">let</span> <span class="n">builder</span> <span class="o">=</span> <span class="n">builder</span> <span class="n">context</span>
+<span class="k">let</span> <span class="n">named_values</span><span class="o">:(</span><span class="kt">string</span><span class="o">,</span> <span class="n">llvalue</span><span class="o">)</span> <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">t</span> <span class="o">=</span> <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">create</span> <span class="mi">10</span>
+<span class="k">let</span> <span class="n">double_type</span> <span class="o">=</span> <span class="n">double_type</span> <span class="n">context</span>
+
+<span class="c">(* Create an alloca instruction in the entry block of the function. This</span>
+<span class="c"> * is used for mutable variables etc. *)</span>
+<span class="k">let</span> <span class="n">create_entry_block_alloca</span> <span class="n">the_function</span> <span class="n">var_name</span> <span class="o">=</span>
+  <span class="k">let</span> <span class="n">builder</span> <span class="o">=</span> <span class="n">builder_at</span> <span class="n">context</span> <span class="o">(</span><span class="n">instr_begin</span> <span class="o">(</span><span class="n">entry_block</span> <span class="n">the_function</span><span class="o">))</span> <span class="k">in</span>
+  <span class="n">build_alloca</span> <span class="n">double_type</span> <span class="n">var_name</span> <span class="n">builder</span>
+
+<span class="k">let</span> <span class="k">rec</span> <span class="n">codegen_expr</span> <span class="o">=</span> <span class="k">function</span>
+  <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Number</span> <span class="n">n</span> <span class="o">-></span> <span class="n">const_float</span> <span class="n">double_type</span> <span class="n">n</span>
+  <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Variable</span> <span class="n">name</span> <span class="o">-></span>
+      <span class="k">let</span> <span class="n">v</span> <span class="o">=</span> <span class="k">try</span> <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">find</span> <span class="n">named_values</span> <span class="n">name</span> <span class="k">with</span>
+        <span class="o">|</span> <span class="nc">Not_found</span> <span class="o">-></span> <span class="k">raise</span> <span class="o">(</span><span class="nc">Error</span> <span class="s2">"unknown variable name"</span><span class="o">)</span>
+      <span class="k">in</span>
+      <span class="c">(* Load the value. *)</span>
+      <span class="n">build_load</span> <span class="n">v</span> <span class="n">name</span> <span class="n">builder</span>
+  <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Unary</span> <span class="o">(</span><span class="n">op</span><span class="o">,</span> <span class="n">operand</span><span class="o">)</span> <span class="o">-></span>
+      <span class="k">let</span> <span class="n">operand</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">operand</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">callee</span> <span class="o">=</span> <span class="s2">"unary"</span> <span class="o">^</span> <span class="o">(</span><span class="nn">String</span><span class="p">.</span><span class="n">make</span> <span class="mi">1</span> <span class="n">op</span><span class="o">)</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">callee</span> <span class="o">=</span>
+        <span class="k">match</span> <span class="n">lookup_function</span> <span class="n">callee</span> <span class="n">the_module</span> <span class="k">with</span>
+        <span class="o">|</span> <span class="nc">Some</span> <span class="n">callee</span> <span class="o">-></span> <span class="n">callee</span>
+        <span class="o">|</span> <span class="nc">None</span> <span class="o">-></span> <span class="k">raise</span> <span class="o">(</span><span class="nc">Error</span> <span class="s2">"unknown unary operator"</span><span class="o">)</span>
+      <span class="k">in</span>
+      <span class="n">build_call</span> <span class="n">callee</span> <span class="o">[|</span><span class="n">operand</span><span class="o">|]</span> <span class="s2">"unop"</span> <span class="n">builder</span>
+  <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Binary</span> <span class="o">(</span><span class="n">op</span><span class="o">,</span> <span class="n">lhs</span><span class="o">,</span> <span class="n">rhs</span><span class="o">)</span> <span class="o">-></span>
+      <span class="k">begin</span> <span class="k">match</span> <span class="n">op</span> <span class="k">with</span>
+      <span class="o">|</span> <span class="sc">'='</span> <span class="o">-></span>
+          <span class="c">(* Special case '=' because we don't want to emit the LHS as an</span>
+<span class="c">           * expression. *)</span>
+          <span class="k">let</span> <span class="n">name</span> <span class="o">=</span>
+            <span class="k">match</span> <span class="n">lhs</span> <span class="k">with</span>
+            <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Variable</span> <span class="n">name</span> <span class="o">-></span> <span class="n">name</span>
+            <span class="o">|</span> <span class="o">_</span> <span class="o">-></span> <span class="k">raise</span> <span class="o">(</span><span class="nc">Error</span> <span class="s2">"destination of '=' must be a variable"</span><span class="o">)</span>
+          <span class="k">in</span>
+
+          <span class="c">(* Codegen the rhs. *)</span>
+          <span class="k">let</span> <span class="n">val_</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">rhs</span> <span class="k">in</span>
+
+          <span class="c">(* Lookup the name. *)</span>
+          <span class="k">let</span> <span class="n">variable</span> <span class="o">=</span> <span class="k">try</span> <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">find</span> <span class="n">named_values</span> <span class="n">name</span> <span class="k">with</span>
+          <span class="o">|</span> <span class="nc">Not_found</span> <span class="o">-></span> <span class="k">raise</span> <span class="o">(</span><span class="nc">Error</span> <span class="s2">"unknown variable name"</span><span class="o">)</span>
+          <span class="k">in</span>
+          <span class="n">ignore</span><span class="o">(</span><span class="n">build_store</span> <span class="n">val_</span> <span class="n">variable</span> <span class="n">builder</span><span class="o">);</span>
+          <span class="n">val_</span>
+      <span class="o">|</span> <span class="o">_</span> <span class="o">-></span>
+          <span class="k">let</span> <span class="n">lhs_val</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">lhs</span> <span class="k">in</span>
+          <span class="k">let</span> <span class="n">rhs_val</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">rhs</span> <span class="k">in</span>
+          <span class="k">begin</span>
+            <span class="k">match</span> <span class="n">op</span> <span class="k">with</span>
+            <span class="o">|</span> <span class="sc">'+'</span> <span class="o">-></span> <span class="n">build_add</span> <span class="n">lhs_val</span> <span class="n">rhs_val</span> <span class="s2">"addtmp"</span> <span class="n">builder</span>
+            <span class="o">|</span> <span class="sc">'-'</span> <span class="o">-></span> <span class="n">build_sub</span> <span class="n">lhs_val</span> <span class="n">rhs_val</span> <span class="s2">"subtmp"</span> <span class="n">builder</span>
+            <span class="o">|</span> <span class="sc">'*'</span> <span class="o">-></span> <span class="n">build_mul</span> <span class="n">lhs_val</span> <span class="n">rhs_val</span> <span class="s2">"multmp"</span> <span class="n">builder</span>
+            <span class="o">|</span> <span class="sc">'<'</span> <span class="o">-></span>
+                <span class="c">(* Convert bool 0/1 to double 0.0 or 1.0 *)</span>
+                <span class="k">let</span> <span class="n">i</span> <span class="o">=</span> <span class="n">build_fcmp</span> <span class="nn">Fcmp</span><span class="p">.</span><span class="nc">Ult</span> <span class="n">lhs_val</span> <span class="n">rhs_val</span> <span class="s2">"cmptmp"</span> <span class="n">builder</span> <span class="k">in</span>
+                <span class="n">build_uitofp</span> <span class="n">i</span> <span class="n">double_type</span> <span class="s2">"booltmp"</span> <span class="n">builder</span>
+            <span class="o">|</span> <span class="o">_</span> <span class="o">-></span>
+                <span class="c">(* If it wasn't a builtin binary operator, it must be a user defined</span>
+<span class="c">                 * one. Emit a call to it. *)</span>
+                <span class="k">let</span> <span class="n">callee</span> <span class="o">=</span> <span class="s2">"binary"</span> <span class="o">^</span> <span class="o">(</span><span class="nn">String</span><span class="p">.</span><span class="n">make</span> <span class="mi">1</span> <span class="n">op</span><span class="o">)</span> <span class="k">in</span>
+                <span class="k">let</span> <span class="n">callee</span> <span class="o">=</span>
+                  <span class="k">match</span> <span class="n">lookup_function</span> <span class="n">callee</span> <span class="n">the_module</span> <span class="k">with</span>
+                  <span class="o">|</span> <span class="nc">Some</span> <span class="n">callee</span> <span class="o">-></span> <span class="n">callee</span>
+                  <span class="o">|</span> <span class="nc">None</span> <span class="o">-></span> <span class="k">raise</span> <span class="o">(</span><span class="nc">Error</span> <span class="s2">"binary operator not found!"</span><span class="o">)</span>
+                <span class="k">in</span>
+                <span class="n">build_call</span> <span class="n">callee</span> <span class="o">[|</span><span class="n">lhs_val</span><span class="o">;</span> <span class="n">rhs_val</span><span class="o">|]</span> <span class="s2">"binop"</span> <span class="n">builder</span>
+          <span class="k">end</span>
+      <span class="k">end</span>
+  <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Call</span> <span class="o">(</span><span class="n">callee</span><span class="o">,</span> <span class="n">args</span><span class="o">)</span> <span class="o">-></span>
+      <span class="c">(* Look up the name in the module table. *)</span>
+      <span class="k">let</span> <span class="n">callee</span> <span class="o">=</span>
+        <span class="k">match</span> <span class="n">lookup_function</span> <span class="n">callee</span> <span class="n">the_module</span> <span class="k">with</span>
+        <span class="o">|</span> <span class="nc">Some</span> <span class="n">callee</span> <span class="o">-></span> <span class="n">callee</span>
+        <span class="o">|</span> <span class="nc">None</span> <span class="o">-></span> <span class="k">raise</span> <span class="o">(</span><span class="nc">Error</span> <span class="s2">"unknown function referenced"</span><span class="o">)</span>
+      <span class="k">in</span>
+      <span class="k">let</span> <span class="n">params</span> <span class="o">=</span> <span class="n">params</span> <span class="n">callee</span> <span class="k">in</span>
+
+      <span class="c">(* If argument mismatch error. *)</span>
+      <span class="k">if</span> <span class="nn">Array</span><span class="p">.</span><span class="n">length</span> <span class="n">params</span> <span class="o">==</span> <span class="nn">Array</span><span class="p">.</span><span class="n">length</span> <span class="n">args</span> <span class="k">then</span> <span class="bp">()</span> <span class="k">else</span>
