[Mlir-commits] [mlir] [MLIR][Linalg][Docs] Add forms to Linalg rationale docs (PR #156859)

[Andrzej Warzyński]

================
@@ -506,6 +506,72 @@ potential by introducing lower-level IR ops and *smaller* Linalg ops.
 This gradually reduces the potential, all the way to Loops + VectorOps
 and LLVMIR.
 
+### Interchangeability of Forms<a name="forms"></a>
+
+#### The Linalg Forms
+
+The core Linalg operation set has four forms:
+* **Generic:** Represented by `linalg.generic` and can encode all perfectly-nested
+loop operations.
+* **Category:** For example, `linalg.contract` and `linalg.elementwise`, that encode
+higher-level semantics of a `linalg.generic` while still representing multiple _named_
+operations via attributes and syntax. In the future, other category operations are
+planned (e.g.: `linalg.convolution` and `linalg.pooling`).
+* **Named:** For example, `linalg.matmul`, `linalg.add`, etc. All _named_ forms that
+can be converted to either a single _category_ or _generic_ forms, ie. are _perfectly nested_.
+* **Composite:** For example `linalg.softmax` and the `winograd` variations. These
+operations are not perfectly nested, and are converted to a list of other operations
+(of various dialects).
+
+The forms correlate in the following manner:
+```
++ generic
+ \__ + category
+      \__ + named
++ composite
+```
+
+The `category` and `named` forms are derived from `linalg.generic` and are *equivalent*.
+It should always be possible to convert a `named` operation into a `category` and that
+into a `generic` and back to `named`. However, it may not be possible to convert a
+`generic` into a `named` if there is no such `named` form.
+
+`Composite` operations cannot be converted to the other three classes and forms a
+sub-set on its own. But they can use other Linalg forms when expanding. There can be
+a pattern-matching transform to detect a graph of operations and convert into a
+`composite` operation.
+
+The various forms in the Linalg dialect are meant to facilitate
+pattern matching (single operations or DAGs) and to be able to consider
+different forms as *canonical* for different transforms.
+
+Linalg's various forms also carry information, and that
+information should be preserved as much as possible during the progressive
+lowering. A `matmul` operation is a special case of a `contract` operation,
+which in turn is a special case of `generic` operation. Transformations on
----------------
banach-space wrote:

```suggestion
which in turn is a special case of a `generic` operation. Transformations on
```

https://github.com/llvm/llvm-project/pull/156859