you're right about interactions in general. but do you think constructor classes specifically would pose any interaction problems with FDs? You have to be more careful with unification in a higher-kinded setting. I am not sure how to do that with CHRs.
to quote from the ATS paper: "just like Jones, we only need first-order unification despite the presence of higher-kinded variables, as we require all applications of associated type synonyms to be saturated".
variant A: I never understood why parameters of a class declaration are limited to variables. the instance parameters just have to match the class parameters, so let's assume we didn't have that variables-only restriction.
class Graph (g e v) where src :: e -> g e v -> v tgt :: e -> g e v -> v
we associate edge and node types with a graph type by making them parameters, and extract them by matching.
The dependency seems to be lost here.
what dependency? the associated types have become parameters to the graph type, so the dependency of association is represented by structural inclusion (type constructors are really constructors, so even phantom types would still be visible in the type construct). any instances of this class would have to be for types matching the form (g e v), fixing the type parameters.
variant B: I've often wanted type destructors as well as constructors. would there be any problem with that?
type Edge (g e v) = e type Vertex (g e v) = v
class Graph g where src :: Edge g -> g -> Vertex g tgt :: Edge g -> g -> Vertex g
Also no dependency and you need higher-order matching, which in general is undecidable.
the dependency is still represented by the type parameters, as in the previous case. and is this any more higher-order than what we have with constructor classes anyway? here's an example implementation of the two destructors, using type classes with constructor instances: {-# OPTIONS_GHC -fglasgow-exts #-} import Data.Typeable data Graph e v = Graph e v class Edge g e | g -> e where edge :: g -> String instance Typeable e => Edge (g e v) e where edge g = show (typeOf (undefined::e)) class Vertex g v | g -> v where vertex :: g -> String instance Typeable v => Vertex (g e v) v where vertex g = show (typeOf (undefined::v)) [the Typeable is only there so that we can see at the value level that the type-level selection works] *Main> edge (Graph (1,1) 1) "(Integer,Integer)" *Main> vertex (Graph (1,1) 1) "Integer"
variant C: the point the paper makes is not so much about the number of class parameters, but that the associations for concepts should not need to be repeated for every combined concept. and, indeed, they need not be
class Edge g e | g -> e instance Edge (g e v) e class Vertex g v | g -> v instance Vertex (g e v) v
class (Edge g e,Vertex g v) => Graph g where src :: e -> g -> v tgt :: e -> g -> v
(this assumes scoped type variables; also, current GHC, contrary to its documentation, does not permit entirely FD-determined variables in superclass contexts)
You still need to get at the parameter somehow from a graph (for which you need an associated type).
oh, please! are you even reading what I write? as should be clear from running the parts of the code that GHC does accept (see above), FDs are quite capable of associating an edge type parameter with its graph.
all three seem to offer possible solutions to the problem posed in that paper, don't they?
Not really.
...
II. The other one is that if you use FDs to define type-indexed types, you cannot make these abstract (ie, the representations leak into user code). For details, please see the "Lack of abstraction." subsubsection in Section 5 of http://www.cse.unsw.edu.au/~chak/papers/#assoc
do they have to? if variant C above would not run into limitations of current implementations, it would seem to extend to cover ATS:
class C a where type CT a
instance C t0 where type CT t0 = t1
would translate to something like:
class CT a t | a -> t instance CT t0 t1
class CT a t => CT a instance CT t0 t1 => C t0
as Martin pointed out when I first suggested this on haskell-cafe, this might lead to parallel recursions for classes C and their type associations CT, so perhaps one might only want to use this to hide the extra parameter from user code (similar to calling auxiliary functions with an initial value for an accumulator).
That doesn't address that problem at all.
come again? CT expresses the type association for C. all of CT can remain on the library side, so the user only needs to see C, without the representation parameter. unless you do want to expose the representation, in which case you can export CT, too. the only remaining problem would be that the main implementations of FDs still seem to have problems with FD type signatures, so they permit keeping both type and associated type abstract f :: CT t at => at -> t but they don't allow you to pretend that you don't know the associated type when you know the type f :: CT Int at => at -> Int but as you point out yourself, that isn't inherent to FDs, and there are FD versions that permit both, so I see that as a bug/oversight in current implementations. without FDs, all type class inference assumed that types are input only. with FDs, some types (those in range of an FD) have become output of the inference process. the second f-signature above does not claim that f is polymorphic in at, it claims that at is determined by CT's FD. so representing at by a rigid, unconstrained, type variable, and then to complain that at is determined by the FD, is not helpful. it should be quite permissible to use a variable in a functional language, even if we already know its value! the question is how useful that would be to the purpose you state in your papers, as you'd really want the code of f to be independent of the representation type (abstract representation), only using methods of CT. but if the representation type is known via the type association/FD, the type checker will happily accept uses of the concrete type where the type variable at is mentioned.
for instance, what would keep us from reserving the last class parameter as the range, and the rest as the domain of a single FD per class? then we could play the old Prolog game of translating expressions involving predicates of n-1 parameters into flat Prolog code involving predicates with n parameters.
That would be a great thing to try if there was a simple formalisation of functional dependencies.
I thought the modified CHR translation we arrived at was rather simple (see thread "alternative translation of type classes to CHR"). any particular problems with that?
Who wants to throw out type classes?
anyone who argues against relational programming via characteristic predicates - type classes are all about predicate entailment, and we don't want that in a functional language. or don't you listen to your own propaganda?-) you have since relented a bit, and functional logic programming at the type level may now be acceptable to you. but you started out with rather extreme views;-) cheers, claus