@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 Scala/Clojure approach for persistent arrays works great with our
`reset/reuse`. We seem to be much more efficient than their
implementations because of `reset/reuse`. The new approach also seems
better than the old one implemented in the runtime, and has a few
advantages:
1- The reroot procedure used in the old approach required
synchronization for multi-threaded code, or we would need to perform
deep copies when sending `parray` objects between threads.
2- We don't need any runtime extension for the new approach.
3- The old approach used "trail lists" for undoing array updates.
This works well for bactracking search use cases, but it is bad
in use cases where we are simultaneously updating the persistent
arrays that have shared nodes.
This commit also removes Array.hmap.
Motivation: I wanted to use Array.hmap as an example in the paper, but
I found it would be too distracting to explain why we had `Array.hmap`
and `Array.map`.
cc @kha
