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48 lines
1.5 KiB
Idris
48 lines
1.5 KiB
Idris
import Data.Vect
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import Data.Nat
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my_filter : (a -> Bool) -> Vect n a -> (p ** Vect p a)
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my_filter p [] = ( _ ** [] )
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my_filter p (x :: xs) with (filter p xs)
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my_filter p (x :: xs) | ( _ ** xs' ) = if (p x) then ( _ ** x :: xs' ) else ( _ ** xs' )
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foo : Int -> Int -> Bool
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foo n m with (n + 1)
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foo _ m | 2 with (m + 1)
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foo _ _ | 2 | 3 = True
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foo _ _ | 2 | _ = False
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foo _ _ | _ = False
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data Parity : Nat -> Type where
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Even : {n : _} -> Parity (n + n)
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Odd : {n : _} ->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
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-- = rewrite plusSuccRightSucc j j in Even {n = S j}
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-- parity (S (S (S (j + j)))) | Odd
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-- = rewrite plusSuccRightSucc j j in Odd {n = S j}
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helpEven : (j : Nat) -> Parity (S j + S j) -> Parity (S (S (plus j j)))
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helpEven j p = rewrite plusSuccRightSucc j j in p
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helpOdd : (j : Nat) -> Parity (S (S (j + S j))) -> Parity (S (S (S (j + j))))
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helpOdd j p = rewrite plusSuccRightSucc j j in p
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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 = helpEven j (Even {n = S j})
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parity (S (S (S (j + j)))) | Odd = helpOdd j (Odd {n = S j})
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natToBin : Nat -> List Bool
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natToBin Z = Nil
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natToBin k with (parity k)
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natToBin (j + j) | Even = False :: natToBin j
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natToBin (S (j + j)) | Odd = True :: natToBin j
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