Programs as Partial Graphs II: Recursion

Abstract In Part I of the paper, we have proposed a unified relational algebra approach using partial graphs for theoretical investigations on semantics, correctness and termination. This approach is extended here to systems of recursive programs, allowing not only sequencing and conditional branching as a control structure but also flow diagrams. An equivalence proof of operational and denotational semantics is obtained which is strictly based on axioms of relational algebra. A short new proof of an important completeness result is given in the generalized setting of systems of recursive flow diagram programs. Finally, Hitchcock-Park's theorem on derivatives is formulated in the general case of nondeterministic recursive flow diagram programs.