`CoeFun` and implicit arguments

[mniip]

Prerequisites

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Description

Function applications going through CoeFun do not respect the implicitness of the parameters declared in the instance head, rather they take the implicitness information from the instance implementation.

Context

Steps to Reproduce

structure Foo where app : ∀α, (x : α) → α

def foo := Foo.mk fun _ => id

instance : CoeFun Foo fun _ => ∀{α}, α → α where
  coe := Foo.app

#check CoeFun.coe foo Nat
#check foo Nat

Expected behavior:

• Both cases desugar as Foo.app foo (α:=Type) (x:=Nat), and infer the type Type

Actual behavior:

• The first one infers the correct type, but the second desugars as Foo.app foo (α:=Nat) and infers the type Nat → Nat.

Versions

4.13.0

Additional Information

The problem can be reversed by making the structure field have implicit ∀{α} and the instance head have the explicit ∀α. https://github.com/leanprover/lean4/issues/1891 seems relevant.

Impact

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[Kha]

CoeFun Foo fun _ => ∀{α}, α → α tells the elaborator to coerce the former type into the latter. I don't see why it should adjust the second type with any other information, at least without further motivation. Thus I'm closing this as by design.

[mniip]

@Kha I think there's a misunderstanding.

CoeFun Foo fun _ => ∀{α}, α → α tells the elaborator to coerce the former type into the latter.

That's exactly what it fails to do, hence this issue.

Instead of coercing to "the latter" -- whatever is written in the instance head, it coerces to what is actually the type of the instance body.