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December 25, 2019 13:18
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{-# LANGUAGE DeriveFunctor #-} | |
module Main where | |
type Algebra f a = f a -> a | |
type Coalgebra f a = a -> f a | |
newtype Fix f = In { out :: f (Fix f) } | |
cata :: Functor f => Algebra f a -> Fix f -> a | |
cata alg = alg . fmap (cata alg) . out | |
ana :: Functor f => Coalgebra f a -> a -> Fix f | |
ana coalg = In . fmap (ana coalg) . coalg | |
hylo :: Functor f => Algebra f b -> Coalgebra f a -> a -> b | |
hylo alg coalg = h where h = alg . fmap h . coalg | |
data NatF a = ZeroF | SuccF a deriving (Functor) | |
fib :: (Show a, Integral a) => Algebra NatF (a, a) | |
fib ZeroF = (0, 1) | |
fib (SuccF (prev, next)) = (next, prev + next) | |
nth :: (Show a, Integral a) => Coalgebra NatF a | |
nth 0 = ZeroF | |
nth n = SuccF (n-1) | |
getNthFib :: Integer -> Integer | |
getNthFib n = fst $ hylo fib nth (n - 1) | |
-- [0,1,1,2,3,5,8,13,21,34,55] | |
main = print $ getNthFib <$> [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11] |
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