We present the fusion calculus as a significant step towards a canonical calculus of concurrency. It simplifies and extends the π-calculus. The fusion calculus contains the polyadic π-calculus as a proper subcalculus and thus inherits all its expressive power. The gain is that fusion contains actions akin to updating a shared state, and a scoping construct for bounding their effects. Therefore it is easier to represent computational models such as concurrent constraints formalisms. It is also easy to represent the so called strong reduction strategies in the lambda-calculus, involving reduction under abstraction. In the π-calculus these tasks require elaborate encodings. The dramatic main point of this paper is that we achieve these improvements by simplifying the π-calculus rather than adding features to it. The fusion calculus has only one binding operator where the π-calculus has two (input and restriction). It has a complete symmetry between input and output actions where the π-calculus has not. There is only one sensible variety of bisimulation congruence where the pi-calculus has at least three (early, late and open). Proofs about the fusion calculus, for example in complete axiomatizations and full abstraction, therefore are shorter and clearer. Our results on the fusion calculus in this paper are the following. We give a structured operational semantics in the traditional style. The novelty lies in a new kind of action, fusion actions for emulating updates of a shared state. We prove that the calculus contains the π-calculus as a subcalculus. We define and motivate the bisimulation equivalence and prove a simple characterization of its induced congruence, which is given two versions of a complete axiomatization for finite terms. The expressive power of the calculus is demonstrated by giving a straight-forward encoding of the strong lazy lambda-calculus, which admits reduction under lambda abstraction.

We study two encodings of the asynchronous #-calculus with input-guarded choice into its choice-free fragment. One encoding is divergence-free, but refines the atomic commitment of choice into gradual commitment. The other preserves atomicity, but introduces divergence. The divergent encoding is fully abstract with respect to weak bisimulation, but the more natural divergence-free encoding is not. Instead, we show that it is fully abstract with respect to coupled simulation, a slightly coarser---but still coinductively defined---equivalence that does not enforce bisimilarity of internal branching decisions. The correctness proofs for the two choice encodings introduce a novel proof technique exploiting the properties of explicit decodings from translations to source terms.

Structural Operational Semantics (SOS) is a widely used formalism for specifying the computational meaning of programs, and is commonly used in specifying the semantics of functional languages. Despite this widespread use there has been relatively little work on the imetatheoryj for such semantics. As a consequence the operational approach to reasoning is considered ad hoc since the same basic proof techniques and reasoning tools are reestablished over and over, once for each operational semantics speciøcation. This paper develops some metatheory for a certain class of SOS language speciøcations for functional languages. We deøne a rule format, Globally Deterministic SOS (gdsos), and establish some proof principles for reasoning about equivalence which are sound for all languages which can be expressed in this format. More speciøcally, if the SOS rules for the operators of a language conform to the syntax of the gdsos format, then ffl a syntactic analogy of continuity holds, which rel...

An improvement theory is a variant of the standard theories of observational approximation (or equivalence) in which the basic observations made of a functional program's execution include some intensionalinformation about, for example, the program's computational cost. One program is an improvement of another if its execution is more efficient in any program context. In this article we give an overview of our work on the theory and applications of improvement. Applications include reasoning about time properties of functional programs, and proving the correctness of program transformation methods. We also introduce a new application, in the form of some bisimulationlike proof techniques for equivalence, with something of the flavour of Sangiorgi's "bisimulation up-to expansion and context".

We show how the #-calculus can express local communications within a distributed system, through an encoding of the local area #-calculus, an enriched system that explicitly represents names which are known universally but always refer to local information. Our translation replaces point-to-point communication with a system of shared local ethers; we prove that this preserves and reflects process behaviour.

Abadi and Cardelli have investigated several versions of the &-calculus, a calculus for describing central features of object-oriented programs, with particular emphasis on various type systems. In this paper we study the properties of a denotational semantics due to Abadi and Cardelli vis-`a-vis the notion of observational congruence for the calculus Ob 1!:¯ . In particular, we prove that the denotational semantics based on partial equivalence relations is correct with respect to observational congruence. By means of a counter-example, we argue that the denotational model is not fully abstract with respect to observational congruence. In fact, the model is able to distinguish objects that have the same behaviour in every Ob 1!:¯ -context. 1 Introduction In [AC96] Abadi and Cardelli present and investigate several versions of the &-calculus, a calculus for describing central features of object-oriented programs, with particular emphasis on various type systems. These object calculi ...

We present an undecidability proof of the notion of communication errors in the polyadic #-calculus. The demonstration follows a general pattern of undecidability proofs -- reducing a well-known undecidable problem to the problem in question. We make use of an encoding of the #-calculus into the #-calculus to show that the decidability of communication errors would solve the problem of deciding whether a lambda term has a normal form.

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