Example of Category instance?

category.hs

{-# LANGUAGE OverloadedStrings, GADTs, NoImplicitPrelude #-}

import Data.Text (Text)
import qualified Data.Text as T
import qualified Data.Text.IO as T
import Control.Monad.Writer

import Prelude hiding ((.),id)
import Control.Category

class Reifiable a where
	reify :: a -> Text

type FuncName = Text

data Chain a b where
	Func :: (a -> b) -> Chain a b
	Func' :: FuncName -> Chain a b
	Chain ::  Chain a c -> Chain c b -> Chain a b
	ChainEnd :: Chain a a

-- the code below can't be typed, because ChainEnd cannot be typed as Chain a a without GADTs.
-- data Chain a b = forall c. Chain (a -> c) (Chain c b) | ChainEnd

instance Category Chain where
	id = ChainEnd
	(.) = flip Chain

-- |evalChain chain1 2 == "6"
chain1 :: Chain Int String
chain1 = Chain (Func (\k -> [k,k,k])) (Chain (Func (show .sum)) ChainEnd)

-- |evalChain chain1' 2 == "6"
chain1' = Func (show . sum) . Func (\k -> [k,k,k])

-- |reify chain2 = "cos().sin()"
chain2 = Func' "sin" . Func' "cos"

evalChain :: Chain a b -> a -> b
evalChain (Chain (Func f) rest) a = evalChain rest (f a)
evalChain ChainEnd a = a
evalChain (Func f) a = f a


instance Reifiable (Chain a b) where
	reify (Chain f ChainEnd) = T.concat [reify f]
	reify (Chain f g) = T.concat [reify f,".",reify g]
	reify (Func f) = "someFunc()"
	reify (Func' name) = T.concat [name,"()"]
	reify ChainEnd = ""