B. Victor. The Fusion Calculus: Expressiveness and Symmetry in Mobile Processes. PhD thesis, Department of Computer Systems, Uppsala University, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....xy. Here, triggers t 1 , t 2 , t 3 guard each input and output command, and also transport the entire environment to every continuation. An encoded term could then be executed directly on the distributed channel machine. The second encoding is based upon the fusion calculus of Parrow and Victor [12], a calculus in which the input command u#y.P is not binding. The encoding [10] uses the sub calculus with only solos u x and u x. It uses the reaction relation (#z) u u#y R) R# where every equivalence class generated by x = y has exactly one element not z, and the ....

....prototype implementation by Wischik [19] and in projects by students at the University of Bologna. With respect to the close correspondence with pilike calculi, we have proved abstraction results which are stronger than those obtained for other implementations. On the contrary, the fusion calculus [12] and the solos calculus [10] are awkward to implement in the fusion machine, even though they are closely related to the explicit fusion calculus. This is because they only allow reaction after a global search for restricted names. We are currently working on a full distributed implementation for ....

J. Parrow and B. Victor. The fusion calculus: Expressiveness and symmetry in mobile processes. In LICS'98, pages 176--185. IEEE, Computer Society Press.

....becomes more symmetrical: symmetric action calculi have a discrete monoid comonoid structure. This means that they are also compact closed (see Chapter 2) and therefore more similar in structure to interaction categories than the standard action calculi. There is an analogy to the fusion calculus [PV98], which tries to resolve the asymmetry between input and output actions in the p calculus. 3.3 A Categorical Type System for CCS like Languages 3.3.1 Motivation We would like to define a category of processes in a language like CCS, along the lines of the models in the previous section: types ....

....of CCS, without restriction. From this process algebra we build a symmetric monoidal co fibration, as required in the construction of Proc. We then extend the process algebra CCS by adding constructors for restriction, and for identification of names, similar to fusions in the fusion calculus [PV98], to obtain a process algebra which we call FCCS. From this latter process algebra, we will then construct a syntactic category, and show that it has the same categorical structure as Proc. We provide translations between the syntactic category, and the instance of Proc, and show that they yield ....

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Joachim Parrow and Bjrn Victor. The fusion calculus: Expressiveness and symmetry in mobile processes. In Proc. LICS, 1998.

....that only one process holds a read capability of a logical variable [46] in which case ask can destroy a message it has received, as will be discussed in detail in this paper. One feature of constraint based concurrency included into name based concurrency only recently by the Fusion calculus [48] is that two channels can be fused into a single channel. 2.4 Locality in Global Store The notion of shared, global store provided by CCP must be understood with care. Unlike conventional shared memory multiprocessing, constraint store of CCP is highly structured and localized. All channels in ....

....escape through Y. Rather, we want to allocate and garbage collect them locally and let Y emit an integer constant. 9 Related Work Relating the family of # calculi and the CCP formalism has been done as proposals of calculi such as the # calculus [33] the # calculus [24] and the Fusion calculus [48], all of which incorporate constraints (or name equation) in some form. The # calculus is unique in that it uses procedures with encapsulated states to model concurrency and communication rather than the other way around. The # calculus introduces constraints into name based concurrency, while ....

Victor, B., The Fusion Calculus: Expressiveness and Symmetry in Mobile Processes, PhD Thesis, Uppsala Univ., 1998.

....its process algebraic formulation. Two of its innovations are adopted in the present work; the unconstrained connectivity of the kind mentioned above, and the explicit fusions here called aliases and coaliases of Gardner and Wischik [11] developed from the fusion calculus of Parrow and Victor [25]. These authors are further developing a calculus of fusion graphs. 3) It may be argued that to allow arcs to link nodes which are distant cousins, i.e. enclosed within distinct parent nodes arbitrarily far apart in the nesting structure, is contrary to reality. But we wish to model not only the ....

....controls are again atomic. In the first and third rules the reactum has a link which makes an alias for . Such an alias is essentially an explicit fusion in the sense of Gardner and Wischik [11] their calculus of explicit fusions was developed from the fusion calculus of Parrow and Victor [25] and from action calculi [22] and has guided the present development. The reactum in the second rule, and the redex in the third rule, both illustrate the use of a closed (i.e. unnamed) edge respectively between the = A B B nodes and between the C D BFEHG I DFJ BFEKG AI ....

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Parrow, J. and Victor, B. (1998), The fusion calculus: expressiveness and symmetry in mobile processes. Proc. LICS'98, IEEE Computer Society Press.

