Universe.hs

{-# LANGUAGE TypeFamilies, MultiParamTypeClasses, FlexibleInstances, TypeOperators #-}

infixr 5 :>

data BigCrunch = BigCrunch
data f :> u = f :> u

class Universe a b u where
    runUniverse :: u -> a -> b

instance (Universe b c u, a0 ~ a) => Universe a0 c ((a -> b) :> u) where
    runUniverse (f :> u) = runUniverse u . f

instance (a0 ~ a) => Universe a0 a BigCrunch where
    runUniverse BigCrunch = id

univ
    :: (Integer -> Integer)
    :> (Integer -> Integer)
    :> (Integer -> String)
    :> ([a] -> [a])
    :> BigCrunch
univ = (*3) :> subtract 3 :> show :> reverse :> BigCrunch

main = print $ runUniverse univ 42