325fab1c1d
* fix: don't try to generate `below` for nested predicates. * doc : document test #2389 * doc : document `mkBelow` * test: extend `2389.lean` * style: fix comments in `IndPredBelow.lean` and `2389.lean`
35 lines
1.4 KiB
Text
35 lines
1.4 KiB
Text
/-!
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# Verify that nested predicates don't trigger the generation of `below` lemmas
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Since the case of nested predicates is not currently handled by `mkBelow` (in `src/Lean/Meta/IndPredBelow.lean`),
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trying to generate `OnlyZeros.below` triggers an error upon defining the inductive type.
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-/
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inductive Forall (P : α → Prop) : List α → Prop
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| nil : Forall P []
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| cons : {x : α} → P x → Forall P l → Forall P (x::l)
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inductive Tree : Type :=
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| leaf : Nat → Tree
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| node : List Tree → Tree
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set_option trace.Meta.IndPredBelow true in
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/-- Despite not having `.below` and `.brecOn`,
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the type is still usable thanks to well-founded recursion. -/
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inductive OnlyZeros : Tree → Prop :=
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| leaf : OnlyZeros (.leaf 0)
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| node (l : List Tree): Forall OnlyZeros l → OnlyZeros (.node l)
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/-- Equivalent definition of `OnlyZeros`, defined by a function instead of an inductive type. -/
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def onlyZeros : Tree → Prop
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| .leaf n => n = 0
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| .node [] => True
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| .node (x::s) => onlyZeros x ∧ onlyZeros (.node s)
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/-- Pattern-matching on `OnlyZeros` works despite `below` and `brecOn` not being generated. -/
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def toFixPoint : OnlyZeros t → onlyZeros t
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| .leaf => rfl
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| .node [] _ => True.intro
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| .node (x::s) (.cons h p) => by
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rw [onlyZeros] -- necessary because `onlyZeros` isn't structurally recursive
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exact And.intro (toFixPoint h) (toFixPoint (.node s p))
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