Proof Systems for Struvtured Algebraic Specifications: An Overview

In this paper an overview on proof systems for structured algebraic specifications is presented. As underlying language we choose an ASL-like kernel language which includes reachability and observability operators. Three different kinds of proof systems are studied. The first two approaches are non-compositional systems where the basic idea is to compute for any structured specification a flat unstructured set of axioms and rules which, combined with some standard proof systems for the underlying logic, may be used for deriving theorems of the specification. In the normal form approach of Bergstra, Hering and Klint, a flat set of axioms is constructed for each structured specification, whereas in the second approach not only individual axioms but also individual proof rules are taken into account. The drawback of the non-compositional proof systems is that they do not reflect the modular structure of specifications. Therefore we present also a structured proof system the derivations of which are performed in accordance with the modular structure of a specification.