lean4-htt/tests/elab/implicitTypesRecCoe.lean
Garmelon 08eb78a5b2
chore: switch to new test/bench suite (#12590)
This PR sets up the new integrated test/bench suite. It then migrates
all benchmarks and some related tests to the new suite. There's also
some documentation and some linting.

For now, a lot of the old tests are left alone so this PR doesn't become
even larger than it already is. Eventually, all tests should be migrated
to the new suite though so there isn't a confusing mix of two systems.
2026-02-25 13:51:53 +00:00

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unsafe def f (n : Nat) :=
let rec g (x : Nat) :=
if x > 0 then
/- This example relies on the instance `coeId {α} (a : α) : CoeT α a α`,
The type of `g` is not provided. Thus, the expected type is
`?m x` since the elaborator assumes it may depend on `x`.
Thus, the expected type for the addition is `?m x`.
The type of `g (x-1)` is `?m (x-1)`. So, we have the unification
problem
```
?m (x-1) =?= ?m x
```
and it is rejected by the unifier. Thus, the elaborator inserts
a coercion from `?m (x-1)` to `?m x` around `g (x-1)` which creates
the pending TC problem:
```
CoeT (?m (x-1)) (g (x-1)) (?m x)
```
Remark: in principle, we could solve it using a heuristic: assume
`?m` is a constant function.
Later, when we elaborate the else branch `0`, we have that
```
?m x =?= Nat
```
which is solved using `?m := (fun _ => Nat)`.
Then, `@coeId Nat (g (x-1))` is used to synthesize
```
CoeT (?m (x-1)) (g (x-1)) (?m x)
```
which is
```
CoeT Nat (g (x-1)) Nat
```
after we apply the assignment `?m := (fun _ => Nat)`
-/
g (x-1) + n
else
0;
g n
/-- info: 100 -/
#guard_msgs in
#eval f 10