+        <span class="k">raise</span> <span class="o">(</span><span class="nc">Error</span> <span class="s2">"incorrect # arguments passed"</span><span class="o">);</span>
+      <span class="k">let</span> <span class="n">args</span> <span class="o">=</span> <span class="nn">Array</span><span class="p">.</span><span class="n">map</span> <span class="n">codegen_expr</span> <span class="n">args</span> <span class="k">in</span>
+      <span class="n">build_call</span> <span class="n">callee</span> <span class="n">args</span> <span class="s2">"calltmp"</span> <span class="n">builder</span>
+  <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">If</span> <span class="o">(</span><span class="n">cond</span><span class="o">,</span> <span class="n">then_</span><span class="o">,</span> <span class="n">else_</span><span class="o">)</span> <span class="o">-></span>
+      <span class="k">let</span> <span class="n">cond</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">cond</span> <span class="k">in</span>
+
+      <span class="c">(* Convert condition to a bool by comparing equal to 0.0 *)</span>
+      <span class="k">let</span> <span class="n">zero</span> <span class="o">=</span> <span class="n">const_float</span> <span class="n">double_type</span> <span class="mi">0</span><span class="o">.</span><span class="mi">0</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">cond_val</span> <span class="o">=</span> <span class="n">build_fcmp</span> <span class="nn">Fcmp</span><span class="p">.</span><span class="nc">One</span> <span class="n">cond</span> <span class="n">zero</span> <span class="s2">"ifcond"</span> <span class="n">builder</span> <span class="k">in</span>
+
+      <span class="c">(* Grab the first block so that we might later add the conditional branch</span>
+<span class="c">       * to it at the end of the function. *)</span>
+      <span class="k">let</span> <span class="n">start_bb</span> <span class="o">=</span> <span class="n">insertion_block</span> <span class="n">builder</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">the_function</span> <span class="o">=</span> <span class="n">block_parent</span> <span class="n">start_bb</span> <span class="k">in</span>
+
+      <span class="k">let</span> <span class="n">then_bb</span> <span class="o">=</span> <span class="n">append_block</span> <span class="n">context</span> <span class="s2">"then"</span> <span class="n">the_function</span> <span class="k">in</span>
+
+      <span class="c">(* Emit 'then' value. *)</span>
+      <span class="n">position_at_end</span> <span class="n">then_bb</span> <span class="n">builder</span><span class="o">;</span>
+      <span class="k">let</span> <span class="n">then_val</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">then_</span> <span class="k">in</span>
+
+      <span class="c">(* Codegen of 'then' can change the current block, update then_bb for the</span>
+<span class="c">       * phi. We create a new name because one is used for the phi node, and the</span>
+<span class="c">       * other is used for the conditional branch. *)</span>
+      <span class="k">let</span> <span class="n">new_then_bb</span> <span class="o">=</span> <span class="n">insertion_block</span> <span class="n">builder</span> <span class="k">in</span>
+
+      <span class="c">(* Emit 'else' value. *)</span>
+      <span class="k">let</span> <span class="n">else_bb</span> <span class="o">=</span> <span class="n">append_block</span> <span class="n">context</span> <span class="s2">"else"</span> <span class="n">the_function</span> <span class="k">in</span>
+      <span class="n">position_at_end</span> <span class="n">else_bb</span> <span class="n">builder</span><span class="o">;</span>
+      <span class="k">let</span> <span class="n">else_val</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">else_</span> <span class="k">in</span>
+
+      <span class="c">(* Codegen of 'else' can change the current block, update else_bb for the</span>
+<span class="c">       * phi. *)</span>
+      <span class="k">let</span> <span class="n">new_else_bb</span> <span class="o">=</span> <span class="n">insertion_block</span> <span class="n">builder</span> <span class="k">in</span>
+
+      <span class="c">(* Emit merge block. *)</span>
+      <span class="k">let</span> <span class="n">merge_bb</span> <span class="o">=</span> <span class="n">append_block</span> <span class="n">context</span> <span class="s2">"ifcont"</span> <span class="n">the_function</span> <span class="k">in</span>
+      <span class="n">position_at_end</span> <span class="n">merge_bb</span> <span class="n">builder</span><span class="o">;</span>
+      <span class="k">let</span> <span class="n">incoming</span> <span class="o">=</span> <span class="o">[(</span><span class="n">then_val</span><span class="o">,</span> <span class="n">new_then_bb</span><span class="o">);</span> <span class="o">(</span><span class="n">else_val</span><span class="o">,</span> <span class="n">new_else_bb</span><span class="o">)]</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">phi</span> <span class="o">=</span> <span class="n">build_phi</span> <span class="n">incoming</span> <span class="s2">"iftmp"</span> <span class="n">builder</span> <span class="k">in</span>
+
+      <span class="c">(* Return to the start block to add the conditional branch. *)</span>
+      <span class="n">position_at_end</span> <span class="n">start_bb</span> <span class="n">builder</span><span class="o">;</span>
+      <span class="n">ignore</span> <span class="o">(</span><span class="n">build_cond_br</span> <span class="n">cond_val</span> <span class="n">then_bb</span> <span class="n">else_bb</span> <span class="n">builder</span><span class="o">);</span>
+
+      <span class="c">(* Set a unconditional branch at the end of the 'then' block and the</span>
+<span class="c">       * 'else' block to the 'merge' block. *)</span>
+      <span class="n">position_at_end</span> <span class="n">new_then_bb</span> <span class="n">builder</span><span class="o">;</span> <span class="n">ignore</span> <span class="o">(</span><span class="n">build_br</span> <span class="n">merge_bb</span> <span class="n">builder</span><span class="o">);</span>
+      <span class="n">position_at_end</span> <span class="n">new_else_bb</span> <span class="n">builder</span><span class="o">;</span> <span class="n">ignore</span> <span class="o">(</span><span class="n">build_br</span> <span class="n">merge_bb</span> <span class="n">builder</span><span class="o">);</span>
+
+      <span class="c">(* Finally, set the builder to the end of the merge block. *)</span>
+      <span class="n">position_at_end</span> <span class="n">merge_bb</span> <span class="n">builder</span><span class="o">;</span>
+
+      <span class="n">phi</span>
+  <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">For</span> <span class="o">(</span><span class="n">var_name</span><span class="o">,</span> <span class="n">start</span><span class="o">,</span> <span class="n">end_</span><span class="o">,</span> <span class="n">step</span><span class="o">,</span> <span class="n">body</span><span class="o">)</span> <span class="o">-></span>
+      <span class="c">(* Output this as:</span>
+<span class="c">       *   var = alloca double</span>
+<span class="c">       *   ...</span>
+<span class="c">       *   start = startexpr</span>
+<span class="c">       *   store start -> var</span>
+<span class="c">       *   goto loop</span>
+<span class="c">       * loop:</span>
+<span class="c">       *   ...</span>
+<span class="c">       *   bodyexpr</span>
+<span class="c">       *   ...</span>
+<span class="c">       * loopend:</span>
+<span class="c">       *   step = stepexpr</span>
+<span class="c">       *   endcond = endexpr</span>
+<span class="c">       *</span>
+<span class="c">       *   curvar = load var</span>
+<span class="c">       *   nextvar = curvar + step</span>
+<span class="c">       *   store nextvar -> var</span>
+<span class="c">       *   br endcond, loop, endloop</span>
+<span class="c">       * outloop: *)</span>
+
+      <span class="k">let</span> <span class="n">the_function</span> <span class="o">=</span> <span class="n">block_parent</span> <span class="o">(</span><span class="n">insertion_block</span> <span class="n">builder</span><span class="o">)</span> <span class="k">in</span>
+
+      <span class="c">(* Create an alloca for the variable in the entry block. *)</span>
+      <span class="k">let</span> <span class="n">alloca</span> <span class="o">=</span> <span class="n">create_entry_block_alloca</span> <span class="n">the_function</span> <span class="n">var_name</span> <span class="k">in</span>
+
+      <span class="c">(* Emit the start code first, without 'variable' in scope. *)</span>
+      <span class="k">let</span> <span class="n">start_val</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">start</span> <span class="k">in</span>
+
+      <span class="c">(* Store the value into the alloca. *)</span>
+      <span class="n">ignore</span><span class="o">(</span><span class="n">build_store</span> <span class="n">start_val</span> <span class="n">alloca</span> <span class="n">builder</span><span class="o">);</span>
+
+      <span class="c">(* Make the new basic block for the loop header, inserting after current</span>
+<span class="c">       * block. *)</span>
+      <span class="k">let</span> <span class="n">loop_bb</span> <span class="o">=</span> <span class="n">append_block</span> <span class="n">context</span> <span class="s2">"loop"</span> <span class="n">the_function</span> <span class="k">in</span>
+
+      <span class="c">(* Insert an explicit fall through from the current block to the</span>
+<span class="c">       * loop_bb. *)</span>
+      <span class="n">ignore</span> <span class="o">(</span><span class="n">build_br</span> <span class="n">loop_bb</span> <span class="n">builder</span><span class="o">);</span>
+
+      <span class="c">(* Start insertion in loop_bb. *)</span>
+      <span class="n">position_at_end</span> <span class="n">loop_bb</span> <span class="n">builder</span><span class="o">;</span>
+
+      <span class="c">(* Within the loop, the variable is defined equal to the PHI node. If it</span>
+<span class="c">       * shadows an existing variable, we have to restore it, so save it</span>
+<span class="c">       * now. *)</span>
+      <span class="k">let</span> <span class="n">old_val</span> <span class="o">=</span>
+        <span class="k">try</span> <span class="nc">Some</span> <span class="o">(</span><span class="nn">Hashtbl</span><span class="p">.</span><span class="n">find</span> <span class="n">named_values</span> <span class="n">var_name</span><span class="o">)</span> <span class="k">with</span> <span class="nc">Not_found</span> <span class="o">-></span> <span class="nc">None</span>
+      <span class="k">in</span>
+      <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="n">named_values</span> <span class="n">var_name</span> <span class="n">alloca</span><span class="o">;</span>
+
+      <span class="c">(* Emit the body of the loop.  This, like any other expr, can change the</span>
+<span class="c">       * current BB.  Note that we ignore the value computed by the body, but</span>
+<span class="c">       * don't allow an error *)</span>
+      <span class="n">ignore</span> <span class="o">(</span><span class="n">codegen_expr</span> <span class="n">body</span><span class="o">);</span>
+
+      <span class="c">(* Emit the step value. *)</span>
+      <span class="k">let</span> <span class="n">step_val</span> <span class="o">=</span>
+        <span class="k">match</span> <span class="n">step</span> <span class="k">with</span>
+        <span class="o">|</span> <span class="nc">Some</span> <span class="n">step</span> <span class="o">-></span> <span class="n">codegen_expr</span> <span class="n">step</span>
+        <span class="c">(* If not specified, use 1.0. *)</span>
