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The Fusion Calculus: Expressiveness and Symmetry in Mobile Processes (Extended Abstract)
 LICS'98
, 1998
"... We present the fusion calculus as a significant step towards a canonical calculus of concurrency. It simplifies and extends the πcalculus.
The fusion calculus contains the polyadic πcalculus as a proper subcalculus and thus inherits all its expressive power. The gain is that fusion contains action ..."
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Cited by 138 (14 self)
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We present the fusion calculus as a significant step towards a canonical calculus of concurrency. It simplifies and extends the πcalculus.
The fusion calculus contains the polyadic πcalculus 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 lambdacalculus, involving reduction under abstraction. In the πcalculus these tasks require elaborate encodings.
The dramatic main point of this paper is that we achieve these improvements by simplifying the πcalculus rather than adding features to it. The fusion calculus has only one binding operator where the πcalculus has two (input and restriction). It has a complete symmetry between input and output actions where the πcalculus has not. There is only one sensible variety of bisimulation congruence where the picalculus 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 πcalculus 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 straightforward encoding of the strong lazy lambdacalculus, which admits reduction under lambda abstraction.
On Asynchrony in NamePassing Calculi
 In
, 1998
"... The asynchronous picalculus 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 c ..."
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Cited by 98 (15 self)
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The asynchronous picalculus 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 bisimulationbased 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 callbyname lambdacalculus; the validity of some laws for Join.
The Update Calculus
, 1997
"... In the update calculus concurrent processes can perform update actions with side effects, and a scoping operator can be used to control the extent of the update. In this way it incorporates fundamental concepts both from imperative languages or concurrent constraints formalisms, and from functional ..."
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Cited by 83 (3 self)
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In the update calculus concurrent processes can perform update actions with side effects, and a scoping operator can be used to control the extent of the update. In this way it incorporates fundamental concepts both from imperative languages or concurrent constraints formalisms, and from functional formalisms such as the  and calculi. Structurally it is similar to but simpler than the calculus; it has only one binding operator and a symmetry between input and output. We define the structured operational semantics and the proper bisimulation equivalence and congruence, and give a complete axiomatization. The calculus turns out to be an asymmetric subcalculus. 1 Introduction Theory of concurrent computation is a diverse field where many different approaches have been proposed and no consensus has emerged on the best paradigms. In this paper we take a step towards unifying two seemingly contradictory schools of thought: global vs local effects of concurrent actions. We define a calc...
Solos in concert
 IN ICALP’99, LNCS 1644:513–523
, 1999
"... We present a calculus of mobile processes without prefix or summation, and using two different encodings we show that it can express both action prefix and guarded summation. One encoding gives a strong correspondence but uses a match operator; the other yields a slightly weaker correspondence but u ..."
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Cited by 21 (4 self)
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We present a calculus of mobile processes without prefix or summation, and using two different encodings we show that it can express both action prefix and guarded summation. One encoding gives a strong correspondence but uses a match operator; the other yields a slightly weaker correspondence but uses no additional operators.
Solo Diagrams
 PROCEEDINGS OF TACS 2001
, 2001
"... We address the problems of implementing the
replication operator efficiently in the solos calculusa calculus of
mobile processes without prefix. This calculus is expressive enough to
admit an encoding of the whole fusion calculus and thus the
picalculus.
We show that nested occurrences of replic ..."
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Cited by 20 (2 self)
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We address the problems of implementing the
replication operator efficiently in the solos calculusa calculus of
mobile processes without prefix. This calculus is expressive enough to
admit an encoding of the whole fusion calculus and thus the
picalculus.
We show that nested occurrences of replication can be avoided, that
the size of replicated terms can be limited to three particles, and
that the usual unfolding semantics of replication can be replaced by
three simple reduction rules. To illustrate the results and show how
the calculus can be efficiently implemented we present a graphic
representation of agents in the solos calculus, adapting ideas from
interaction diagrams and pinets.
Dfusion: a distinctive fusion calculus
 In Proc. of APLAS04, volume 3302 of LNCS
, 2004
"... Abstract. Fusion calculus is commonly regarded as a generalisation of picalculus. Actually, we prove that there is no uniform fully abstract embedding of picalculus into Fusion. This fact motivates the introduction of a new calculus, DFusion, with two binders, λ and ν. We show that DFusion is str ..."
