25 lines
583 B
Text
25 lines
583 B
Text
/- Well-founded recursion -/
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def ack : Nat → Nat → Nat
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| 0, y => y+1
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| x+1, 0 => ack x 1
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| x+1, y+1 => ack x (ack (x+1) y)
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termination_by ack x y => (x, y)
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def sum (a : Array Int) : Int :=
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let rec go (i : Nat) :=
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if i < a.size then
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a[i] + go (i+1)
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else
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0
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go 0
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termination_by go i => a.size - i
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set_option pp.proofs true
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#print sum.go
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/-
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def sum.go : Array Int → Nat → Int :=
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fun a =>
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WellFounded.fix (sum.go.proof_1 a) fun i a_1 =>
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if h : i < Array.size a then Array.getOp a i + a_1 (i + 1) (sum.go.proof_2 a i h) else 0
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-/
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