Unversity of Glasgow Talk: A graphical language for closed monoidal categories

A graphical language for closed monoidal categories, by Dan Ghica.

Diagrams, schematics, blueprints and so on play an important role in engineering, architecture, construction, and other activities where projects need to be formally specified. In mathematics the role of diagrams has been, at least until recently, mostly that of illustrating concepts, rather than specifying formally mathematical objects, including proofs. This has started to change with the increasing popularity of string diagrams, a formal graphical representation based on monoidal categories. String diagrams have been used successfully in quantum communication and computation, computational linguistics, electronic circuits and more. In this talk I will present some recent work in progress on using hierarchical graphs to give a string-diagram representation to closed monoidal categories, and using it as an alternative (improved) syntax for the lambda calculus of explicit substitution. Further applications to abstract machines and equational reasoning in programming languages will be briefly sketched out.

Seminar information: https://samoa.dcs.gla.ac.uk/events/viewtalk.jsp?id=17215

Slides: https://www.dropbox.com/s/wuuxy5q921hdk5s/plug%20seminar%20hierarchical%20graphs.pdf?dl=0