f20cae3729
This PR sets the `irreducible` attribute before generating the equations for recursive definitions. This prevents these equations to be marked as `defeq`, which could lead to `simp` generation proofs that do not type check at default transparency. This issue is surfacing more easily since well-founded recursion on `Nat` is implemented with a dedicated fix point operator (#7965). Before that, `WellFounded.fix` was used, which is inherently not reducing, so we did get the desired result even without the explicit reducibility setting. Fixes #12398.
146 lines
2.9 KiB
Text
146 lines
2.9 KiB
Text
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def foo : Nat → Nat → Nat
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| 0, m => match m with | 0 => 0 | m => m
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| n+1, m => foo n m
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termination_by n => n
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/--
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info: equations:
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theorem foo.eq_1 : foo 0 0 = 0
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theorem foo.eq_2 : ∀ (x : Nat), (x = 0 → False) → foo 0 x = x
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theorem foo.eq_3 : ∀ (x n : Nat), foo n.succ x = foo n x
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-/
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#guard_msgs in
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#print equations foo
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/--
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info: foo.eq_def (x✝ x✝¹ : Nat) :
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foo x✝ x✝¹ =
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match x✝, x✝¹ with
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| 0, m =>
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match m with
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| 0 => 0
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| m => m
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| n.succ, m => foo n m
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-/
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#guard_msgs in
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#check foo.eq_def
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/-- error: Unknown identifier `foo.eq_4` -/
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#guard_msgs in
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#check foo.eq_4
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/--
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info: foo._unary.eq_def (_x : (_ : Nat) ×' Nat) :
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foo._unary _x =
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PSigma.casesOn _x fun a a_1 =>
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match a, a_1 with
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| 0, m =>
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match m with
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| 0 => 0
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| m => m
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| n.succ, m => foo._unary ⟨n, m⟩
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-/
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#guard_msgs in
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#check foo._unary.eq_def
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set_option backward.eqns.deepRecursiveSplit false in
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def bar : Nat → Nat → Nat
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| 0, m => match m with | 0 => 0 | m => m
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| n+1, m => bar n m
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termination_by n => n
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/--
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info: equations:
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theorem bar.eq_1 : ∀ (x : Nat),
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bar 0 x =
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match x with
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| 0 => 0
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| m => m
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theorem bar.eq_2 : ∀ (x n : Nat), bar n.succ x = bar n x
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-/
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#guard_msgs in
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#print equations bar
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/--
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info: bar.eq_def (x✝ x✝¹ : Nat) :
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bar x✝ x✝¹ =
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match x✝, x✝¹ with
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| 0, m =>
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match m with
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| 0 => 0
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| m => m
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| n.succ, m => bar n m
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-/
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#guard_msgs in
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#check bar.eq_def
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-- Now the same for structural recursion
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namespace Structural
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def foo : Nat → Nat → Nat
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| 0, m => match m with | 0 => 0 | m => m
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| n+1, m => foo n m
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termination_by structural n => n
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/--
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info: equations:
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@[defeq] theorem Structural.foo.eq_1 : foo 0 0 = 0
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theorem Structural.foo.eq_2 : ∀ (x : Nat), (x = 0 → False) → foo 0 x = x
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@[defeq] theorem Structural.foo.eq_3 : ∀ (x n : Nat), foo n.succ x = foo n x
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-/
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#guard_msgs in
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#print equations foo
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/--
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info: Structural.foo.eq_def (x✝ x✝¹ : Nat) :
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foo x✝ x✝¹ =
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match x✝, x✝¹ with
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| 0, m =>
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match m with
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| 0 => 0
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| m => m
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| n.succ, m => foo n m
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-/
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#guard_msgs in
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#check foo.eq_def
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/-- error: Unknown identifier `Structural.foo.eq_4` -/
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#guard_msgs in
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#check Structural.foo.eq_4
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set_option backward.eqns.deepRecursiveSplit false in
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def bar : Nat → Nat → Nat
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| 0, m => match m with | 0 => 0 | m => m
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| n+1, m => bar n m
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termination_by n => n
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/--
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info: equations:
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theorem Structural.bar.eq_1 : ∀ (x : Nat),
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bar 0 x =
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match x with
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| 0 => 0
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| m => m
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theorem Structural.bar.eq_2 : ∀ (x n : Nat), bar n.succ x = bar n x
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-/
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#guard_msgs in
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#print equations bar
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/--
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info: Structural.bar.eq_def (x✝ x✝¹ : Nat) :
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bar x✝ x✝¹ =
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match x✝, x✝¹ with
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| 0, m =>
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match m with
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| 0 => 0
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| m => m
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| n.succ, m => bar n m
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-/
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#guard_msgs in
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#check bar.eq_def
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end Structural
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