Overlapping Instances with Functional Dependencies
I have the following three programs: class Foo a b instance Foo (a -> b) (a -> [b]) instance Foo a a class Bar a b | a -> b instance Bar (a -> b) (a -> b) instance Bar a a class Baz a b | a -> b instance Baz (a -> b) (a -> [b]) instance Baz a a When compiled in ghc 6.4 (with -fglasgow-exts -fallow-overlapping-instances -fallow-undecidable-instances) Foo and Bar compile fine, but Baz fails with this error: Baz.hs:2:0: Functional dependencies conflict between instance declarations: Baz.hs:2:0: instance Baz (a -> b) (a -> [b]) Baz.hs:3:0: instance Baz a a This is how I interpret the error: The fundep says "a uniquely determines b", but if you have `Baz (Int -> Int) b`, b is `Int -> [Int]` according to the first instance and `Int -> Int` according to the second instance. b isn't uniquely determined by a, so the functional dependency isn't functional -- thus the conflict. When confronted with overlapping instances, the compiler chooses the most specific one (if it is unique), e.g. `Baz (a -> b) (a -> [b])` is more specific than `Baz a a`. But it seems that the combination of the two features is broken: if the most specific instance is chosen before checking the functional dependency, then the fundep is satisfied; if the fundep is checked before choosing the most specific instance, then it isn't. Is this a bug, or am I confused? Dan
Hi, I wouldn't call this a bug, overlapping instances and in particular the combination with functional dependencies are something which is not well studied yet. Hence, GHC is very conservative here. I feel like you, this program should work. As you correctly point out, there's a conflict among the two improvement rules (resulting from the instances and FD). A sensible decision is to apply the same "ad-hoc" mechanism to improvement rules that is currently applied to overlapping instances. Of course, we need some formal system to express such conditions precisely. You find some hints how to achieve this in G. J. Duck, S. Peyton-Jones, P. J. Stuckey, and M. Sulzmann. Sound and decidable type inference for functional dependencies. In Proc. of ESOP'04 Martin Daniel Brown writes:
I have the following three programs:
class Foo a b instance Foo (a -> b) (a -> [b]) instance Foo a a
class Bar a b | a -> b instance Bar (a -> b) (a -> b) instance Bar a a
class Baz a b | a -> b instance Baz (a -> b) (a -> [b]) instance Baz a a
When compiled in ghc 6.4 (with -fglasgow-exts -fallow-overlapping-instances -fallow-undecidable-instances) Foo and Bar compile fine, but Baz fails with this error:
Baz.hs:2:0: Functional dependencies conflict between instance declarations: Baz.hs:2:0: instance Baz (a -> b) (a -> [b]) Baz.hs:3:0: instance Baz a a
This is how I interpret the error: The fundep says "a uniquely determines b", but if you have `Baz (Int -> Int) b`, b is `Int -> [Int]` according to the first instance and `Int -> Int` according to the second instance. b isn't uniquely determined by a, so the functional dependency isn't functional -- thus the conflict.
When confronted with overlapping instances, the compiler chooses the most specific one (if it is unique), e.g. `Baz (a -> b) (a -> [b])` is more specific than `Baz a a`.
But it seems that the combination of the two features is broken: if the most specific instance is chosen before checking the functional dependency, then the fundep is satisfied; if the fundep is checked before choosing the most specific instance, then it isn't.
Is this a bug, or am I confused?
Dan _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Daniel Brown wrote:
class Baz a b | a -> b instance Baz (a -> b) (a -> [b]) instance Baz a a ...but Baz fails with this error...
When confronted with overlapping instances, the compiler chooses the most specific one (if it is unique), e.g. `Baz (a -> b) (a -> [b])` is more specific than `Baz a a`.
But it seems that the combination of the two features is broken: if the most specific instance is chosen before checking the functional dependency, then the fundep is satisfied; if the fundep is checked before choosing the most specific instance, then it isn't.
