409c6cac4c
Recursive predefinitions contains “rec app” markers as mdata in the predefinitions, but sometimes these get in the way of termination checking, when you have ``` [mdata (fun x => f)] arg ``` Therefore, the `preprocess` pass floats them out of applications (originally only for structural recursion, since #2818 also for well-founded recursion). But the code was incomplete: Because `Meta.transform` calls `post` on `f x y` only once (and not also on `f x`) one has to float out of nested applications as well. A consequence of this can be that in a recursive proof, `rw [foo]` does not work although `rw [foo _ _]` does. Also adding the testcase where @david-christiansen and I stumbled over this (Maybe the two preprocess modules can be combined, now that #2973 is landed, will try that in a follow-up).
90 lines
1.5 KiB
Text
90 lines
1.5 KiB
Text
/-!
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Test that parentheses don't get in the way of structural recursion.
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https://github.com/leanprover/lean4/issues/2810
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-/
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namespace Unary
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def f (n : Nat) : Nat :=
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match n with
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| 0 => 0
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| n + 1 => (f) n
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-- TODO: How can we assert that this was compiled structurally?
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-- with beta-reduction
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def f2 (n : Nat) : Nat :=
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match n with
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| 0 => 0
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| n + 1 => (fun n' => (f2) n') n
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-- structural recursion
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def f3 (n : Nat) : Nat :=
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match n with
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| 0 => 0
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| n + 1 => (f3) n
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termination_by n
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-- Same with rewrite
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theorem f_zero (n : Nat) : f n = 0 := by
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match n with
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| .zero => rfl
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| .succ n =>
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unfold f
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rewrite [f_zero]
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rfl
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-- Same with simp
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theorem f_zero' (n : Nat) : f n = 0 := by
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match n with
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| .zero => rfl
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| .succ n =>
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unfold f
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simp only [f_zero']
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end Unary
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namespace Binary
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def f (n m : Nat) : Nat :=
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match n with
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| 0 => 0
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| n + 1 => (f) n m
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-- TODO: How can we assert that this was compiled structurally?
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-- with beta-reduction
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def f2 (n m : Nat) : Nat :=
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match n with
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| 0 => 0
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| n + 1 => (fun n' => (f2) n' m) n
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-- structural recursion
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def f3 (n m : Nat) : Nat :=
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match n with
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| 0 => 0
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| n + 1 => (f3) n m
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termination_by n
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-- Same with rewrite
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theorem f_zero (n m : Nat) : f n m = 0 := by
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match n with
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| .zero => rfl
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| .succ n =>
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unfold f
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rewrite [f_zero]
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rfl
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-- Same with simp
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theorem f_zero' (n m : Nat) : f n m = 0 := by
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match n with
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| .zero => rfl
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| .succ n =>
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unfold f
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simp only [f_zero']
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end Binary
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