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23 lines
525 B
Plaintext
23 lines
525 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 $n)) (Odd $n) = n
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data Baz : Nat -> Type where
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AddThings : (x : Nat) -> (y : Nat) -> Baz (plus x y)
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addBaz : (x : Nat) -> Baz x -> Nat
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addBaz (plus $x $y) (AddThings $x $y) = plus x y
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