type families not advertised for 6.8

[Wolfgang Jeltsch]

Am Freitag, 19. Oktober 2007 09:25 schrieb Simon Peyton-Jones:
> […]

> Our current plan is to regard FDs as syntactic sugar for indexed type
> families.  We think this can be done -- see our IFL workshop paper
> http://research.microsoft.com/%7Esimonpj/papers/assoc-types

I doubt this can be done in all cases.  Take the following code which is more 
or less from HList:

    {-# LANGUAGE
        MultiParamTypeClasses,
        FunctionalDependencies,
        FlexibleInstances,
        OverlappingInstances,
        UndecidableInstances,
        TypeFamilies,
        EmptyDataDecls
    #-}

    data False

    data True

    class TypeEq t1 t2 b | t1 t2 -> b where
        typeEq :: t1 -> t2 -> b

    instance TypeEq t t True where
        typeEq = undefined

    instance (b ~ False) => TypeEq t1 t2 b where
        typeEq = undefined

If you convert this code according to the above-cited paper to use type 
families instead of functional dependencies, you run into several problems.

First, type families don’t allow overlapping with conflicting results.  
Interestingly, the compiler doesn’t complain about the overlapping but about 
two other things.  In the first instance declaration you have something like

    type TypeEqTF t t = True

which results in the error “Conflicting definitions for `t'”.  In addition, 
the second instance declaration which includes something like

    type TypeEqTF t1 t2 = b

causes the error “Not in scope: type variable `b'”.  This latter problem can 
be circumvented by writing

    type TypeEqTF t1 t2 = False

but it shows that the automatic translation doesn’t work here.

In fact, after thinking and experimenting I came to the conclusion that it’s 
probably just not possible to define a type function TypeEqTF t1 t2 which for 
*all* types t1 and t2 yields True or False, depending on whether t1 and t2 
are equal or not.

> […]

> Simon

Best wishes,
Wolfgang