Bisimulations up-to: beyond first-order transition systems

International audienceThe bisimulation proof method can be enhanced by employing 'bisimulations up-to' techniques. A comprehensive theory of such enhancements has been developed for first-order (i.e., CCS-like) labelled transition systems (LTSs) and bisimilarity, based on the notion of compatible function for fixed-point theory. We transport this theory onto languages whose bisimilarity and LTS go beyond those of first-order models. The approach consists in exhibiting fully abstract translations of the more sophisticated LTSs and bisimilarities onto the first-order ones. This allows us to reuse directly the large corpus of up-to techniques that are available on first-order LTSs. The only ingredient that has to be manually supplied is the compatibility of basic up-to techniques that are specific to the new languages. We investigate the method on the pi-calculus, the lambda-calculus, and a (call-by-value) lambda-calculus with references

A Separation Logic for Heap Space under Garbage Collection

International audienceWe present SL⋄, a Separation Logic that allows controlling the heap space consumption of a program in the presence of dynamic memory allocation and garbage collection. A user of the logic works with space credits, a resource that is consumed when an object is allocated and produced when a group of objects is logically deallocated, that is, when the user is able to prove that it has become unreachable and therefore can be collected. To prove such a fact, the user maintains pointed-by assertions that record the immediate predecessors of every object. Our calculus, SpaceLang, has mutable state, shared-memory concurrency, and code pointers. We prove that SL⋄ is sound and present several simple examples of its use

A behavioural theory for a π-calculus with preorders

We study the behavioural theory of piP, a pi-calculus featuring restriction as the only binder. In contrast with calculi such as Fusions and Chi, reduction in piP generates a preorder on names rather than an equivalence relation. We present two characterisations of barbed congruence in piP: the fi rst is based on a compositional LTS, and the second is an axiomatisation. The results in this paper bring out basic properties of piP, mostly related to the interplay between the restriction operator and the preorder on name

Name-passing calculi: from fusions to preorders and types

This is the appendix of the paper "Name-passing calculi: from fusions to preorders and types" (D Hirschkoff, JM. Madiot, D. Sangiorgi), to appear in LICS'2013

