leanprover / leanprover/lean4

`match` requires explicitly listing dependencies as scrutinees or causes "type mismatch"

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Description

Prerequisites

Please put an X between the brackets as you perform the following steps:

Description

Consider a situation like this:

inductive Nat' : Nat → Type where
  | zero : Nat' 0
  | succ (x : Nat' n) : Nat' (n + 1)

example (n : Nat) (xs : Nat' n) : Vector Nat n :=
  match xs with
  | .zero => #v[]
  | _ => sorry

Here, it suffices to specify xs and Lean automatically detects that it also needs to scrutinize n. However, there are situations in which this mechanism fails, requiring the user to tediously use _, _, _, ... in the match arms.

Context

This happened in a type theory formalization project.

Steps to Reproduce

Consider this:

inductive Expr : Nat → Type where
  | next (m : Expr n) : Expr (n + 1)

inductive X : Expr n → Type where
  | x {m : Expr n} : X (.next m)

/--
error: Type mismatch
  X.x
has type
  X (Expr.next ?m.6)
but is expected to have type
  X e
---
error: Case tag `rhs` not found.

Note: There are no cases to select.
-/
#guard_msgs in
def fails {e f : Expr n} (x : X e) :
    X f := by
  match x with
  | .x => sorry

def works {e f : Expr n} (x : X e) :
    X f := by
  match n, e, x with
  | _, _, .x => sorry

Expected behavior:

Lean should automatically match over n and e, too, and resolve the type mismatch this way.

Actual behavior:

The user gets a "type mismatch" error that e cannot be identified with .next _.

Versions
Lean 4.24.0-nightly-2025-09-02
Target: x86_64-unknown-linux-gnu
Additional Information

The symptoms of this issue look similar to this issue, except that adding more scrutinees doesn't help there.

Impact

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Contributor guide

Open the contributing guide

First steps

  1. Read the whole issue, then the project's contributing guide.
  2. Comment on the issue to say you are picking it up — it saves two people doing the same work.
  3. Fork the repository and make your change on a branch.
  4. Open a pull request that references the issue number.

Research direction

Start by running the minimal reproducer from the issue against the referenced Lean nightly version, comparing fails with works. Investigate how match x selects scrutinees for indexed inductive types such as Expr and X; the issue is done when the shorter match automatically scrutinizes n and e without the type mismatch.

Written by the indexing model from the issue text.

Assessment

Domain
compilers
Issue type
Bug
Difficulty
5/5
Estimated time
Over a week
Activity status
Stale
Clarity
Mostly clear
Newbie friendliness
35/100

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