....to u, and w(z) P deployed to w. The result is that the large continuations are already placed at their correct locations; all that is needed is a small message to trigger them. Technically, we have shown elsewhere [2] how the triggers can be encoded in a version of the pi calculus with fusions [3, 7]. A fusion makes two channels become equivalent, in the sense that a message sent to either will have the same effect) Our machine therefore implements this fusion version of the calculus, rather than the pure pi calculus, and we leave pre deployment as a compiletime optimisation. Note that in ....

J. Parrow and B. Victor. The fusion calculus: Expressiveness and symmetry in mobile processes. In LICS'98, pages 176--185. Computer Society Press.

....We start by brie y recalling the fusion calculus, then we de ne an inductive translation of fusion processes into terms and eventually we prove that the translation preserves transitions. We report here the reduction semantics for the recursion free fragment of the guarded fusion calculus from [14] whose syntax in BNF like style is P : 0 j :P 0 :Q j P 1 jP 2 j (x)P with ; 0 being either u x for the input or u x for the output. Note that the objects x of input actions are not bound by the input pre x in the process pre xed as instead happens in the calculus [7] The only ....

.... The structural congruence in the rule Str is the smallest congruence on processes satisfying: F ; 0) and (F ; j = 0) are commutative monoids; z)0 0, x) y)P (y) x)P , x) P Q) x)P (x)Q; x)P jQ (x) P jQ) if x 62 fn(Q) Finally note that fusion pre xes as f y = xg:P [14] can be viewed as derived forms for processes as (u) u x:0ju y:P ) with u a fresh name. We start with a function [ that maps fusion processes into terms. De nition 7. Let [ F T be de ned by structural induction as [ 0] 0 [ x u:P ] x u:P ] x u) P ] P jQ] ....

Bjorn Victor. The Fusion Calculus: Expressiveness and Symmetry in Mobile Processes. PhD thesis, Dept. of Computer Science, Uppsala University, 1998.

....functions and arguments is lost. Indeed a computation is possible when two objects interact and evolve generating other interaction or modifying their environments via substitutions. We also address the issue of encoding concurrent computations by showing as an example how the fusion calculus [9] (and hence [7] 10] and [8] calculi) can be expressed in our formalism. Finally we propose an encoding of proof nets in the calculus and we introduce the question of typing in relation with linear logic. The paper is organized as follows. In the next section we introduce the basic ....

....X;B [ x]fj ( u]fj u ta ; a jg x ) v]fj v tb ; b jg x ) jg X;A u B Table 3. Additive fragment. 5 Concurrency In this section we show how concurrent computations are included into calculus computations by providing an encoding of the fusion calculus [9] into our calculus. We start by brie y recalling the fusion calculus, then we de ne an inductive translation of fusion processes into terms and eventually we prove that the translation preserves transitions. We report here the reduction semantics for the recursion free fragment of the guarded ....

Joachim Parrow and Bjorn Victor. The fusion calculus: Expressiveness and symmetry in mobile processes. In Proceedings of LICS '98, pages 176-185. IEEE, Computer Society Press, June 1998.

....final graph of the rewriting by merging the corresponding nodes. As is done in calculus, we allow to merge new nodes with other nodes (new or old) Merging among already existing nodes is not allowed. Relaxing this constraint, would permit fusions of nodes in the style of the fusion calculus [7]. Instead, in [2] we consider a syntactic restriction of our formalisms in which we allow merging new nodes only, in the style of the I calculus [6] These policies of which nodes are shared are independent of the synchronization mechanisms applied. To formalize synchronized rewriting we use, as ....

Victor, B. The Fusion Calculus: Expressiveness and Symmetry in Mobile Processes. PhD thesis, Uppsala University, 1998.

....Q = xy: xy:0. Only one transition is incident out of the abstract state corresponding to Q, while two of them are incident out of the abstract state for P , one for the case y = x and one for all the remaining values of y. Symmetric handling of input and output is a goal of the fusion calculus [26]. Notice that the states of the nal model in Coalg form a algebra. So, in particular, a support supp(X) is de ned for each of these states. The support of a calculus agent in lts de nes the free names of the agent; the support of the corresponding state in the nal model, instead, de ne ....

J. Parrow and B. Victor. The fusion calculus: Expressiveness and symmetry in mobile processes. In Proc. LICS'98, IEEE. Computer Society Press, 1998.