+        <span class="o">|</span> <span class="nc">None</span> <span class="o">-></span> <span class="n">const_float</span> <span class="n">double_type</span> <span class="mi">1</span><span class="o">.</span><span class="mi">0</span>
+      <span class="k">in</span>
+
+      <span class="c">(* Compute the end condition. *)</span>
+      <span class="k">let</span> <span class="n">end_cond</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">end_</span> <span class="k">in</span>
+
+      <span class="c">(* Reload, increment, and restore the alloca. This handles the case where</span>
+<span class="c">       * the body of the loop mutates the variable. *)</span>
+      <span class="k">let</span> <span class="n">cur_var</span> <span class="o">=</span> <span class="n">build_load</span> <span class="n">alloca</span> <span class="n">var_name</span> <span class="n">builder</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">next_var</span> <span class="o">=</span> <span class="n">build_add</span> <span class="n">cur_var</span> <span class="n">step_val</span> <span class="s2">"nextvar"</span> <span class="n">builder</span> <span class="k">in</span>
+      <span class="n">ignore</span><span class="o">(</span><span class="n">build_store</span> <span class="n">next_var</span> <span class="n">alloca</span> <span class="n">builder</span><span class="o">);</span>
+
+      <span class="c">(* Convert condition to a bool by comparing equal to 0.0. *)</span>
+      <span class="k">let</span> <span class="n">zero</span> <span class="o">=</span> <span class="n">const_float</span> <span class="n">double_type</span> <span class="mi">0</span><span class="o">.</span><span class="mi">0</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">end_cond</span> <span class="o">=</span> <span class="n">build_fcmp</span> <span class="nn">Fcmp</span><span class="p">.</span><span class="nc">One</span> <span class="n">end_cond</span> <span class="n">zero</span> <span class="s2">"loopcond"</span> <span class="n">builder</span> <span class="k">in</span>
+
+      <span class="c">(* Create the "after loop" block and insert it. *)</span>
+      <span class="k">let</span> <span class="n">after_bb</span> <span class="o">=</span> <span class="n">append_block</span> <span class="n">context</span> <span class="s2">"afterloop"</span> <span class="n">the_function</span> <span class="k">in</span>
+
+      <span class="c">(* Insert the conditional branch into the end of loop_end_bb. *)</span>
+      <span class="n">ignore</span> <span class="o">(</span><span class="n">build_cond_br</span> <span class="n">end_cond</span> <span class="n">loop_bb</span> <span class="n">after_bb</span> <span class="n">builder</span><span class="o">);</span>
+
+      <span class="c">(* Any new code will be inserted in after_bb. *)</span>
+      <span class="n">position_at_end</span> <span class="n">after_bb</span> <span class="n">builder</span><span class="o">;</span>
+
+      <span class="c">(* Restore the unshadowed variable. *)</span>
+      <span class="k">begin</span> <span class="k">match</span> <span class="n">old_val</span> <span class="k">with</span>
+      <span class="o">|</span> <span class="nc">Some</span> <span class="n">old_val</span> <span class="o">-></span> <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="n">named_values</span> <span class="n">var_name</span> <span class="n">old_val</span>
+      <span class="o">|</span> <span class="nc">None</span> <span class="o">-></span> <span class="bp">()</span>
+      <span class="k">end</span><span class="o">;</span>
+
+      <span class="c">(* for expr always returns 0.0. *)</span>
+      <span class="n">const_null</span> <span class="n">double_type</span>
+  <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Var</span> <span class="o">(</span><span class="n">var_names</span><span class="o">,</span> <span class="n">body</span><span class="o">)</span> <span class="o">-></span>
+      <span class="k">let</span> <span class="n">old_bindings</span> <span class="o">=</span> <span class="n">ref</span> <span class="bp">[]</span> <span class="k">in</span>
+
+      <span class="k">let</span> <span class="n">the_function</span> <span class="o">=</span> <span class="n">block_parent</span> <span class="o">(</span><span class="n">insertion_block</span> <span class="n">builder</span><span class="o">)</span> <span class="k">in</span>
+
+      <span class="c">(* Register all variables and emit their initializer. *)</span>
+      <span class="nn">Array</span><span class="p">.</span><span class="n">iter</span> <span class="o">(</span><span class="k">fun</span> <span class="o">(</span><span class="n">var_name</span><span class="o">,</span> <span class="n">init</span><span class="o">)</span> <span class="o">-></span>
+        <span class="c">(* Emit the initializer before adding the variable to scope, this</span>
+<span class="c">         * prevents the initializer from referencing the variable itself, and</span>
+<span class="c">         * permits stuff like this:</span>
+<span class="c">         *   var a = 1 in</span>
+<span class="c">         *     var a = a in ...   # refers to outer 'a'. *)</span>
+        <span class="k">let</span> <span class="n">init_val</span> <span class="o">=</span>
+          <span class="k">match</span> <span class="n">init</span> <span class="k">with</span>
+          <span class="o">|</span> <span class="nc">Some</span> <span class="n">init</span> <span class="o">-></span> <span class="n">codegen_expr</span> <span class="n">init</span>
+          <span class="c">(* If not specified, use 0.0. *)</span>
+          <span class="o">|</span> <span class="nc">None</span> <span class="o">-></span> <span class="n">const_float</span> <span class="n">double_type</span> <span class="mi">0</span><span class="o">.</span><span class="mi">0</span>
+        <span class="k">in</span>
+
+        <span class="k">let</span> <span class="n">alloca</span> <span class="o">=</span> <span class="n">create_entry_block_alloca</span> <span class="n">the_function</span> <span class="n">var_name</span> <span class="k">in</span>
+        <span class="n">ignore</span><span class="o">(</span><span class="n">build_store</span> <span class="n">init_val</span> <span class="n">alloca</span> <span class="n">builder</span><span class="o">);</span>
+
+        <span class="c">(* Remember the old variable binding so that we can restore the binding</span>
+<span class="c">         * when we unrecurse. *)</span>
+        <span class="k">begin</span>
+          <span class="k">try</span>
+            <span class="k">let</span> <span class="n">old_value</span> <span class="o">=</span> <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">find</span> <span class="n">named_values</span> <span class="n">var_name</span> <span class="k">in</span>
+            <span class="n">old_bindings</span> <span class="o">:=</span> <span class="o">(</span><span class="n">var_name</span><span class="o">,</span> <span class="n">old_value</span><span class="o">)</span> <span class="o">::</span> <span class="o">!</span><span class="n">old_bindings</span><span class="o">;</span>
+          <span class="k">with</span> <span class="nc">Not_found</span> <span class="o">-></span> <span class="bp">()</span>
+        <span class="k">end</span><span class="o">;</span>
+
+        <span class="c">(* Remember this binding. *)</span>
+        <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="n">named_values</span> <span class="n">var_name</span> <span class="n">alloca</span><span class="o">;</span>
+      <span class="o">)</span> <span class="n">var_names</span><span class="o">;</span>
+
+      <span class="c">(* Codegen the body, now that all vars are in scope. *)</span>
+      <span class="k">let</span> <span class="n">body_val</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">body</span> <span class="k">in</span>
+
+      <span class="c">(* Pop all our variables from scope. *)</span>
+      <span class="nn">List</span><span class="p">.</span><span class="n">iter</span> <span class="o">(</span><span class="k">fun</span> <span class="o">(</span><span class="n">var_name</span><span class="o">,</span> <span class="n">old_value</span><span class="o">)</span> <span class="o">-></span>
+        <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="n">named_values</span> <span class="n">var_name</span> <span class="n">old_value</span>
+      <span class="o">)</span> <span class="o">!</span><span class="n">old_bindings</span><span class="o">;</span>
+
+      <span class="c">(* Return the body computation. *)</span>
+      <span class="n">body_val</span>
+
+<span class="k">let</span> <span class="n">codegen_proto</span> <span class="o">=</span> <span class="k">function</span>
+  <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Prototype</span> <span class="o">(</span><span class="n">name</span><span class="o">,</span> <span class="n">args</span><span class="o">)</span> <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">BinOpPrototype</span> <span class="o">(</span><span class="n">name</span><span class="o">,</span> <span class="n">args</span><span class="o">,</span> <span class="o">_)</span> <span class="o">-></span>
+      <span class="c">(* Make the function type: double(double,double) etc. *)</span>
+      <span class="k">let</span> <span class="n">doubles</span> <span class="o">=</span> <span class="nn">Array</span><span class="p">.</span><span class="n">make</span> <span class="o">(</span><span class="nn">Array</span><span class="p">.</span><span class="n">length</span> <span class="n">args</span><span class="o">)</span> <span class="n">double_type</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">ft</span> <span class="o">=</span> <span class="n">function_type</span> <span class="n">double_type</span> <span class="n">doubles</span> <span class="k">in</span>
+      <span class="k">let</span> <span class="n">f</span> <span class="o">=</span>
+        <span class="k">match</span> <span class="n">lookup_function</span> <span class="n">name</span> <span class="n">the_module</span> <span class="k">with</span>
+        <span class="o">|</span> <span class="nc">None</span> <span class="o">-></span> <span class="n">declare_function</span> <span class="n">name</span> <span class="n">ft</span> <span class="n">the_module</span>
+
+        <span class="c">(* If 'f' conflicted, there was already something named 'name'. If it</span>
+<span class="c">         * has a body, don't allow redefinition or reextern. *)</span>
+        <span class="o">|</span> <span class="nc">Some</span> <span class="n">f</span> <span class="o">-></span>
+            <span class="c">(* If 'f' already has a body, reject this. *)</span>
+            <span class="k">if</span> <span class="n">block_begin</span> <span class="n">f</span> <span class="o"><></span> <span class="nc">At_end</span> <span class="n">f</span> <span class="k">then</span>
+              <span class="k">raise</span> <span class="o">(</span><span class="nc">Error</span> <span class="s2">"redefinition of function"</span><span class="o">);</span>
+
+            <span class="c">(* If 'f' took a different number of arguments, reject. *)</span>
+            <span class="k">if</span> <span class="n">element_type</span> <span class="o">(</span><span class="n">type_of</span> <span class="n">f</span><span class="o">)</span> <span class="o"><></span> <span class="n">ft</span> <span class="k">then</span>
+              <span class="k">raise</span> <span class="o">(</span><span class="nc">Error</span> <span class="s2">"redefinition of function with different # args"</span><span class="o">);</span>
+            <span class="n">f</span>
+      <span class="k">in</span>
+
+      <span class="c">(* Set names for all arguments. *)</span>
+      <span class="nn">Array</span><span class="p">.</span><span class="n">iteri</span> <span class="o">(</span><span class="k">fun</span> <span class="n">i</span> <span class="n">a</span> <span class="o">-></span>
