We add a new configuration flag for `isDefEq`:
`Meta.Config.univApprox`.
When it is true, we approximate the solution for universe constraints
such as
- `u =?= max u ?v`, we use `?v := u`, and ignore the solution `?v := 0`.
- `max u v =?= max u ?w`, we use `?w := v`, and ignore the solution `?w
:= max u v`.
We only apply these approximations when there the contraints cannot be
postponed anymore. These approximations prevent error messages such as
```
error: stuck at solving universe constraint
max u ?u.3430 =?= u
```
This kind of error seems to appear in several Mathlib files.
We currently do not use these approximations while synthesizing type
class instances.
The new class specifies an interface for saving and restoring the
backtrackable part of the state.
This commit also fixes a few issues.
- `commitWhen` at `LevelDefEq` was defining a checkpoint for
the `isDefEq` methods, and it affects how postponed universe
constraints are handled. However, the name suggests it is
similar to `commitWhenSome?`, and consequently it was used
in other places that had nothing to do with `isDefEq`.
So, I renamed it, and provided the generic `commitWhen` at the new
`MonadBacktrack.lean` file.
- We were restoring more state then needed in a few places.
For example, we were discarding all caches.
- At `SyntheticMVars.lean`, we were using the `Meta.commitWhenSome?`
method which does not restore the `Term.State`.
@Kha I marked the corresponding methods as `protected`.
I currently can't stand `throw_error`, and I am optimistic about
server highlighting feature you are working on :)
Before this commit, each `isDefEq u v` invocation would fail if there
were pending universe level constraints. This commit, moves the
postponed universe constraints back to the `MetaM` state.
It also adds the combinator
```lean
withoutPostponingUniverseConstraints x
```
which executes `x` and throws an error if there are pending universe
constraints. We use the combinator at `elabApp` and `elabBinders`.
Without this commit, we would fail to elaborate simple terms such as
```lean
Functor.map Prod.fst (x s)
```
because after elaborating `Prod.fst` and trying to ensure its type
match the expected one, we would be stuck at the universe constraint:
```
u =?= max u ?v
```
Another benefit of the new approach is better error messages. Instead
of getting a mysterious type mismatch constraint, we get a list of
universe contraints the system is stuck at.
cc @Kha
The idea is to make clear that the field `posponed` is transient
state. It is only used during `isDefEq`.
The refactoring was motivated by a bug I found where the `posponed`
constraints were not being handled correctly. For example,
the `check (e : Expr)` method was returning `true`, but leaving pending
universe constraints at `postponed`.
cc @Kha
