failed to generate equational theorem
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Description
Prerequisites
Please put an X between the brackets as you perform the following steps:
- Check that your issue is not already filed:
https://github.com/leanprover/lean4/issues - Reduce the issue to a minimal, self-contained, reproducible test case.
Avoid dependencies to Mathlib or Batteries. - Test your test case against the latest nightly release, for example on
https://live.lean-lang.org/#project=lean-nightly
(You can also use the settings there to switch to “Lean nightly”)
Description
Starting in version 4.18.0, Lean fails to generate equational theorems for certain well-founded recursive definitions.
Steps to Reproduce
inductive IsZero : Nat → Type
| mk : IsZero .zero
def isZero : ∀ n, Option (IsZero n)
| .zero => some .mk
| .succ n => match isZero n with
| none => none
| some .mk => none
termination_by n => n
Expected behavior: Code succeeds with no errors.
Actual behavior: The following error:
error: failed to generate equational theorem for 'isZero'
case h_2
x n : Nat
⊢ ((match (motive :=
(n : Nat) →
Option (IsZero n) →
((y : Nat) → (invImage (fun x => x) instWellFoundedRelationOfSizeOf).1 y n.succ → Option (IsZero y)) →
Option (IsZero n.succ))
n, isZero n with
| n, none => fun x => none
| .(Nat.zero), some IsZero.mk => fun x => none)
fun y a => isZero y) =
match n, isZero n with
| n, none => none
| .(Nat.zero), some IsZero.mk => none
Versions
v4.18.0-rc1, v4.18.0, v4.19.0-rc1, v4.19.0-rc2
Impact
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Contributor guide
First steps
- Read the whole issue, then the project's contributing guide.
- Comment on the issue to say you are picking it up — it saves two people doing the same work.
- Fork the repository and make your change on a branch.
- Open a pull request that references the issue number.
Research direction
Start by running the self-contained IsZero/isZero reproducer against the listed Lean versions and the latest nightly release. Compare the expected successful compilation with the equational-theorem generation error and use that failure as the regression boundary. Done means the reproducer compiles without errors while preserving its well-founded recursive definition.
Written by the indexing model from the issue text.
Assessment
- Domain
- compilers
- Issue type
- Bug
- Difficulty
- 4/5
- Estimated time
- 3-5 days
- Activity status
- Stale
- Clarity
- Clearly specified
- Newbie friendliness
- 35/100