def Lean.Elab.Term.setElabConfig (cfg : Lean.Meta.Config) : Lean.Meta.Config

Set isDefEq configuration for the elaborator. Note that we enable all approximations but quasiPatternApprox

In Lean3 and Lean 4, we used to use the quasi-pattern approximation during elaboration. The example:

def ex : StateT δ (StateT σ Id) σ :=
monadLift (get : StateT σ Id σ)

demonstrates why it produces counterintuitive behavior. We have the Monad-lift application:

@monadLift ?m ?n ?c ?α (get : StateT σ id σ) : ?n ?α

It produces the following unification problem when we process the expected type:

?n ?α =?= StateT δ (StateT σ id) σ
==> (approximate using first-order unification)
?n := StateT δ (StateT σ id)
?α := σ

Then, we need to solve:

?m ?α =?= StateT σ id σ
==> instantiate metavars
?m σ =?= StateT σ id σ
==> (approximate since it is a quasi-pattern unification constraint)
?m := fun σ => StateT σ id σ

Note that the constraint is not a Milner pattern because σ is in the local context of ?m. We are ignoring the other possible solutions:

?m := fun σ' => StateT σ id σ
?m := fun σ' => StateT σ' id σ
?m := fun σ' => StateT σ id σ'

We need the quasi-pattern approximation for elaborating recursor-like expressions (e.g., dependent match with expressions).

If we had use first-order unification, then we would have produced the right answer: ?m := StateT σ id

Haskell would work on this example since it always uses first-order unification.

Equations

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