+        <span class="k">let</span> <span class="n">n</span> <span class="o">=</span> <span class="n">args</span><span class="o">.(</span><span class="n">i</span><span class="o">)</span> <span class="k">in</span>
+        <span class="n">set_value_name</span> <span class="n">n</span> <span class="n">a</span><span class="o">;</span>
+        <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="n">named_values</span> <span class="n">n</span> <span class="n">a</span><span class="o">;</span>
+      <span class="o">)</span> <span class="o">(</span><span class="n">params</span> <span class="n">f</span><span class="o">);</span>
+      <span class="n">f</span>
+
+<span class="c">(* Create an alloca for each argument and register the argument in the symbol</span>
+<span class="c"> * table so that references to it will succeed. *)</span>
+<span class="k">let</span> <span class="n">create_argument_allocas</span> <span class="n">the_function</span> <span class="n">proto</span> <span class="o">=</span>
+  <span class="k">let</span> <span class="n">args</span> <span class="o">=</span> <span class="k">match</span> <span class="n">proto</span> <span class="k">with</span>
+    <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Prototype</span> <span class="o">(_,</span> <span class="n">args</span><span class="o">)</span> <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">BinOpPrototype</span> <span class="o">(_,</span> <span class="n">args</span><span class="o">,</span> <span class="o">_)</span> <span class="o">-></span> <span class="n">args</span>
+  <span class="k">in</span>
+  <span class="nn">Array</span><span class="p">.</span><span class="n">iteri</span> <span class="o">(</span><span class="k">fun</span> <span class="n">i</span> <span class="n">ai</span> <span class="o">-></span>
+    <span class="k">let</span> <span class="n">var_name</span> <span class="o">=</span> <span class="n">args</span><span class="o">.(</span><span class="n">i</span><span class="o">)</span> <span class="k">in</span>
+    <span class="c">(* Create an alloca for this variable. *)</span>
+    <span class="k">let</span> <span class="n">alloca</span> <span class="o">=</span> <span class="n">create_entry_block_alloca</span> <span class="n">the_function</span> <span class="n">var_name</span> <span class="k">in</span>
+
+    <span class="c">(* Store the initial value into the alloca. *)</span>
+    <span class="n">ignore</span><span class="o">(</span><span class="n">build_store</span> <span class="n">ai</span> <span class="n">alloca</span> <span class="n">builder</span><span class="o">);</span>
+
+    <span class="c">(* Add arguments to variable symbol table. *)</span>
+    <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="n">named_values</span> <span class="n">var_name</span> <span class="n">alloca</span><span class="o">;</span>
+  <span class="o">)</span> <span class="o">(</span><span class="n">params</span> <span class="n">the_function</span><span class="o">)</span>
+
+<span class="k">let</span> <span class="n">codegen_func</span> <span class="n">the_fpm</span> <span class="o">=</span> <span class="k">function</span>
+  <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">Function</span> <span class="o">(</span><span class="n">proto</span><span class="o">,</span> <span class="n">body</span><span class="o">)</span> <span class="o">-></span>
+      <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">clear</span> <span class="n">named_values</span><span class="o">;</span>
+      <span class="k">let</span> <span class="n">the_function</span> <span class="o">=</span> <span class="n">codegen_proto</span> <span class="n">proto</span> <span class="k">in</span>
+
+      <span class="c">(* If this is an operator, install it. *)</span>
+      <span class="k">begin</span> <span class="k">match</span> <span class="n">proto</span> <span class="k">with</span>
+      <span class="o">|</span> <span class="nn">Ast</span><span class="p">.</span><span class="nc">BinOpPrototype</span> <span class="o">(</span><span class="n">name</span><span class="o">,</span> <span class="n">args</span><span class="o">,</span> <span class="n">prec</span><span class="o">)</span> <span class="o">-></span>
+          <span class="k">let</span> <span class="n">op</span> <span class="o">=</span> <span class="n">name</span><span class="o">.[</span><span class="nn">String</span><span class="p">.</span><span class="n">length</span> <span class="n">name</span> <span class="o">-</span> <span class="mi">1</span><span class="o">]</span> <span class="k">in</span>
+          <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="nn">Parser</span><span class="p">.</span><span class="n">binop_precedence</span> <span class="n">op</span> <span class="n">prec</span><span class="o">;</span>
+      <span class="o">|</span> <span class="o">_</span> <span class="o">-></span> <span class="bp">()</span>
+      <span class="k">end</span><span class="o">;</span>
+
+      <span class="c">(* Create a new basic block to start insertion into. *)</span>
+      <span class="k">let</span> <span class="n">bb</span> <span class="o">=</span> <span class="n">append_block</span> <span class="n">context</span> <span class="s2">"entry"</span> <span class="n">the_function</span> <span class="k">in</span>
+      <span class="n">position_at_end</span> <span class="n">bb</span> <span class="n">builder</span><span class="o">;</span>
+
+      <span class="k">try</span>
+        <span class="c">(* Add all arguments to the symbol table and create their allocas. *)</span>
+        <span class="n">create_argument_allocas</span> <span class="n">the_function</span> <span class="n">proto</span><span class="o">;</span>
+
+        <span class="k">let</span> <span class="n">ret_val</span> <span class="o">=</span> <span class="n">codegen_expr</span> <span class="n">body</span> <span class="k">in</span>
+
+        <span class="c">(* Finish off the function. *)</span>
+        <span class="k">let</span> <span class="o">_</span> <span class="o">=</span> <span class="n">build_ret</span> <span class="n">ret_val</span> <span class="n">builder</span> <span class="k">in</span>
+
+        <span class="c">(* Validate the generated code, checking for consistency. *)</span>
+        <span class="nn">Llvm_analysis</span><span class="p">.</span><span class="n">assert_valid_function</span> <span class="n">the_function</span><span class="o">;</span>
+
+        <span class="c">(* Optimize the function. *)</span>
+        <span class="k">let</span> <span class="o">_</span> <span class="o">=</span> <span class="nn">PassManager</span><span class="p">.</span><span class="n">run_function</span> <span class="n">the_function</span> <span class="n">the_fpm</span> <span class="k">in</span>
+
+        <span class="n">the_function</span>
+      <span class="k">with</span> <span class="n">e</span> <span class="o">-></span>
+        <span class="n">delete_function</span> <span class="n">the_function</span><span class="o">;</span>
+        <span class="k">raise</span> <span class="n">e</span>
+</pre></div>
+</div>
+</dd>
+<dt>toplevel.ml:</dt>
+<dd><div class="first last highlight-ocaml"><div class="highlight"><pre><span class="c">(*===----------------------------------------------------------------------===</span>
+<span class="c"> * Top-Level parsing and JIT Driver</span>
+<span class="c"> *===----------------------------------------------------------------------===*)</span>
+
+<span class="k">open</span> <span class="nc">Llvm</span>
+<span class="k">open</span> <span class="nc">Llvm_executionengine</span>
+
+<span class="c">(* top ::= definition | external | expression | ';' *)</span>
+<span class="k">let</span> <span class="k">rec</span> <span class="n">main_loop</span> <span class="n">the_fpm</span> <span class="n">the_execution_engine</span> <span class="n">stream</span> <span class="o">=</span>
+  <span class="k">match</span> <span class="nn">Stream</span><span class="p">.</span><span class="n">peek</span> <span class="n">stream</span> <span class="k">with</span>
+  <span class="o">|</span> <span class="nc">None</span> <span class="o">-></span> <span class="bp">()</span>
+
+  <span class="c">(* ignore top-level semicolons. *)</span>
+  <span class="o">|</span> <span class="nc">Some</span> <span class="o">(</span><span class="nn">Token</span><span class="p">.</span><span class="nc">Kwd</span> <span class="sc">';'</span><span class="o">)</span> <span class="o">-></span>
+      <span class="nn">Stream</span><span class="p">.</span><span class="n">junk</span> <span class="n">stream</span><span class="o">;</span>
+      <span class="n">main_loop</span> <span class="n">the_fpm</span> <span class="n">the_execution_engine</span> <span class="n">stream</span>
+
+  <span class="o">|</span> <span class="nc">Some</span> <span class="n">token</span> <span class="o">-></span>
+      <span class="k">begin</span>
+        <span class="k">try</span> <span class="k">match</span> <span class="n">token</span> <span class="k">with</span>
+        <span class="o">|</span> <span class="nn">Token</span><span class="p">.</span><span class="nc">Def</span> <span class="o">-></span>
+            <span class="k">let</span> <span class="n">e</span> <span class="o">=</span> <span class="nn">Parser</span><span class="p">.</span><span class="n">parse_definition</span> <span class="n">stream</span> <span class="k">in</span>
+            <span class="n">print_endline</span> <span class="s2">"parsed a function definition."</span><span class="o">;</span>
+            <span class="n">dump_value</span> <span class="o">(</span><span class="nn">Codegen</span><span class="p">.</span><span class="n">codegen_func</span> <span class="n">the_fpm</span> <span class="n">e</span><span class="o">);</span>
+        <span class="o">|</span> <span class="nn">Token</span><span class="p">.</span><span class="nc">Extern</span> <span class="o">-></span>
+            <span class="k">let</span> <span class="n">e</span> <span class="o">=</span> <span class="nn">Parser</span><span class="p">.</span><span class="n">parse_extern</span> <span class="n">stream</span> <span class="k">in</span>
+            <span class="n">print_endline</span> <span class="s2">"parsed an extern."</span><span class="o">;</span>
+            <span class="n">dump_value</span> <span class="o">(</span><span class="nn">Codegen</span><span class="p">.</span><span class="n">codegen_proto</span> <span class="n">e</span><span class="o">);</span>
+        <span class="o">|</span> <span class="o">_</span> <span class="o">-></span>
+            <span class="c">(* Evaluate a top-level expression into an anonymous function. *)</span>
+            <span class="k">let</span> <span class="n">e</span> <span class="o">=</span> <span class="nn">Parser</span><span class="p">.</span><span class="n">parse_toplevel</span> <span class="n">stream</span> <span class="k">in</span>
+            <span class="n">print_endline</span> <span class="s2">"parsed a top-level expr"</span><span class="o">;</span>
+            <span class="k">let</span> <span class="n">the_function</span> <span class="o">=</span> <span class="nn">Codegen</span><span class="p">.</span><span class="n">codegen_func</span> <span class="n">the_fpm</span> <span class="n">e</span> <span class="k">in</span>
+            <span class="n">dump_value</span> <span class="n">the_function</span><span class="o">;</span>
+
+            <span class="c">(* JIT the function, returning a function pointer. *)</span>
+            <span class="k">let</span> <span class="n">result</span> <span class="o">=</span> <span class="nn">ExecutionEngine</span><span class="p">.</span><span class="n">run_function</span> <span class="n">the_function</span> <span class="o">[||]</span>
+              <span class="n">the_execution_engine</span> <span class="k">in</span>
+
+            <span class="n">print_string</span> <span class="s2">"Evaluated to "</span><span class="o">;</span>
