This PR improves the “expected type mismatch” error message by omitting
the type's types when they are defeq, and putting them into separate
lines when not.
I found it rather tediuos to parse the error message when the expected
type is long, because I had to find the `:` in the middle of a large
expression somewhere. Also, when both are of sort `Prop` or `Type` it
doesn't add much value to print the sort (and it’s only one hover away
anyways).
This PR fixes a bug where the monad lift coercion elaborator would
partially unify expressions even if they were not monads. This could be
taken advantage of to propagate information that could help elaboration
make progress, for example the first `change` worked because the monad
lift coercion elaborator was unifying `@Eq _ _` with `@Eq (Nat × Nat)
p`:
```lean
example (p : Nat × Nat) : p = p := by
change _ = ⟨_, _⟩ -- used to work (yielding `p = (p.fst, p.snd)`), now it doesn't
change ⟨_, _⟩ = _ -- never worked
```
As such, this is a breaking change; you may need to adjust expressions
to include additional implicit arguments.
Where before we had
```lean
#check fun x : Nat => ?a
-- fun x ↦ ?m.7 x : (x : Nat) → ?m.6 x
```
Now by default we have
```lean
#check fun x : Nat => ?a
-- fun x => ?a : (x : Nat) → ?m.6 x
```
In particular, delayed assignment metavariables such as `?m.7` pretty
print using the name of the metavariable they are delayed assigned to,
suppressing the bound variables used in the delayed assignment (hence
`?a` rather than `?a x`). Hovering over `?a` shows `?m.7 x`.
The benefit is that users can see the user-provided name in local
contexts. A justification for this pretty printing choice is that `?m.7
x` is supposed to stand for `?a`, and furthermore it is just as opaque
to assignment in defeq as `?a` is (however, when synthetic opaque
metavariables are made assignable, delayed assignments can be a little
less assignable than true synthetic opaque metavariables).
The original pretty printing behavior can be recovered using `set_option
pp.mvars.delayed true`.
This PR also extends the documentation for holes and synthetic holes,
with some technical details about what delayed assignments are. This
likely should be moved to the reference manual, but for now it is
included in this docstring.
(This PR is a simplified version of #3494, which has a round-trippable
notation for delayed assignments. The pretty printing in this PR is
unlikely to round trip, but it is better than the current situation,
which is that delayed assignment metavariables never round trip, and
plus it does not require introducing a new notation.)
Floris van Doorn [reported on
Zulip](https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/have.20tactic.20error.20recovery/near/425283053)
that it is confusing that the `have : T := e` tactic completely fails if
the body `e` is not of type `T`. This is in contrast to `have : T := by
exact e`, which does not completely fail when `e` is not of type `T`.
This ends up being caused by `elabTermEnsuringType` throwing an error
when it fails to insert a coercion. Now, it detects this case, and it
checks the `errToSorry` flag to decide whether to throw the error or to
log the error and insert a `sorry`.
This is justified by `elabTermEnsuringType` being a frontend to
`elabTerm`, which inserts `sorry` on error.
An alternative would be to make `ensureType` respect `errToSorry`, but
there exists code that expects being able to catch when `ensureType`
fails. Making such code manipulate `errToSorry` seems error prone, and
this function is not a main entry point to the term elaborator, unlike
`elabTermEnsuringType`.
It had two problems:
- It was preventing coercions from being applied.
- It was compromising error recovery. The body of the lambda was not
being elaborated when the exception was thrown.
The new error message is more verbose and potentially confusing, but
it is better than the one produced this morning.
