Proof theory for hybrid(ised) logics

Hybridisation is a systematic process along which the characteristic features of hybrid logic, both at the syntactic and the semantic levels, are developed on top of an arbitrary logic framed as an institution. In a series of papers this process has been detailed and taken as a basis for a specification methodology for reconfigurable systems. The present paper extends this work by showing how a proof calculus (in both a Hilbert and a tableau based format) for the hybridised version of a logic can be systematically generated from a proof calculus for the latter. Such developments provide the basis for a complete proof theory for hybrid(ised) logics, and thus pave the way to the development of (dedicated) proof support.The authors are grateful to Torben Bräuner for helpful, inspiring discussions, and to the anonymous referees for their detailed comments. This work is funded by ERDF—European Regional Development Fund, through the COMPETE Programme, and by National Funds through Fundação para a Ciência e a Tecnologia(FCT) within project PTDC/EEI-CTP/4836/2014. Moreover, the first and the second authors are sponsored by FCT grants SFRH/BD/52234/2013 and SFRH/BPD/103004/2014, respectively. M. Mar-tins is also supported by the EU FP7 Marie Curie PIRSES-GA-2012-318986 project GeTFun: Generalizing Truth-Functionality and FCT project UID/MAT/04106/2013 through CIDMA. L.Barbosa is further supported by FCT in the context of SFRH/B-SAB/113890/2015

Refinement in hybridised institutions

Hybrid logics, which add to the modal description of transition structures the ability to refer to specific states, offer a generic framework to approach the specification and design of reconfigurable systems, i.e., systems with reconfiguration mechanisms governing the dynamic evolution of their execution configurations in response to both external stimuli or internal performance measures. A formal representation of such systems is through transition structures whose states correspond to the different configurations they may adopt. Therefore, each node is endowed with, for example, an algebra, or a first-order structure, to precisely characterise the semantics of the services provided in the corresponding configuration. This paper characterises equivalence and refinement for these sorts of models in a way which is independent of (or parametric on) whatever logic (propositional, equational, fuzzy, etc) is found appropriate to describe the local configurations. A Hennessy–Milner like theorem is proved for hybridised logics.This work is funded by ERDF-European Regional Development Fund, through the COMPETE Programme, and by National Funds through FCT within project FCOMP-01-0124-FEDER-028923 and by project NORTE-07-0124-FEDER-000060, co-financed by the North Portugal Regional Operational Programme (ON.2), under the National Strategic Reference Framework (NSRF), through the European Regional Development Fund (ERDF). The work had also partial financial assistance by the project PEst-OE/MAT/UI4106/2014 at CIDMA, FCOMP-01-0124-FEDER-037281 at INESC TEC and the Marie Curie project FP7-PEOPLE-2012-IRSES (GetFun)

Reuse and integration of specification logics: the hybridisation perspective

Hybridisation is a systematic process along which the characteristic features of hybrid logic, both at the syntactic and the semantic levels, are developed on top of an arbitrary logic framed as an institution. It also captures the construction of first-order encodings of such hybridised institutions into theories in first-order logic. The method was originally developed to build suitable logics for the specification of reconfigurable software systems on top of whatever logic is used to describe local requirements of each system’s configuration. Hybridisation has, however, a broader scope, providing a fresh example of yet another development in combining and reusing logics driven by a problem from Computer Science. This paper offers an overview of this method, proposes some new extensions, namely the introduction of full quantification leading to the specification of dynamic modalities, and exemplifies its potential through a didactical application. It is discussed how hybridisation can be successfully used in a formal specification course in which students progress from equational to hybrid specifications in a uniform setting, integrating paradigms, combining data and behaviour, and dealing appropriately with systems evolution and reconfiguration.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 FCT (Portuguese Foundation for Science and Technology) within project POCI-01-0145-FEDER-006961. M. Martins was further supported by project UID/MAT/04106/2013. A. Madeira and R. Neves research was carried out in the context of a post-doc and a Ph.D. grant with references SFRH/BPD/103004/2014 and SFRH/BD/52234/2013, respectively. L.S. Barbosa is also supported by SFRH/BSAB/ 113890/2015