+            <span class="n">print_float</span> <span class="o">(</span><span class="nn">GenericValue</span><span class="p">.</span><span class="n">as_float</span> <span class="nn">Codegen</span><span class="p">.</span><span class="n">double_type</span> <span class="n">result</span><span class="o">);</span>
+            <span class="n">print_newline</span> <span class="bp">()</span><span class="o">;</span>
+        <span class="k">with</span> <span class="nn">Stream</span><span class="p">.</span><span class="nc">Error</span> <span class="n">s</span> <span class="o">|</span> <span class="nn">Codegen</span><span class="p">.</span><span class="nc">Error</span> <span class="n">s</span> <span class="o">-></span>
+          <span class="c">(* Skip token for error recovery. *)</span>
+          <span class="nn">Stream</span><span class="p">.</span><span class="n">junk</span> <span class="n">stream</span><span class="o">;</span>
+          <span class="n">print_endline</span> <span class="n">s</span><span class="o">;</span>
+      <span class="k">end</span><span class="o">;</span>
+      <span class="n">print_string</span> <span class="s2">"ready> "</span><span class="o">;</span> <span class="n">flush</span> <span class="n">stdout</span><span class="o">;</span>
+      <span class="n">main_loop</span> <span class="n">the_fpm</span> <span class="n">the_execution_engine</span> <span class="n">stream</span>
+</pre></div>
+</div>
+</dd>
+<dt>toy.ml:</dt>
+<dd><div class="first last highlight-ocaml"><div class="highlight"><pre><span class="c">(*===----------------------------------------------------------------------===</span>
+<span class="c"> * Main driver code.</span>
+<span class="c"> *===----------------------------------------------------------------------===*)</span>
+
+<span class="k">open</span> <span class="nc">Llvm</span>
+<span class="k">open</span> <span class="nc">Llvm_executionengine</span>
+<span class="k">open</span> <span class="nc">Llvm_target</span>
+<span class="k">open</span> <span class="nc">Llvm_scalar_opts</span>
+
+<span class="k">let</span> <span class="n">main</span> <span class="bp">()</span> <span class="o">=</span>
+  <span class="n">ignore</span> <span class="o">(</span><span class="n">initialize_native_target</span> <span class="bp">()</span><span class="o">);</span>
+
+  <span class="c">(* Install standard binary operators.</span>
+<span class="c">   * 1 is the lowest precedence. *)</span>
+  <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="nn">Parser</span><span class="p">.</span><span class="n">binop_precedence</span> <span class="sc">'='</span> <span class="mi">2</span><span class="o">;</span>
+  <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="nn">Parser</span><span class="p">.</span><span class="n">binop_precedence</span> <span class="sc">'<'</span> <span class="mi">10</span><span class="o">;</span>
+  <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="nn">Parser</span><span class="p">.</span><span class="n">binop_precedence</span> <span class="sc">'+'</span> <span class="mi">20</span><span class="o">;</span>
+  <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="nn">Parser</span><span class="p">.</span><span class="n">binop_precedence</span> <span class="sc">'-'</span> <span class="mi">20</span><span class="o">;</span>
+  <span class="nn">Hashtbl</span><span class="p">.</span><span class="n">add</span> <span class="nn">Parser</span><span class="p">.</span><span class="n">binop_precedence</span> <span class="sc">'*'</span> <span class="mi">40</span><span class="o">;</span>    <span class="c">(* highest. *)</span>
+
+  <span class="c">(* Prime the first token. *)</span>
+  <span class="n">print_string</span> <span class="s2">"ready> "</span><span class="o">;</span> <span class="n">flush</span> <span class="n">stdout</span><span class="o">;</span>
+  <span class="k">let</span> <span class="n">stream</span> <span class="o">=</span> <span class="nn">Lexer</span><span class="p">.</span><span class="n">lex</span> <span class="o">(</span><span class="nn">Stream</span><span class="p">.</span><span class="n">of_channel</span> <span class="n">stdin</span><span class="o">)</span> <span class="k">in</span>
+
+  <span class="c">(* Create the JIT. *)</span>
+  <span class="k">let</span> <span class="n">the_execution_engine</span> <span class="o">=</span> <span class="nn">ExecutionEngine</span><span class="p">.</span><span class="n">create</span> <span class="nn">Codegen</span><span class="p">.</span><span class="n">the_module</span> <span class="k">in</span>
+  <span class="k">let</span> <span class="n">the_fpm</span> <span class="o">=</span> <span class="nn">PassManager</span><span class="p">.</span><span class="n">create_function</span> <span class="nn">Codegen</span><span class="p">.</span><span class="n">the_module</span> <span class="k">in</span>
+
+  <span class="c">(* Set up the optimizer pipeline.  Start with registering info about how the</span>
+<span class="c">   * target lays out data structures. *)</span>
+  <span class="nn">DataLayout</span><span class="p">.</span><span class="n">add</span> <span class="o">(</span><span class="nn">ExecutionEngine</span><span class="p">.</span><span class="n">target_data</span> <span class="n">the_execution_engine</span><span class="o">)</span> <span class="n">the_fpm</span><span class="o">;</span>
+
+  <span class="c">(* Promote allocas to registers. *)</span>
+  <span class="n">add_memory_to_register_promotion</span> <span class="n">the_fpm</span><span class="o">;</span>
+
+  <span class="c">(* Do simple "peephole" optimizations and bit-twiddling optzn. *)</span>
+  <span class="n">add_instruction_combination</span> <span class="n">the_fpm</span><span class="o">;</span>
+
+  <span class="c">(* reassociate expressions. *)</span>
+  <span class="n">add_reassociation</span> <span class="n">the_fpm</span><span class="o">;</span>
+
+  <span class="c">(* Eliminate Common SubExpressions. *)</span>
+  <span class="n">add_gvn</span> <span class="n">the_fpm</span><span class="o">;</span>
+
+  <span class="c">(* Simplify the control flow graph (deleting unreachable blocks, etc). *)</span>
+  <span class="n">add_cfg_simplification</span> <span class="n">the_fpm</span><span class="o">;</span>
+
+  <span class="n">ignore</span> <span class="o">(</span><span class="nn">PassManager</span><span class="p">.</span><span class="n">initialize</span> <span class="n">the_fpm</span><span class="o">);</span>
+
+  <span class="c">(* Run the main "interpreter loop" now. *)</span>
+  <span class="nn">Toplevel</span><span class="p">.</span><span class="n">main_loop</span> <span class="n">the_fpm</span> <span class="n">the_execution_engine</span> <span class="n">stream</span><span class="o">;</span>
+
+  <span class="c">(* Print out all the generated code. *)</span>
+  <span class="n">dump_module</span> <span class="nn">Codegen</span><span class="p">.</span><span class="n">the_module</span>
+<span class="o">;;</span>
+
+<span class="n">main</span> <span class="bp">()</span>
+</pre></div>
+</div>
+</dd>
+<dt>bindings.c</dt>
+<dd><div class="first last highlight-c"><div class="highlight"><pre><span class="cp">#include <stdio.h></span>
+
+<span class="cm">/* putchard - putchar that takes a double and returns 0. */</span>
+<span class="k">extern</span> <span class="kt">double</span> <span class="nf">putchard</span><span class="p">(</span><span class="kt">double</span> <span class="n">X</span><span class="p">)</span> <span class="p">{</span>
+  <span class="n">putchar</span><span class="p">((</span><span class="kt">char</span><span class="p">)</span><span class="n">X</span><span class="p">);</span>
+  <span class="k">return</span> <span class="mi">0</span><span class="p">;</span>
+<span class="p">}</span>
+
+<span class="cm">/* printd - printf that takes a double prints it as "%f\n", returning 0. */</span>
+<span class="k">extern</span> <span class="kt">double</span> <span class="nf">printd</span><span class="p">(</span><span class="kt">double</span> <span class="n">X</span><span class="p">)</span> <span class="p">{</span>
+  <span class="n">printf</span><span class="p">(</span><span class="s">"%f</span><span class="se">\n</span><span class="s">"</span><span class="p">,</span> <span class="n">X</span><span class="p">);</span>
+  <span class="k">return</span> <span class="mi">0</span><span class="p">;</span>
+<span class="p">}</span>
+</pre></div>
+</div>
+</dd>
+</dl>
+<p><a class="reference external" href="OCamlLangImpl8.html">Next: Conclusion and other useful LLVM tidbits</a></p>
+</div>
+</div>
+
+
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+  <div class="section" id="kaleidoscope-conclusion-and-other-useful-llvm-tidbits">
+<h1>8. Kaleidoscope: Conclusion and other useful LLVM tidbits<a class="headerlink" href="#kaleidoscope-conclusion-and-other-useful-llvm-tidbits" title="Permalink to this headline">¶</a></h1>
+<div class="contents local topic" id="contents">
+<ul class="simple">
+<li><a class="reference internal" href="#tutorial-conclusion" id="id2">Tutorial Conclusion</a></li>
+<li><a class="reference internal" href="#properties-of-the-llvm-ir" id="id3">Properties of the LLVM IR</a><ul>
+<li><a class="reference internal" href="#target-independence" id="id4">Target Independence</a></li>
+<li><a class="reference internal" href="#safety-guarantees" id="id5">Safety Guarantees</a></li>
+<li><a class="reference internal" href="#language-specific-optimizations" id="id6">Language-Specific Optimizations</a></li>
+</ul>
+</li>
+<li><a class="reference internal" href="#tips-and-tricks" id="id7">Tips and Tricks</a><ul>
+<li><a class="reference internal" href="#implementing-portable-offsetof-sizeof" id="id8">Implementing portable offsetof/sizeof</a></li>
+<li><a class="reference internal" href="#garbage-collected-stack-frames" id="id9">Garbage Collected Stack Frames</a></li>
+</ul>
+</li>
+</ul>
+</div>
+<div class="section" id="tutorial-conclusion">
+<h2><a class="toc-backref" href="#id2">8.1. Tutorial Conclusion</a><a class="headerlink" href="#tutorial-conclusion" title="Permalink to this headline">¶</a></h2>
+<p>Welcome to the final chapter of the “<a class="reference external" href="index.html">Implementing a language with
+LLVM</a>” tutorial. In the course of this tutorial, we have
+grown our little Kaleidoscope language from being a useless toy, to
+being a semi-interesting (but probably still useless) toy. :)</p>
+<p>It is interesting to see how far we’ve come, and how little code it has
+taken. We built the entire lexer, parser, AST, code generator, and an
+interactive run-loop (with a JIT!) by-hand in under 700 lines of
+(non-comment/non-blank) code.</p>
+<p>Our little language supports a couple of interesting features: it
+supports user defined binary and unary operators, it uses JIT
+compilation for immediate evaluation, and it supports a few control flow
+constructs with SSA construction.</p>
+<p>Part of the idea of this tutorial was to show you how easy and fun it
+can be to define, build, and play with languages. Building a compiler
+need not be a scary or mystical process! Now that you’ve seen some of
+the basics, I strongly encourage you to take the code and hack on it.
+For example, try adding:</p>
+<ul class="simple">
+<li><strong>global variables</strong> - While global variables have questional value
+in modern software engineering, they are often useful when putting
+together quick little hacks like the Kaleidoscope compiler itself.
+Fortunately, our current setup makes it very easy to add global
+variables: just have value lookup check to see if an unresolved
+variable is in the global variable symbol table before rejecting it.
+To create a new global variable, make an instance of the LLVM
+<tt class="docutils literal"><span class="pre">GlobalVariable</span></tt> class.</li>
+<li><strong>typed variables</strong> - Kaleidoscope currently only supports variables
+of type double. This gives the language a very nice elegance, because
+only supporting one type means that you never have to specify types.
