`csimp` assumes constructors and `casesOn` applications match. That
is, given `I.casesOn x ...`, then if `x` is an constructor, then it is
a constructor of the inductive datatype `I`.
The transformation `erase_irrelevant` was violating this property when
it mixes `Decidable` and `Bool`. We fix this issue by mapping
`Decidable.casesOn`, `Decidable.isTrue` and `Decidable.isFalse` to
`Bool.casesOn`, `Bool.true` and `Bool.false` respectively.
For example, in the new test `qsort64.lean`, the new optimization
prevents the repeated execution of `box UInt64.inhabited`.
On my machine
```
./run.sh qsort64.lean 2000000
```
Goes from 1.22s to 0.355s
@kha @dselsam: I added a small repro for the bug reported by Daniel on
Zulip. The current fix is not polished at all since we will replace
the equation compiler with one implemented in Lean. The bug is once
again on the code that handle nested `match`-expressions containing
recursive calls. We had problems in this module before, and the
current compilation strategy using auxiliary `*._match_<id>` functions
is also very inconvenient for users. They are often puzzled when they
see these auxiliary functions appearing in proof goals after unfolding
and/or simplification. They usually don't know what to do with these
auxiliary definitions, and have no idea how they were defined and what
they correspond to if the function has several nested
`match`-expression. Right now, the best option is to use `#print
<fun-name>._match_<id>` which is far from ideal.
@kha: @dselsam and I discussed an alternative approach where we do not
create the auxiliary definitions, annotate the generated `cases_on`
applications with meta-data indicating they correspond to a nested
match, and modify the pretty printer to display these annotated
`cases_on` applications using the `match` syntax. With these
modifications, the behavior will be similar to the one in Coq where
complex `match`-expressions are reduced to atomic ones. The only
difference is that we represent these "atomic" `match`-expressions
using `cases_on` applications.
This commit uses a simpler version of this approach where we do not
create auxiliary `*._match_<id>` functions, and more importantly do
not use the dreadful `pull_nested_rec_fn` code.
