102 lines
2.3 KiB
Haskell
102 lines
2.3 KiB
Haskell
{-# LANGUAGE LambdaCase, DeriveFunctor, DeriveFoldable, MultiParamTypeClasses #-}
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import Prelude hiding (length, sum, fix)
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length :: [a] -> Int
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length [] = 0
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length (_:xs) = 1 + length xs
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lengthF :: ([a] -> Int) -> [a] -> Int
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lengthF rec [] = 0
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lengthF rec (_:xs) = 1 + rec xs
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lengthF' = \rec -> \case
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[] -> 0
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_:xs -> 1 + rec xs
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fix f = let x = f x in x
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length' = fix lengthF
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data MyList = MyNil | MyCons Int MyList
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data MyListF a = MyNilF | MyConsF Int a
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newtype Fix f = Fix { unFix :: f (Fix f) }
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testList :: Fix MyListF
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testList = Fix (MyConsF 1 (Fix (MyConsF 2 (Fix (MyConsF 3 (Fix MyNilF))))))
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myOut :: MyList -> MyListF MyList
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myOut MyNil = MyNilF
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myOut (MyCons i xs) = MyConsF i xs
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myIn :: MyListF MyList -> MyList
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myIn MyNilF = MyNil
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myIn (MyConsF i xs) = MyCons i xs
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instance Functor MyListF where
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fmap f MyNilF = MyNilF
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fmap f (MyConsF i a) = MyConsF i (f a)
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mySumF :: MyListF Int -> Int
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mySumF MyNilF = 0
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mySumF (MyConsF i rest) = i + rest
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mySum :: MyList -> Int
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mySum = mySumF . fmap mySum . myOut
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myCata :: (MyListF a -> a) -> MyList -> a
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myCata f = f . fmap (myCata f) . myOut
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myLength = myCata $ \case
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MyNilF -> 0
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MyConsF _ l -> 1 + l
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myMax = myCata $ \case
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MyNilF -> 0
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MyConsF x y -> max x y
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myMin = myCata $ \case
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MyNilF -> 0
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MyConsF x y -> min x y
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myTestList = MyCons 2 (MyCons 1 (MyCons 3 MyNil))
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pack :: a -> (Int -> a -> a) -> MyListF a -> a
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pack b f MyNilF = b
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pack b f (MyConsF x y) = f x y
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unpack :: (MyListF a -> a) -> (a, Int -> a -> a)
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unpack f = (f MyNilF, \i a -> f (MyConsF i a))
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class Functor f => Cata a f where
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out :: a -> f a
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cata :: Cata a f => (f b -> b) -> a -> b
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cata f = f . fmap (cata f) . out
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instance Cata MyList MyListF where
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out = myOut
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data ListF a b = Nil | Cons a b deriving Functor
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instance Cata [a] (ListF a) where
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out [] = Nil
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out (x:xs) = Cons x xs
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sum :: Num a => [a] -> a
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sum = cata $ \case
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Nil -> 0
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Cons x xs -> x + xs
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data BinaryTree a = Node a (BinaryTree a) (BinaryTree a) | Leaf deriving (Show, Foldable)
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data BinaryTreeF a b = NodeF a b b | LeafF deriving Functor
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instance Cata (BinaryTree a) (BinaryTreeF a) where
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out (Node a l r) = NodeF a l r
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out Leaf = LeafF
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invert :: BinaryTree a -> BinaryTree a
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invert = cata $ \case
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LeafF -> Leaf
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NodeF a l r -> Node a r l
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