+Different languages have different ways of handling this. The easiest
+way is to require the user to specify types for every variable
+definition, and record the type of the variable in the symbol table
+along with its Value*.</li>
+<li><strong>arrays, structs, vectors, etc</strong> - Once you add types, you can start
+extending the type system in all sorts of interesting ways. Simple
+arrays are very easy and are quite useful for many different
+applications. Adding them is mostly an exercise in learning how the
+LLVM <a class="reference external" href="../LangRef.html#i_getelementptr">getelementptr</a> instruction
+works: it is so nifty/unconventional, it <a class="reference external" href="../GetElementPtr.html">has its own
+FAQ</a>! If you add support for recursive types
+(e.g. linked lists), make sure to read the <a class="reference external" href="../ProgrammersManual.html#TypeResolve">section in the LLVM
+Programmer’s Manual</a> that
+describes how to construct them.</li>
+<li><strong>standard runtime</strong> - Our current language allows the user to access
+arbitrary external functions, and we use it for things like “printd”
+and “putchard”. As you extend the language to add higher-level
+constructs, often these constructs make the most sense if they are
+lowered to calls into a language-supplied runtime. For example, if
+you add hash tables to the language, it would probably make sense to
+add the routines to a runtime, instead of inlining them all the way.</li>
+<li><strong>memory management</strong> - Currently we can only access the stack in
+Kaleidoscope. It would also be useful to be able to allocate heap
+memory, either with calls to the standard libc malloc/free interface
+or with a garbage collector. If you would like to use garbage
+collection, note that LLVM fully supports <a class="reference external" href="../GarbageCollection.html">Accurate Garbage
+Collection</a> including algorithms that
+move objects and need to scan/update the stack.</li>
+<li><strong>debugger support</strong> - LLVM supports generation of <a class="reference external" href="../SourceLevelDebugging.html">DWARF Debug
+info</a> which is understood by common
+debuggers like GDB. Adding support for debug info is fairly
+straightforward. The best way to understand it is to compile some
+C/C++ code with “<tt class="docutils literal"><span class="pre">clang</span> <span class="pre">-g</span> <span class="pre">-O0</span></tt>” and taking a look at what it
+produces.</li>
+<li><strong>exception handling support</strong> - LLVM supports generation of <a class="reference external" href="../ExceptionHandling.html">zero
+cost exceptions</a> which interoperate with
+code compiled in other languages. You could also generate code by
+implicitly making every function return an error value and checking
+it. You could also make explicit use of setjmp/longjmp. There are
+many different ways to go here.</li>
+<li><strong>object orientation, generics, database access, complex numbers,
+geometric programming, ...</strong> - Really, there is no end of crazy
+features that you can add to the language.</li>
+<li><strong>unusual domains</strong> - We’ve been talking about applying LLVM to a
+domain that many people are interested in: building a compiler for a
+specific language. However, there are many other domains that can use
+compiler technology that are not typically considered. For example,
+LLVM has been used to implement OpenGL graphics acceleration,
+translate C++ code to ActionScript, and many other cute and clever
+things. Maybe you will be the first to JIT compile a regular
+expression interpreter into native code with LLVM?</li>
+</ul>
+<p>Have fun - try doing something crazy and unusual. Building a language
+like everyone else always has, is much less fun than trying something a
+little crazy or off the wall and seeing how it turns out. If you get
+stuck or want to talk about it, feel free to email the <a class="reference external" href="http://lists.cs.uiuc.edu/mailman/listinfo/llvmdev">llvmdev mailing
+list</a>: it has lots
+of people who are interested in languages and are often willing to help
+out.</p>
+<p>Before we end this tutorial, I want to talk about some “tips and tricks”
+for generating LLVM IR. These are some of the more subtle things that
+may not be obvious, but are very useful if you want to take advantage of
+LLVM’s capabilities.</p>
+</div>
+<div class="section" id="properties-of-the-llvm-ir">
+<h2><a class="toc-backref" href="#id3">8.2. Properties of the LLVM IR</a><a class="headerlink" href="#properties-of-the-llvm-ir" title="Permalink to this headline">¶</a></h2>
+<p>We have a couple common questions about code in the LLVM IR form - lets
+just get these out of the way right now, shall we?</p>
+<div class="section" id="target-independence">
+<h3><a class="toc-backref" href="#id4">8.2.1. Target Independence</a><a class="headerlink" href="#target-independence" title="Permalink to this headline">¶</a></h3>
+<p>Kaleidoscope is an example of a “portable language”: any program written
+in Kaleidoscope will work the same way on any target that it runs on.
+Many other languages have this property, e.g. lisp, java, haskell,
+javascript, python, etc (note that while these languages are portable,
+not all their libraries are).</p>
+<p>One nice aspect of LLVM is that it is often capable of preserving target
+independence in the IR: you can take the LLVM IR for a
+Kaleidoscope-compiled program and run it on any target that LLVM
+supports, even emitting C code and compiling that on targets that LLVM
+doesn’t support natively. You can trivially tell that the Kaleidoscope
+compiler generates target-independent code because it never queries for
+any target-specific information when generating code.</p>
+<p>The fact that LLVM provides a compact, target-independent,
+representation for code gets a lot of people excited. Unfortunately,
+these people are usually thinking about C or a language from the C
+family when they are asking questions about language portability. I say
+“unfortunately”, because there is really no way to make (fully general)
+C code portable, other than shipping the source code around (and of
+course, C source code is not actually portable in general either - ever
+port a really old application from 32- to 64-bits?).</p>
+<p>The problem with C (again, in its full generality) is that it is heavily
+laden with target specific assumptions. As one simple example, the
+preprocessor often destructively removes target-independence from the
+code when it processes the input text:</p>
+<div class="highlight-c"><div class="highlight"><pre><span class="cp">#ifdef __i386__</span>
+  <span class="kt">int</span> <span class="n">X</span> <span class="o">=</span> <span class="mi">1</span><span class="p">;</span>
+<span class="cp">#else</span>
+  <span class="kt">int</span> <span class="n">X</span> <span class="o">=</span> <span class="mi">42</span><span class="p">;</span>
+<span class="cp">#endif</span>
+</pre></div>
+</div>
+<p>While it is possible to engineer more and more complex solutions to
+problems like this, it cannot be solved in full generality in a way that
+is better than shipping the actual source code.</p>
+<p>That said, there are interesting subsets of C that can be made portable.
+If you are willing to fix primitive types to a fixed size (say int =
+32-bits, and long = 64-bits), don’t care about ABI compatibility with
+existing binaries, and are willing to give up some other minor features,
+you can have portable code. This can make sense for specialized domains
+such as an in-kernel language.</p>
+</div>
+<div class="section" id="safety-guarantees">
+<h3><a class="toc-backref" href="#id5">8.2.2. Safety Guarantees</a><a class="headerlink" href="#safety-guarantees" title="Permalink to this headline">¶</a></h3>
+<p>Many of the languages above are also “safe” languages: it is impossible
+for a program written in Java to corrupt its address space and crash the
+process (assuming the JVM has no bugs). Safety is an interesting
+property that requires a combination of language design, runtime
+support, and often operating system support.</p>
+<p>It is certainly possible to implement a safe language in LLVM, but LLVM
+IR does not itself guarantee safety. The LLVM IR allows unsafe pointer
+casts, use after free bugs, buffer over-runs, and a variety of other
+problems. Safety needs to be implemented as a layer on top of LLVM and,
+conveniently, several groups have investigated this. Ask on the <a class="reference external" href="http://lists.cs.uiuc.edu/mailman/listinfo/llvmdev">llvmdev
+mailing list</a> if
+you are interested in more details.</p>
+</div>
+<div class="section" id="language-specific-optimizations">
+<h3><a class="toc-backref" href="#id6">8.2.3. Language-Specific Optimizations</a><a class="headerlink" href="#language-specific-optimizations" title="Permalink to this headline">¶</a></h3>
+<p>One thing about LLVM that turns off many people is that it does not
+solve all the world’s problems in one system (sorry ‘world hunger’,
+someone else will have to solve you some other day). One specific
+complaint is that people perceive LLVM as being incapable of performing
+high-level language-specific optimization: LLVM “loses too much
+information”.</p>
+<p>Unfortunately, this is really not the place to give you a full and
+unified version of “Chris Lattner’s theory of compiler design”. Instead,
+I’ll make a few observations:</p>
+<p>First, you’re right that LLVM does lose information. For example, as of
+this writing, there is no way to distinguish in the LLVM IR whether an
+SSA-value came from a C “int” or a C “long” on an ILP32 machine (other
+than debug info). Both get compiled down to an ‘i32’ value and the
+information about what it came from is lost. The more general issue
+here, is that the LLVM type system uses “structural equivalence” instead
+of “name equivalence”. Another place this surprises people is if you
+have two types in a high-level language that have the same structure
+(e.g. two different structs that have a single int field): these types
+will compile down into a single LLVM type and it will be impossible to
+tell what it came from.</p>
+<p>Second, while LLVM does lose information, LLVM is not a fixed target: we
+continue to enhance and improve it in many different ways. In addition
+to adding new features (LLVM did not always support exceptions or debug
+info), we also extend the IR to capture important information for
+optimization (e.g. whether an argument is sign or zero extended,
+information about pointers aliasing, etc). Many of the enhancements are
+user-driven: people want LLVM to include some specific feature, so they
+go ahead and extend it.</p>
+<p>Third, it is <em>possible and easy</em> to add language-specific optimizations,
+and you have a number of choices in how to do it. As one trivial
+example, it is easy to add language-specific optimization passes that
+“know” things about code compiled for a language. In the case of the C
+family, there is an optimization pass that “knows” about the standard C
+library functions. If you call “exit(0)” in main(), it knows that it is
+safe to optimize that into “return 0;” because C specifies what the
+‘exit’ function does.</p>
+<p>In addition to simple library knowledge, it is possible to embed a
+variety of other language-specific information into the LLVM IR. If you
+have a specific need and run into a wall, please bring the topic up on
+the llvmdev list. At the very worst, you can always treat LLVM as if it
+were a “dumb code generator” and implement the high-level optimizations
+you desire in your front-end, on the language-specific AST.</p>
+</div>
+</div>
+<div class="section" id="tips-and-tricks">
+<h2><a class="toc-backref" href="#id7">8.3. Tips and Tricks</a><a class="headerlink" href="#tips-and-tricks" title="Permalink to this headline">¶</a></h2>
+<p>There is a variety of useful tips and tricks that you come to know after
+working on/with LLVM that aren’t obvious at first glance. Instead of
+letting everyone rediscover them, this section talks about some of these
+issues.</p>
+<div class="section" id="implementing-portable-offsetof-sizeof">
+<h3><a class="toc-backref" href="#id8">8.3.1. Implementing portable offsetof/sizeof</a><a class="headerlink" href="#implementing-portable-offsetof-sizeof" title="Permalink to this headline">¶</a></h3>
+<p>One interesting thing that comes up, if you are trying to keep the code
+generated by your compiler “target independent”, is that you often need
+to know the size of some LLVM type or the offset of some field in an
+llvm structure. For example, you might need to pass the size of a type
+into a function that allocates memory.</p>
+<p>Unfortunately, this can vary widely across targets: for example the
+width of a pointer is trivially target-specific. However, there is a
+<a class="reference external" href="http://nondot.org/sabre/LLVMNotes/SizeOf-OffsetOf-VariableSizedStructs.txt">clever way to use the getelementptr
+instruction</a>
+that allows you to compute this in a portable way.</p>
+</div>
+<div class="section" id="garbage-collected-stack-frames">
+<h3><a class="toc-backref" href="#id9">8.3.2. Garbage Collected Stack Frames</a><a class="headerlink" href="#garbage-collected-stack-frames" title="Permalink to this headline">¶</a></h3>
+<p>Some languages want to explicitly manage their stack frames, often so
+that they are garbage collected or to allow easy implementation of
+closures. There are often better ways to implement these features than
+explicit stack frames, but <a class="reference external" href="http://nondot.org/sabre/LLVMNotes/ExplicitlyManagedStackFrames.txt">LLVM does support
+them,</a>
+if you want. It requires your front-end to convert the code into
+<a class="reference external" href="http://en.wikipedia.org/wiki/Continuation-passing_style">Continuation Passing
+Style</a> and
+the use of tail calls (which LLVM also supports).</p>
+</div>
+</div>
+</div>
+
+
+          </div>
+      </div>
+      <div class="clearer"></div>
+    </div>
+    <div class="related">
+      <h3>Navigation</h3>
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+          <a href="../genindex.html" title="General Index"
