The Fusion Calculus: Expressiveness and Symmetry in Mobile Processes

Joachim Parrow and Björn Victor

Abstract:

We present the fusion calculus as a significant step towards a canonical calculus of concurrency. It simplifies and extends the pi-calculus.

The fusion calculus contains the polyadic pi-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 pi-calculus these tasks require elaborate encodings.

The dramatic main point of this paper is that we achieve these improvements by simplifying the pi-calculus rather than adding features to it. The fusion calculus has only one binding operator where the pi-calculus has two (input and restriction). It has a complete symmetry between input and output actions where the pi-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 pi-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.

Extended abstract: Published in the Proceedings of LICS'98 (Postscript, compressed)

See also these related papers:

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• The Fusion Calculus: Expressiveness and Symmetry in Mobile Processes, by Joachim Parrow and Björn Victor, LICS'98.
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• Concurrent Constraints in the Fusion Calculus, by Björn Victor and Joachim Parrow, ICALP'98.
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• The Tau-Laws of Fusion, by Joachim Parrow and Björn Victor, CONCUR'98.
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• The Fusion Calculus: Expressiveness and Symmetry in Mobile Processes, PhD thesis by Björn Victor.
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• Symbolic Characterizations and Algorithms for Hyperequivalence, by Björn Victor, technical report DoCS 98/96.
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• Solos in Concert, by Cosimo Laneve and Björn Victor, ICALP'99 / MSCS 13(5) 2003.
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• Solo Diagrams, by Cosimo Laneve, Joachim Parrow and Björn Victor, TACS2001.