There is a way to write your example in Haskell as it is. The key idea is that functional dependencies can be given *per instance* rather than per class. To assert such dependencies, you need the `TypeCast' constraint, which is throughly discussed in the HList technical report. http://homepages.cwi.nl/~ralf/HList/ The following is the complete code for the example, which runs on GHC 6.4. We see that the functional dependencies work indeed: the compiler figures out the types of test1 and test2 and test3 (and thus resolved overloading) without any type signatures or other intervention on our part. {-# OPTIONS -fglasgow-exts #-} {-# OPTIONS -fallow-undecidable-instances #-} {-# OPTIONS -fallow-overlapping-instances #-} module Foo where {- class Baz a b | a -> b instance Baz (a -> b) (a -> [b]) instance Baz a a -} -- No functional dependencies here! class Baz a b where baz :: a -> b -- Rather, dependencies are here instance TypeCast a r => Baz a r where baz a = typeCast a instance TypeCast (a -> [b]) r => Baz (a -> b) r where baz f = let r = \a -> [f a] in typeCast r -- Chooses the instance Baz a a test1 = baz True -- True -- Chooses the instance Baz (a -> b) (a -> [b]) test2 = (baz show) (1::Int) -- ["1"] test3 x = (baz show) x test3' = test3 (Just True) -- ["Just True"] -- copied verbatim 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
This is still an ad-hoc solution, cause you lose the `most-specific' instance property. You really have to impose a `fixed' ordering in which instance-improvement rules fire. Recap: The combination of overlapping instances and type improvement leads to a `non-confluent' system, i.e. there're too many (inconsistent) choices how to improve and reduce constraints. The standard approach to deal with overlapping instances is to impose a fixed order among the resulting reduction rules (the `most-specific' order can be seen as a special instance of a fixed order). FDs imply improvement rules. In case of overlapping instances these improvement rules are immediately non-confluent. As Simon pointed out: "...what ever mechanism is used for instance matching, the same would be used for type dependencies..." Hence, combining instances and improvement rules is the obvious `solution'. Hints can be found in my first two replies where I said: 1) "... You find some hints how to achieve this in ... ESOP'04". 2) "...instances and type dependencies are closer linked to each other then one might think..." Concretely, the TypeCast trick already appears in the ESOP'04 paper on p8 (mid-page). Conclusion: I think it's wrong to explain a new feature in terms of an implementation-specific encoding. We need something more principled here. Otherwise, we'll face some unexpected behavior (eventually) again. Martin oleg@pobox.com writes:
Daniel Brown wrote:
class Baz a b | a -> b instance Baz (a -> b) (a -> [b]) instance Baz a a ...but Baz fails with this error...
When confronted with overlapping instances, the compiler chooses the most specific one (if it is unique), e.g. `Baz (a -> b) (a -> [b])` is more specific than `Baz a a`.
But it seems that the combination of the two features is broken: if the most specific instance is chosen before checking the functional dependency, then the fundep is satisfied; if the fundep is checked before choosing the most specific instance, then it isn't.
There is a way to write your example in Haskell as it is. The key idea is that functional dependencies can be given *per instance* rather than per class. To assert such dependencies, you need the `TypeCast' constraint, which is throughly discussed in the HList technical report. http://homepages.cwi.nl/~ralf/HList/
The following is the complete code for the example, which runs on GHC 6.4. We see that the functional dependencies work indeed: the compiler figures out the types of test1 and test2 and test3 (and thus resolved overloading) without any type signatures or other intervention on our part.
{-# OPTIONS -fglasgow-exts #-} {-# OPTIONS -fallow-undecidable-instances #-} {-# OPTIONS -fallow-overlapping-instances #-}
module Foo where
{- class Baz a b | a -> b instance Baz (a -> b) (a -> [b]) instance Baz a a -}
-- No functional dependencies here! class Baz a b where baz :: a -> b
-- Rather, dependencies are here instance TypeCast a r => Baz a r where baz a = typeCast a
instance TypeCast (a -> [b]) r => Baz (a -> b) r where baz f = let r = \a -> [f a] in typeCast r
-- Chooses the instance Baz a a test1 = baz True -- True
-- Chooses the instance Baz (a -> b) (a -> [b]) test2 = (baz show) (1::Int) -- ["1"]
test3 x = (baz show) x test3' = test3 (Just True) -- ["Just True"]
-- copied verbatim 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
participants (3)
-
Daniel Brown -
Martin Sulzmann -
oleg＠pobox.com