This is partly a continuation from: http://groups.google.ca/group/haskell-cafe/browse_thread/thread/4ee2ca1f5eb8... and http://hpaste.org/fastcgi/hpaste.fcgi/view?id=25265 Also of relevance: http://groups.google.ca/group/haskell-cafe/browse_thread/thread/9cc8858a2e51... http://www.haskell.org/haskellwiki/GHC/AdvancedOverlap http://homepages.cwi.nl/~ralf/HList/paper.pdf http://okmij.org/ftp/Haskell/typecast.html http://www.haskell.org/haskellwiki/User:ConradParker/InstantInsanity http://okmij.org/ftp/Haskell/types.html (haven't looked at this link yet) I will continue to try to solve the problem on my own but at the moment I'm able to get IsSuperSet to work but not the classes Isa, Child and IsSubSet to work. Unlike set theory IsSubSet is not the same as switching the order arguments in IsSuperSet because the searching is done in the opposite direction. In one case we are searching the parents and each child only has one parent. In the other Case we are searching the children and each parent could have multiple children). Bellow is my current code: {-# LANGUAGE EmptyDataDecls, MultiParamTypeClasses, ScopedTypeVariables, FunctionalDependencies, OverlappingInstances, FlexibleInstances, UndecidableInstances, TypeFamilies #-} {-# LANGUAGE TypeOperators #-} --10 {-# LANGUAGE FlexibleContexts #-} --{-# LANGUAGE IncoherentInstances #-} ----------------------IsSubSet ----------------------------------- data ItsNotAParrent class IsSubSet a b c | a b -> c where -- General Definition isSubSet :: a->b->c class Child a b|b->a where {} instance ( Parrent b a2, TypeEq a2 a itsAParrent, -- Child' itsAParrent a b ) => Child a b class Child' itsAParrent a b where {} instance (TypeCast b ItsNotAParrent)=>Child' F a b --No Childern instance (TypeCast b c, Parrent c b)=>Child' T a b instance (TypeCast b M)=>Child' itsAParrent a b --- Fail Case instance ( TypeEq ItsNotAParrent a itsNotAParrent, TypeEq a b iseq, IsSubSet' itsNotAParrent iseq a b c3 -- ) => IsSubSet a b c3 where -- isSubSet a b = undefined::c3 class IsSubSet' itsNotAParrent iseq a b c| itsNotAParrent iseq a b -> c where {} instance (TypeCast c T)=>IsSubSet' F T a b c where {} instance (TypeCast c F)=>IsSubSet' T iseq a b c where {} --Not sure which logic value is best for this case. instance (TypeCast c M)=>IsSubSet' itsNotAParrent iseq a b c where {} --Fail Case instance ( Child a d, IsSubSet d b c )=> IsSubSet' F F a b c where {} --bla11=isSubSet Cat Animal -----------------------Isa --------------------------------------------- class Isa' a b c|a b->c where {} --Direct Relationship class Isa a b c|a b->c where isa::a->b->c instance ( Isa' a1 b1 c1, --Direct Relationship IsSuperSet a1 a c2, --Check --20 IsSuperSet b b1 c3, -- Isa'' c1 c2 c3 a1 b1 c4 -- Decesion function -- )=>Isa a b c4 where isa a b = undefined::c4 class Isa'' c1 c2 c3 a b c4|c1 c2 c3 a b->c4 where {} -- isa :: c1->c2->c3->a->b->c4 instance Isa'' T T T a1 b1 T where {} -- isa'' c1 c2 c3 a b = T --30 instance Isa'' F c2 c3 a1 b1 F where {} -- -- isa'' c1 c2 c3 a b = F instance Isa'' c1 F c3 a1 b1 F where {} -- isa'' c1 c2 c3 a b = F instance Isa'' c1 c2 F a1 b1 F where {} -- isa'' c1 c2 c3 a b = F ---------------- Instance Isa Relations ---------------------------------- instance Isa' Animal Noun T instance (TypeCast F result) => Isa' a b result -----------------Test Relationships ----------------------------------40 --bla6 = isa Cat Noun -- --bla4 = isa Cat Verb -----------------------Basic Type Declarations --------------------------- 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) --50 data Cat = Cat deriving (Show) data Taby_Cat=Taby_Cat deriving (Show) -----------------------Instance SubType Relations -------------------------------- data ItsAnOrphan = ItsAnOrphan instance Show ItsAnOrphan where show _ = "ItsAnOrphan" --60 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 -- instance (TypeCast result ItsAnOrphan) => Parrent anyChild result where parrent a = undefined::result ----------------------- Generic subType Relations ------------------------------ 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 ItsAnOrphan b isOrphan, TypeEq a b iseq, IsSuperSet' isOrphan iseq a b c3 -- ) => IsSuperSet a b c3 where --S isSuperSet a b = undefined::c3 -- isSuperSet a b=(isSuperSet' (u::isaninmal) (u::iseq) (a::a) (b::b))::c3 class IsSuperSet' isOrphan iseq a b c| isOrphan iseq a b -> c where {} -- isSuperSet' :: isOrphan->iseq->a->b->c instance (TypeCast c T)=>IsSuperSet' F T a b c where {} -- isSuperSet' isOrphan iseq a b = T instance (TypeCast c F)=>IsSuperSet' T T a b c where {} --Not sure which logic value is best for this case. instance ( Parrent b d, IsSuperSet a d c )=> IsSuperSet' F F a b c where {} -- isSuperSet' isOrphan iseq a b = (isSuperSet a ((parrent (b::b))::d))::c instance (TypeCast c F)=>IsSuperSet' T F a b c where {} -- isSuperSet' isOrphan iseq a b = F ----------- Logical Types ------------------ data T=T -- deriving (Show) data F=F -- deriving (Show) --25 data M=M -- Fail case instance Show T where show _ = "T" instance Show F where show _ = "F" instance Show M where show _ = "M" class ToBool a where toBool :: a->Bool instance ToBool T where toBool a = True instance ToBool F where toBool a = False -----------------------Loical Type Relations ----------------------------- 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 ----------------------- OKMIJ ------------------------------------------ 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 ----------------------- Testing Code -------------------------------- myCat=Cat bla=isSuperSet Animal Cat bla2=isSuperSet Cat Animal bla3=isSuperSet Animal Noun bla4=isSuperSet Noun Animal bla5=isSuperSet Noun Noun