Graph algorithms with a functional flavour

Abstract

Graph algorithms have long been a challenge to program in a pure functional language. Previous attempts have either tended to be unreadable, or have failed to achieve standard asymptotic complexity measures. We explore a number of graph search algorithms in which we achieve standard complexities, while significantly improving upon traditional imperative presentations, In particular, we construct the algorithms from reusable components, so providing a greater level of modularity than is typical elsewhere. Furthermore, we provide examples of correctness proofs which are quite different from traditional proofs, largely because they are not based upon reasoning about the dynamic process of graph traversal, but rather reason about a static value.