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
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