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.

Contextual equivalences for cryptographic process calculi, like the spi-calculus, can be used to reason about correctness of protocols, but their definition suffers from quantification over all possible contexts. Here, we focus on two such equivalences, namely may-testing and barbed equivalence, and investigate tractable proof methods for them. To this aim, we design an enriched labelled transition system, where transitions are constrained by the knowledge the environment has of names and keys. The new transition system is then used to define a trace equivalence and a weak bisimulation equivalence, that avoid quantification over contexts. Our main results are soundness and completeness of trace and weak bisimulation equivalence with respect to may-testing and barbed equivalence, respectively. They lead to more direct proof methods for equivalence checking. The use of these methods is illustrated with a few examples, concerning implementation of secure channels and verification of proto...

We propose an object-oriented calculus with internal concurrency and class-based inheritance that is built upon the join calculus. Method calls, locks, and states are handled in a uniform manner, using asynchronous messages. Classes are partial message definitions that can be combined and transformed. We design operators for behavioral and synchronization inheritance. We also give a type system that statically enforces basic safety properties. Our model is compatible with the JoCaml implementation

Abstract. safeDpi is a distributed version of the Picalculus, in which processes are located at dynamically created sites. Parametrised code may be sent between sites using so-called ports, which are essentially higher-order versions of Picalculus communication channels. A host location may protect itself by only accepting code which conforms to a given type associated to the incoming port. We define a sophisticated static type system for these ports, which restrict the capabilities and access rights of any processes launched by incoming code. Dependent and existential types are used to add flexibility, allowing the behaviour of these launched processes, encoded as process types, to depend on the host’s instantiation of the incoming code. We also show that a natural contextually defined behavioural equivalence can be characterised coinductively, using bisimulations based on typed actions. The characterisation is based on the idea of knowledge acquisition by a testing environment and makes explicit some of the subtleties of determining equivalence in this language of highly constrained distributed code. 1

We define a typed bisimulation equivalence for the language Dpi, a distributed version of the π-calculus in which processes may migrate between dynamically created locations. It takes into account resource access policies, which can be implemented in Dpi using a novel form of dynamic capability types. The equivalence, based on typed actions between configurations, is justified by showing that it is fully-abstract with respect to a natural distributed version of a contextual equivalence. In the second part

We study typed behavioural equivalences for the -calculus, in which the type system allows a form of subtyping. This enables processes to selectively distribute dierent capabilities on communication channels.

Developing a theory of bisimulation in higher-order languages can be hard. Particularly challenging can be: (1) the proof of congruence, as well as enhancements of the bisimulation proof method with “up-to context ” techniques, and (2) obtaining definitions and results that scale to languages with different features. To meet these challenges, we present environmental bisimulations, a form of bisimulation for higher-order languages, and its basic theory. We consider four representative calculi: pure λ-calculi (call-by-name and call-byvalue), call-by-value λ-calculus with higher-order store, and then Higher-Order π-calculus. In each case: we present the basic properties of environmental bisimilarity, including congruence; we show that it coincides with contextual equivalence; we develop some up-to techniques, including up-to context, as examples of possible enhancements of the associated bisimulation method. Unlike previous approaches (such as applicative bisimulations, logical relations, Sumii-Pierce-Koutavas-Wand), our method does not require induction/indices on evaluation derivation/steps (which may complicate the proofs of congruence, transitivity, and the combination with up-to techniques), or sophisticated methods such as Howe’s for proving congruence. It also scales from the pure λ-calculi to the richer calculi with simple congruence proofs. 1

We give a labeled characterization of barbed congruence in asynchronous -calculus, which, unlike previous characterizations, does not use the matching construct. In absence of matching the observer cannot directly distinguish two names. In asynchronous -calculus the fact that two names are indistinguishable can be modeled by means of Honda and Yoshida's notion of equator. Our labeled characterization is based on such a notion. As an application of our theory we provide a fully abstract encoding w.r.t. barbed congruence of external mobility (communication of free names) in terms of internal mobility (communication of private names).

Abstract. We re-examine the standard structural operational semantics of the π-calculus with the view that both process structure and contextual observational power should play roles in describing the behavioural theory. To that end we provide a decomposition of the operational semantics of π which allows for a systematic definition of labelled transitions. These are derived from the calculus ’ underlying reduction rules by following the contexts-as-labels philosophy while being presented using the structural approach. Our novel transition system refines to a composite description of the standard early lts. We generalise our technique to higher-order and asynchronous variants.

The impact of types on the algebraic theory of the π-calculus is studied. The type system has capability types. They allow one to distinguish between the ability to read from a channel, to write to a channel, and both to read and to write. They also give rise to a natural and powerful subtyping relation. Two variants...