Hidden Congruent Deduction

Cleverly designed software often fails to satisfy its requirements strictly, but instead satisfies them behaviorally, in the sense that they appear to be satisfied under every experiment that can be performed on the system. A good example is the traditional implementation of sets by lists, where union as implemented by append fails to strictly satisfy basic laws like commutativity and idempotency, but does satisfy them behaviorally. It is becoming increasingly clear that behavioral specification is more appropriate to software engineering than traditional approaches that rely on strict satisfaction of axioms, and it is therefore becoming increasingly important to develop powerful techniques for behavioral verification. This paper presents some techniques of this kind in the area called hidden algebra, clustered around the central notion of coinduction. We believe hidden algebra is the natural next step in the evolution of algebraic semantics and its first order proof technology. Hidden algebra originated in [7], and was developed further in [8,10,3,12,5] among other places; the most comprehensive survey currently available is [12].