FUNCTIONAL PEARLS Proof-Directed Debugging

The close relationship between writing programs and proving theorems has frequently been cited as an advantage of functional programming languages. We illustrate the interplay between programming and proving in the development of a program for regular expression matching. The presentation is inspired by Lakatos's method of proofs and refutations in which the attempt to prove a plausible conjecture leads to a revision not only of the proof, but of the theorem itself. We give a plausible implementation of a regular expression matcher that contains a aw that is uncovered in an attempt to prove its correctness. The failure of the proof suggests a revision of the speci cation, rather than a change to the code. We then show that a program meeting the revised speci cation is nevertheless su cient to solve the original problem.