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

3 Sep 2006

      Bulat, Stefan,

My question wasn't clear. I understand already that classes with associated
types are are alternative to MPTC with fundeps.

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)

What is the practical difference between class A and class B? With class A
we can define instances so that f is overloaded (Int -> Bool), (String ->
Bool), (Bool -> Bool) by defining instances of A for Int, String, and Bool,
but we cannot overload it more (Int -> String), (Int -> Int) because we can
only have on "instance A Int". The converse is true for class B. Is that the
only difference?

If so, then why do we have "associated types" instance of "associated
classes" like this?:

    class A a where
       class B b where
           f :: a -> b

    instance A Int where
        instance B Bool where
            f = (==0)

The made-up syntax I presented in my previous message was just a different
way of writing the above (which is also made-up syntax):

    class A a, B b where f :: a -> b
    instance A Int, B Bool where f = (==0)

    class Elem elem, Collect collect where
        empty :: collect
        insert :: elem -> collect -> collect
        toList :: collect -> [elem]

Thanks for your help,
Brian

On 9/1/06, Bulat Ziganshin <bulat.ziganshin@gmail.com> wrote:
...
Hello Brian,
Friday, September 1, 2006, 8:32:55 PM, you wrote:
...
I read the easy parts of the "Associated Types with Class" and
"Associated Type Synonyms" papers. An associated type synonym seems
to kind of work similarly to a restricted form of class. In what way
are the two following examples different?
...
-- define a class with a type synonym, and a set of operations
class A a where
type B b
foo :: a -> B b
...
instance A Int where
type B = Bool
foo = (==0)
...
-- define two classes, and an function that .
class A a, B b where
foo :: a -> b
...
instance A Int, B Bool where
foo = (==0)
where you've find such unusual syntax? :)  GHC/Hugs supports
multi-parameter type classes (MPTC):
class AB a b where
    foo :: a -> b
instance AB Int Bool where
foo = (==0)
AT replaces MPTC with FD (functional dependency), which allows to
specify which type parameter of MPTC is detremined by another one, i.e.:
class AB a b | a->b where ....
for further details about MPTC+FD see chapter 7.1.1 in the
http://cvs.haskell.org/Hugs/pages/hugsman/exts.html
...
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_Haske...
--
Best regards,
Bulat                            mailto:Bulat.Ziganshin@gmail.com

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

Brian Smith