Here is an even better and earlier reference to category theory and Axiom:
http://dl.acm.org/citation.cfm?id=988127
A language for computational algebra
Authors:
Richard D. Jenks IBM Research Center, Yorktown Heights, New York
Barry M. Trager IBM Research Center, Yorktown Heights, New York
Volume 16 Issue 11, November 1981
ACM New York, NY, USA
I've also put a copy here in case you don't have access to acm publications:
http://axiom-portal.newsynthesis.org/refs/articles/p22-jenks.pdf
Regards,
Bill Page.
On Tue, Nov 8, 2011 at 7:23 PM, Bill Page <bill.p...@newsynthesis.org> wrote:
> Martin,
>
> Why do you say:
>
>> It may well be that I'm just approaching what you
>> call 'domain constructors' from a different direction, I don't know,
>> but there is obviously no consensus about that terminology either.
>
> The term 'domain constructor' is used throughout the Axiom Book:
>
> http://axiom-wiki.newsynthesis.org/Mirrors?go=/public/book2.pdf&it=Axiom+Book
>
> For example, section 2.1.1, page 131
>
> If you given the command in Axiom
>
> )show X
>
> and X is a domain, then it says:
>
> X is a domain constructor
> ...
>
> As far as I know I am not using this term in any other way then it is
> used in the Axiom Book. I have not heard anyone dispute the use of
> this term.
>
> The issue that I was discussing with Gaby earlier today involved
> contrasting domain constructors with other types of functions in
> Axiom. Again as far as I know there is no dispute about this
> difference although it might be sufficiently subtle that not everyone
> is aware of it. This is made a bit more complicated because to some
> extent the Aldor language tries to minimize this difference.
>
> Actual the word 'functor' as a synonym of domain constructor in the
> context of category theory was used very early on in the design of
> Axiom. See for example: Davenport, 1991:
>
> http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.7694
>
> (bottom page 11).
>
> Regards,
> Bill Page.
>
>
>
> On Tue, Nov 8, 2011 at 6:02 PM, Martin Baker <ax87...@martinb.com> wrote:
>>> I don't really want to talk about what a 'List' is in general. I want
>>> to do what you said at first:
>>>
>>> "trying to understand how to implement these category theory concepts in
>>> various computer languages".
>>
>> So I was suggesting that, for a language like SPAD, which does not
>> appear to have the concept of 'functor' built into the core of the
>> language then perhaps this might be modelled in the type system in the
>> way I described. It may well be that I'm just approaching what you
>> call 'domain constructors' from a different direction, I don't know,
>> but there is obviously no consensus about that terminology either.
>>
>> Martin
>
--
You received this message because you are subscribed to the Google Groups
"FriCAS - computer algebra system" group.
To post to this group, send email to fricas-devel@googlegroups.com.
To unsubscribe from this group, send email to
fricas-devel+unsubscr...@googlegroups.com.
For more options, visit this group at
http://groups.google.com/group/fricas-devel?hl=en.
