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112 lines
2.5 KiB
112 lines
2.5 KiB
{# LANGUAGE LambdaCase, DeriveFunctor, DeriveFoldable, MultiParamTypeClasses #}


import Prelude hiding (length, sum, fix)




length :: [a] > Int


length [] = 0


length (_:xs) = 1 + length xs




lengthF :: ([a] > Int) > [a] > Int


lengthF rec [] = 0


lengthF rec (_:xs) = 1 + rec xs




lengthF' = \rec > \case


[] > 0


_:xs > 1 + rec xs




fix f = let x = f x in x




length' = fix lengthF




data MyList = MyNil  MyCons Int MyList


data MyListF a = MyNilF  MyConsF Int a




newtype Fix f = Fix { unFix :: f (Fix f) }




testList :: Fix MyListF


testList = Fix (MyConsF 1 (Fix (MyConsF 2 (Fix (MyConsF 3 (Fix MyNilF))))))




myOut :: MyList > MyListF MyList


myOut MyNil = MyNilF


myOut (MyCons i xs) = MyConsF i xs




myIn :: MyListF MyList > MyList


myIn MyNilF = MyNil


myIn (MyConsF i xs) = MyCons i xs




instance Functor MyListF where


fmap f MyNilF = MyNilF


fmap f (MyConsF i a) = MyConsF i (f a)




mySumF :: MyListF Int > Int


mySumF MyNilF = 0


mySumF (MyConsF i rest) = i + rest




mySum :: MyList > Int


mySum = mySumF . fmap mySum . myOut




myCata :: (MyListF a > a) > MyList > a


myCata f = f . fmap (myCata f) . myOut




myLength = myCata $ \case


MyNilF > 0


MyConsF _ l > 1 + l




myMax = myCata $ \case


MyNilF > 0


MyConsF x y > max x y




myMin = myCata $ \case


MyNilF > 0


MyConsF x y > min x y




myTestList = MyCons 2 (MyCons 1 (MyCons 3 MyNil))




pack :: a > (Int > a > a) > MyListF a > a


pack b f MyNilF = b


pack b f (MyConsF x y) = f x y




unpack :: (MyListF a > a) > (a, Int > a > a)


unpack f = (f MyNilF, \i a > f (MyConsF i a))




class Functor f => Cata a f where


out :: a > f a




cata :: Cata a f => (f b > b) > a > b


cata f = f . fmap (cata f) . out




instance Cata MyList MyListF where


out = myOut




data ListF a b = Nil  Cons a b deriving Functor




instance Cata [a] (ListF a) where


out [] = Nil


out (x:xs) = Cons x xs




sum :: Num a => [a] > a


sum = cata $ \case


Nil > 0


Cons x xs > x + xs




data BinaryTree a = Node a (BinaryTree a) (BinaryTree a)  Leaf deriving (Show, Foldable)


data BinaryTreeF a b = NodeF a b b  LeafF deriving Functor




instance Cata (BinaryTree a) (BinaryTreeF a) where


out (Node a l r) = NodeF a l r


out Leaf = LeafF




invert :: BinaryTree a > BinaryTree a


invert = cata $ \case


LeafF > Leaf


NodeF a l r > Node a r l




data MaybeF a b = NothingF  JustF a deriving Functor




instance Cata (Maybe a) (MaybeF a) where


out Nothing = NothingF


out (Just x) = JustF x




getOrDefault :: a > Maybe a > a


getOrDefault d = cata $ \case


NothingF > d


JustF a > a