A method for rigorous design of reconfigurable systems

Reconfigurability, understood as the ability of a system to behave differently in different modes of operation and commute between them along its lifetime, is a cross-cutting concern in modern Software Engineering. This paper introduces a specification method for reconfigurable software based on a global transition structure to capture the system's reconfiguration space, and a local specification of each operation mode in whatever logic (equational, first-order, partial, fuzzy, probabilistic, etc.) is found expressive enough for handling its requirements. In the method these two levels are not only made explicit and juxtaposed, but formally interrelated. The key to achieve such a goal is a systematic process of hybridisation of logics through which the relationship between the local and global levels of a specification becomes internalised in the logic itself.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 – Fundação para a Ciência e a Tecnologia within projects POCI-01-0145-FEDER-016692 and UID/MAT/04106/2013. The first author is further supported by the BPD FCT Grant SFRH/BPD/103004/2014, and R. Neves is sponsored by FCT Grant SFRH/BD/52234/2013. M.A. Martins is also funded by the EU FP7 Marie Curie PIRSESGA-2012-318986 project GeTFun: Generalizing Truth-Functionality

Foundations and techniques for software reconfigurability

Programa de doutoramento em Informática das Universidades do Minho, de Aveiro e do PortoThe qualifier reconfigurable is used for software systems which behave differently in different modes of operation (often called configurations) and commute between them along their lifetime. Such systems, which evolve in response to external or internal stimulus, are everywhere: from e-Health or e-Government integrated services to sensor networks, from domestic appliances to complex systems distributed and collaborating over the web, from safety or mission-critical applications to massive parallel software. There are two basic approaches to formally capture requirements of this sort of systems: one emphasizes behaviour and its evolution; the other focus on data and their transformations. Within the first paradigm, reconfigurable systems are regarded as (some variant of) state-machines whose states correspond to the different configurations they may assume. On the other hand, in data-oriented approaches the system’s functionality is specified in terms of input-output relations modelling operations on data. A specification presents a theory in a suitable logic, expressed over a signature which captures its syntactic interface. Its semantics is a class of concrete algebras or relational structures, acting as models for the specified theory. The observation that whatever services a reconfigurable system may offer, at each moment, may depend on the stage of its evolution, suggests that both dimensions (data and behaviour) are interconnected and should be combined. In particular, each node in the transition system which describes a reconfiguration space, may be endowed with a local structure modelling the functionality of the respective configuration. This is the basic insight of a configurations-as-local-models specification style. These specifications are modeled by structured state-machines, states denoting complex structures, rather than sets. A specification for this sort of system should be able to make assertions both about the transition dynamics and, locally, about each particular configuration. This leads to the adoption of hybrid logic, which adds to the modal description of transition structures the ability to refer to specific states, as the lingua franca for a suitable specification method. On the other hand, specific applications may require specific logics to describe their configurations. For example, requirements expressed equationally lead to a configurations-as-algebras perspective. But depending on their nature one could also naturally end up in configurations-as-relational-structutres, or probabilistic spaces or even in configurations-as-Kripke-structutres, if first-order, fuzzy or modal logic is locally used. The aim of this thesis is to develop the foundations for a specification method based on these principles. To subsume all the possibilities above our approach builds on very general grounds. Therefore, instead of committing to a particular version of hybrid logic, we start by choosing a specific logic for expressing requirements at the configuration (static) level. This is later taken as the base logic on top of which the characteristic features of hybrid logic, both at the level of syntax (i.e. modalities, nominals, etc.) and of the semantics (i.e. possible worlds), are developed. This process is called hybridisation and is one of the main technical contributions of this thesis. To be completely general, it is framed in the context of the theory of institutions of J. Goguen and R. Burstall, each logic (base and hybridised) being treated abstractly as an institution. In this setting the thesis’ contributions are the following: A method to hybridise arbitrary institutions; this can be understood as a source of logics to support arbitrary configurations-as-local-models specifications. A method to lift encodings (technically, comorphisms) from an institution to a presentation in first-order logic, into encodings from its hybridisation to a presentation in first-order logic; this result paves the way to the introduction of suitable automatised proof support for a wide range of hybridised logics. Suitable characterisations of bisimulation and refinement for models