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

Reactive systems, proposed by Leifer and Milner, represent a meta-framework aimed at deriving behavioral congruences for those specification formalisms whose operational semantics is provided by rewriting rules. Despite its applicability, reactive systems suffered so far from two main drawbacks. First of all, no technique was found for recovering a set of inference rules, e.g. in the so-called SOS style, for describing the distilled observational semantics. Most importantly, the efforts focussed on strong bisimilarity, tackling neither weak nor barbed semantics. Our paper addresses both issues, instantiating them on a calculus whose semantics is still in a flux: Cardelli and Gordon’s mobile ambients. While the solution to the first issue is tailored over our case study, we provide a general framework for recasting (weak) barbed equivalence in the reactive systems formalism. Moreover, we prove that our proposal captures the behavioural semantics for mobile ambients proposed by Rathke and Sobociński and by Merro and Zappa Nardelli.

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Mobile computation, in which executing computations can move from one physical computing device to another, is a recurring theme: from OS process migration, to language-level mobility, to virtual machine migration. This paper reports on the design, implementation, and verification of overlay networks to support reliable communication between migrating computations, in the Nomadic Pict project. We define two levels of abstraction as calculi with precise semantics: a low-level Nomadic π-calculus with migration and location-dependent communication, and a high-level calculus that adds location-independent communication. Implementations of locationindependent communication, as overlay networks that track migrations and forward messages, can be expressed as translations of the high-level calculus into the low. We discuss the design space of such overlay network algorithms and define three precisely, as such translations. Based on the calculi, we design and implement the Nomadic Pict distributed programming language, to let such algorithms (and simple applications above them) to be quickly prototyped. We go on to develop the semantic theory of the Nomadic π-calculi, proving correctness of one example overlay network. This requires novel equivalences and congruence results that take migration into account, and reasoning principles for agents that are temporarily immobile (e.g. waiting on a lock

Abstract. Behavioral theory for higher-order process calculi is less well developed than for first-order ones such as the π-calculus. In particular, effective coinductive characterizations of barbed congruence, such as the notion of normal bisimulation developed by Sangiorgi for the higherorder π-calculus, are difficult to obtain. In this paper, we study bisimulations in two simple higher-order calculi with a passivation operator, that allows the interruption and thunkification of a running process. We develop a normal bisimulation that characterizes barbed congruence, in the strong and weak cases, for the first calculus which has no name restriction operator. We then show that this result does not hold in the calculus extended with name restriction. 1

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The aim of this work is to verify an algebra for high level languages for reading and writing Linked Data. Linked Data refers to a collection of standards which aim to enhance the world’s data, by interlinking datasets through the Web. The starting point is as simple as using URIs as global identifiers in data, but the technical challenges of managing data in this distributed setting are immense. An algebra is an essential contribution to this application domain. To verify the algebra several useful things are established. A high level language is defined that concisely captures query and update languages for Linked Data. The language is provided with a concise operational semantics. The natural notions of equivalence, contextual equivalence, is shown to coincide with the bisimulation proof technique. Ultimately, bisimulation allows the algebra proven to be correct. Some novel techniques are used in establishing these results.

The Sπ-calculus is a synchronous π-calculus which is based on the SL model. The latter is a relaxation of the Esterel model where the reaction to the absence of a signal within an instant can only happen at the next instant. In the present work, we study the notions of determinacy and (local) confluence for the Sπ-calculus and we introduce a typing system that guarantees determinacy. 1

The paper presents a case study on the synthesis of labelled transition systems (LTSs) for process calculi, choosing as testbed Cardelli and Gordon’s Mobile Ambients (MAs). The proposal is based on a graphical encoding: each process is mapped into a graph equipped with suitable interfaces, such that the denotation is fully abstract with respect to the usual structural congruence. Graphs with interfaces are amenable to the synthesis mechanism proposed by Ehrig and König and based on borrowed contexts (BCs), an instance of relative pushouts, introduced by Leifer and Milner. The BC mechanism allows the effective construction of a LTS that has graphs with interfaces as both states and labels, and such that the associated bisimilarity is automatically a congruence. Our paper focuses on the analysis of a LTS over (processes as) graphs with interfaces, as distilled by exploiting the graphical encoding of MAs. In particular, we use the LTS on graphs to recover a suitable LTS directly defined over the structure of MAs processes. Keywords: Labelled transition system, mobile ambients, borrowed contexts

Abstract. G-Reactive Systems (GRSs) are a framework for the derivation of labelled transition systems (LTSs) from a set of unlabelled rules. A label for a transition from A to B is a context C[−] such that C[A] may perform a reaction and reach B. If either all contexts, or just the “minimal” ones, are considered, the resulting LTS is called saturated (GIPO, respectively). The borrowed contexts (BCs) technique addresses the issue in the setting of the DPO approach. Indeed, from an adhesive rewriting system (ARS) a GRS can be defined such that DPO derivations correspond to reactions, and BC derivations to transitions of the GIPO LTS. This paper extends the BCs technique in order to derive saturated LTSs for ARSs, applying it to capture bisimilarity for asynchronous calculi. 1