Martin, If you are thinking about category theory and graphical calculus you might be interesting in
http://sites.google.com/site/quantomatic/ http://dream.inf.ed.ac.uk/projects/quantomatic/ https://groups.google.com/forum/#!forum/quantomatic http://sites.google.com/site/quantomatic/publications A lot of this work is being done in the context of quantum computation but the tools are much more general. The system uses the theorem proving package Isabelle http://www.cl.cam.ac.uk/research/hvg/Isabelle/ to reason about graphs and Poly/ML (a variant of standard ML that is even more like SPAD) and Java for data structures and GUI. This video http://www.cs.ox.ac.uk/quantum/content/1005019/ is a pretty good introduction. I became especially interested in this while implementing linear operators as an extension of the Axiom CartesianTensor domain. See: http://axiom-wiki.newsynthesis.org/LinearOperator I think it would be great if there was a group of people who were motivated to add something like this to Axiom. Regards, Bill Page. On Wed, Aug 17, 2011 at 12:52 PM, Martin Baker <ax87...@martinb.com> wrote: > On Wednesday 17 Aug 2011 05:24:41 d...@axiom-developer.org wrote: >> It seems that the Category Theory discussion has come around again on the >> great wheel of life. These talks might be helpful for those who are lost. >> >> part 1: http://vimeo.com/17207564 >> part 2: http://www.youtube.com/watch?v=yilkBvVDB_w > > Tim, > > These are very good, I haven't come across them before. > > I especially like part 2 and the link between category theory string diagrams > and combinators. Its interesting about adding iterators to combinators, it > would be good to implement that. > > Also there was a throwaway line, something about removing the crossover > cancellation rule from combinators gives braids. I thought before that it > would be interesting to implement braid groups and I wonder if it could be > done using combinators? > > Also string diagrams/combinators being so graphical reminds me once again how > much I would like a 2-way graphical interface to Axiom. > > Martin > > _______________________________________________ > Axiom-developer mailing list > Axiom-developer@nongnu.org > https://lists.nongnu.org/mailman/listinfo/axiom-developer > _______________________________________________ Axiom-developer mailing list Axiom-developer@nongnu.org https://lists.nongnu.org/mailman/listinfo/axiom-developer