[Haskell-cafe] Functional Dependencies Help

[John Creighton]

I've been trying to apply some stuff I learned about functional
dependencies, but I run into one of two problems. I either end up with
inconsistent dependencies (OverlappingInstances  doesn't seem to
apply) or I end up with infinite recursion. I want to be able to do
simple things like if a is a subset of b and b is a subset of c then a
is a subset of c. If a is a is a subset of b and b is a c then a is a
c.

Before I added the equality functions I had infinite recursion. Once I
put them them in then I have trouble with overlapping isntances.

{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE OverlappingInstances #-}
{-# LANGUAGE UndecidableInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE FlexibleContexts #-}


data Noun = Noun deriving (Show) --10
data Verb = Verb deriving (Show) --
data Adjactive = Adjactive deriving (Show)

data Animal=Animal deriving (Show)
data Feline=Feline deriving (Show)
data Cat = Cat deriving (Show)

data Taby_Cat=Taby_Cat deriving (Show)
data T=T deriving (Show)
data F=F deriving (Show) --20


class Isa a b c | a b->c where isa::a->b->c

instance Isa Animal Noun T where isa a b = T --25

class IsSuperSet a b c | a b->c where
    isSuperSet :: a->b->c

instance IsSuperSet Feline Cat T where --30
   isSuperSet a b=T
instance IsSuperSet Animal Feline T where
   isSuperSet a b=T
instance IsSuperSet a Animal F where
   isSuperSet a b=F --35

class TypeNotEq d b c | d b->c where
   typeNotEq :: a->b->c

instance (IsSuperSet d b c, --40
          IsSuperSet a d c,
          TypeNotEq a d T,
          TypeNotEq b d T,
          TypeEq c T T
         )=>
    IsSuperSet a b c where
      isSuperSet a b=undefined::c

instance TypeNotEq a a c where
    typeNotEq a b = undefined::c --50
instance TypeNotEq a b c where
    typeNotEq a b = undefined::c
class TypeEq a b c | a b->c where
    typeEq :: a->b->c
instance TypeEq a a c where
    typeEq a b = undefined::c
instance TypeEq a b c where
    typeEq a b = undefined::c

class ToBool a where
   toBool :: a->Bool

instance ToBool T where
   toBool a = True

instance ToBool F where
   toBool a = False

myCat=Cat
bla=isSuperSet Animal Cat