{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances, FlexibleContexts #-}

import Control.Monad.Instances
import Coalgebra

-- F X = A x X, for a fixed A, this has a functor instance
type F a = (,) a

-- This will give the fixpoint, ie a coalgebra, because F is a functor
type Stream a = Nu (F a)

-- auxiliary functions
toList :: Stream a -> [a]
toList s = a0 : toList a' where (a0, a') = psi s


-- example with a very simple (F Int)-coalgebra, 1 -> 2, 2 -> 3, 3 -> 2
data X = One | Two | Three
instance Coalgebra (F Int) X where
	psi One = (1, Two)
	psi Two = (2, Three)
	psi Three = (3, Two)

main :: IO ()
main = do
	putStrLn $ show $ take 20 $ toList $ (semantics One :: Stream Int)