[Haskell-cafe] Are associated types synonyms like type classes?

[Manuel M T Chakravarty]

Brian Smith:
> When using AT then we have to decide what part of the abstraction is
> the class and what part is the associated type. Sometimes this seams
> arbitrary. If we have: 
> 
>     class A a where
>         type B b
>         f :: a -> B b
>     instance A Int where
>         type B = Bool
>         f  = (==0)
> 
> Can't we also rewrite it as:
>     
>     class B b where
>         type A a
>         f :: A a -> b
>     instance B Bool where
>         type A = Int
>         f = (==0)

If it is arbitrary, you should use a two parameter class.  The bias in
an associated type is on purpose; ie, an associated type should be used
if one type depends on the other.

Bulat wrote:
> > Also, has anybody written a paper on the differences between
> > typeclasses + associated types and ML's module system +
> overloading? 
> 
> "ML Modules and Haskell Type Classes: A Constructive Comparison"
> http://www.informatik.uni-freiburg.de/~wehr/diplom/Wehr_ML_modules_and_Haskell_type_classes.pdf

In addition to this comparison, there is now also a proposal for type
classes with associated types as a mode of use of ML modules.  See our
forthcoming POPL paper:

  http://www.cse.unsw.edu.au/~chak/papers/DHC07.html

Ie, this gives you ML modules + overloading.

Manuel