Galois Connections and Fixed Point Calculus

Abstract

Fixed point calculus is about the solution of recursive equations defined by a monotonic endofunction on a partially ordered set. This tutorial presents the basic theory of fixed point calculus together with a number of applications of direct relevance to the construction of computer programs. The tutorial also summarises the theory and application of Galois connections between partially ordered sets. In particular, the intimate relation between Galois connections and fixed point equations is amply demonstrated.