Behavioural and abstractor specifications revisited

In the area of algebraic specification there are two main approaches for defining observational abstraction: behavioural specifications use a notion of observational satisfaction for the axioms of a specification, whereas abstractor specifications define an abstraction from the standard semantics of a specification w.r.t. an observational equivalence relation between algebras. Earlier work by Bidoit, Hennicker, Wirsing has shown that in the case of first-order logic specifications both concepts coincide semantically under mild assumptions. Analogous results have been shown by Sannella and Hofmann for higher-order logic specifications and recently, by Hennicker and Madeira, for specifications of reactive systems using a dynamic logic with binders. In this paper, we bring these results into a common setting: we isolate a small set of characteristic principles to express the behaviour/abstractor equivalence and show that all three mentioned specification frameworks satisfy these principles and therefore their behaviour and abstractor specifications coincide semantically (under mild assumptions). As a new case we consider observational modal logic where observational satisfaction of Hennessy–Milner logic formulae is defined “up to” silent transitions and observational abstraction is defined by weak bisimulation. We show that in this case the behaviour/abstractor equivalence can only be obtained, if we restrict models to weakly deterministic labelled transition systems.publishe

A logic for the stepwise development of reactive systems

D↓is a new dynamic logic combining regular modalities with the binder constructor typical of hybrid logic, which provides a smooth framework for the stepwise development of reactive systems. Actually, the logic is able to capture system properties at different levels of abstraction, from high-level safety and liveness requirements, to constructive specifications representing concrete processes. The paper discusses its semantics, given in terms of reachable transition systems with initial states, its expressive power and a proof system. The methodological framework is in debt to the landmark work of D.Sannella and A.Tarlecki, instantiating the generic concepts of constructor and abstractor implementations by standard operators on reactive components, e.g. relabelling and parallel composition, as constructors, and bisimulation for abstraction.This work was funded by ERDF European Regional Development Fund, through the COMPETE Programme, and by National Funds through FCT – Portuguese Foundation for Science and Technology – within projects POCI-01-0145-FEDER-016692 (DaLí – Dynamic logics for cyber-physical systems: towards contract based design) and UID/MAT/04106/2013 at CIDMA. Further support was given by the project SmartEGOV, NORTE-01-0145-FEDER000037, supported by Norte Portugal Regional Operational Programme (NORTE 2020), under the PORTUGAL 2020 Partnership Agreement, through the EFDR. The first author is also supported by a FCT individual grant SFRH/BPD/103004/201

Program equivalence for a concurrent lambda calculus with futures

Reasoning about the correctness of program transformations requires a notion of program equivalence. We present an observational semantics for the concurrent lambda calculus with futures Lambda(fut), which formalizes the operational semantics of the programming language Alice ML. We show that natural program optimizations, as well as partial evaluation with respect to deterministic rules, are correct for Lambda(fut). This relies on a number of fundamental properties that we establish for our observational semantics

Formal mechanization of device interactions with a process algebra

The principle emphasis is to develop a methodology to formally verify correct synchronization communication of devices in a composed hardware system. Previous system integration efforts have focused on vertical integration of one layer on top of another. This task examines 'horizontal' integration of peer devices. To formally reason about communication, we mechanize a process algebra in the Higher Order Logic (HOL) theorem proving system. Using this formalization we show how four types of device interactions can be represented and verified to behave as specified. The report also describes the specification of a system consisting of an AVM-1 microprocessor and a memory management unit which were verified in previous work. A proof of correct communication is presented, and the extensions to the system specification to add a direct memory device are discussed

A Logical Verification Methodology for Service-Oriented Computing

We introduce a logical verification methodology for checking behavioural properties of service-oriented computing systems. Service properties are described by means of SocL, a branching-time temporal logic that we have specifically designed to express in an effective way distinctive aspects of services, such as, e.g., acceptance of a request, provision of a response, and correlation among service requests and responses. Our approach allows service properties to be expressed in such a way that they can be independent of service domains and specifications. We show an instantiation of our general methodology that uses the formal language COWS to conveniently specify services and the expressly developed software tool CMC to assist the user in the task of verifying SocL formulae over service specifications. We demonstrate feasibility and effectiveness of our methodology by means of the specification and the analysis of a case study in the automotive domain

