> It seems to me that the name 'Functor' is fine from the point of view
> of established usage in Haskell and other similar programming
> languages.
>
> Also the name 'Functorial' is good from the point of view of
> mathematical category theory.
>
> The use of 'Functor' to refer to type constructors should be deprecated.
Your argument is good! If we use the name "Functor" for this
category because of the Haskell context, and don't refer type
constructors to 'Functor', and use non-capitalized 'functor' for
the category theory functor, then there's not much confusion
about "Functor".
>> the actually meaning of "map" can be very
>> different. (This is more obvious for Monad.)
>>
>
> I do not think that this is the case. If it were, then there would be
> some doubt that it was the appropriate abstraction of the underlying
> concept. At most the "actual meaning" should be a special and specific
> case of the more general notion.
Take AbelianMonoidRing for example:
map : (R -> R, %) -> %
++ map(fn, u) maps function fn onto the coefficients
++ of the non-zero monomials of u.
A 'map' function can also operate on its degree, but this documentation
says it operates on the coefficients. This information should be preserved
when showing documentation of map from AbelianMonoidRing.
Maybe we can change how compiler work:
For
Functor(R) with
map : (R -> R, %) -> %
++ new doc
We don't show this map signature again in ')display operation map',
just update the documentation with "new doc".
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