Claus Reinke:
For example, AFAIK the CHR formalisation doesn't consider higher kinds (ie, no constructor classes).
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.
Two serious problems have little to do with type theory. They are more like software engineering problems:
I. One is nicely documented in http://www.osl.iu.edu/publications/prints/2003/comparing_generic_programming...
that paper isn't bad as far as language comparisons go, but it focusses on a rather restricted problem, so I'm surprised that this was part of the motivation to launch ATS: to reduce the number of parameters in combined "concepts", we might as well associate types with each other, instead of types with instances.
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.
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.
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).
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.
you reply to a message that is about a month old.
That's what re-locating around half of the planet does to your email responsiveness...but the topic is still of interest and I got the impression that your position is still the same.
definitely. I was just unsure how to react - if you really hadn't seen the messages of the last month, it would be better to let you catch up (perhaps via the mailing list archive). if you just took that message as the natural place to attach your contribution to, there's no need to wait.
The latter.
ATs are not about special syntax. Type checking with ATs doesn't not use "improvement", but rather a rewrite system on type terms interleaved with unification. This leads to similar effects, but seems to have slightly different properties.
that's what I'm complaining about. if ATs were identified as a subset of FDs with better properties and nicer syntax, it would be easy to compare. unless you claim that the different formalization is essential to achieving the properties of ATs, it is just an unfortunate incidental difference.
Our formalisation of ATs stays very close to the formalisation of qualified types, which to me is the state of the art of formalising type classes.
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.
Actually, I think, much of our disagreement is due to a different idea of the purpose of a language standard. You appear to be happy to standardise a feature that may be replaced in the next standard.
I'm pragmatic. Most of us thought the features in questions were well defined, and just needed to be written up. I still don't see why MPTCs or some form of FDs would necessarily be replaced, unless someone did the major overhaul of throwing out type classes and defining a functional replacement.
Who wants to throw out type classes? Manuel