....: A1 #A2 (Seal Algo) # ## x : Id A # ## P : A # # ## x [P ] A # # A 4 This is due to the specificity of the receive action: when a seal is received it is activated at the same level as the process that received it. The movement actions look like interactions in the Fusion Calculus [14]. 4.4 Properties The typing algorithm defined above is sound and complete with respect to the type system. Theorem 1 (Soundness and completeness) 1. If # ## P : A then # ## P : A. 2. If # ## P : A then #A # such that A # # A and # ## P : A # . A corollary of this theorem is the ....

J. Parrow and B. Victor. The Fusion Calculus: Expressiveness and symmetry in mobile processes. In Logic in Computer Science. IEEE Computer Society Press, 1998.

....a aussi ete proposee dans [38] o u la composition resulte de ce que Honda appelle une substitution ouverte . Independamment, Parrow et Victor developperent le calcul Fusion [65] comme une evolution polyadique de leur calcul Update [64] La theorie du calcul Fusion fut etudiee en detail dans [87]. Le calcul Chi, independamment introduit par Fu [28] peut etre vu comme une variante monadique du calcul Fusion. Les objets mobiles sous forme de processus mobiles Le travail le plus proche du n otre est [42] dans lequel une interpretation en calcul type du Calcul des Objets Imperatif d Abadi ....

....way has been proposed in [38] where the composition results in what Honda calls an open substitution . Independently, Parrow and Victor have developed the Fusion calculus [65] as a polyadic evolution of their Update calculus [64] The theory of Fusion calculus has been studied in detail in [87]. The Chi calculus, independently introduced by Fu [28] can be seen as a monadic variant of the Fusion calculus. Mobile objects as mobile processes The work closest to our is [42] where an interpretation of Abadi and Cardelli s Imperative Object Calculus into typed calculus is 1.5. OUTLINE OF ....

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Bj orn Victor. The Fusion Calculus: Expressiveness and Symmetry in Mobile Processes. PhD thesis, Dept. of Computer Systems, Uppsala University, Sweden, June 1998. Available from http://www.docs.uu.se/ victor/thesis.shtml.

.... a concrete instance of the model from a CCS like process algebra without restriction, and gave an alternative construction of the category as a syntactic category based on the same process algebra extended by restriction and global fusions, similar to a CCS version of the fusion calculi in [PV98] and [GW00] Translations between the instance of the abstract model and the syntactic category were given, establishing an isomorphism between the categories. We presented a process calculus with a transition semantics and observational equivalence based on bisimulation, and showed that it had ....

Joachim Parrow and Bjrn Victor. The fusion calculus: Expressiveness and symmetry in mobile processes. In Proc. LICS, 1998.

....[10] Theorem 1 P J P 0 , P ] J ffi [ P 0 ] J Proof. Appendix A. 3.2. Semantics of the Fusion calculus To probe further on the expressive power of Spots, we consider a calculus with asynchronous composition and synchronous communications, the solos variant [15] of theFusion calculus [23]. In the Fusion calculus, a process P consists of input and output messages x(u) and x(u) asynchronous composition P j P 0 , restriction (v)P , replication P and the guard [u = u 0 ]P of a process P by an equation u = u 0 . P : 0 j x(u) j x(u) j P j P 0 j (v)P j P j [u = u 0 ]P ....

J. Parrow, B. Victor. The Fusion calculus: expressiveness and symmetry in mobile computing. In Symposium on Logic in Computer Science. Ieee Press, 1998.

....P v quantifies to only those elements that are equal to t. This feature cannot be expressed if quantification is combined with action prefixing. Hence, our method does not directly apply to languages with input prefixing, such as the # calculus. In this respect, we mention the fusion calculus of Parrow and Victor (1998), an extension of the # calculus in which action prefixing is separated from quantification. We conjecture that it can be provided with an algebraic semantics in a similar fashion. Acknowledgements The author thanks Vincent van Oostrom and Piet Rodenburg for carefully reading earlier versions of ....

Parrow, J. and Victor, B. (1998). The fusion calculus: Expressiveness and symmetry in mobile processes. In Proceedings of LICS'98 , pages 176--185. IEEE Computer Society Press.

....becomes more symmetrical: symmetric action calculi have a discrete monoid comonoid structure. This means that they are also compact closed (see Chapter 2) and therefore more similar in structure to interaction categories than the standard action calculi. There is an analogy to the fusion calculus [PV98], which tries to resolve the asymmetry between input and output actions in the pi calculus, 3.3 A Categorical Type System for CCS like Languages 3.3.1 Motivation We would like to formalize a model for processes with type information, as presented graphically in the introduction to this chapter. ....

