[Haskell-cafe] Restricted type classes
wren ng thornton
wren at freegeek.org
Mon Sep 6 22:18:45 EDT 2010
On 9/6/10 2:35 AM, Ivan Lazar Miljenovic wrote:
> Well, if we consider what this does, pure is equivalent to singleton
> for container types. The actual definition of pure (or any other
> aspect of Pointed) doesn't require Functor; however there are
> properties for types that are instances of Functor and Pointed.
Right, that's what I was meaning to highlight. If we were doing this in
Coq, for example, then not having Functor as a superclass of Pointed
would mean that we'd need a third class PointedFunctor which has both as
superclasses. In Haskell, since we don't have proofs, PointedFunctor
wouldn't have any methods and would therefore just be unnecessary
complication. Though this raises the question of which one makes more
sense to keep around: Pointed (with no superclass), or PointedFunctor.
> So, from a proof/testing POV having Functor as a superclass is nice;
> from an implementation POV it doesn't seem to be needed.
Though, again, I wonder what the use case would be. Your example of
singleton collections doesn't seem quite right. I'd expect the singleton
functions to obey various "spatial" laws (i.e., module-like or vector
space-like laws). For example,
union (singleton a) x = insert a x
This isn't exactly like Applicative because 'a' is an element instead of
a function. And it's not quite like Alternative either, since it only
requires union to be a semigroup instead of a monoid.
However, I can see some pointed functors that don't have this law,
either because insert or union don't make sense or because the obvious
implementations don't fit the pattern. Consider, for instance, the
ZipList applicative functor which has pure=repeat. It satisfies the
pointed law just fine, but it's not clear what insert or union should
mean (interleaving, perhaps? It still wouldn't be an Alternative though).
Perhaps this just means that union/insert should be part of some other
class. Of course, I'd expect singleton to obey the pointed law as well,
so that other class would (most likely) be a subclass of pointed
functors. In any case, it does mean there's something of a mismatch
between singleton vs return/pure/point/unit.
--
Live well,
~wren
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