Seminars & Colloquia Calendar

Abstract: Lambda calculus has its origins almost a century ago, in Alonzo Church's ambitious project to build a foundation for mathematics based on the concept of function. Although that project ultimately failed due to logical inconsistency, lambda calculus continues to serve as an important everyday tool for functional programmers, not to mention researchers in programming languages, type systems, and proof assistants.

In the talk, I will survey some surprising connections found over recent years between certain natural subsystems of lambda calculus and the study of graphs on surfaces, or "maps", and in particular the enumerative theory of maps initiated by Tutte in the 1960s. As with so many other such connections, this one owes its existence to the OEIS, and so I will present some practical background on how lambda terms may be efficiently enumerated, generated, and manipulated. Finally, as an illustration of one of the more amusing mashups of these explorations, I will explain how to give a reformulation of the Four Color Theorem as a simple statement about typing of lambda terms.