The foundational legacy of ASL

Abstract. We recall the kernel algebraic specification language ASL and outline its main features in the context of the state of research on algebraic specification at the time it was conceived in the early 1980s. We discuss the most significant new ideas in ASL and the influence they had on subsequent developments in the field and on our own work in particular.

Building Specifications in the Event-B Institution

This paper describes a formal semantics for the Event-B specification language using the theory of institutions. We define an institution for Event-B, EVT, and prove that it meets the validity requirements for satisfaction preservation and model amalgamation. We also present a series of functions that show how the constructs of the Event-B specification language can be mapped into our institution. Our semantics sheds new light on the structure of the Event-B language, allowing us to clearly delineate three constituent sub-languages: the superstructure, infrastructure and mathematical languages. One of the principal goals of our semantics is to provide access to the generic modularisation constructs available in institutions, including specification-building operators for parameterisation and refinement. We demonstrate how these features subsume and enhance the corresponding features already present in Event-B through a detailed study of their use in a worked example. We have implemented our approach via a parser and translator for Event-B specifications, EBtoEVT, which also provides a gateway to the Hets toolkit for heterogeneous specification.Comment: 54 pages, 25 figure

Encoding hybridised institutions into first order logic

"First published online: 12 November 2014"A ‘hybridization’ of a logic, referred to as the base logic, consists of developing the characteristic features of hybrid logic on top of the respective base logic, both at the level of syntax (i.e. modalities, nominals, etc.) and of the semantics (i.e. possible worlds). By ‘hybridized institutions’ we mean the result of this process when logics are treated abstractly as institutions (in the sense of the institution theory of Goguen and Burstall). This work develops encodings of hybridized institutions into (many-sorted) first order logic (abbreviated FOL) as a ‘hybridization’ process of abstract encodings of institutions into FOL, which may be seen as an abstraction of the well known standard translation of modal logic into first order logic. The concept of encoding employed by our work is that of comorphism from institution theory, which is a rather comprehensive concept of encoding as it features encodings both of the syntax and of the semantics of logics/institutions. Moreover we consider the so-called theoroidal version of comorphisms that encode signatures to theories, a feature that accommodates a wide range of concrete applications. Our theory is also general enough to accomodate various constraints on the possible worlds semantics as well a wide variety of quantifications. We also provide pragmatic sufficient conditions for the conservativity of the encodings to be preserved through the hybridization process, which provides the possibility to shift a formal verification process from the hybridized institution to FOL.We thank both Till Mossakowski and Andrzej Tarlecki for the technical suggestion of using the predicates D. The work of the first author has been supported by a grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-ID-PCE-2011-3-0439. The work of the second author was funded by the European Regional Development Fund through the COMPETE Programme, and by the Portuguese Foundation for Science and Technology through the projects FCOMP-01-0124-FEDER-028923 and NORTE-01-0124-FEDER-000060