The asynchronous pi-calculus is considered the basis of experimental programming languages (or proposal of programming languages) like Pict, Join, and Blue calculus. However, at a closer inspection, these languages are based on an even simpler calculus, called Local (L), where: (a) only the output capability of names may be transmitted; (b) there is no matching or similar constructs for testing equality between names. We study the basic operational and algebraic theory of Lpi. We focus on bisimulation-based behavioural equivalences, precisely on barbed congruence. We prove two coinductive characterisations of barbed congruence in Lpi, and some basic algebraic laws. We then show applications of this theory, including: the derivability of delayed input; the correctness of an optimisation of the encoding of call-by-name lambda-calculus; the validity of some laws for Join.

ABSTRACT. As informal methods do little to help their use for concurrent and distributed programming, one of the most challenging current tasks is to build tools based on formal method in order to ease the development of such applications. In this context, we propose precise type systems for concurrent object and actor oriented programming languages. This paper analyzes the type systems that we have developed for realistic languages and presents their benefits and limits. First, it introduces the kernel of an actor language used to describe and validate the proposed technic. Then, the errors we wish to detect are precisely defined. Afterwards, the first type system is defined and its properties are presented. Finally, insights are given on a second more powerful type system, which is the basis of our future work. RÉSUMÉ. Face à l’échec des méthodes informelles dans l’assistance à la programmation concurrente et distribuée, un des enjeux majeurs actuels consiste à fournir des outils d’aide basés sur des méthodes formelles. Dans ce contexte, nous proposons des systèmes de type précis et pertinents pour des langages à objets concurrents ou à acteurs. Cet article est un premier bilan des systèmes que nous avons mis au point pour des langages réalistes, il expose à la fois leurs avantages et leurs limites. Pour présenter ces systèmes de type, nous introduisons le noyau d’un langage d’acteurs qui sert de support pour valider les techniques proposées. Nous décrivons ensuite, de manière approfondie, les types d’erreurs que nous souhaitons détecter. Nous définissons un premier système de type et présentons ses propriétés. Enfin, nous terminons sur une brève introduction d’un second système de type plus puissant, base de nos futurs travaux.

The Blue calculus is a direct extension of both the lambda and the pi calculi. In this report, we dene an equivalence for this calculus based on barbed congruence, and we prove the validity of the replication laws. For example, we prove that a replicated resource, shared by many processes, can be safely copied and distributed.

. We describe a model of concurrent objects based on the blue calculus ( ? ), a typed variant of the asynchronous -calculus in which the notion of function is directly embedded. We propose a definition for a simple concurrent object-based calculus and show how objects can be translated in ? . We also present the type system for objects derived from our definition and we verify the expressiveness of the object calculus by giving a direct and adequate interpretation of Abadi and Cardelli object calculus: Ob1!: , that preserves subtyping. 1 Introduction In his article [21], Milner states that the reduction relation of the -calculus () is based on the object paradigm, in the sense that "what is transmitted and bound is never an object, but rather access to the object". There is a strong connection with object-oriented programming here: processes are objects (and states), and communication channels are the references used to name/access objects. But the object-oriented paradigm is mor...