54 lines
987 B
Text
54 lines
987 B
Text
namespace Ex1
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mutual
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def f : Nat → α → α → α
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| 0, a, b => a
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| n, a, b => g a n b |>.1
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def g : α → Nat → α → (α × α)
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| a, 0, b => (a, b)
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| a, n, b => (h a b n, a)
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def h : α → α → Nat → α
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| a, b, 0 => b
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| a, b, n+1 => f n a b
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end
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termination_by'
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invImage
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(fun
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| PSum.inl ⟨n, _, _⟩ => (n, 2)
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| PSum.inr <| PSum.inl ⟨_, n, _⟩ => (n, 1)
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| PSum.inr <| PSum.inr ⟨_, _, n⟩ => (n, 0))
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(Prod.lex sizeOfWFRel sizeOfWFRel)
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#print f
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#print g
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#print h
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#eval f 5 'a' 'b'
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end Ex1
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namespace Ex2
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mutual
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def f : Nat → α → α → α
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| 0, a, b => a
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| n, a, b => g a n b |>.1
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def g : α → Nat → α → (α × α)
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| a, 0, b => (a, b)
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| a, n, b => (h a b n, a)
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def h : α → α → Nat → α
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| a, b, 0 => b
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| a, b, n+1 => f n a b
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end
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termination_by
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f n _ _ => (n, 2)
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g _ n _ => (n, 1)
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h _ _ n => (n, 0)
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#print f
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#print g
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#print h
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#eval f 5 'a' 'b'
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end Ex2
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