The basic idea of an information flow was introduced by Hartmanis and Stearns in the algebraic structure theory of sequential machines. This is a beautiful and elegant formalism for describing how information flows in sequential machines. Now using new mathematics I have put this theory on its highest level of generality. But its not enough that this should be a mathematical theory, so I also discuss its implementation.

At the center of an implementation of information flows is the idea of a partition image. This codifies how a particular function maps a piece of information into some other piece of information. To implement this intuitive idea, I define a type hierarchy of different partition and function classes and use multiple dispatch on them to determine the right algorithm to use on a case-by-case basis.