[Haskell-cafe] Re: ANN: data-category, restricted categories

[Ashley Yakeley]

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) 
are not.

That's a fuzzy lens...

-- 
Ashley Yakeley