induction does not populate instance-implicit arguments

[eric-wieser]

Prerequisites

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Description

The induction tactic does not handle instance-implicit arguments, as it treats them as regular implicits.

Context

Zulip thread

Steps to Reproduce

1. Run the following:

class Foo (α : Type)

instance : Foo Nat where

@[elab_as_elim]
def Foo.induction_no (P : ∀ (α : Type) [Foo α], Prop) (nat : P Nat) (α : Type) [ohno : Foo α] : P α := sorry
@[elab_as_elim]
def Foo.induction_ok (P : ∀ (α : Type) [Foo α], Prop) (nat : P Nat) (α : Type) (ohok : Foo α) : P α := sorry


example (α : Type) [Foo α] : α = Nat := by
  induction α using Foo.induction_no with
  | nat => rfl

example (α : Type) [Foo α] : α = Nat := by
  induction α, ‹Foo α› using Foo.induction_ok with
  | nat => rfl

Expected behavior: Both inductions should succeed

Actual behavior: The first one fails with "failed to infer implicit target ohno". It should be synthesizing the target via typeclass search, since it is in square brackets.

Versions

• 4.8.0-rc1
• 4.9.0-nightly-2024-05-21

Additional Information

[Additional information, configuration or data that might be necessary to reproduce the issue]

Impact

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[Kha]

@eric-wieser or others: could you say more about the (positive) impact of fixing this bug? Has it come up more often than with the single theorem mentioned on Zulip?

[eric-wieser]

I think probably it does only come up with the handful of theorems mentioned on Zulip, but only because it is rare to have an induction principle that inducts on a typeclass argument. Finiteness is precisely the case where this is most likely to happen.