Tuple

{-# LANGUAGE MultiParamTypeClasses,FlexibleInstances,FunctionalDependencies ,UndecidableInstances#-}

data Pair a b = Pair a b
data Zero = Zero
data Succ a = Succ a

class Tuple t n c | t n -> c where
    nth :: t -> n -> c

instance Tuple (Pair a b) Zero a where
    nth (Pair a _) _ = a

instance Tuple t n c => Tuple (Pair a t) (Succ n) c where
    nth (Pair _ b) (Succ n) = nth b n

_0 = Zero
_1 = Succ _0
_2 = Succ _1
_3 = Succ _2
_4 = Succ _3
_5 = Succ _4
_6 = Succ _5
_7 = Succ _6
_8 = Succ _7
_9 = Succ _8

class TupleLike t p | t -> p where
    fromTuple :: t -> p
    toTuple :: p -> t

instance TupleLike (a,b) (Pair a (Pair b ())) where
    fromTuple (a,b) = Pair a (Pair b ())
    toTuple (Pair a (Pair b ())) = (a,b)

instance TupleLike (a,b,c) (Pair a (Pair b (Pair c ()))) where
    fromTuple (a,b,c) = Pair a (Pair b (Pair c ()))
    toTuple (Pair a (Pair b (Pair c ()))) = (a,b,c)

instance TupleLike (a,b,c,d) (Pair a (Pair b (Pair c (Pair d ())))) where
    fromTuple (a,b,c,d) = Pair a (Pair b (Pair c (Pair d ())))
    toTuple (Pair a (Pair b (Pair c (Pair d ())))) = (a,b,c,d)

main = do
    print $ fromTuple (0,"hoge") `nth` _0
    print $ fromTuple (0,"hoge") `nth` _1
    --print $ fromTuple (0,"hoge") `nth` _2 -- type error
    print $ fromTuple (0,"hoge",True) `nth` _1
    print $ fromTuple (0,"hoge",True) `nth` _2
    print $ fromTuple (0,"hoge",True,"piyo") `nth` _3
    --print $ fromTuple (0,"hoge",True,"piyo") `nth` _4