....of CCS, without restriction. From this process algebra we build a symmetric monoidal co fibration, as required in the construction of Proc. We then extend the process algebra CCS by adding constructors for restriction, and for identification of names, similar to fusions in the fusion calculus [PV98], to obtain a process algebra which we call FCCS. From this latter process algebra, we will then construct a syntactic category, and show that it has the same categorical structure as Proc. We provide translations between the syntactic category, and the instance of Proc, and show that they yield ....

[Article contains additional citation context not shown here]

Joachim Parrow and Bjrn Victor. The fusion calculus: Expressiveness and symmetry in mobile processes. In Proc. LICS, 1998.

....School of Computer Science McGill University Montreal, Quebec, Canada Introduction The Fusion Calculus is a foundational calculus for concurrency, particularly a calculus for mobile processes. It is introduced as a [ significant step towards a canonical calculus of concurrency . [V98] In the framework of concurrent systems we refer to mobility as the dynamic change of the communication interactions between processes. That is, the structure of the communications network of processes evolves during execution as opposed to being statically determined. The means of communication ....

....output operations are completely symmetric. Another important simplification is that there is only one sensible bisimulation equivalence. The present paper intends to give a brief overview of the fusion calculus. For a more comprehensive treatment, the reader is referred to Victor s Ph.D. thesis [V98] and related papers [VP98] PV98 1] and [PV98 2] Concurrent Constraint Programming As a motivation to the fusion calculus a reminder of the Concurrent Constraint Programming paradigm is presented. In Constraint Programming the central notion is that of a constraint. A constraint can be seen ....

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Victor, B. The Fusion Calculus: Expressiveness and Symmetry in Mobile Processes. Ph.D. Thesis. Uppsala University. June 1998. URL: http://www.docs.uu.se/~victor/tr/thesis.shtml

....symmetric. Another important simplification is that there is only one sensible bisimulation equivalence. The present paper intends to give a brief overview of the fusion calculus. For a more comprehensive treatment, the reader is referred to Victor s Ph.D. thesis [V98] and related papers [VP98] [PV98 1], and [PV98 2] Concurrent Constraint Programming As a motivation to the fusion calculus a reminder of the Concurrent Constraint Programming paradigm is presented. In Constraint Programming the central notion is that of a constraint. A constraint can be seen as a guard that must be satisfied ....

....direct predecessor of the fusion calculus is the update calculus , developed by Victor and Parrow earlier. It had the same purpose of simplifying and extending the p calculus, but it was monadic (only one object transmitted during communication) and it didn t generalize to polyadic interactions [PV98 1]. A very similar approach called the c calculus was developed by Fu, but it adds more constructs to the p calculus. Sangiorgi developed the pI calculus, that also simplifies the p calculus, by taking a different approach, in which both input and output are symmetric as in fusion, but unlike ....

Parrow, J., Victor, B. The Fusion Calculus: Expressiveness and Symmetry in Mobile Processes (extended abstract). In Proceedings of LICS'98. IEEE, Computer Society Press. June 1998. URL: http://www.docs.uu.se/~victor/tr/fusion.html

....polarities; and there is some relationship between the number of (t 0 ; d) pairs and thvi and d pairs. 7 Conclusions and further work. One of the aims of this project was to find an abstract model of various calculi: including a calculus, the Ambient Calculus [2] and the Fusion Calculus [11]. It was hoped that this new model would give us more expressive power in constructing specifications for calculus programs: we would have the whole of mathematics at our disposal. Also, the mathematician can use informal, but rigorous, powerful and familiar techniques for reasoning in the ....

J. Parrow and B. Victor, The Fusion Calculus: Expressiveness and Symmetry in Mobile Processes. Proceedings of LICS '98, 1998.

....In particular, the model of communication adopted in the applied pi calculus is deliberately classical: communication is through named channels, and value computation is rather separate from communication. Fur ther, active substitutions are reminiscent of the constraints of the fusion calculus [43]. They are especially close to the substitution environments that Boreale et al. employ in their proof techniques for a variant of the spi calculus with a symmetric cryptosystem [12] we incorporate substitutions into processes, systematize them, and generalize from symmetric cryptosystems to ....

Bjorn Victor. The Fusion Calculus: Expressiveness and Symmetry in Mobile Processes. PhD thesis, Dept. of Computer Systems, Uppsala University, Sweden, June 1998.

....respects arity and binding, i.e. E AR : ar H V = ar G E BIND : bind H ( V u) P (bind G u) This implies that P is defined, and hence R undefined, on all binding ports of G. In Section 3 we shall define the composition of edge embeddings, and thereby establish in Theorem 15 a category of edge embeddings. Relying on that result, we now define the category of graph embeddings. Definition 5 (category of graphs and embeddings) The category G Emb s has graphs as objects and graph embeddings as arrows. The composition of arrows is given by def = V V ; E ....