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Cited by 17 (2 self)
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Abstract. Fusion calculus is commonly regarded as a generalisation of picalculus. Actually, we prove that there is no uniform fully abstract embedding of picalculus into Fusion. This fact motivates the introduction of a new calculus, DFusion, with two binders, λ and ν. We show that DFusion is strictly more expressive than both picalculus and Fusion. The expressiveness gap is further clarified by the existence of a fully abstract encoding of mixed guarded choice into the choicefree fragment of DFusion. 1
Concurrent Constraints in the Fusion Calculus (Extended Abstract)
 In (Larsen et al
, 1998
"... . We use the fusion calculus, a generalization and simplification of the calculus, to model concurrent constraint programming. In particular we encode three basic variants of the aecalculus, which is a foundational calculus for the concurrent constraint programming language Oz. Using a new redu ..."
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Cited by 16 (3 self)
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. We use the fusion calculus, a generalization and simplification of the calculus, to model concurrent constraint programming. In particular we encode three basic variants of the aecalculus, which is a foundational calculus for the concurrent constraint programming language Oz. Using a new reductionbased semantics and weak barbed congruences for the fusion calculus we formally establish an operational correspondence between the aecalculi and their encodings. These barbed congruences are shown to coincide with the hyperequivalences previously adopted for the fusion calculus. 1 Introduction In this paper we use the fusion calculus to model concurrent constraint programming, thereby relating the paradigm of communicating processes to that of concurrent constraints. In the first, parallel agents interact with each other by sending and receiving data over named ports; in the second, agents produce constraints on the values of variables, which are combined to resolve queries abou...
Tau laws for pi calculus
 Theoretical Computer Science
"... The paper investigates the nonsymbolic algebraic semantics of the weak bisimulation congruences on finite pi processes. The weak bisimulation congruences are studied both in the absence and in the presence of the mismatch operator. Some interesting phenomena about the open congruences are revealed. ..."
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Cited by 11 (4 self)
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The paper investigates the nonsymbolic algebraic semantics of the weak bisimulation congruences on finite pi processes. The weak bisimulation congruences are studied both in the absence and in the presence of the mismatch operator. Some interesting phenomena about the open congruences are revealed. Several new tau laws are discovered and their relationship is discussed. The contributions of the paper are mainly as follows: 1. It is proved that Milner’s three tau laws fail to lift a complete system for the strong open congruence to a complete system for the weak open congruence in the absence of both the mismatch operator and the restriction operator. A fourth tau law is proposed to deal with the match operator under the prefix operation. It is shown that for this calculus a complete system for the strong open congruence extended with all the four tau laws is complete for the weak open congruence. 2. It is verified that the four tau laws are also enough for the weak open congruence of the pi calculus without the mismatch operator. Two complete systems are given, one using distinctions and the other using a schematic law for the restriction operator.
The Ground Congruence for Chi Calculus
 Information and Computation
, 1974
"... Chi calculus was proposed as a process calculus that has a uniform treatment of names. Preliminary properties of chi calculus have been examined in literature. In this paper a more systematic study of bisimilarities for chi processes is carried out. The notion of Lbisimilarity is introduced to give ..."
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Cited by 6 (3 self)
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Chi calculus was proposed as a process calculus that has a uniform treatment of names. Preliminary properties of chi calculus have been examined in literature. In this paper a more systematic study of bisimilarities for chi processes is carried out. The notion of Lbisimilarity is introduced to give a possible classification of bisimilarities on chi processes. It is shown that the set of Lbisimilarities form a four element lattice and that wellknown bisimilarities for chi processes fit into the lattice hierarchy. The four distinct Lbisimilarities give rise to four congruence relations. Complete axiomatization system is given for each of the four congruences.
Locality and Polyadicity in Asynchronous NamePassing Calculi
 LNCS 1784 (2000
, 2000
"... We give a divergencefree encoding of polyadic Local π into its monadic variant. Local π is a subcalculus of asynchronous πcalculus where the recipients of a channel are local to the process that has created the channel. We prove the encoding fullyabstract with respect to bar ..."
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Cited by 5 (1 self)
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We give a divergencefree encoding of polyadic Local &pi; into its monadic variant. Local &pi; is a subcalculus of asynchronous &pi;calculus where the recipients of a channel are local to the process that has created the channel. We prove the encoding fullyabstract with respect to barbed congruence. This implies that in Local &pi; (i) polyadicity does not add extra expressive power, and (ii) when studying the theory of polyadic Local &pi; we can focus on the simpler monadic variant. Then, we show how the idea of our encoding can be adapted to namepassing calculi with nonbinding input prefix, such as Chi, Fusion and &pi;F calculi .