On 20 October 2016 at 06:16, oldk1331 <oldk1...@gmail.com> wrote: > About abstracting the signature 'map : (S->S,%)->%' > into a category, there are 2 problems so far: > >> - Functor is quite loaded name and may lead to confusion. >> Something like 'MapCategory2' seem to fit better existing >> naming scheme. >> - What documentatin do you propose for the 'map' function? >> Current scheme with several signatures has a separate >> documentation slot per signature. Common signature would >> be quite abstract, so hard to specify. > > First, the name. Yes, the name "Functor" may lead to > confusion, for example, to be mixed with the category > theory "Functor". (Well, "Category" has similar problem.) > OpenAxiom uses "Functorial", which is similar to "Functor"? > I think we can also consider the name "MapCategory".
I am against category names that include the word Category in the name. 'SetCategory' is already annoying enough. I think the name should reflect the terminology used in the (preferably widely accepted) mathematical literature for the relevant concept. 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. I do not see any problem with the use of the name Category by Axiom and derivatives. Although there are significant formal differences between Axiom categories and mathematical categories, it is clear that the intended use and probably even the origin of the term is very similar. > > Second, the documentation. Yes, it's impossible to give a > precise documentation for "map", the doc will depend on the > domain that implements "map". Because this category just > specifies the signature and a few axioms that "map" > should obey, I think this is exactly the documentation that one needs for a category. > 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. > So I suggest the following change: > map:(S->S,%)->% > ++ map docstring > to > MapCategory(S) > ++ map docstring > > However such changes will not update the docstring > showed in HyperDoc. > > OpenAxiom just removes those documentation, which is > a loss of information. (See the OpenAxiom changes on > 2013-05-20, or commit 1316b335). > Why not include this information in the general information provided for the specific domain? I.e. say in this documentation why the domain satisfies 'Functor' in other words: why it is functorial. Bill Page. -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