of (generic) hybridisations, which provide canonical, satisfaction preserving relations to identify and relate models. A two-stage specification method for reconfigurable systems based on a global transition structure to capture the system’s reconfiguration space, and a local specification of configurations in whatever logic is found expressive enough for the requirements at hands. A set of additional technics to assist the process of specifying and verifying requirements for reconfigurable systems, with partial tool support.O termo reconfigurável é usado para sistemas de software que se comportam de forma diferente em diferentes modos de operação (frequentemente chamados de configurações) comutando entre eles, ao longo do seu ciclo de vida. Estes sistemas, que evoluem em resposta a estímulos externos e internos, estão por toda a parte, desde sistemas de e-Health ou sistemas integrados de e-Governement, às redes de sensores, das aplicações domésticas aos complexos sistemas distribuidos, dos sistemas críticos de missão ao software de computação paralela. Existem duas abordagens formais para captar requisitos deste tipo de sistemas: uma focada no comportamento e evolução; e outra focada nos dados e respectivas transformações. Segundo o primeiro paradigma, os sistemas reconfiguráveis são abordados por (alguma variante) de máquinas-de-estados, correspondendo, cada um dos seus estados, a uma configuração que o sistema possa assumir. A outra abordagem, orientada aos dados, especifica as funcionalidades do sistema em função de relações de input-output, que modelam operações nos dados. Uma especificação apresenta uma teoria numa lógica adequada, expressa sobre uma assinatura que capta a sua interface sintática. A sua semântica consiste na classe de álgebras, ou estruturas de primeira ordem, que modelam a teoria especificada. A observação de que, a cada momento, os serviços oferecidos por um sistema reconfigurável possam depender do estado da sua evolução, sugere-nos que ambas as dimensões (dados e comportamento) estejam interligados e devam ser combinados. Em particular, cada nó do sistema de transição, que descreve o espaço de reconfigurabilidade, pode ser dotado de uma estrutura local onde as funcionalidades do sistema, na respectiva configuração, são modeladas. Esta é a ideia base da especificação configurações-como-modeloslocais. Tecnicamente, as especificações são modeladas por máquinas de estados estruturadas, onde cada estado denota uma estrutura complexa, ao invés de um conjunto. Uma especificação para este tipo de sistemas deve ser adequada à expressão de asserções acerca da dinâmica de transições, assim como, ao nível local de cada configuração particular. Isto leva-nos à adopção de lógica híbrida, que adiciona, mecanismos para referir estados específicos à expressividade modal dos sistemas de transição, como lingua franca para um método adequado de especificação. Por outro lado, aplicações podem requerer lógicas específicas para descrever as suas configurações. Por exemplo, requisitos expressos por equações devem ser modelados numa perspectiva configurações-como-álgebras. Dependendo da sua natureza, podemos considerar configurações-como-estruturas de primeira ordem, ou configurações-como-espaços probabilísticos ou mesmo configurações-como-estruturas de Kripke quando usadas, localmente, lógica de primeira ordem, lógica fuzzy, ou lógica modal respectivamente. O objectivo da tese é desenvolver os fundamentos para um método de especificação baseado nestes princípios. Por forma a acomodar todas estas possibilidades, a abordagem é desenvolvida sob fundamentos muito genéricos. Ao invés de comprometer a abordagem com uma lógica híbrida particular, partimos da escolha da lógica específica para especificar requisitos ao nível (estáctico) local. Esta lógica é então tomada como lógica de base, sobre a qual os mecanismos da lógica híbrida, tanto ao nível sintáctico (i.e., modalidades, nominais, etc.) como ao semântico (i.e., mundos possíveis), são desenvolvidos. Este processo, que chamamos de hibridização, é uma das principais contribuições técnicas da tese. A generalidade do método resulta do seu desenvolvimento no contexto da teoria das instituições de J. Goguen e R. Burstall. As peincipais contribuições da tese são: • um método para hibridizar instituições arbitrárias; o que pode ser entendido como uma fonte de lógicas para suportar especificações configurações- como-modelos-locais arbitrárias • um método para transportar codificações de uma instituição nas apresentações de primeira ordem (tecnicamente comorfismos), em codificações da sua hibridização em apresentações em primeira ordem; este resultado abre o caminho para a introdução do suporte de prova automático para uma ampla classe de lógicas híbridas; • caracterização de relações de bissimulação e de refinamento para modelos de hibridizações genéricas. Isto oferece relações canónicas, que preservam satisfação, para identificar e relacionar modelos; • um método de especificação para sistemas reconfiguráveis com dois estágios, baseado numa estrutura de transição global, onde o espaço de reconfigurações do sistema é modelado; e numa especificação local das configurações expressa numa lógica escolhida como adequada, aos requisitos a tratar; • um conjunto de técnicas adicionais para assistir o processo de especificação e de verificação de requisitos de sistemas reconfiguráveis com suporte parcial de ferramentas.Fundação para a Ciência e Tecnologia (FCT) and Critical Software S.A., under BDE grant under the contract SFRH/BDE/33650/2009 and by the MONDRIAN Project (FCT) under the contract PTDC/EIA-CCO/108302/2008