Langages d'ordre supérieur : dualités et techniques de bisimulation

The behaviours of concurrent processes can be expressed using process calculi, which are simple formal languages that let us establish precise mathematical results on the behaviours and interactions between processes. A very simple example is CCS, another one is the pi-calculus, which is more expressive thanks to a name-passing mechanism. The pi-calculus supports the addition of type systems (to refine the analysis to more subtle environments) and the encoding of the lambda-calculus (which represents sequential computations).Some of these calculi, like CCS or variants of the pi-calculus such as fusion calculi, enjoy a property of symmetry. First, we use this symmetry as a tool to prove that two encodings of the lambda-calculus in the pi-calculus are in fact equivalent.This proof using a type system and a form of symmetry, we wonder if other existing symmetric calculi can support the addition of type systems. We answer negatively to this question with an impossibility theorem.Investigating this theorem leads us to a fundamental constraint of these calculi that forbids types: they induce an equivalence relation on names. Relaxing this constraint to make it a preorder relation yields another calculus that recovers important notions of the pi-calculus, that fusion calculi do not satisfy: the notions of types and of privacy of names. The first part of this thesis focuses on the study of this calculus, a pi-calculus with preorders on names.The second part of this thesis focuses on bisimulation, a proof method for equivalence of agents in higher-order languages, like the pi- or the lambda-calculi. An enhancement of this method is the powerful theory of bisimulations up to, which unfortunately only applies for first-order systems, like automata or CCS.We then proceed to describe higher-order languages as first-order systems. This way, we inherit the general theory of up-to techniques for these languages, by proving correct the translations and up-to techniques that are specific to each language. We give details on the approach, to provide the necessary tools for future applications of this method to other higher-order languages.Les comportements des processus concurrents peuvent être exprimés en utilisant des calculs de processus, des langages formels simples qui permettent de démontrer des résultats mathématiques précis sur les interactions entre processus. Un exemple très simple est CCS, un autre exemple est le pi-calcul, plus expressif grâce à un mécanisme de communication de canaux. Dans ce dernier, on peut instaurer un système de types (pour raffiner l'analyse aux environnements plus contraints) et encoder le lambda-calcul (qui représente les calculs séquentiels).Certains de ces calculs, comme CCS ou des variantes du pi-calcul comme les calculs de fusions, ont une certaine propriété de symétrie. On utilise dans un premier temps cette symétrie comme un outil, pour prouver que deux encodages du lambda-calcul dans le pi-calcul sont en fait équivalents.Cette preuve nécessitant un système de types et une forme de symétrie, on se pose la question de l'existence d'un système de types pour les autres calculs symétriques, notamment les calculs de fusion, à laquelle on répond par la négative avec un théorème d'impossibilité.En analysant ce théorème, on découvre un contrainte fondamentale de ces calculs qui empêche l'utilisation des types, à savoir la présence d'une notion de relation d'équivalence entre les canaux de communication. Le relâchement de cette contrainte pour obtenir une relation de pré-ordre engendre un calcul intéressant qui recouvre des notions importantes du pi-calcul, absentes dans les calculs de fusion : les types et les noms privés. La première partie de la thèse se concentre sur l'étude de ce calcul.La deuxième partie de la thèse se concentre sur la bisimulation, une méthode pour établir l'équivalence de deux agents dans des langages d'ordre supérieur, par exemple le pi-calcul ou le lambda-calcul. Une amélioration de cette méthode est la théorie des techniques modulo, très puissante, mais qui malheureusement s'applique uniquement aux systèmes de premier ordre, comme les automates ou CCS.Cette thèse s'applique alors à décrire les langages d'ordre supérieur en tant que systèmes du premier ordre. On récupère ainsi la théorie générale des techniques modulo pour ces langages, en prouvant correctes la correspondance induite et les techniques spécifiques à chaque langage. On détaille les tenants et aboutissants de cette approche, pour fournir les outils nécessaires à son utilisation pour d'autres langages d'ordre supérieur

A behavioural theory for a π-calculus with preorders

We study the behavioural theory of piP, a pi-calculus featuring restriction as the only binder. In contrast with calculi such as Fusions and Chi, reduction in piP generates a preorder on names rather than an equivalence relation. We present two characterisations of barbed congruence in piP: the fi rst is based on a compositional LTS, and the second is an axiomatisation. The results in this paper bring out basic properties of piP, mostly related to the interplay between the restriction operator and the preorder on name

Modular coinduction up-to for higher-order languages via first-order transition systems

International audienceThe bisimulation proof method can be enhanced by employing `bisimulations up-to' techniques. A comprehensive theory of such enhancements has been developed for first-order (i.e., CCS-like) labelled transition systems (LTSs) and bisimilarity, based on abstract fixed-point theory and compatible functions. We transport this theory onto languages whose bisimilarity and LTS go beyond those of first-order models. The approach consists in exhibiting fully abstract translations of the more sophisticated LTSs and bisimilarities onto the first-order ones. This allows us to reuse directly the large corpus of up-to techniques that are available on first-order LTSs. The only ingredient that has to be manually supplied is the compatibility of basic up-to techniques that are specific to the new languages. We investigate the method on the pi-calculus, the lambda-calculus, and a (call-by-value) lambda-calculus with references

Name-passing calculi: from fusions to preorders and types

Abstract—The fusion calculi are a simplification of the picalculus in which input and output are symmetric and restriction is the only binder. We highlight a major difference between these calculi and the pi-calculus from the point of view of types, proving some impossibility results for subtyping in fusion calculi. We propose a modification of fusion calculi in which the name equivalences produced by fusions are replaced by name preorders, and with a distinction between positive and negative occurrences of names. The resulting calculus allows us to import subtype systems, and related results, from the picalculus. We examine the consequences of the modification on behavioural equivalence (e.g., context-free characterisations of barbed congruence) and expressiveness (e.g., full abstraction of the embedding of the asynchronous pi-calculus). Index Terms—process calculus; fusions; types; subtyping; I

Name-passing calculi: From fusions to preorders and types

International audienc