On Sun, 2 Jan 2005 karczma@info.unicaen.fr wrote:
I tried to generalize one of my old packages for quantum *abstract* computations, where state vectors are defined as functional objects, whose codomain has some arithmetic. It is easy to see that you can define (f <+> g) = \x -> f x + g x etc.
The problem that you were trying to solve can be solved, and has been solved. Please refer to the message on keyword arguments: http://www.haskell.org/pipermail/haskell/2004-August/014416.html Functional dependencies _are_ kept. Here's one of the tests test4 = ((\x y -> x <+> y) <+> (\x y -> ((2 *> x) <+> (3 *> y)))) (1::Int) (2::Int) it typechecks and computes. Perhaps this solution also solves the problems in the numericprelude. The compiler is GHCi 6.2.1 {-# OPTIONS -fglasgow-exts #-} {-# OPTIONS -fallow-undecidable-instances #-} {-# OPTIONS -fallow-overlapping-instances #-} module Q where class Vspace a v | v -> a where (<+>) :: v -> v -> v (*>) :: a -> v -> v instance (IsFunction v f, Vspace' f a v) => Vspace a v where (<+>) = doplus (undefined::f) (*>) = dostar (undefined::f) class Vspace' f a v | f v -> a where doplus :: f -> v -> v -> v dostar :: f -> a -> v -> v instance Num a => Vspace' HFalse a a where doplus _ = (+) dostar _ = (*) -- etc. No problem. instance (IsFunction v f, Vspace' f a v, Vspace a v) => Vspace' HTrue a (c->v) where doplus _ f g = \x -> f x <+> g x dostar _ a f x = a *> (f x) test1 = (1::Int) <+> 2 test2 = ((\x -> x <+> (10::Int)) <+> (\x -> x <+> (10::Int))) 1 test3 = ((\x y -> x <+> y) <+> (\x y -> (x <+> y) <+> x)) (1::Int) (2::Int) test4 = ((\x y -> x <+> y) <+> (\x y -> ((2 *> x) <+> (3 *> y)))) (1::Int) (2::Int) data HTrue data HFalse class IsFunction a b | a -> b instance IsFunction (x->y) HTrue instance TypeCast f HFalse => IsFunction a f -- literally lifted from the HList library 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 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