Death to data types

die-data-types.purs

module Main where 

import Debug.Trace
import Prelude (flip, const, id, ($), (+), (<<<), show)

type Tuple a b = forall z. (a -> b -> z) -> z

mkTuple :: forall a b. a -> b -> Tuple a b
mkTuple a b = \f -> f a b

fst :: forall a b. Tuple a b -> a
fst = flip ($) (flip $ const id)

snd :: forall a b. Tuple a b -> b
snd = flip ($) (const id)

bimap :: forall a b c d. (a -> c) -> (b -> d) -> Tuple a b -> Tuple c d
bimap f g = \t -> mkTuple (f $ fst t) (g $ snd t)

type List a = forall z. (z -> a -> z) -> z -> z

nil :: forall a. List a 
nil = const id

cons :: forall a. a -> List a -> List a
cons a xs = \f -> \z -> xs f (f z a)

list :: List Number
list = cons 1 (cons 2 (cons 3 (nil)))

foldl :: forall z a. (z -> a -> z) -> z -> List a -> z
foldl f z l = l f z

main = trace <<< show $ foldl (+) 0 list