lean4-htt/tests/lean/run/univCnstrApprox.lean
Leonardo de Moura 1630d9b803
feat: universe constraint approximations (#3981)
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.
2024-04-24 20:27:51 +00:00

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Text

universe u v
-- This is a mock-up of the `HasLimitsOfSize` typeclass in mathlib4.
class HLOS.{a,b} (C : Type b) where
P : Type a
-- We only have an instance when there is a "universe inequality".
instance HLOS_max : HLOS.{a} (Type max a b) := sorry
-- In mathlib4 we currently make use of the following workaround:
abbrev TypeMax := Type max u v
instance (priority := high) HLOS_max' : HLOS.{a} (TypeMax.{a, b}) := sorry
example : HLOS.{a} (TypeMax.{a, b}) := HLOS_max'.{a} -- Success
example : HLOS.{a} (TypeMax.{a, b}) := inferInstance -- Success
-- We solve the following examples using approximations
example : Type max v u = TypeMax.{v} := rfl -- Previously failed with: `max u v =?= max v ?u`
example : Type max v u = TypeMax.{u} := rfl -- Previously failed with: `max u v =?= max u ?u`