41a2e9af19
This PR makes functions defined by well-founded recursion use an `opaque` well-founded proof by default. This reliably prevents kernel reduction of such definitions and proofs, which tends to be prohibitively slow (fixes #2171), and which regularly causes hard-to-debug kernel type-checking failures. This changes renders `unseal` ineffective for such definitions. To avoid the opaque proof, annotate the function definition with `@[semireducible]`.
38 lines
1.5 KiB
Text
38 lines
1.5 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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/-- info: [Meta.IndPredBelow] Nested or not recursive -/
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#guard_msgs 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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if we make `onlyZeros` semireducible-/
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def toFixPoint : OnlyZeros t → onlyZeros t
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| .leaf => by simp [onlyZeros]
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| .node [] _ => by simp [onlyZeros]
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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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