A single complete relational rule for coalgebraic refinement

A transition system can be presented either as a binary relation or as a coalgebra for the powerset functor, each representation being obtained from the other by transposition. More generally, a coalgebra for a functor F generalises transition systems in the sense that a shape for transitions is determined by F, typically encoding a signature of methods and observers. This paper explores such a duality to frame in purely relational terms coalgebraic refinement, showing that relational (data) refinement of transition relations, in its two variants, downward and upward (functional) simulations, is equivalent to coalgebraic refinement based on backward and forward morphisms, respectively. Going deeper, it is also shown that downward simulation provides a complete relational rule to prove coalgebraic refinement. With such a single rule the paper defines a pre-ordered calculus for refinement of coalgebras, with bisimilarity as the induced equivalence. The calculus is monotonic with respect to the main relational operators and arbitrary relator F, therefore providing a framework for structural reasoning about refinement

The composition of Event-B models

The transition from classical B [2] to the Event-B language and method [3] has seen the removal of some forms of model structuring and composition, with the intention of reinventing them in future. This work contributes to thatreinvention. Inspired by a proposed method for state-based decomposition and refinement [5] of an Event-B model, we propose a familiar parallel event composition (over disjoint state variable lists), and the less familiar event fusion (over intersecting state variable lists). A brief motivation is provided for these and other forms of composition of models, in terms of feature-based modelling. We show that model consistency is preserved under such compositions. More significantly we show that model composition preserves refinement

Galois: a language for proofs using galois connections and fork algebras

Galois is a domain specific language supported by the Galculator interactive proof-assistant prototype. Galculator uses an equational approach based on Galois connections with indirect equality as an additional inference rule. Galois allows for the specification of different theories in a point-free style by using fork algebras, an extension of relation algebras with expressive power of first-order logic. The language offers sub-languages to derive proof rules from Galois connections, to express proof tactics, and to organize axioms and theorems into modular definitions. In this paper, we describe how the algebraic theory underlying the proof-method drives the design of the Galois language. We provide the syntax and semantics of important fragments of Galois and show how they are hierarchically combined into a complete language.Theauthorsthanktheanonymousrefereesforinsightfulcomments which improved the quality of the original submission. This research was supported by FCT (the Portuguese Foundation for Science and Technology), in the context of the MATHIS Project under contract PTDC/EIA/73252/2006. The first author was supported by FCT under grant number SFRH/BD/19195/2004

Strategic term rewriting and its application to a VDM-SL to SQL conversion

We constructed a tool, called VooDooM, which converts datatypes in Vdm-sl into Sql relational data models. The conversion involves transformation of algebraic types to maps and products, and pointer introduction. The conversion is specified as a theory of refinement by calculation. The implementation technology is strategic term rewriting in Haskell, as supported by the Strafunski bundle. Due to these choices of theory and technology, the road from theory to practise is straightforward.Fundação para a Ciência e a Tecnologia (FCT) - POSI/ICHS/44304/2002Agência de Inovação (ADI) - ∑!223

Basic completion strategies as another application of the Maude strategy language

The two levels of data and actions on those data provided by the separation between equations and rules in rewriting logic are completed by a third level of strategies to control the application of those actions. This level is implemented on top of Maude as a strategy language, which has been successfully used in a wide range of applications. First we summarize the Maude strategy language design and review some of its applications; then, we describe a new case study, namely the description of completion procedures as transition rules + control, as proposed by Lescanne.Comment: In Proceedings WRS 2011, arXiv:1204.531

From algebras to objects : generation and composition

This paper addresses objectification, a formal specification technique which inspects the potential for object-orientation of a declarative model and brings the 'implicit objects' explicit. Criteria for such objectification are formalized and implemented in a runnable prototype tool which embeds Vdm-sl into Vdm++. The paper also includes a quick presentation of a (coinductive) calculus of such generated objects, framed as generalised Moore machines.Fundação para a Ciência e a Tecnologia (FCT

A Conceptual Framework for Adapation

This paper presents a white-box conceptual framework for adaptation that promotes a neat separation of the adaptation logic from the application logic through a clear identification of control data and their role in the adaptation logic. The framework provides an original perspective from which we survey archetypal approaches to (self-)adaptation ranging from programming languages and paradigms, to computational models, to engineering solutions

A Conceptual Framework for Adapation

This paper presents a white-box conceptual framework for adaptation that promotes a neat separation of the adaptation logic from the application logic through a clear identification of control data and their role in the adaptation logic. The framework provides an original perspective from which we survey archetypal approaches to (self-)adaptation ranging from programming languages and paradigms, to computational models, to engineering solutions