### The Lax Braided Structure of Streaming I/O

Alan Jeffrey & Julian Rathke
We investigate and implement a model of typed streaming I/O. Each type determines a language of traces analogous to regular expressions on strings, and programs are modelled by certain monotone functions on these traces. We show that sequential composition forms a lax braided monoid in the category of types and programs. This lax braided structure allows programs to be represented diagrammatically using Joyal and Street's string diagrams in 3D space. Monotone functions over traces cannot...