On May 4, 9:46 am, Bartek Ćwikłowski <paczesi...@gmail.com> wrote: > hello, > > 2010/5/4 John Creighton <johns2...@gmail.com>: > > > 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). > > Since Subset is the opposite of Superset, you can search in the > "easier" (up) direction, so it really is as easy as reversing the > order of arguments. > > It's not possible to write class/type-level function Child a b | a -> > b, because functions (classes with fun-deps) must be deterministic. If > you want to enumerate all children (based on Parent class instances), > it's also impossible in this setup,
That's the approach I finally ended up taking. It seems to work so far but I haven't tried using my child function to build a subset or an isa function. My code is rather ugly but it's the best I came up with. The following are examples of the enumerations: instance Parrent' () d Z Cat Feline -- instance Parrent' () d Z Feline Animal -- Z: means the first child S Z: would be the second child instance d is a type variable letting the relationship be bidirectional: () is a dumby argument which is used in the case where their is no instance. It is used as follows: instance (Parrent'' q d z anyChild anyParrent)=>Parrent' q d z anyChild anyParrent instance (ItsAnOrphan ~ anyParrent)=>Parrent'' q P1 n anyChild anyParrent instance (HasNoChildern ~ anyChild)=>Parrent'' q N1 Z anyChild anyParrent instance (HasNoMoreChildern ~ anyChild)=>Parrent'' q N1 (S n) anyChild anyParrent N1 is short for S Z P1 is short for P Z (Negative numbers, P stands for previous) > it's probably possible with Oleg's > second-order typeclass programming[1]. > > [1]http://okmij.org/ftp/Haskell/types.html#poly2 > But what are you actually trying to achieve? I can't thing of anything > useful that would require walking down the hierarchy tree (and > backtracking) and it has to be done at the type level. Well, I need it for my Isa relationship defined so that "a" isa "d" if their exists a "b" and "c" such that the following conditions hold: "a" isa subset of "b", "b" isa "c" "c" is a subset of "d" Thus we know d, but we need to search backwards to find c. Anyway, I don't have the code for isa or subset yet but here is my code for child (some more testing warranted): Any hints on making it cleaner or more readable would be appreciated. ------------------------------------------------------------------------------------- {-# LANGUAGE EmptyDataDecls, MultiParamTypeClasses, ScopedTypeVariables, FunctionalDependencies, OverlappingInstances, FlexibleInstances, UndecidableInstances, TypeFamilies #-} {-# LANGUAGE TypeOperators #-} --10 {-# LANGUAGE FlexibleContexts #-} {-# LANGUAGE TypeSynonymInstances #-} u=undefined bla = child Z Animal bla2 = child (u::P1) Animal bla3 = child (u::Z) Cat bla4 = child (u::P1) Cat bla5 = parrent Cat bla6 = parrent Feline bla7 = parrent Animal --20 -----------------------Instance SubType Relations -------------------------------- data ItsAnOrphan = ItsAnOrphan instance (Show ItsAnOrphan) where show _ = "ItsAnOrphan" data HasNoMoreChildern = HasNoMoreChildern instance (Show HasNoMoreChildern) where show _ = "HasNoMoreChildern" data HasNoChildern = HasNoChildern instance (Show HasNoChildern) where show _ = "HasNoChildern" --30 class Parrent' () P1 Z a b =>Parrent a b| a->b where -- Specific Cases parrent :: a->b -- instance Parrent' () P1 Z a b => Parrent a b where parrent _ = undefined::b class Parrent' q d n a b | q d n a-> b, q d n b ->a class Parrent'' q d n a b | q d n a -> b,q d n b -> a --class Parrent''' q n a b | q n b -> a instance Parrent' () d Z Cat Feline -- instance Parrent' () d Z Feline Animal -- instance (Parrent'' q d z anyChild anyParrent)=>Parrent' q d z anyChild anyParrent instance (ItsAnOrphan ~ anyParrent)=>Parrent'' q P1 n anyChild anyParrent instance (HasNoChildern ~ anyChild)=>Parrent'' q N1 Z anyChild anyParrent instance (HasNoMoreChildern ~ anyChild)=>Parrent'' q N1 (S n) anyChild anyParrent class Child n a b|n a->b where -- a2 is the parrent of b child :: n->a->b child _ _ = undefined::b instance ( Parrent' () N1 n b2 a, Child' b2 n a b --b2==b or b2=HasNoChildern or b2==HasNoMoreChildern )=> Child n a b class Child' b2 n a b | b2 n a -> b --a2==a or a2=HasNoChildern or a2==HasNoMoreChildern class Child'' q b2 n a b|q b2 n a b ->b class Child''' q b2 n a b|q b2 n a b ->b instance Child' HasNoChildern Z a HasNoChildern instance Child' HasNoMoreChildern (S n) a HasNoMoreChildern instance (b2~b) => Child' b2 n a b --instance Child'' () b2 n a b => Child' b2 n a b --instance (Child''' q b2 n a b)=>Child''' q b2 n a b ----------- 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 ---------------------- Peno Numbers ------------------------- data Z=Z type family Simple a type instance Simple (P (S n)) = n type instance Simple (S (P n)) = n type instance Simple Z = Z data S n = S n data P n = P n type P1 = S Z type P2 = S P1 type P3 = S P2 type P4 = S P3 type N1 = P Z type N2 = P N1 type N3 = P N2 type N4 = P N3 -----------------------Basic Type Declarations ---------------------------50 data Noun = Noun deriving (Show) --15 data Verb = Verb deriving (Show) -- data Adjactive = Adjactive deriving (Show) data Animal=Animal -- deriving (Show) instance Show Animal where show _ = "Animal" data Feline=Feline -- deriving (Show) --50 instance Show Feline where show _ = "Feline" data Cat = Cat -- deriving (Show) instance Show Cat where show _ = "Cat" data Taby_Cat=Taby_Cat deriving (Show) --60 ----------------------- 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 _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
