Martin Sulzmann <sulzmann@comp.nus.edu.sg> writes:
Hi,
I was wondering whether other people made similiar observations. Functional dependencies seem to be expressiveness enough to encode some of the kinding rules required for Constructor Classes.
read this page: http://cvs.haskell.org/Hugs/pages/hugsman/exts.html I think that the designer of constructor class and functionnal depedencies is the same person si it makes sense that one generalise the other. nevertheless i found constructor class more elegant for many problems. Your solution is less elegant that the one using constructor classes. I found too that type error messages of class using functionnal depedencies are not easy to read. There is often ambiguity in code that are not easy to solver. this problem does not appear with constructor classes.
Take a look at the Haskell code below (runs under hugs -98 or ghci -fglasgow-exts-fallow-undecidable-instances)
Martin
-- An alternative to constructor classes
module Fmap where
{- Instead of class Functor f where fmap :: (a->b)->(f a->f b)
use -}
class Fmap a b fa fb | a fb -> b fa, b fa -> a fb, fa fb -> a b where fmap2 :: (a->b)->(fa -> fb)
{- We require:
(1) fmap2 transforms a function into another function, i.e. fmap2's type should always be of shape (a->b)->(fa->fb)
(2) b, fa uniquely determine a and fb
(3) a, fb " b and fa
(4) fa, fb " a and b
Note that (1) is enforced by the class definition. (2)-(4) are enforced by FDs.
My guess/conjecture is that the above axiomatization of functors is equivalent to the one found in Haskell98. -}
-- some Examples
{- The following is a variation of an example taken from Mark Jones original paper "A System of Constructor Classes: Overloading and Implicit Higher-Order Polymorphism". He used this example to motivate the introduction of constructor classes. The example is type correct using the alternative formulation of functors. -}
cmap :: (Fmap a b fb1 fb, Fmap a1 b1 fa fb1) => (a1 -> b1) -> (a -> b) -> fa -> fb cmap f g = (fmap2 g) . (fmap2 f)
-- identity functor instance Fmap a a a a where fmap2 h = h
-- functor composition -- Instance is not allowed, cause leads to undecidable type inference
{- instance (Fmap a b c d, Fmap e f a b) => Fmap e f c d where fmap2 h = fmap2 (fmap2 h) -}
comp :: (Fmap fa1 fb1 fa fb, Fmap a b fa1 fb1) => (a -> b) -> fa -> fb comp h = fmap2 (fmap2 h)
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