| So, obviously, the next version of Haskell should have a type system
| with subtyping, don't you agree? :-)
It's always delightful to find that some awkward fumbling has
been Done Properly by someone else earlier. My claim was that
forall a. Show a => T
could be implemented by passing a bottom dictionary for Show. I didn't
say
this, but the obvious thing to do is to fix 'a' to be some vacuous type
Empty,
and arrange that Empty is an instance of every class, with a bottom
dictionary. And you're telling us that the subtyping folk worked this
out
yonks ago. Excellent! (Reference, for this particular point?)
In a system with subtyping this would work even if T contained a free,
as you say. But even in a system *without* subtyping, if 'a' is not
free in T,
we can safely remove the 'forall a' and fix a=Empty. (A calling context
can only "see" the types in T, so this places no constraints on the
calling context, which is why we don't need subtyping.) I think this is
what your PPS suggested, yes?
So in fact, all we need do is:
for each class, find the variance of each of its parameters
in an ambiguous type, zap any positive parameters to Empty
That sounds pretty easy. We don't need Haskell 2 for that. I feel
a little implementation coming on.
Hmm. One question. Suppose I have
forall a. C (a->Int) Int => T
and C is positive in its first parameter. Can I zap 'a' to Empty?
It looks as if it still occurs positively. What about data types?
| PS In some previous version of Haskell (1.3?), the Prelude defined an
| empty type called Void, but it has since been removed. Apparently,
| people didn't see the potential of Void...
Void was a type with one element. What we really want here is
a type with no elements. It's also useful to be able to introduce
such empty types for phantom-type purposes, so GHC now lets you say
data T
and get a type T with no values.
Simon
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