Up to date, this is the most comprehensive introduction to graphic lambda calculus. Is available as arxiv:1305.5786. It does not contain all the material on the subject, but it is, I hope, a fair exposition of what you can do with it. See also the tutorial page on graphic lambda calculus on this blog.
- it shows that it can be used for much more than just visually representing lambda calculus for pedagogical reasons, you can turn it into a programming language which mixes differential calculus, manipulation of spatial quantities, with lambda calculus,
- it is the visual language appropriated for giving a rigorous formulation of the constructions done in Computing with space.
If you have comments or corrections to make, or peer-reviews, let me know! For the moment I can’t stand to look at it, I have to detach a bit, but it would surely benefit from a fresh eye.
UPDATE: The article has been accepted for publication in Wolfram’s Complex Systems. This is good news for the emergent algebras – computing with space subject. (Btw, thumbs up for the reviewing process, which made me update the previous version arXiv:1207.0332 to a much more comprehensive presentation, which also benefited from several postings on this blog and from one question on mathoverflow.)