Re: [sage-devel] Re: [fricas-devel] Re: categories

2015-10-02 Thread Bill Hart
Bill, you may also like to see the HomAlg project: http://homalg.math.rwth-aachen.de/ I know of this through some of its authors, Mohamed Barakat and Sebastian Gutsche, who both still list their affiliation on that website as Kaiserslautern. That project is homological algebra. It is an innova

Re: [sage-devel] Re: [fricas-devel] Re: categories

2015-10-01 Thread Bill Page
Thanks. https://github.com/homalg-project/CAP_project https://github.com/homalg-project/CAP_project/blob/master/CAPManual.pdf On 1 October 2015 at 18:43, Simon King wrote: > PS: > > On 2015-10-01, Bill Page wrote: >> I am very interested in the use of adjunction in programming languages >> and

[sage-devel] Re: [fricas-devel] Re: categories

2015-10-01 Thread Simon King
PS: On 2015-10-01, Bill Page wrote: > I am very interested in the use of adjunction in programming languages > and the definition of types by construction of universals. Perhaps CAP > is relevant? Can you provide a reference to a relevant paper? The talk on CAP here was presented by Sebastian Gu

[sage-devel] Re: [fricas-devel] Re: categories

2015-10-01 Thread Simon King
Hi Bill, On 2015-10-01, Bill Page wrote: > On 1 October 2015 at 17:38, Simon King wrote: >> ... >> When I first encountered Sage's category framework, I expected to see >> something similar to what we now have in CAP, but it has in fact a rather >> different flavour and purpose. > > I am very in

Re: [sage-devel] Re: [fricas-devel] Re: categories

2015-10-01 Thread Bill Page
On 1 October 2015 at 17:38, Simon King wrote: > ... > When I first encountered Sage's category framework, I expected to see > something similar to what we now have in CAP, but it has in fact a rather > different flavour and purpose. > Understood. I am not arguing against the way this was done in

[sage-devel] Re: [fricas-devel] Re: categories

2015-10-01 Thread Simon King
Hi Bill, On 2015-10-01, 'Bill Hart' via sage-devel wrote: > One reason is that it easily leads to functions that are not > type-consistent. You can quite easily write functions whose output type > depends on the values, rather than the types of the inputs. This completely > screws with type infer

[sage-devel] Re: [fricas-devel] Re: categories

2015-10-01 Thread Simon King
Hi William and Bill! On 2015-10-01, William Stein wrote: >> Is there a reasonably short description of categories in Sage "for >> category theorists"? There is something about both parent-element scheme and category framework in the thematic tutorial http://doc.sagemath.org/html/en/thematic_tuto

[sage-devel] Re: [fricas-devel] Re: categories

2015-10-01 Thread Simon King
Hi Bill, On 2015-10-01, Bill Page wrote: >> I would expect that somebody who doesn't know category theory (the >> mathematical area) would find the category framework in Sage very >> confusing, just like somebody who doesn't know calculus might find the >> symbolic functionality confusing. > > No