25 lines
1.1 KiB
Text
25 lines
1.1 KiB
Text
/--
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Tests that `partial_fixpoint` is not picking up the partial order structure on Prop, that is exclusively used for defining (co)inductive predicates. Since `Prop` is inhabitted, `partial_fixpoint` will synthetise a `FlatOrder` instance, but in the provided example, it will not be able to prove that the recursive calls are monotone in their arguments.
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-/
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-- This works as `∨` is monotone in its arguments with respect to the (`ImplicationOrder`/`ReverseImplicationOrder` on `Prop`.
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def f (x : Nat) : Prop :=
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f (x + 1) ∨ f ( x + 2)
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coinductive_fixpoint
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def f' (x : Nat) : Prop :=
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f' (x + 1) ∨ f' ( x + 2)
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inductive_fixpoint
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/--
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error: Could not prove 'f''' to be monotone in its recursive calls:
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Cannot eliminate recursive call `f'' (x + 1)` enclosed in
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f'' (x + 1) ∨ f'' (x + 2)
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Tried to apply 'Lean.Order.implication_order_monotone_or' and 'Lean.Order.coind_monotone_or', but failed.
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Possible cause: A missing `Lean.Order.MonoBind` instance.
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Use `set_option trace.Elab.Tactic.monotonicity true` to debug.
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-/
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#guard_msgs in
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def f'' (x : Nat) : Prop :=
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f'' (x + 1) ∨ f'' ( x + 2)
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partial_fixpoint
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