On Multi-Language Semantics: Semantic Models, Equational Logic, and Abstract Interpretation of Multi-Language Code

Modern software development rarely takes place within a single programming language. Often, programmers appeal to cross-language interoperability. Benefits are two-fold: exploitation of novel features of one language within another, and cross-language code reuse. For instance, HTML, CSS, and JavaScript yield a form of interoperability, working in conjunction to render webpages. Some object oriented languages have interoperability via a virtual machine host (.NET CLI compliant languages in the Common Language Runtime, and JVM compliant languages in the Java Virtual Machine). A high-level language can interact with a lower level one (Apple's Swift and Objective-C). Whilst this approach enables developers to benefit from the strengths of each base language, it comes at the price of a lack of clarity of formal properties of the new multi-language, mainly semantic specifications. Developing such properties is a key focus of this thesis. Indeed, while there has been some research exploring the interoperability mechanisms, there is little development of theoretical foundations. In this thesis, we broaden the boundary functions-based approach à la Matthews and Findler to propose an algebraic framework that provides systematic and more general ways to define multi-languages, regardless of the inherent nature of the underlying languages. The aim of this strand of research is to overcome the lack of a formal model in which to design the combination of languages. Main contributions are an initial algebra semantics and a categorical semantics for multi-languages. We then give ways in which interoperability can be reasoned about using equations over the blended language. Formally, multi-language equational logic is defined, within which one may deduce valid equations starting from a collection of axioms that postulate properties of the combined language. Thus, we have the notion of a multi-language theory and part of the thesis is devoted to exploring the properties of these theories. This is accomplished by way of both universal algebra and category theory, giving us a very general and flexible semantics, and hence a wide collection of models. Classifying categories are constructed, and hence equational theories furnish each categorical model with an internal language. From this we establish soundness and completeness of the multi-language equational logic. As regards static analysis, the heterogeneity of the multi-language context opens up new and unexplored scenarios. In this thesis, we provide a general theory for the combination of abstract interpretations of existing languages in order to gain an abstract semantics of multi-language programs. As a part of this general theory, we show that formal properties of interest of multi-language abstractions (e.g., soundness and completeness) boil down to the features of the interoperability mechanism that binds the underlying languages together. We extend many of the standard concepts of abstract interpretation to the framework of multi-languages. Finally, a minor contribution of the thesis concerns language specification formalisms. We prove that longstanding syntactical transformations between context-free grammars and algebraic signatures give rise to adjoint equivalences that preserve the abstract syntax of the generated terms. Thus, we have methods to move from context-free languages to the algebraic signature formalisms employed in the thesis