[Haskell-cafe] Re: Functional Dependencies Help

30 Apr 2010


      On Apr 29, 7:47 am, John Creighton  wrote:
...
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 instances.
I've been doing some reading and I think the following is an
improvement but I end up hanging the compiler so I can't tell what the
errors are. I'll see if their are any trace options that might be
helpfully for GHC.
{-# LANGUAGE EmptyDataDecls,
             MultiParamTypeClasses,
             ScopedTypeVariables,
             FunctionalDependencies,
             FlexibleInstances #-}

{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE UndecidableInstances #-} --10
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE FlexibleContexts #-}


data Noun = Noun deriving (Show) --15
data Verb = Verb deriving (Show) --
data Adjactive = Adjactive deriving (Show)

data Animal=Animal deriving (Show)
data Feline=Feline deriving (Show) --20
data Cat = Cat deriving (Show)

data Taby_Cat=Taby_Cat deriving (Show)
data T=T deriving (Show)
data F=F deriving (Show) --25
--data Z=Z
--data S i = S i
--type One = S Z
--type Zero = Z
class Isa a b c | a b->c where isa::a->b->c --30

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


class Parrent a b| a->b where -- Specific Cases
    parrent :: a->b --

instance Parrent Cat Feline where --
   parrent a = Feline --40
instance Parrent Feline Animal where --
   parrent a= Animal --


class TypeOr a b c|a b->c where
   typeOr :: a->b->c
instance TypeOr T T T where
   typeOr a b = T --50
instance TypeOr T F T where
   typeOr a b = T
instance TypeOr F T T where
   typeOr a b = T
instance TypeOr F F T where
   typeOr a b = T

class TypeEq' () x y b => TypeEq x y b | x y -> b
instance TypeEq' () x y b => TypeEq x y b
class TypeEq' q x y b | q x y -> b --60
class TypeEq'' q x y b | q x y -> b

instance TypeCast b T => TypeEq' () x x b
instance TypeEq'' q x y b => TypeEq' q x y b
instance TypeEq'' () x y F

-- see http://okmij.org/ftp/Haskell/typecast.html
class TypeCast   a b   | a -> b, b->a   where typeCast   :: a -> b
class TypeCast'  t a b | t a -> b, t b -> a where typeCast'  :: t->a-
...
b
class TypeCast'' t a b | t a -> b, t b -> a where typeCast'' :: t->a-
b --70
instance TypeCast'  () a b => TypeCast a b where typeCast x =
typeCast' () x
instance TypeCast'' t a b => TypeCast' t a b where typeCast' =
typeCast''
instance TypeCast'' () a a where typeCast'' _ x  = x

-- overlapping instances are used only for ShowPred
class EqPred a flag | a->flag where {}

                                  -- Used only if the other
                                  -- instances don't apply -- 80

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

--instance (TypeEq b Animal T,TypeEq c F T)=>IsSuperSet a b c where
--85
--   isSuperSet a b = F --
u=undefined
instance (
           TypeEq a b iseq, --90
           TypeEq Animal b isaninmal,
           IsSuperSet' isaninmal iseq a b c3 --
         ) =>
         IsSuperSet a b c3 where --
         isSuperSet a b=(isSuperSet' (u::isaninmal) (u::iseq) (a::a)
(b::b))::c3

class IsSuperSet' isanimal iseq a b c| isanimal iseq a b->c where
    isSuperSet' :: a->b->c

instance IsSuperSet' isanimal T a b T where
   isSuperSet' a b = T

instance (Parrent b d, IsSuperSet a b c)=>IsSuperSet' F F a b c where
   isSuperSet' a b = (isSuperSet a ((parrent (b::b)::d)))::c

instance IsSuperSet' T F a b F where
   isSuperSet' a b = F


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