....category of edgings and embeddings. Definition 14 (category of edgings and embeddings) The category E Emb has edgings as objects and edge embeddings as arrows, with composition as defined in Def. 8. Its identity embedding on each edging E = P; edg) is id E : E E def = Id P ; Theorem 15 E Emb is a category. Proof The associativity of composition is proved in Prop. 13, and it is easy to check that = id E = id F for any embedding : E F . 4 Directed edgings and graphs We now define the categories E Emb d of directed edgings and G Emb sd of shallow directed graphs, ....

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Parrow, J. and Victor, B. (1998), The fusion calculus: expressiveness and symmetry in mobile processes. Proc. LICS'98, IEEE Computer Society Press.

....due to the specificity of the receive action: when a seal is received it is activated at the same level as the process that received it. Therefore it would be strange that the scope of its name were bound to the receiving process. The movement actions look like interactions in the Fusion Calculus [11]. 13 4.3 Typing algorithm The type rules in the previous section just need some slight modification to be converted into a type algorithm. As usual in type systems with subtyping, we must eliminate the subsumption rule by embedding subtyping in the other rules. Actually there are only two rules ....

J. Parrow and B. Victor. The Fusion Calculus: Expressiveness and symmetry in mobile processes. In Logic in Computer Science. IEEE Computer Society Press, 1998.

....# There exist many di#erent calculi for rescribing interactive and sequential behaviour. The goal of action calculi [1] is to unify these calculi at a syntactic and operation level. We introduce a symmetric variant which extends the reach of action calculi to cover for example the Fusion calculus [2] and Yoshida s process graphs [3] These symmetric action calculi conservatively extend the reflexive action calculi [4] and have close links to category theory. Background Action calculi and their extensions [4] have constructs for names and nameabstraction in common. The intention is that ....

....calculi have operators for names, co names and restriction (see Figure 2) Conventional action calculi meanwhile combine the last two into a single abstraction operator. In this respect, the move from conventional action calculi to symmetric mirrors that from the # calculus to the Fusion calculus [2]. a) x out C (b) x out C (c) xyout C (#x) x.C) x) x.C) x=y x.C Figure 2: a) Restriction is a primitive operator in symmetric action calculi. Graphically we indicate a restricted (local) name with a line through it. b) Abstraction is composed from two parts: a co name, ....

Parrow and Victor. The fusion calculus: Expressiveness and symmetry in mobile processes. In LICS: IEEE Symposium, 1998.

....to replace abstracted names in the input process; this replacement is represented with a substitution. In contrast a #F reaction is directionless and fuses names; this is recorded with an explicit fusion. The #F calculus is similar in many respects to the fusion calculus of Parrow and Victor [10, 13], and to the chi calculus of Fu [1] These calculi also have a directionless reaction which fuses names. The difference is in how the name fusions have effect. In the fusion calculus, fusions occur implicitly within the reaction relation and their effect is immediate. In the #F calculus, fusions ....

....ljw1004 cam.ac.uk. 1 compositional, in contrast with the analogous embeddings in the # calculus and fusion calculus. We provide a bisimulation congruence for the #F calculus, which is automatically closed with respect to substitution. We compare it with hyper equivalence in the fusion calculus [10] and open bisimulation in the # calculus [12] 2The# F calculus To illustrate the key features of the #F calculus, we contrast it to the fusion calculus. Both calculi have symmetric input and output processes. They have no abstraction operator. Instead, they interpret the # calculus abstraction ....

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J. Parrow and B. Victor. The fusion calculus: expressiveness and symmetry in mobile processes. In LICS. IEEE, Computer Society Press, 1998.

....as to reason about the essential properties of the protocol. 1 Introduction The eld of process calculi has seen major advances in the decades since the introduction of CCS [21] CSP [14] and ACP [5] In particular, with the advent of the calculus [23] and other name passing process calculi [9,15,24,26], it has been found that diverse computational structures in both sequential and concurrent computing are uniformly representable as interacting processes. This enables us to apply standard syntactic reasoning methods developed for process calculi to a wide variety of computational phenomena. ....

Joachim Parrow and Bjorn Victor. The fusion calculus: Expressiveness and symmetry in mobile processes. In Proceedings of LICS'98, 1998.

