@kha This is another instance of a problem we discussed last summer.
I guess there are many more instances like this one that we are not handling.
Recall that we want to preserve types at `csimp` because we eventually
want to allow users to use equational theorems as rewriting rules during
compilation.
However, some of the transformations that `csimp` perform do not
preserve typeability in CIC.
Moreover, some of the optimizations require type inference.
I see the possible long term solutions:
1- Erase types and proofs as soon as possible. The main drawback here is
that we would have to develop an approach for translating Lean theorems
into valid rewriting rules for lambda pure. For example, the following
theorem should not be used as a rewriting rule after we erase types.
```
forall (xs : List Unit) (f : Unit -> Unit), List.map f xs = List.map id xs
```
BTW, I don't want to abandon the idea of using lemmas as rewriting rules in
the compiler.
2- Go over `csimp` and other compiler steps and make sure they work
properly even when `type_checker::infer_type` fails.
The array read and write operations are now called:
- "Comfortable" version (with runtime bound checks):
`Array.get` and `Array.set` like OCaml.
It is also consistent with `Ref.get` and `Ref.put`,
and `get` and `set` for `MonadState`.
- `Fin` version (without runtime bound checks):
`Array.index` and `Array.update` like in F*.
- `USize` version (without runtime bound checks and unboxing):
`Array.idx` and `Array.updt`.
cc @kha
@kha I have disabled this check. It was implemented 2 years ago by
Daniel, and I don't want to fix it. It seems you have already fixed a
bug there. AFAICT, this check is just for improving error messages.
I believe we may not even need it since the kernel now supports nested
inductive types. AFAIR, Daniel implemented this check here because the
inductive compiler was introducing a lot of auxiliary declarations
that were making the kernel error messages unreadable.
The bug occurs when floating `cases_on` application in code of the form
```
let x := C.cases_on ...
in t
```
and when the type of `t` depends on `x`.
The issue here is that the `x` declaration disappears after the float, but the resulting type still depends on it.
We fix the bug by replacing `x` with its value in the type.
cc @kha
