The compiler tries to generate code for `let rec`s inside a proof

Prerequisites

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Description

Declaring a non-computable function within a proof with let rec ends up with an error that the function should be marked noncomputable, but:

1. There is no place to mark a let rec as noncomputable.
2. There is no point making a let rec computable anyway, since we're inside a proof.

Context

This came up in APAP when doing a measure theoretic argument requiring to define a simple function recursively.

Steps to Reproduce

noncomputable def foo (n : Nat) : Nat := n

-- Uncomment the next line to fix
-- noncomputable section

example : True := by
  -- Always works fine
  let bar : Nat → Nat := foo
  -- Works iff `noncomputable section` is uncommented
  let rec baz : Nat → Nat
  | 0 => 0
  | n + 1 => foo n + 1
  /-
  failed to compile definition, compiler IR check failed at '_example.baz'. Error: depends on declaration 'foo', which has no executable code; consider marking definition as 'noncomputable'
  -/
  trivial

Expected behavior: The let rec works

Actual behavior: The let rec doesn't work

Additional information

If a variant of #2719 were implemented for noncomputable, then we could work around this issue by using noncomputable let rec instead of let rec.

Versions

Lean 4.18.0
Target: x86_64-unknown-linux-gnu

Impact

Add 👍 to issues you consider important. If others are impacted by this issue, please ask them to add 👍 to it.

Start with the minimal reproducer in the issue and inspect the compiler path that emits _example.baz and performs the compiler IR check. Confirm the behavior for a recursive let inside a proof, then verify that the example compiles without requiring a noncomputable section.