Dynamic logic with binders and its application to the development of reactive systems

Publicado em "Theoretical aspects of computing - ICTAC 2016: 13th International Colloquium, Taipei, Taiwan, ROC, October 24–31, 2016, Proceedings". ISBN 978-3-319-46749-8This paper introduces a logic to support the specification and development of reactive systems on various levels of abstraction, from property specifications, concerning e.g. safety and liveness requirements, to constructive specifications representing concrete processes. This is achieved by combining binders of hybrid logic with regular modalities of dynamic logics in the same formalism, which we call D↓-logic. The semantics of our logic focuses on effective processes and is therefore given in terms of reachable transition systems with initial states. The second part of the paper resorts to this logic to frame stepwise development of reactive systems within the software development methodology proposed by Sannella and Tarlecki. In particular, we instantiate the generic concepts of constructor and abstractor implementations by using standard operators on reactive components, like relabelling and parallel composition, as constructors, and bisimulation for abstraction. We also study vertical composition of implementations which relies on the preservation of bisimularity by the constructions on labeleld transition systems.FCT individual grants SFRH/BPD/103004/2014 and SFRH/BSAB/113890/2015ERDF European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT - Fundação para a Cência e a Tecnologia within project POCI-01-0145-FEDER-016692 and UID/MAT/04106/2013 at CIDM

Specification and analysis of SOC systems using COWS: a finance case study

Service-oriented computing, an emerging paradigm for distributed computing based on the use of services, is calling for the development of tools and techniques to build safe and trustworthy systems, and to analyse their behaviour. Therefore many researchers have proposed to use process calculi, a cornerstone of current foundational research on specification and analysis of concurrent and distributed systems. We illustrate this approach by focussing on COWS, a process calculus expressly designed for specifying and combining services, while modelling their dynamic behaviour. We present the calculus and one of the analysis techniques it enables, that is based on the temporal logic SocL and the associated model checker CMC. We demonstrate applicability of our tools by means of a large case study, from the financial domain, which is first specified in COWS, and then analysed by using SocL to express many significant properties and CMC to verify them

Towards a specification theory for fuzzy modal logic

Fuzziness, as a way to express imprecision, or uncertainty, in computation is an important feature in a number of current application scenarios: from hybrid systems interfacing with sensor networks with error boundaries, to knowledge bases collecting data from often non-coincident human experts. Their abstraction in e.g. fuzzy transition systems led to a number of mathematical structures to model this sort of systems and reason about them. This paper adds two more elements to this family: two modal logics, framed as institutions, to reason about fuzzy transition systems and the corresponding processes. This paves the way to the development, in the second part of the paper, of an associated theory of structured specification for fuzzy computational systems.This work is financed by the ERDF - European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation -COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT -Fundacao para a Ciencia e a Tecnologia within project POCI-01-0145-FEDER-029946 -PTDC/CCI-COM/29946/2017

Imperative Object-based Calculi in (Co)Inductive Type Theories

We discuss the formalization of Abadi and Cardelli's imps, a paradigmatic object-based calculus with types and side effects, in Co-Inductive Type Theories, such as the Calculus of (Co)Inductive Constructions (CC(Co)Ind). Instead of representing directly the original system "as it is", we reformulate its syntax and semantics bearing in mind the proof-theoretical features provided by the target metalanguage. On one hand, this methodology allows for a smoother implementation and treatment of the calculus in the metalanguage. On the other, it is possible to see the calculus from a new perspective, thus having the occasion to suggest original and cleaner presentations. We give hence anew presentation of imps, exploiting natural deduction semantics, (weak) higher-order abstract syntax, and, for a significant fragment of the calculus, coinductive typing systems. This presentation is easier to use and implement than the original one, and the proofs of key metaproperties, e.g. subject reduction, are much simpler. Although all proof developments have been carried out in the Coq system, the solutions we have devised in the encoding of and metareasoning on imps can be applied to other imperative calculi and proof environments with similar features