Much of the research reported in the article “On graphic lambda calculus and the dual of the graphic beta move” arXiv:1303.0778 appeared first time in posts from this blog, in places indicated by links given in the article (here is the link to the preview, before the appearance in the arxiv).
The abstract is:
This is a short description of graphic lambda calculus, with special emphasis on a duality suggested by the two different appearances of knot diagrams, in lambda calculus and emergent algebra sectors of the graphic lambda calculus respectively. This duality leads to the introduction of the dual of the graphic beta move. While the graphic beta move corresponds to beta reduction in untyped lambda calculus, the dual graphic beta move appears in relation to emergent algebras.
See the page Graphic lambda calculus for details.
I played also with the bibliography, in two ways: I tried to cite only articles from arxiv and I give each time in the text the link to the respective article, also I preferred to indicate web pages as sources of bibliographic information whenever possible. This way, the bibliography is reduced to the bare minimum, it is there mostly by convention. Finally, there are no theorems or definitions in the text (I mean, there are, as well as proofs, only that they are not “encrypted” into the respective formats), I preferred instead to use a more relaxed writing, more alike wiki pages, according to views expressed in “Comments in epijournals: we may learn from Wikipedia” and “Wiki journals over arxiv“.
I first wanted to make a tutorial article on graphic lambda calculus, but for the moment I don’t see the point, there already is such a tutorial here; much of it is in several arxiv articles. But probably this article will have updates, if it will be submitted to a “regular” publisher. For the moment it is a bit of an experiment (but mind you, it is a rigorous mathematical article).