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+          <div class="body">
+            
+  <div class="section" id="llvm-tutorial-table-of-contents">
+<h1>LLVM Tutorial: Table of Contents<a class="headerlink" href="#llvm-tutorial-table-of-contents" title="Permalink to this headline">¶</a></h1>
+<div class="section" id="kaleidoscope-implementing-a-language-with-llvm">
+<h2>Kaleidoscope: Implementing a Language with LLVM<a class="headerlink" href="#kaleidoscope-implementing-a-language-with-llvm" title="Permalink to this headline">¶</a></h2>
+<div class="toctree-wrapper compound">
+<ul>
+<li class="toctree-l1"><a class="reference internal" href="LangImpl1.html">1. Kaleidoscope: Tutorial Introduction and the Lexer</a><ul class="simple">
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="LangImpl2.html">2. Kaleidoscope: Implementing a Parser and AST</a><ul class="simple">
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="LangImpl3.html">3. Kaleidoscope: Code generation to LLVM IR</a><ul class="simple">
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="LangImpl4.html">4. Kaleidoscope: Adding JIT and Optimizer Support</a><ul class="simple">
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="LangImpl5.html">5. Kaleidoscope: Extending the Language: Control Flow</a><ul class="simple">
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="LangImpl6.html">6. Kaleidoscope: Extending the Language: User-defined Operators</a><ul class="simple">
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="LangImpl7.html">7. Kaleidoscope: Extending the Language: Mutable Variables</a><ul class="simple">
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="LangImpl8.html">8. Kaleidoscope: Conclusion and other useful LLVM tidbits</a><ul class="simple">
+</ul>
+</li>
+</ul>
+</div>
+</div>
+<div class="section" id="kaleidoscope-implementing-a-language-with-llvm-in-objective-caml">
+<h2>Kaleidoscope: Implementing a Language with LLVM in Objective Caml<a class="headerlink" href="#kaleidoscope-implementing-a-language-with-llvm-in-objective-caml" title="Permalink to this headline">¶</a></h2>
+<div class="toctree-wrapper compound">
+<ul>
+<li class="toctree-l1"><a class="reference internal" href="OCamlLangImpl1.html">1. Kaleidoscope: Tutorial Introduction and the Lexer</a><ul class="simple">
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="OCamlLangImpl2.html">2. Kaleidoscope: Implementing a Parser and AST</a><ul class="simple">
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="OCamlLangImpl3.html">3. Kaleidoscope: Code generation to LLVM IR</a><ul class="simple">
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="OCamlLangImpl4.html">4. Kaleidoscope: Adding JIT and Optimizer Support</a><ul class="simple">
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="OCamlLangImpl5.html">5. Kaleidoscope: Extending the Language: Control Flow</a><ul class="simple">
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="OCamlLangImpl6.html">6. Kaleidoscope: Extending the Language: User-defined Operators</a><ul class="simple">
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="OCamlLangImpl7.html">7. Kaleidoscope: Extending the Language: Mutable Variables</a><ul class="simple">
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="OCamlLangImpl8.html">8. Kaleidoscope: Conclusion and other useful LLVM tidbits</a><ul class="simple">
+</ul>
+</li>
+</ul>
+</div>
+</div>
+<div class="section" id="external-tutorials">
+<h2>External Tutorials<a class="headerlink" href="#external-tutorials" title="Permalink to this headline">¶</a></h2>
+<dl class="docutils">
+<dt><a class="reference external" href="http://jonathan2251.github.com/lbd/">Tutorial: Creating an LLVM Backend for the Cpu0 Architecture</a></dt>
+<dd>A step-by-step tutorial for developing an LLVM backend. Under
+active development at <a class="reference external" href="https://github.com/Jonathan2251/lbd">https://github.com/Jonathan2251/lbd</a> (please
+contribute!).</dd>
+<dt><a class="reference external" href="http://www.embecosm.com/appnotes/ean10/ean10-howto-llvmas-1.0.html">Howto: Implementing LLVM Integrated Assembler</a></dt>
+<dd>A simple guide for how to implement an LLVM integrated assembler for an
+architecture.</dd>
+</dl>
+</div>
+<div class="section" id="advanced-topics">
+<h2>Advanced Topics<a class="headerlink" href="#advanced-topics" title="Permalink to this headline">¶</a></h2>
+<ol class="arabic simple">
+<li><a class="reference external" href="http://llvm.org/pubs/2004-09-22-LCPCLLVMTutorial.html">Writing an Optimization for LLVM</a></li>
+</ol>
+</div>
+</div>
+
+
+          </div>
+      </div>
+      <div class="clearer"></div>
+    </div>
+    <div class="related">
+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="../genindex.html" title="General Index"
+             >index</a></li>
+        <li class="right" >
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+             >next</a> |</li>
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+             >previous</a> |</li>
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+    <div class="document">
+      <div class="documentwrapper">
+          <div class="body">
+            
+  <div class="section" id="yaml2obj">
+<h1>yaml2obj<a class="headerlink" href="#yaml2obj" title="Permalink to this headline">¶</a></h1>
+<p>yaml2obj takes a YAML description of an object file and converts it to a binary
+file.</p>
+<blockquote>
+<div>$ yaml2obj input-file</div></blockquote>
+<p>Outputs the binary to stdout.</p>
+<div class="section" id="coff-syntax">
+<h2>COFF Syntax<a class="headerlink" href="#coff-syntax" title="Permalink to this headline">¶</a></h2>
+<p>Here’s a sample COFF file.</p>
+<div class="highlight-yaml"><div class="highlight"><pre><span class="l-Scalar-Plain">header</span><span class="p-Indicator">:</span>
+  <span class="l-Scalar-Plain">Machine</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">IMAGE_FILE_MACHINE_I386</span> <span class="c1"># (0x14C)</span>
+
+<span class="l-Scalar-Plain">sections</span><span class="p-Indicator">:</span>
+  <span class="p-Indicator">-</span> <span class="l-Scalar-Plain">Name</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">.text</span>
+    <span class="l-Scalar-Plain">Characteristics</span><span class="p-Indicator">:</span> <span class="p-Indicator">[</span> <span class="nv">IMAGE_SCN_CNT_CODE</span>
+                     <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_ALIGN_16BYTES</span>
+                     <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_MEM_EXECUTE</span>
+                     <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_MEM_READ</span>
+                     <span class="p-Indicator">]</span> <span class="c1"># 0x60500020</span>
+    <span class="l-Scalar-Plain">SectionData</span><span class="p-Indicator">:</span>
+      <span class="s">"</span><span class="se">\x83\xEC\x0C\xC7\x44\x24\x08\x00\x00\x00\x00\xC7\x04\x24\x00\x00\x00\x00\xE8\x00\x00\x00\x00\xE8\x00\x00\x00\x00\x8B\x44\x24\x08\x83\xC4\x0C\xC3</span><span class="s">"</span> <span class="c1"># |....D$.......$...............D$.....|</span>
+
+<span class="l-Scalar-Plain">symbols</span><span class="p-Indicator">:</span>
+  <span class="p-Indicator">-</span> <span class="l-Scalar-Plain">Name</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">.text</span>
+    <span class="l-Scalar-Plain">Value</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">0</span>
+    <span class="l-Scalar-Plain">SectionNumber</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">1</span>
+    <span class="l-Scalar-Plain">SimpleType</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">IMAGE_SYM_TYPE_NULL</span> <span class="c1"># (0)</span>
+    <span class="l-Scalar-Plain">ComplexType</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">IMAGE_SYM_DTYPE_NULL</span> <span class="c1"># (0)</span>
+    <span class="l-Scalar-Plain">StorageClass</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">IMAGE_SYM_CLASS_STATIC</span> <span class="c1"># (3)</span>
+    <span class="l-Scalar-Plain">NumberOfAuxSymbols</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">1</span>
+    <span class="l-Scalar-Plain">AuxiliaryData</span><span class="p-Indicator">:</span>
+      <span class="s">"</span><span class="se">\x24\x00\x00\x00\x03\x00\x00\x00\x00\x00\x00\x00\x01\x00\x00\x00\x00\x00</span><span class="s">"</span> <span class="c1"># |$.................|</span>
+
+  <span class="p-Indicator">-</span> <span class="l-Scalar-Plain">Name</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">_main</span>
+    <span class="l-Scalar-Plain">Value</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">0</span>
+    <span class="l-Scalar-Plain">SectionNumber</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">1</span>
+    <span class="l-Scalar-Plain">SimpleType</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">IMAGE_SYM_TYPE_NULL</span> <span class="c1"># (0)</span>
+    <span class="l-Scalar-Plain">ComplexType</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">IMAGE_SYM_DTYPE_NULL</span> <span class="c1"># (0)</span>
+    <span class="l-Scalar-Plain">StorageClass</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">IMAGE_SYM_CLASS_EXTERNAL</span> <span class="c1"># (2)</span>
+</pre></div>
+</div>
+<p>Here’s a simplified <a class="reference external" href="http://www.kuwata-lab.com/kwalify/ruby/users-guide.html">Kwalify</a> schema with an extension to allow alternate types.</p>
+<div class="highlight-yaml"><div class="highlight"><pre><span class="l-Scalar-Plain">type</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">map</span>
+  <span class="l-Scalar-Plain">mapping</span><span class="p-Indicator">:</span>
+    <span class="l-Scalar-Plain">header</span><span class="p-Indicator">:</span>
+      <span class="l-Scalar-Plain">type</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">map</span>
+      <span class="l-Scalar-Plain">mapping</span><span class="p-Indicator">:</span>
+        <span class="l-Scalar-Plain">Machine</span><span class="p-Indicator">:</span> <span class="p-Indicator">[</span> <span class="p-Indicator">{</span><span class="nv">type</span><span class="p-Indicator">:</span> <span class="nv">str</span><span class="p-Indicator">,</span> <span class="nv">enum</span><span class="p-Indicator">:</span>
+                               <span class="p-Indicator">[</span> <span class="nv">IMAGE_FILE_MACHINE_UNKNOWN</span>
+                               <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_MACHINE_AM33</span>
+                               <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_MACHINE_AMD64</span>
+                               <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_MACHINE_ARM</span>
+                               <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_MACHINE_ARMNT</span>
+                               <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_MACHINE_EBC</span>
+                               <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_MACHINE_I386</span>
+                               <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_MACHINE_IA64</span>
+                               <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_MACHINE_M32R</span>
+                               <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_MACHINE_MIPS16</span>
+                               <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_MACHINE_MIPSFPU</span>
+                               <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_MACHINE_MIPSFPU16</span>
+                               <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_MACHINE_POWERPC</span>
+                               <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_MACHINE_POWERPCFP</span>
+                               <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_MACHINE_R4000</span>
+                               <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_MACHINE_SH3</span>
+                               <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_MACHINE_SH3DSP</span>
+                               <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_MACHINE_SH4</span>
+                               <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_MACHINE_SH5</span>
+                               <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_MACHINE_THUMB</span>
+                               <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_MACHINE_WCEMIPSV2</span>
+                               <span class="p-Indicator">]}</span>
+                 <span class="p-Indicator">,</span> <span class="p-Indicator">{</span><span class="nv">type</span><span class="p-Indicator">:</span> <span class="nv">int</span><span class="p-Indicator">}</span>
+                 <span class="p-Indicator">]</span>
+        <span class="l-Scalar-Plain">Characteristics</span><span class="p-Indicator">:</span>
+          <span class="p-Indicator">-</span> <span class="l-Scalar-Plain">type</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">seq</span>
+            <span class="l-Scalar-Plain">sequence</span><span class="p-Indicator">:</span>
+              <span class="p-Indicator">-</span> <span class="l-Scalar-Plain">type</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">str</span>
+                <span class="l-Scalar-Plain">enum</span><span class="p-Indicator">:</span> <span class="p-Indicator">[</span> <span class="nv">IMAGE_FILE_RELOCS_STRIPPED</span>
+                      <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_EXECUTABLE_IMAGE</span>
+                      <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_LINE_NUMS_STRIPPED</span>
+                      <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_LOCAL_SYMS_STRIPPED</span>
+                      <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_AGGRESSIVE_WS_TRIM</span>
+                      <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_LARGE_ADDRESS_AWARE</span>
+                      <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_BYTES_REVERSED_LO</span>
+                      <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_32BIT_MACHINE</span>