....define an inductive translation of fusion processes into terms and eventually we prove that the translation preserves transitions. 4 THE CALCULUS AND CONCURRENCY 6 4. 1 The fusion calculus We report here the reduction semantics for the recursion free fragment of the guarded fusion calculus from [15] whose syntax in BNF like style is P : 0 j ff:P ff 0 :Q j P 1 jP 2 j (x)P with ff; ff 0 being either u x for the input or u x for the output. Note that the objects x of input actions are not bound by the input prefix in the process prefixed as instead happens in the calculus [9] The ....

.... The structural congruence j in the rule Str is the smallest congruence on processes satisfying: F ; j ; 0) and (F ; j =j ; 0) are commutative monoids; z)0 j 0, x) y)P j (y) x)P , x) P Q) j (x)P (x)Q; x)P jQ j (x) P jQ) if x 62 fn(Q) Finally note that fusion prefixes as f y = xg:P [15] can be viewed as derived forms for processes as (u) u x:0ju y:P ) with u a fresh name. 4 THE CALCULUS AND CONCURRENCY 7 4.2 Encoding We start with a function [ Gamma] that maps fusion processes into terms. Definition 4.1. Let [ Gamma] F T be defined by structural induction as [ 0] ....

Bjorn Victor. The Fusion Calculus: Expressiveness and Symmetry in Mobile Processes. PhD thesis, Dept. of Computer Science, Uppsala University, 1998.

.... via substitutions of a placeholder (represented by a variable) with something else (a process) We show here that designing systems in a multiset style and equipping them with a simple interaction mechanism is enough to express the computations of the calculus [2] of the fusion calculus [11] (and hence [9] fl [12] and ae [10] calculi) and of the proof nets [7] 2 The basic calculus In this section we introduce our calculus. We first define its syntax and then its operational semantics. Finally, we discuss confluence properties of the calculus. 2.1 Syntax Definition 2.1. Let ....

.... [x]fj [ M 0 ] jg = x)fj x [ N ] M 0 ] jg (x)fj [ M 0 ] N ] x] jg [ M 0 ] N ] x] M 0 [N=x] 2 4 The calculus and concurrency In this section we show how concurrent computations are included into calculus computations by providing an encoding of the fusion calculus [11] into our calculus. We start by briefly recalling the fusion calculus, then we define an inductive translation of fusion processes into terms and eventually we prove that the translation preserves transitions. 4 THE CALCULUS AND CONCURRENCY 6 4.1 The fusion calculus We report here the ....

Joachim Parrow and Bjorn Victor. The fusion calculus: Expressiveness and symmetry in mobile processes. In Proceedings of LICS '98, pages 176--185. IEEE, Computer Society Press, June 1998.

....[10] Theorem 1 P J P 0 , P ] J ffi [ P 0 ] J Proof. Appendix A. 3.2. Semantics of the Fusion calculus To probe further on the expressive power of Spots, we consider a calculus with asynchronous composition and synchronous communications, the solos variant [15] of theFusion calculus [23]. In the Fusion calculus, a process P consists of input and output messages x(u) and x(u) asynchronous composition P j P 0 , restriction (v)P , replication P and the guard [u = u 0 ]P of a process P by an equation u = u 0 . P : 0 j x(u) j x(u) j P j P 0 j (v)P j P j [u = u 0 ]P ....

J. Parrow, B. Victor. The Fusion calculus: expressiveness and symmetry in mobile computing. In Symposium on Logic in Computer Science. Ieee Press, 1998.

....congruence by graph isomorphism. This gives a denotational semantics to at least part of the reduction relation and can be very useful in the design of new process calculi. Especially in fusion calculus and its variants a process calculus where a process may choose to fuse two channel names [PV98] it is not obvious how the structural congruence should look like. Furthermore string based process calculi have to deal with alpha conversion, i.e. the renaming of bound names, which often impedes the analysis of processes. Also interaction is done in a non local way, i.e. parts of a process ....

....to (C) aa] j (B) aa] which requires a non local de nition of a rewriting step. The same problem arises when de ning process calculi where processes are able to fuse two names on their own (another feature of these calculi is the fact that the input pre x is nonbinding) The fusion calculus [PV98] solves the problem by having non local reduction rules. One appropriate solution would be to give a name based notation (with a complete set of equations) for hypergraphs with duplicates in their external nodes and to use the equivalence rules for the structural congruence of the corresponding ....

Joachim Parrow and Bjorn Victor. The fusion calculus: Expressiveness and symmetry in mobile processes. In Proc. of LICS '98, 1998.

