Unfolds, coalgebras and anamorphisms

Unfold.hs

{-# LANGUAGE DeriveFunctor #-}
import Data.Functor.Foldable
import Data.Function

unfold1 :: Unfold Int [Int]
unfold1 = xana coalgebra1

xana :: Unfoldable b => Coalgebra a b -> Unfold a b
xana = ana

type Coalgebra a b = a -> Base b a
type Unfold a b = a -> b

coalgebra1 :: Coalgebra Int [Int]
coalgebra1 5 = Nil
coalgebra1 x = Cons x (x + 1)

main = print "ho"

unfold2 :: Unfold Int [Int]
unfold2 5 = []
unfold2 x = x : unfold2 (x + 1)


unfold3 :: Unfold Int [Int]
unfold3 = fix f where
	f _ 5 = []
	f self x = x : self (x + 1)

unfold4 = fix f' where
	f' self x = coalgebra x where
		nil = []
		cons a b = a : self b
		coalgebra 5 = nil
		coalgebra x = cons x (x + 1)

unfold3'' :: Unfold Int [Int]
unfold3'' = fix f' where
	f' self x = foo' $ coalgebra1 x where
		foo' = embed . fmap self
		foo Nil = []
		foo (Cons a b) = a : self b

type OurList a = Fix (OurBase a)

data OurBase a b = OurCons a b | OurNil deriving (Functor)

coalgebra2 :: Coalgebra Int (OurList Int)
coalgebra2 5 = OurNil
coalgebra2 x = OurCons x (x + 1)

coalgebra3 :: Coalgebra (OurList a) [a]
coalgebra3 (Fix OurNil) = Nil

coalgebra3 (Fix (OurCons a b)) = Cons a b

toList1 :: OurList a -> [a]
toList1 = cata algebra where
	algebra OurNil = []
	algebra (OurCons a b) = a : b 

toList2 :: OurList a -> [a]
toList2 = ana coalgebra3 

unfold5 :: Unfold Int (OurList Int)
unfold5 = ana coalgebra2