{-# OPTIONS_GHC -fno-warn-missing-methods #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE UndecidableInstances #-}

nil = undefined

data True
data False

data S n
data Z

data Nil
data Cons h t

data IsCell
data IsOddAtom
data IsEvenAtom

class Not t b | t -> b
instance Not True False
instance Not False True

class And a b r | a b -> r
instance And True True True
instance And True False False
instance And False True False
instance And False False False

class If c t f r | c t f -> r
instance If True t f t
instance If False t f f

class IsEven a b | a -> b
instance IsEven Z True
instance IsEven (S Z) False
instance (IsEven n r)
   => IsEven (S (S n)) r
instance IsEven (Cons xs x) False

class Wutpam t b | t -> b
instance Wutpam Z True
instance Wutpam (S n) True
instance Wutpam Nil False
instance Wutpam (Cons x xs) False

class Wutket t b | t -> b
instance (Wutpam t b, Not b r)
   => Wutket t r

class Solution n r | n -> r
   where solution :: n -> r
instance ( Wutket n c
         , Not c a
         , IsEven n m
         , If m IsEvenAtom IsOddAtom e
         , If c IsCell e o
         )
   => Solution n o where solution = nil