....in terms of eOEciency. The notion of normal form appears in the literature through axiomatisations; axiomatisations of nite control processes have been given for example for open bisimulation [San96b] this axiomatisation is used in the Mobility WorkBench) as well as for the fusion calculus [PV98], that is a promising language for the task of the implementation of verication methods. For replicated terms in the general case, EG96] proves decidability for an extended version of structural congruence; in this work, any form of process can be replicated; we have chosen a smaller language to ....

J. Parrow and B. Victor. The fusion calculus: Expressiveness and symmetry in mobile processes. In Proceedings of LICS' 98, 1998. to appear.

....prefixes can be regarded as derived forms since f y = zg : P has exactly the same transitions as (u) u y : 0 j u z : P ) when u 62 fn(P ) In the same way the prefix can be regarded as derived in CCS and in the calculus. For further examples and explanations we refer the reader to [7] and [14]. 2.2 Equivalences From [7] we recall the definition of strong bisimulation in the fusion calculus. Definition 5. A substitution oe agrees with the fusion if 8x; y : x y , oe(x) oe(y) A substitutive effect of a fusion is a substitution oe agreeing with such that 8x; y : oe(x) y ) x ....

....any relevant substitutions at any time, and show that if two agents are equivalent in that context, which they must be if they are congruent, then they are also weakly hyperequivalent. The context used is the same as in [7] Due to space limitations, we refer to the first author s PhD thesis [14] for the full proof. 3 The Barbed Congruences We shall here provide a reduction semantics for the fusion calculus and prove that it in a precise way corresponds to the transition semantics. This lends credibility to our transition laws and equivalence definitions. A reduction semantics is also ....

B. Victor. The Fusion Calculus: Expressiveness and Symmetry in Mobile Processes. PhD thesis, Dept. of Computer Systems, Uppsala University, Sweden, June 1998. URL: http://www.docs.uu.se/~victor/thesis.shtml.

....cases, the major obstacle has been expressing logical variables, which can be updated from several processes and not only at their binding occurrence. The variables are modelled by separate processes which can be read, updated etc. by sending requests and receiving responses. In a previous paper [7] we show how the calculus can be simplified into the fusion calculus while at the same time extending its expressiveness. The heart of the fusion calculus is the fusion action, which in interplay with the scope operator can express changes to names shared between several processes in the system. ....

....The semantics of the ae calculus is given in [6] using reduction rules and a structural congruence resulting in an unlabelled transition system. Term rewriting systems such as the calculus also have reduction semantics. The semantics of the fusion calculus, on the other hand, is given in [7] using rules for labelled transitions (and a similar structural congruence) as traditionally has been done for process calculi such as CCS or the calculus. To relate the calculi we give a reduction semantics for the fusion calculus. The behaviour of an agent must then be considered together with ....

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J. Parrow and B. Victor. The fusion calculus: Expressiveness and symmetry in mobile processes. In Proceedings of LICS'98. IEEE, Computer Society Press, June 1998. URL: http://www.docs.uu.se/~victor/tr/fusion.html.

....much of it is really necessary in order to attain the expressive power. This has led to several interesting and expressive subcalculi. For example, in the more easily implemented asynchronous subcalculus [2, 8] the output pre x u v : P is replaced by the output particle u v. In the fusion calculus [19] the reduction of an input and output results in a fusion of names rather than a substitution. In that calculus both input and output pre x can be replaced by their corresponding particles, in other words, there is no need for explicit representation of temporal precedence. These particles are ....

....P P 0 Side conditions in the rst rule: jexj = jeyj; agrees with fex = e yg; ran( e z = and dom( e z: Fig. 4. Reduction rules for the calculus of solos. set. The free names in P , denoted fn(P ) are the names in P with a non bound occurrence. The (choice free) fusion calculus [19] consists of the above agents and those formed using the pre x operator, namely agents of the form : P . Operational semantics. We begin by de ning a structural congruence which equates all agents we will never want to distinguish for any semantic reason, and then use this when giving the ....

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J. Parrow and B. Victor. The fusion calculus: Expressiveness and symmetry in mobile processes. In Proc. of LICS '98, pages 176-185. IEEE, Computer Society Press, July 1998.

....x is said to be bound in (x)P . We write (ex)P for (x 1 ) x n )P , n 0, and often Q i2I P i for the composition of all P i for i 2 I , where I is a nite set. The free names in P , denoted fn(P ) are the names in P with a non bound occurrence. The ( nite, choice free) fusion calculus [16] consists of the above agents and the pre x operator, namely agents of the form : P . Operational semantics. In the style of the Chemical Abstract Machine [2] we begin by de ning a structural congruence which equates all agents we will never want to distinguish for any semantic reason, and ....

