Unique Solutions of Contractions, CCS, and their HOL Formalisation

The unique solution of contractions is a proof technique for bisimilarity that overcomes certain syntactic constraints of Milner's "unique solution of equations" technique. The paper presents an overview of a rather comprehensive formalisation of the core of the theory of CCS in the HOL theorem prover (HOL4), with a focus towards the theory of unique solutions of contractions. (The formalisation consists of about 20,000 lines of proof scripts in Standard ML.) Some refinements of the theory itself are obtained. In particular we remove the constraints on summation, which must be weakly-guarded, by moving to rooted contraction, that is, the coarsest precongruence contained in the contraction preorder.Comment: In Proceedings EXPRESS/SOS 2018, arXiv:1808.0807

Confluence Competition 2019

The Confluence Competition (CoCo)4 is an annual competition of software tools that aim to prove or disprove confluence and related (undecidable) properties of a variety of rewrite formalisms automatically. Initiated in 2012, CoCo runs live in a single slot at a conference or workshop and is executed on the crosscommunity competition platform StarExec [20]. For each category, 100 suitable problems are randomly selected from the online database of confluence problems (COPS). Participating tools must answer YES or NO within 60 seconds, followed by a justification that is understandable by a human expert; any other output signals that the tool could not determine the status of the problem. CoCo 2019 features new categories on commutation, infeasibility problems, and confluence of string rewrite systems. Confluence provides a general notion of determinism and has been conceived as one of the central properties of rewriting. A rewrite system R is a set of directed equations, so called rewrite rules, which induces a rewrite relation →R on terms. We provide a simple exampl

Up-to Techniques for Branching Bisimilarity

Ever since the introduction of behavioral equivalences on processes one has been searching for efficient proof techniques that accompany those equivalences. Both strong bisimilarity and weak bisimilarity are accompanied by an arsenal of up-to techniques: enhancements of their proof methods. For branching bisimilarity, these results have not been established yet. We show that a powerful proof technique is sound for branching bisimilarity by combining the three techniques of up to union, up to expansion and up to context for Bloom's BB cool format. We then make an initial proposal for casting the correctness proof of the up to context technique in an abstract coalgebraic setting, covering branching but also {\eta}, delay and weak bisimilarity

Essay on Semantics Definition in MDE. An Instrumented Approach for Model Verification

International audienceIn the context of MDE (Model-Driven Engineering), our objective is to define the semantics for a given DSL (Domain Specific Language) either to simulate its models or to check properties on them using model-checking techniques. In both cases, the purpose is to formalize the DSL semantics as it is known by the DSL designer but often in an informal way. After several experiments to define operational semantics on the one hand, and translational semantics on the other hand, we discuss both approaches and we specify in which cases these semantics seem to be judicious. As a second step, we introduce a pragmatic and instrumented approach to define a translational semantics and to validate it against a reference operational semantics expressed by the DSL designer. We apply this approach to the xSPEM process description language in order to verify process models

(Bi)Simulations Up-to Characterise Process Semantics

We define (bi)simulations up-to a preorder and show how we can use them to provide a coinductive, (bi)simulation-like, characterisation of semantic (equivalences) preorders for processes. In particular, we can apply our results to all the semantics in the linear time-branching time spectrum that are defined by preorders coarser than the ready simulation preorder. The relation between bisimulations up-to and simulations up-to allows us to find some new relations between the equivalences that define the semantics and the corresponding preorders. In particular, we have shown that the simulation up-to an equivalence relation is a canonical preorder whose kernel is the given equivalence relation. Since all of these canonical preorders are defined in an homogeneous way, we can prove properties for them in a generic way. As an illustrative example of this technique, we generate an axiomatic characterisation of each of these canonical preorders, that is obtained simply by adding a single axiom to the axiomatization of the original equivalence relation. Thus we provide an alternative axiomatization for any axiomatizable preorder in the linear time-branching time spectrum, whose correctness and completeness can be proved once and for all. Although we first prove, by induction, our results for finite processes, then we see, by using continuity arguments, that they are also valid for infinite (finitary) processes

Unique solutions of contractions, CCS, and their HOL formalisation

International audienceThe unique solution of contractions is a proof technique for (weak) bisimilarity that overcomes certainsyntactic limitations of Milner’s “unique solution of equations” theorem. This paper presents an overview ofa comprehensive formalisation of Milner’s Calculus of Communicating Systems (CCS) in the HOL theoremprover (HOL4), with a focus towards the theory of unique solutions of equations and contractions. Theformalisation consists of about 24,000 lines (1MB) of code in total. Some refinements of the “unique solutionof contractions” theory itself are obtained. In particular we remove the constraints on summation, whichmust be guarded, by moving from contraction to rooted contraction. We prove the “unique solution ofrooted contractions” theorem and show that rooted contraction is the coarsest precongruence contained inthe contraction preorder

Approche de métamodélisation pour la simulation et la vérification de modèle. Application à l'ingénierie des procédés

Nous proposons dans cette thèse une démarche permettant de décrire un DSML (Domain Specific Modeling Language) et les outils nécessaires à l'exécution, la vérification et la validation des modèles. La démarche que nous proposons offre une architecture générique de la syntaxe abstraite du DSML pour capturer les informations nécessaires à l'exécution d'un modèle et définir les propriétés temporelles qui doivent être vérifiées. Nous nous appuyons sur cette architecture pour expliciter la sémantique de référence et l'implanter. Plus particulièrement, nous étudions les moyens : – d'exprimer et de valider la définition d'une traduction vers un domaine formel dans le but de réutiliser des outils de model-checking. – de compléter la syntaxe abstraite par le comportement ; et profiter d'outils génériques pour pouvoir simuler les modèles construits. Enfin, de manière à valider les différentes sémantiques implantées vis-à-vis de la sémantique de référence, nous proposons un cadre formel de métamodélisation. ABSTRACT : We propose in this thesis a specific taxonomy of the mechanisms allowing to express an execution semantics for Domain Specific Modeling Languages (DSMLs). Then, we integrate these different mechanisms within a comprehensive approach describing DSMLs and tools required for model execution, verification and validation. The proposed approach provides a rigorous and generic architecture for DSML abstract syntax in order to capture the information required for model execution. We rely on this generic architecture to make the reference semantics explicit and implement it. More specifically, we study the means : – to express and validate the definition of a translation into a formal domain in order to re-use model-checking techniques. – to enrich the abstract syntax with the definition of the DSML behaviour and take advantage of generic tools so to simulate the built models. Finally, for the purpose of validating the equivalence of different semantics implemented according to the reference semantics, we also propose a formal metamodeling framewor

New Up-To Techniques for Weak Bisimulation

International audienceUp-to techniques have been introduced to enhance the bisimulation proof method for establishing bisimilarity results. While up-to techniques for strong bisimilarity are well understood, the irregularities that appear in the weak case make it difficult to give a unified presentation. We propose a uniform and modular theory of up-to techniques for weak bisim-ulation that captures most of the existing proof technology and introduces new techniques. Some proofs rely on nontrivial – and new – commutation results based on termination guarantees. All results presented in this paper have been formally proved using the Coq proof assistant