Monday, July 14, 2014

The algebra of processes XI

We have been thinking about categorical algebra for computer science now for 25 years. I want to discuss the problems of thinking seriously about two distinct disciplines, and how one might avoid the danger of falling between two stools.
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Sunday, July 13, 2014

The seeds of homotopy type theory

I was recently very surprised to find a lecture (http://www.math.ias.edu/~vladimir/Site3/Univalent_Foundations_files/2014_IAS.pdf) of Vladimir Voevodsky explaining his motivation for working on homotopy type theory and the mechanization of mathematics.

In brief the reason was that a group of well-known mathematicians working on "higher dimensional mathematics" since the 1980's were making errors which were not discovered for years, in one case not till more than 20 years after publication. Voevodsky refers to this situation as "outrageous".

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Friday, June 27, 2014

Shag on a rock

Well, it turns out that I cannot go to the Cambridge meeting, Category Theory 2014, after all. I will be having some treatment next week. I will try to put up on arXiv an account of the lecture I intended to give.

In an earlier post I said that my talk seemed to have no connection with any other that I could see from the titles. However looking a bit more closely perhaps there are one or two related.
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Friday, June 06, 2014

The algebra of processes X

Wednesday, June 04, 2014

Our house on the lake




Steve Bloom's tree

When Steve died in 2010 we said we would plant a tree in his memory at our mountain house. Here it is:

Saturday, May 31, 2014

The algebra of processes IX

I have had some problems so there has been a break in this series of posts. But also I was not quite sure how to explain what I called the distributive laws with the rather primitive mathematical resources of my blogspot. I should really find out how to incorporate TeX.
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Thursday, May 15, 2014

The algebra of processes VIII - the distributive laws

I want to first say something about the abstract setting. In the arXiv paper (arXiv:0909.4136 ) we considered a more complicated notion of process (mentioned in the second post of this series) with nine graphs, and we described many operations. We now believe that this definition was too general, and instead a process should consist of five graphs A,B,X,Y, G and four morphisms δ0: G → A,  δ1: G → B, γ0: X → G, γ1: Y → G  as we have been discussing in these posts.

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The algebra of processes VII

PARALLEL PROGRAMMING in Span(Graph)

Last post I promised to give an example of a parallel program. Here is a very simple one which is the parallel composite of two components both having state space N+N+N (N= natural numbers).
I have distinguished the different summands by subscripts to make the description of the composite clearer:

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