The Proof Technique of Unique Solutions of Contractions

International audienceWe review some recent work aimed at understanding proof techniques for behavioural equivalence on processes based on the concept of unique solution of equations. The schema of equations is refined to that of contraction, based on partial orders rather than equalities

Formalisation de HOCore en Coq

National audienceNous présentons les premiers résultats de la formalisation de propriétés du calcul de processus d'ordre supérieur HOCore [I. Lanese, J. A. Pérez, D. Sangiorgi et A. Schmitt : On the expressiveness and decidability of higher-order process calculi. Information and Computation, 209(2):198-226, fév. 2011.] dans l'assistant de preuve Coq. Nous décrivons notre choix de représentation des lieurs de HOCore, nous basant sur l'approche canonique de Pollack et al .[R. Pollack, M. Sato et W. Ricciotti : A canonical locally named representation of binding. Journal of Automated Reasoning, p. 1-23, mai 2011. 10.1007/s10817-011-9229-y.] Nous donnons la représentation de différentes notions de bissimulations, puis la preuve formelle de la correction de l'IO-bissimilarité par rapport à l'équivalence contextuelle barbue, correspondant à un des théorèmes fondamentaux de [I. Lanese, J. A. Pérez, D. Sangiorgi et A. Schmitt : On the expressiveness and decidability of higher-order process calculi. Information and Computation, 209(2):198-226, fév. 2011.]. Nous montrons également que l'IO-bissimilarité est décidable. L'objectif de ce travail est de montrer l'utilité de Coq et de la représentation canonique pour prouver des propriétés de calculs d'ordre supérieur

Adaptable processes

We propose the concept of adaptable processes as a way of overcoming the limitations that process calculi have for describing patterns of dynamic process evolution. Such patterns rely on direct ways of controlling the behavior and location of running processes, and so they are at the heart of the adaptation capabilities present in many modern concurrent systems. Adaptable processes have a location and are sensible to actions of dynamic update at runtime; this allows to express a wide range of evolvability patterns for concurrent processes. We introduce a core calculus of adaptable processes and propose two verification problems for them: bounded and eventual adaptation. While the former ensures that the number of consecutive erroneous states that can be traversed during a computation is bound by some given number k, the latter ensures that if the system enters into a state with errors then a state without errors will be eventually reached. We study the (un)decidability of these two problems in several variants of the calculus, which result from considering dynamic and static topologies of adaptable processes as well as different evolvability patterns. Rather than a specification language, our calculus intends to be a basis for investigating the fundamental properties of evolvable processes and for developing richer languages with evolvability capabilities

Environmental Bisimulations for Probabilistic Higher-Order Languages

International audienceEnvironmental bisimulations for probabilistic higher-order languages are studied. In contrast with applicative bisimulations, environmental bisimulations are known to be more robust and do not require sophisticated techniques such as Howe's in the proofs of congruence. As representative calculi, call-by-name and call-by-value λ-calculus, and a (call-by-value) λ-calculus extended with references (i.e., a store) are considered. In each case full abstraction results are derived for probabilistic environmental similarity and bisimilarity with respect to contextual preorder and contextual equivalence, respectively. Some possible enhancements of the (bi)simulations, as 'up-to techniques', are also presented. Probabilities force a number of modifications to the definition of environmental bisimulations in non-probabilistic languages. Some of these modifications are specific to probabilities, others may be seen as general refinements of environmental bisimulations, applicable also to non-probabilistic languages. Several examples are presented, to illustrate the modifications and the differences

Characterizing contextual equivalence in calculi with passivation

AbstractWe study the problem of characterizing contextual equivalence in higher-order languages with passivation. To overcome the difficulties arising in the proof of congruence of candidate bisimilarities, we introduce a new form of labeled transition semantics together with its associated notion of bisimulation, which we call complementary semantics. Complementary semantics allows to apply the well-known Howeʼs method for proving the congruence of bisimilarities in a higher-order setting, even in the presence of an early form of bisimulation. We use complementary semantics to provide a coinductive characterization of contextual equivalence in the HOπP calculus, an extension of the higher-order π-calculus with passivation, obtaining the first result of this kind. We then study the problem of defining a more effective variant of bisimilarity that still characterizes contextual equivalence, along the lines of Sangiorgiʼs notion of normal bisimilarity. We provide partial results on this difficult problem: we show that a large class of test processes cannot be used to derive a normal bisimilarity in HOπP, but we show that a form of normal bisimilarity can be defined for HOπP without restriction