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
