Iowa Type Theory Commute

A system of word equations is called quadratic if no variable occurs more than twice in it.  There is an interesting simple algorithm to solve quadratic systems of word equations, which I talk through in this episode.  My source is Chapter 12 of "Algebraic Combinatorics on Words" by Lothaire.

The problem of word equations is a rather storied one, including frustrated connections to Hilbert's Tenth problem.  Word equations relate expressions consisting of concatenations of variables and constant symbols.  An example is a X = X a, where X is a variable and a is a constant.  A solution maps variables to strings of constant symbols making the two sides identical.  In this episode, I discuss the problem a little, and what I learned so far about how it is solved.

In this episode, I give further arguments in favor of coercive subtyping from a software-engineering perspective.  I also explain the critical concept of coherence.

I explain the story from last episode.

The Curry-Howard isomorphism for the law of excluded middle, as a radio drama.  I first saw a version of this story performed by Phil Wadler and Frank Pfenning (wearing fake horns!) at RTA in Nara, Japan in 2005.  This is my take on it.  In a subsequent episode, I will explain how the story illustrates the computational interpretation of the law of excluded middle.