....equivalence if 8x; y : x y , x) y) We say that two names are fused by a reduction if they are made equal by the resulting substitution. The side condition of Figure 3 bans reductions that fuse two di erent free names. For instance, the agent x y j x z is irreducible. See section 7 and [16] for alternative semantics allowing such reductions. Equivalence. To de ne an extensional semantics, we use the standard notion of barbed bisimulation developed in [13, 17] De nition 3. The observation relation is the least relation satisfying the rules below. x e y # x (P j Q) # x if P # x or ....

[Article contains additional citation context not shown here]

J. Parrow and B. Victor. The fusion calculus: Expressiveness and symmetry in mobile processes. In Proceedings of LICS '98, pages 176-185. IEEE, Computer Society Press, July 1998.

....axiomatizations in two versions, with and without the mismatch operator. Finally in Section 5 we demonstrate how the strong lazy reduction strategy in the calculus has a straightforward encoding. The proofs are presented in the full version of this paper [12] and in the second author s PhD thesis [19]. 2 Syntax and Semantics We assume an infinite set N of names ranged over by u; v; z. Like in the calculus, names represent communication ports, which are also the values transmitted. We write x for a (possibly empty) finite sequence x 1 Delta Delta Delta xn of names. ranges over ....

B. Victor. The Fusion Calculus: Expressiveness and Symmetry in Mobile Processes. PhD thesis, Dept. of Computer Systems, Uppsala University, Sweden, June 1998. URL: http://www.docs.uu.se/~victor/ thesis.shtml.

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B. Victor. The Fusion Calculus: Expressiveness and Symmetry in Mobile Processes. PhD thesis, Department of Computer Systems, Uppsala University, 1998.

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J. Parrow and B. Victor. The Fusion Calculus: Expressiveness and Symmetry in Mobile Processes. In Proc. of LICS'98. IEEE Computer Society Press, 1998.

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Parrow, J. and Victor, B. (1998), The fusion calculus: expressiveness and symmetry in mobile processes. Proc. LICS'98, IEEE Computer Society Press.

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B. Victor. The Fusion Calculus: Expressiveness and Symmetry in Mobile Processes. PhD thesis, Department of Computer Systems, Uppsala University, 1998.

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Parrow, J. and Victor, B. (1998), The fusion calculus: expressiveness and symmetry in mobile processes. Proc. LICS'98, IEEE Computer Society Press.

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J. Parrow and B. Victor. The fusion calculus: Expressiveness and symmetry in mobile processes. In Thirteenth Annual Symposium on Logic in Computer Science (LICS 1998), pages 176--185. IEEE, IEEE Computer Society, 1998.

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Joachim Parrow and Bjorn Victor. The fusion calculus: Expressiveness and symmetry in mobile processes. In Proceedings of LICS'98, 1998. 25

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Parrow, J. and Victor, B. (1998), The fusion calculus: expressiveness and symmetry in mobile processes. Proc. LICS'98, IEEE Computer Society Press.

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J. Parrow and B. Victor. The fusion calculus: Expressiveness and symmetry in mobile processes. In Proc. LICS'98, IEEE Computer Society Press, 1998.

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Bjorn Victor. The Fusion Calculus: Expressiveness and Symmetry in Mobile Processes. PhD thesis, Dept. of Computer Systems, Uppsala University, Sweden, June 1998.

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Joachim Parrow and Bjorn Victor. The Fusion Calculus: Expressiveness and symmetry in mobile processes. In Proceedings of LICS '98 [IEE98], pages 176{ 185.

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B. Victor. The Fusion Calculus : Expressiveness and Symmetry in Mobile Processes, Phd Dissertation, Department of Computer Science, Uppsala University, June 1998.

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J. Parrow and B. Victor. The Fusion Calculus: Expressiveness and Symmetry in Mobile Processes(extended abstract), Poceedings of the LICS'98, 21-24 June 1998, Indianapolis.

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Joachim Parrow and Bjorn Victor. The fusion calculus: Expressiveness and symmetry in mobile processes. In Proceedings of LICS '98, 1998.

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Joachim Parrow and Bjorn Victor. The fusion calculus: Expressiveness and symmetry in mobile processes. In Proceedings of LICS'98. IEEE, June 1998.

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Parrow, J. and Victor, B. (1998) The fusion calculus: expressiveness and symmetry in mobile processes. In Proc. 13th Ann. IEEE Symp. Logic in Computer Science.

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