Program Composition via Unification

Program composition and compositional proof systems have proven them­ selves important for simplifying the design and the verification of programs. The paper presents a version of the jigsaw program composition operator pre­ viously defined in [FFG90, FFG91]. Here, the jigsaw operator is defined as the unification of its components by their most general unifier. The jigsaw operator generalizes and unifies the traditional sequential and parallel program composi­ tion operators and the newly proposed union and superposition operators. We consider a family of frameworks each consisting of a programming language, a specification language and a compositional syntax-directed proof system. We present syntactic rules to augment any given framework in the family with the Jigsaw operator. The augmented framework is syntax-directed and composi­ tional. Moreover, it is sound and complete with respect to the given framework. Program composition and compositional proof systems have proven themselves impor­ tant fpr simplifying the design and verification of programs. In this approach, small parts of a software system are programmed and verified separately and then composed into a larger system. To develop a system such that its syntactic structure reflects the intuitive structure of the algorithm it implements, program composition operators able to reflect common relations among components of algorithms are required. Tradi­ tional program composition operators are the sequential and the parallel composition operators. Recently, other program composition operators have been suggested [BF88, CM88, FF90, KFE90]. In this paper a composition operator, called jigsaw, is considered. The jigsaw composition operator generalizes and unifies the sequential and the parallel operators together with the newly proposed union and superposition operators [BF88,CM88]. • A preliminary version of this paper appears in [FFG92]. Abstract Program composition and compositional proof systems have proven themselves important for simplifying the design and the verification of programs. The paper presents a version of the jigsaw program composition operator previously defined in [FFG90, FFG91]. Here, the jigsaw operator is defined as the unification of its components by their most general unifier. The jigsaw operator generalizes and unifies the traditional sequential and parallel program composition operators and the newly proposed union and superposition operators. We consider a family of frameworks each consisting of a programming language, a specification language and a compositional syntax-directed proof system. We present syntactic rules to augment any given framework in the family with the Jigsaw operator. The augmented framework is syntax-directed and composi-tional. Moreover, it is sound and complete with …