Heterogeneous Specification and the Heterogeneous Tool Set Habilitation thesis

Formal specification of software systems has become more and more important, especially in safetycritical areas where one cannot take the risk of malfunction. Casl, the Common Algebraic Specification Language, is a standard for axiomatic specification of conventional software; and several extensions of Casl deal with temporal, reactive, higher-order etc. aspects. That is, we are faced with a multitude of specification languages and underlying logics. In this work, we argue that for the specification of large software systems, heterogeneous multilogic specifications are needed, since complex problems have different aspects that are best specified in different logics. A combination of all the used logics would become too complex in many cases. Moreover, using heterogeneous specifications, different approaches being developed at different sites can be related, i.e. there is a formal interoperability among languages and tools. In many cases, specialized languages and tools often have their strengths in particular aspects. Using heterogeneous specification, these strengths can be combined with comparably small effort. The specification language Casl is an expressive specification language. At the level of basic specifications, it provides first-order logic with induction, powerful datatype constructs, subsorting and partial functions. Casl also provides constructs for structuring specifications-in-the-large. Several extensions of Casl (concurrent, modal-temporal, coalgebraic and higher-order) are formalized as so-called institutions, which means that Casl’s structuring constructs can also be used for these extensions. We extend Casl’s powerful logic-independent structuring constructs to heterogeneous specification, obtaining the specification language Heterogeneous Casl (HetCasl). HetCasl allows mixing specifications written in different logics (using translations between the logics). It extends Casl only at the level of structuring constructs, by adding constructs for choosing the logic and translating specifications among logics. HetCasl is needed when combining specifications written in Casl with specifications written in its sublanguages and extensions. HetCasl also allows the integration of logics that are completely different from the Casl logic. Heterogeneous specification in HetCasl is based on an arbitrary but fixed graph of logics (formalized as institutions) and logic translations (formalized as various kinds of institution morphisms). We provide an initial logic graph covering a range of different specification paradigms, and then study heterogeneous specification in general. In order to obtain a semantic foundation for heterogeneous specification, we extend Diaconescu’s morphism-based Grothendieck institutions to the case of comorphisms. This is not just a dualization, because we obtain more general results, especially concerning amalgamation properties. We also introduce a proof calculus for structured heterogeneous specifications and study its soundness and completeness (where amalgamation properties play a rôle for obtaining the latter). Last but not least, we show how this theory can be brought into practice. The Heterogeneous Tool Set (Hets). Hets provides an abstract interface for logics and provides a parser, static analysis and proof engine for heterogeneous Casl— based on corresponding tools for the logics involved in the given logic graph.