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16 lines
351 B
Plaintext
16 lines
351 B
Plaintext
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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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data Parity : Nat -> Type where
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Even : (n : Nat) -> Parity (plus n n)
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Odd : (n : Nat) -> Parity (S (plus n n))
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half : (n : Nat) -> Parity n -> Nat
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half (plus $n $n) (Even $n) = n
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half (S (plus $n $m)) (Odd $n) = n
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