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51 lines
856 B
Plaintext
51 lines
856 B
Plaintext
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data Bool : Type where
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False : Bool
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True : Bool
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not : Bool -> Bool
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not False = True
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not True = False
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data Nat : Type where
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Z : Nat
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S : Nat -> Nat
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plus : Nat -> Nat -> Nat
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plus Z y = y
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plus (S k) y = S (plus k y)
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ack : Nat -> Nat -> Nat
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ack Z n = S n
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ack (S k) Z = ack k (S Z)
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ack (S j) (S k) = ack j (ack (S j) k)
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foo : Nat -> Nat
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foo Z = Z
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foo (S Z) = (S Z)
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foo (S (S k)) = foo (S k)
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foo' : Nat -> Nat
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foo' Z = Z
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foo' (S Z) = (S Z)
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foo' (S p@(S k)) = foo' p
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data Bin : Type where
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EPS : Bin
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C0 : Bin -> Bin
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C1 : Bin -> Bin
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foom : Bin -> Nat
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foom EPS = Z
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foom (C0 EPS) = Z
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foom (C0 (C1 x)) = S (foom (C1 x))
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foom (C0 (C0 x)) = foom (C0 x)
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foom (C1 x) = S (foom x)
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pfoom : Bin -> Nat
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pfoom EPS = Z
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pfoom (C0 EPS) = Z
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pfoom (C0 (C1 x)) = S (pfoom (C0 x))
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pfoom (C0 (C0 x)) = pfoom (C0 x)
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pfoom (C1 x) = S (foom x)
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