Reasoning algebraically about recursion

Abstract

An algebraic technique for reasoning about recursive programs is proposed. The technique is based on Tarski's axioms of least fixed points of monotonic functions and the existence of weak-op-inverses. The algebraic style gives rise to elegant proofs, although the requirement of existence of weak-op-inverse may limit applicability. When such inverses do exist, the method can be used in presence of noncontinuous but monotonic operators occuring in languages containing unbounded nondeterminism, fairness constraints and specification statements.