29 lines
1.1 KiB
Text
29 lines
1.1 KiB
Text
inductive Tree (α : Type _) : Type _
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| leaf : α → Tree α
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| branch : Tree α → Tree α → Tree α
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inductive Path {α : Type _} : Tree α → Type _
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| term (x : α) : Path (Tree.leaf x)
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| left (tl tr : Tree α) : Path tl → Path (Tree.branch tl tr)
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| right (tl tr : Tree α) : Path tr → Path (Tree.branch tl tr)
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section map
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variables {α : Type _} {β : Type _} (f : α → β)
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protected def Tree.map : Tree α → Tree β
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| Tree.leaf x => Tree.leaf (f x)
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| Tree.branch tl tr => Tree.branch (Tree.map tl) (Tree.map tr)
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protected def Path.map : {t : Tree α} → Path t → Path (t.map f)
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| Tree.leaf _, Path.term x => Path.term (f x)
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| Tree.branch _ _, Path.left tl tr p => Path.left (tl.map f) (tr.map f) (Path.map p)
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| Tree.branch _ _, Path.right tl tr p => Path.right (tl.map f) (tr.map f) (Path.map p)
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protected def Path.unmap : {t : Tree α} → Path (t.map f) → Path t
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| Tree.leaf x, Path.term _ => Path.term x
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| Tree.branch tl tr, Path.left _ _ p => Path.left tl tr (Path.unmap p)
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| Tree.branch tl tr, Path.right _ _ p => Path.right tl tr (Path.unmap p)
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#print Path.unmap
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end map
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