When we declare a `simp` set using `register_simp_attr`, we
automatically create `simproc` set. However, users may create `simp`
sets programmatically, and the associated `simproc` set may be missing
and vice-versa.
Before this commit, `Simproc`s were defined as `Expr -> SimpM (Option Step)`, where `Step` is inductively defined as follows:
```
inductive Step where
| visit : Result → Step
| done : Result → Step
```
Here, `Result` is a structure containing the resulting expression and a proof demonstrating its equality to the input. Notably, the proof is optional; in its absence, `simp` assumes reflexivity.
A simproc can:
- Fail by returning `none`, indicating its inapplicability. In this case, the next suitable simproc is attempted, along with other simp extensions.
- Succeed and invoke further simplifications using the `.visit`
constructor. This action returns control to the beginning of the
simplification loop.
- Succeed and indicate that the result should not undergo further
simplifications. However, I find the current approach unsatisfactory, as it does not align with the methodology employed in `Transform.lean`, where we have the type:
```
inductive TransformStep where
/-- Return expression without visiting any subexpressions. -/
| done (e : Expr)
/--
Visit expression (which should be different from current expression) instead.
The new expression `e` is passed to `pre` again.
-/
| visit (e : Expr)
/--
Continue transformation with the given expression (defaults to current expression).
For `pre`, this means visiting the children of the expression.
For `post`, this is equivalent to returning `done`. -/
| continue (e? : Option Expr := none)
```
This type makes it clearer what is going on. The new `Simp.Step` type is similar but use `Result` instead of `Expr` because we need a proof.
Allow `simproc`s to be declared without setting the `[simproc]`
attribute. A `simproc` declaration is function + pattern.
Motivation: allow them to be provided as arguments to `simp` **and** `simp only`.
TODO: track their use in `simp`.
TODO: builtin simprocs
