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https://github.com/ilyakooo0/Idris-dev.git
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62 lines
1.3 KiB
Idris
62 lines
1.3 KiB
Idris
module Main
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data Binary : Nat -> Type where
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bEnd : Binary Z
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bO : Binary n -> Binary (n + n)
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bI : Binary n -> Binary (S (n + n))
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instance Show (Binary n) where
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show (bO x) = show x ++ "0"
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show (bI x) = show x ++ "1"
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show bEnd = ""
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data Parity : Nat -> Type where
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even : Parity (n + n)
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odd : Parity (S (n + n))
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parity : (n:Nat) -> Parity n
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parity Z = even {n=Z}
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parity (S Z) = odd {n=Z}
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parity (S (S k)) with (parity k)
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parity (S (S (j + j))) | even ?= even {n=S j}
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parity (S (S (S (j + j)))) | odd ?= odd {n=S j}
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natToBin : (n:Nat) -> Binary n
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natToBin Z = bEnd
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natToBin (S k) with (parity k)
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natToBin (S (j + j)) | even = bI (natToBin j)
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natToBin (S (S (j + j))) | odd ?= bO (natToBin (S j))
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intToNat : Int -> Nat
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intToNat 0 = Z
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intToNat x = if (x>0) then (S (intToNat (x-1))) else Z
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main : IO ()
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main = do putStr "Enter a number: "
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x <- getLine
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print (natToBin (fromInteger (cast x)))
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---------- Proofs ----------
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Main.natToBin_lemma_1 = proof
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intros
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rewrite plusSuccRightSucc j j
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rewrite sym (plusSuccRightSucc j j)
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trivial
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parity_lemma_1 = proof
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intros
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rewrite sym (plusSuccRightSucc j j)
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trivial
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parity_lemma_2 = proof {
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intro;
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intro;
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rewrite sym (plusSuccRightSucc j j);
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trivial;
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}
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