Constructive Automata Theory Implemented with the Nuprl Proof Development System

Abstract

The Nuprl proof development system was designed for the computer-assisted problem solving in mathematics and programming. In particular it can be used for the development of mathematical proofs and of programs which are guaranteed to meet their specifications. The implementation of the theory of finite automata gave lots of insights into its strengths and weaknesses and shows that Nuprl is indeed powerful enough now to obtain nontrivial results within reasonable amounts of time. Its success shall encourage people to actually use the system and build theories within it. This report describes the techniques and the user-defined extensions to the Nuprl object language which were necessary to formulate and prove theorems from the theory of finite automata. It also describes the experiences which came from actually working with the current Nuprl system and gave some useful insights into its strenghts and weaknesses. A complete Nuprl-proof of the pumping lemma and its computational evaluation are presented and an outline for future development is given.