[Haskell-cafe] Re: ANN: data-category, restricted categories
ashley at semantic.org
Tue Mar 30 16:34:10 EDT 2010
Ashley Yakeley wrote:
> Edward Kmett wrote:
>> Of course, you can argue that we already look at products and
>> coproducts through fuzzy lenses that don't see the extra bottom, and
>> that it is close enough to view () as Unit and Unit as Void, or go so
>> far as to unify Unit and Void, even though one is always inhabited and
>> the other should never be.
> The alternative is to use _consistently_ "fuzzy lenses" and not consider
> bottom to be a value. I call this the "bottomless" interpretation. I
> prefer it, because it's easier to reason about.
> In the bottomless interpretation, laws for Functor, Monad etc. work.
> Many widely-accepted instances of these classes fail these laws when
> bottom is considered a value. Even reflexivity of Eq fails.
Worse than that, if bottom is a value, then Hask is not a category! Note
that while undefined is bottom, (id . undefined) and (undefined . id)
That's a fuzzy lens...
More information about the Haskell-Cafe