The unifier used to implement the `cases` tactic should not discard
equations of the form `x = t` and `t = x` using proof irrelanvance.
The new test demonstrates the issue. The unifier was reaching the
state
```
x : Conw Con.nil
|- x = Conw.nilw -> x = Conw.nilw
```
and discarding the equality instead of substituting `x`
because `x` and `Conw.nilw` are definionally equal due to
proof irrelevance.
@javra Do you have more complicated examples that were being
affected by this issue?
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 after I enabled elaboration on syntactically incorrect terms, the
fallback is activated more often, and the raw term seems to have
little value for most users, and it is just scary.
Not sure whether the flag is a good idea, but it produces are more
user friendly output.
We need `MetaM` methods such as `isProp` to improve `ppGoal`.
This commit also moves `currNamespace` and `openDecls` to
`Core.Context`. Without this change, `Meta.ppExpr` was not taking
`open` commands into account.
@Kha I was tired of writing `arbitrary _` :)
There 0 places in the stdlib where the type needs to be provided.
If in the future we need to specify the type we can use
`arbitrary (α := <type>)`
There is no reason for having `MonadIO` anymore. The `MonadLift` type
class is well behaved in the new frontend, the `MonadFinally` solves
the problem at monad stacks such as `ExcepT e IO`.
This commit also changes the type of the IO printing functions.
For example, the type of `IO.println` was
```
def IO.println {m} [MonadIO m] {α} [ToString α] (s : α) : m Unit
```
and now it is just
```
def IO.println {α} [ToString α] (s : α) : IO Unit
```
We rely on the new frontend auto-lifting feature.
That is, if there is an instance `[MonadLiftT IO m]`, then
a term of type `IO a` is automatically coerced to `m a`
We also want a simpler `IO.println` for writing tests.
For example,
```
```
doesn't work because there isn't sufficient information for inferring
the parameter `m` in the previous `IO.println`.
The shortest workaround looked very weird
```
```
I considered adding `IO` as a default value for `m` when we have
`MonadIO m`, as we use `Nat` as the default for `ofNat a`, but it felt
like uncessary complexity.
@Kha The commit seems to work well. The auto-lifting featuring has
been working great for me. There is still room for improvement.
For example, given `MonadLiftT m n`, it doesn't automatically lift
`a -> m b` into `a -> n b`. So, code such as
`foo >>= IO.println`
had to be rewritten as
`foo >>= fun x => IO.println x`
I will add this feature later.
If you have time, please try to play with this feature and figure out
if it is stable enough for making it the default.
That is, if it roboust enough, we can stop using the following idiom
for writing functions that can be lifted automatically.
```
def instantiateLevelMVarsImp (u : Level) : MetaM Level :=
...
def instantiateLevelMVars {m} [MonadLiftT MetaM m] (u : Level) : m Level :=
liftMetaM $ instantiateLevelMVarsImp u
```
I think we only need this idiom when using `MonadControlT` which is
not as common as `MonadLiftT`.
