Proof Assistants and the Dynamic Nature of Formal Theories

Abstract

This article shows that theory exploration arises naturally from the need to progressively modify applied formal theories, especially those underpinning deployed systems that change over time or need to be attack-tolerant. Such formal theories require us to explore a problem space with a proof assistant and are naturally dynamic. The examples in this article are from our on-going decade-long eort to formally synthesize critical components of modern distributed systems. Using the Nuprl proof assistant we created event logic and its protocol theories. I also mention the impact over this period of extensions to the constructive type theory implemented by Nuprl. One of them led to our solution of a long standing open problem in constructive logic. Proof exchange among theorem provers is promising for improving the \super tactics" that provide domain specic reasoners our protocol theories. Both theory exploration and proof exchange illustrate the dynamic nature of applied formal theories built using modern proof assistants. These activities dispel the false impression that formal theories are rigid and brittle artifacts that become less relevant over time in a fast moving eld like computer science.