+                      <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_DEBUG_STRIPPED</span>
+                      <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_REMOVABLE_RUN_FROM_SWAP</span>
+                      <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_NET_RUN_FROM_SWAP</span>
+                      <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_SYSTEM</span>
+                      <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_DLL</span>
+                      <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_UP_SYSTEM_ONLY</span>
+                      <span class="p-Indicator">,</span> <span class="nv">IMAGE_FILE_BYTES_REVERSED_HI</span>
+                      <span class="p-Indicator">]</span>
+          <span class="p-Indicator">-</span> <span class="l-Scalar-Plain">type</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">int</span>
+    <span class="l-Scalar-Plain">sections</span><span class="p-Indicator">:</span>
+      <span class="l-Scalar-Plain">type</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">seq</span>
+      <span class="l-Scalar-Plain">sequence</span><span class="p-Indicator">:</span>
+        <span class="p-Indicator">-</span> <span class="l-Scalar-Plain">type</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">map</span>
+          <span class="l-Scalar-Plain">mapping</span><span class="p-Indicator">:</span>
+            <span class="l-Scalar-Plain">Name</span><span class="p-Indicator">:</span> <span class="p-Indicator">{</span><span class="nv">type</span><span class="p-Indicator">:</span> <span class="nv">str</span><span class="p-Indicator">}</span>
+            <span class="l-Scalar-Plain">Characteristics</span><span class="p-Indicator">:</span>
+              <span class="p-Indicator">-</span> <span class="l-Scalar-Plain">type</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">seq</span>
+                <span class="l-Scalar-Plain">sequence</span><span class="p-Indicator">:</span>
+                  <span class="p-Indicator">-</span> <span class="l-Scalar-Plain">type</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">str</span>
+                    <span class="l-Scalar-Plain">enum</span><span class="p-Indicator">:</span> <span class="p-Indicator">[</span> <span class="nv">IMAGE_SCN_TYPE_NO_PAD</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_CNT_CODE</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_CNT_INITIALIZED_DATA</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_CNT_UNINITIALIZED_DATA</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_LNK_OTHER</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_LNK_INFO</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_LNK_REMOVE</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_LNK_COMDAT</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_GPREL</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_MEM_PURGEABLE</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_MEM_16BIT</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_MEM_LOCKED</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_MEM_PRELOAD</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_ALIGN_1BYTES</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_ALIGN_2BYTES</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_ALIGN_4BYTES</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_ALIGN_8BYTES</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_ALIGN_16BYTES</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_ALIGN_32BYTES</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_ALIGN_64BYTES</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_ALIGN_128BYTES</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_ALIGN_256BYTES</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_ALIGN_512BYTES</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_ALIGN_1024BYTES</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_ALIGN_2048BYTES</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_ALIGN_4096BYTES</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_ALIGN_8192BYTES</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_LNK_NRELOC_OVFL</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_MEM_DISCARDABLE</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_MEM_NOT_CACHED</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_MEM_NOT_PAGED</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_MEM_SHARED</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_MEM_EXECUTE</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_MEM_READ</span>
+                          <span class="p-Indicator">,</span> <span class="nv">IMAGE_SCN_MEM_WRITE</span>
+                          <span class="p-Indicator">]</span>
+              <span class="p-Indicator">-</span> <span class="l-Scalar-Plain">type</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">int</span>
+            <span class="l-Scalar-Plain">SectionData</span><span class="p-Indicator">:</span> <span class="p-Indicator">{</span><span class="nv">type</span><span class="p-Indicator">:</span> <span class="nv">str</span><span class="p-Indicator">}</span>
+    <span class="l-Scalar-Plain">symbols</span><span class="p-Indicator">:</span>
+      <span class="l-Scalar-Plain">type</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">seq</span>
+      <span class="l-Scalar-Plain">sequence</span><span class="p-Indicator">:</span>
+        <span class="p-Indicator">-</span> <span class="l-Scalar-Plain">type</span><span class="p-Indicator">:</span> <span class="l-Scalar-Plain">map</span>
+          <span class="l-Scalar-Plain">mapping</span><span class="p-Indicator">:</span>
+            <span class="l-Scalar-Plain">Name</span><span class="p-Indicator">:</span> <span class="p-Indicator">{</span><span class="nv">type</span><span class="p-Indicator">:</span> <span class="nv">str</span><span class="p-Indicator">}</span>
+            <span class="l-Scalar-Plain">Value</span><span class="p-Indicator">:</span> <span class="p-Indicator">{</span><span class="nv">type</span><span class="p-Indicator">:</span> <span class="nv">int</span><span class="p-Indicator">}</span>
+            <span class="l-Scalar-Plain">SectionNumber</span><span class="p-Indicator">:</span> <span class="p-Indicator">{</span><span class="nv">type</span><span class="p-Indicator">:</span> <span class="nv">int</span><span class="p-Indicator">}</span>
+            <span class="l-Scalar-Plain">SimpleType</span><span class="p-Indicator">:</span> <span class="p-Indicator">[</span> <span class="p-Indicator">{</span><span class="nv">type</span><span class="p-Indicator">:</span> <span class="nv">str</span><span class="p-Indicator">,</span> <span class="nv">enum</span><span class="p-Indicator">:</span> <span class="p-Indicator">[</span> <span class="nv">IMAGE_SYM_TYPE_NULL</span>
+                                            <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_TYPE_VOID</span>
+                                            <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_TYPE_CHAR</span>
+                                            <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_TYPE_SHORT</span>
+                                            <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_TYPE_INT</span>
+                                            <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_TYPE_LONG</span>
+                                            <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_TYPE_FLOAT</span>
+                                            <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_TYPE_DOUBLE</span>
+                                            <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_TYPE_STRUCT</span>
+                                            <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_TYPE_UNION</span>
+                                            <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_TYPE_ENUM</span>
+                                            <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_TYPE_MOE</span>
+                                            <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_TYPE_BYTE</span>
+                                            <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_TYPE_WORD</span>
+                                            <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_TYPE_UINT</span>
+                                            <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_TYPE_DWORD</span>
+                                            <span class="p-Indicator">]}</span>
+                        <span class="p-Indicator">,</span> <span class="p-Indicator">{</span><span class="nv">type</span><span class="p-Indicator">:</span> <span class="nv">int</span><span class="p-Indicator">}</span>
+                        <span class="p-Indicator">]</span>
+            <span class="l-Scalar-Plain">ComplexType</span><span class="p-Indicator">:</span> <span class="p-Indicator">[</span> <span class="p-Indicator">{</span><span class="nv">type</span><span class="p-Indicator">:</span> <span class="nv">str</span><span class="p-Indicator">,</span> <span class="nv">enum</span><span class="p-Indicator">:</span> <span class="p-Indicator">[</span> <span class="nv">IMAGE_SYM_DTYPE_NULL</span>
+                                             <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_DTYPE_POINTER</span>
+                                             <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_DTYPE_FUNCTION</span>
+                                             <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_DTYPE_ARRAY</span>
+                                             <span class="p-Indicator">]}</span>
+                         <span class="p-Indicator">,</span> <span class="p-Indicator">{</span><span class="nv">type</span><span class="p-Indicator">:</span> <span class="nv">int</span><span class="p-Indicator">}</span>
+                         <span class="p-Indicator">]</span>
+            <span class="l-Scalar-Plain">StorageClass</span><span class="p-Indicator">:</span> <span class="p-Indicator">[</span> <span class="p-Indicator">{</span><span class="nv">type</span><span class="p-Indicator">:</span> <span class="nv">str</span><span class="p-Indicator">,</span> <span class="nv">enum</span><span class="p-Indicator">:</span>
+                                        <span class="p-Indicator">[</span> <span class="nv">IMAGE_SYM_CLASS_END_OF_FUNCTION</span>
+                                        <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_CLASS_NULL</span>
+                                        <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_CLASS_AUTOMATIC</span>
+                                        <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_CLASS_EXTERNAL</span>
+                                        <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_CLASS_STATIC</span>
+                                        <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_CLASS_REGISTER</span>
+                                        <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_CLASS_EXTERNAL_DEF</span>
+                                        <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_CLASS_LABEL</span>
+                                        <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_CLASS_UNDEFINED_LABEL</span>
+                                        <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_CLASS_MEMBER_OF_STRUCT</span>
+                                        <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_CLASS_ARGUMENT</span>
+                                        <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_CLASS_STRUCT_TAG</span>
+                                        <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_CLASS_MEMBER_OF_UNION</span>
+                                        <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_CLASS_UNION_TAG</span>
+                                        <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_CLASS_TYPE_DEFINITION</span>
+                                        <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_CLASS_UNDEFINED_STATIC</span>
+                                        <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_CLASS_ENUM_TAG</span>
+                                        <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_CLASS_MEMBER_OF_ENUM</span>
+                                        <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_CLASS_REGISTER_PARAM</span>
+                                        <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_CLASS_BIT_FIELD</span>
+                                        <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_CLASS_BLOCK</span>
+                                        <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_CLASS_FUNCTION</span>
+                                        <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_CLASS_END_OF_STRUCT</span>
+                                        <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_CLASS_FILE</span>
+                                        <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_CLASS_SECTION</span>
+                                        <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_CLASS_WEAK_EXTERNAL</span>
+                                        <span class="p-Indicator">,</span> <span class="nv">IMAGE_SYM_CLASS_CLR_TOKEN</span>
+                                        <span class="p-Indicator">]}</span>
+                          <span class="p-Indicator">,</span> <span class="p-Indicator">{</span><span class="nv">type</span><span class="p-Indicator">:</span> <span class="nv">int</span><span class="p-Indicator">}</span>
+                          <span class="p-Indicator">]</span>
+</pre></div>
+</div>
+</div>
+</div>
+
+
+          </div>
+      </div>
+      <div class="clearer"></div>
+    </div>
+    <div class="related">
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