B. Thomsen, Plain CHOCS: A second generation calculus for higher order processes, Acta Informatica 30 (1) (1993) 1--59.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....primitive calculi of concurrency. We conclude the paper by discussing the related calculi and future works (Section 8) 1.5 Remarks No knowledge is assumed of CBS or any other process calculus. The formal development in this paper is selfcontained. For readers familiar with CCS [11] CHOCS [18] and CBS: Roughly, HOBS is to CBS what CHOCS is to CCS. The extended version of the paper (available online [14] gives details of all de nitions, proofs and some additional results. 2. SYNTAX AND SEMANTICS HOBS has eleven process constructs, formally de ned in the next subsection. Their ....

....following notion of message extension for convenience. Definition 1 (Message Extension) Let R P P be a relation on process terms. Its message extension R M M is de ned by the following rules R TauExt p R q p R q MsgExt Thomsen s notion of applicative higher order simulation [18] is suitable for strong simulation in HOBS, because we have to take the non grounded (higher order) nature of the messages into account. Definition 2 (Applicative Simulation) A relation R P P on closed process terms is a (strong, higher order) applicative simulation, written S(R) when ....

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Bent Thomsen. Plain CHOCS: A second generation calculus for higher order processes. Acta Informatica, 30(1):1-59, January 1993.

....an arrow in Prof I that maps the late interpretation onto the early one. This chapter is based on a joint paper with Ian Stark and Glynn Winskel [25] that appeared in the proceedings of CTCS 97. Chapter 8 shows the state of our knowledge as far as the modelling of higher order process calculi [130, 116, 118] with presheaves is concerned and is part of ongoing research. A denotational model for a linear higher order process language over a fixed set of channels is deducible from the work of the previous chapters. It comes equipped with a notion of bisimulation and a proof that bisimulation is a ....

....tie together the wide selection of customised # calculi proposed in recent years. As we have already mentioned we do not have a general function space in Prof I . Where it does exist we are no longer be constrained to passing just names or other ground values. Process passing systems like CHOCS [130] or even the full higher order # calculus of [116] could then fit into our framework. The di#culties here lie not just in writing plausible equations, but also in extracting their operational content to see if the semantics and bisimilarities that arise fit any existing scheme as we shall see in ....

Bent Thomsen. Plain CHOCS: A second generation calculus for higher order processes. Acta Informatica, 30(1):1--59, 1993.

....We show that the induced equivalence is a congruence using Howe s method [8] This method is becoming standard, but its application is nonetheless a sizeable task. It is worth noting here that this same approach may not have been possible if HOBS had channel names (See for example CHOCS [15]) Second, and more importantly, finding a reasonable set of constructs for controlling broadcast has proven to be a substantial challenge. The design of primitive calculi for broadcasting is largely uncharted territory, and thus many (and varied) intermediate proposals had to be considered. Also, ....

....calculi of concurrency. We conclude the paper by discussing the related calculi and future works (Section 7) 1.2 Remarks No knowledge is assumed of CBS or any other process calculus; the formal development in this paper is self contained. A side comment for readers familiar with CCS [9] CHOCS [15] and CBS: Roughly, HOBS is to CBS what CHOCS is to CCS. A key over simplification in this analogy, however, is that HOBS has a fundamentally di#erent and novel encapsulation mechanism than CBS. 2 HOBS: Higher Order Broadcasting Systems HOBS has eight process constructors, formally defined in ....

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Bent Thomsen. Plain CHOCS: A second generation calculus for higher order processes. Acta Informatica, 30(1):1--59, January 1993.

....calculi of concurrency. We conclude the paper by discussing the related calculi and future works (Section 7) 1.5 Remarks No knowledge is assumed of CBS or any other process calculus; the formal development in this paper is self contained. A side comment for readers familiar with CCS [9] CHOCS [15] and CBS: Roughly, HOBS is to CBS what CHOCS is to CCS. An extended version of the paper available online [11] gives details of all definitions, proofs and further development. 2 Syntax and Semantics HOBS has eight process constructors, formally defined in the next subsection. Their informal ....

.... Gamma p 0 2 p1 x p2 Gamma p 0 1 x p 0 2 Feed f q Gamma f q g1 p 2 Gamma p 0 1 g1 p2 Gamma p 0 1 f1 Gamma p 0 1 f1 p2 Gamma p 0 1 p2 Fig. 2. Semantics 7 Adaptation of Thomsen s definition of applicative higher order simulation [15] seems as a most suitable notion of strong simulation for HOBS. There are two reasons for this: first, simulation in a higher order calculus has to account for structure of messages; second, HOBS can be viewed as an extension of the lazy calculus [1] in which applicative bisimulation is widely ....

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Bent Thomsen. Plain CHOCS: A second generation calculus for higher order processes. Acta Informatica, 30(1):1--59, January 1993.

....calculi of concurrency. We conclude the paper by discussing the related calculi and future works (Section 7) 1.5 Remarks No knowledge is assumed of CBS or any other process calculus; the formal development in this paper is self contained. A side comment for readers familiar with CCS [9] CHOCS [16] and CBS: Roughly, HOBS is to CBS what CHOCS is to CCS. 2 Syntax and Semantics HOBS has eight process constructors, formally defined in the next subsection. Their informal meaning is as follows: 0 is a process that says nothing and ignores everything it hears. 4 x is a variable name. ....

....relations to message relations. Definition 1 (Message Extension) Let R P Theta P be a relation on process terms. Its message extension R M Theta M is defined by the following rules R TauExt p R q p R q MsgExt Adaptation of Thomsen s definition of applicative higher order simulation [16] seems as a most suitable notion of strong simulation for HOBS. There are two reasons for this: first, simulation in a higher order calculus has to account for structure of messages; second, HOBS can be viewed as an extension of the lazy calculus [1] in which applicative bisimulation is widely ....

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Bent Thomsen. Plain CHOCS: A second generation calculus for higher order processes. Acta Informatica, 30(1):1--59, January 1993.

.... of expressions representing three statements executed concurrently by two processors as follows: Machine 2 (P1 Before Q1) P2 Before Q2 ) P3 Before Q3) 6 Note that P Before 0 #= P and P Before ( Q Before R ) #= P Before Q ) Before R, unlike the Before combinators developed in [11, 14, 20, 21]. # (run) # idle.Processor run.idle.Processor ( P1 [b done] b.#0, idle.Q1 # t stat ) b ) P2 Before Q2) P3 Before Q3 ) # (run) # idle.Processor idle.Processor ( P1 [b done] b.#0, idle.Q1 # t stat ) b ) P2 [b done] b.#0, idle.Q2# t stat ) b ) P3 Before ....

....a communication must be executed as soon as it becomes executable. Consequently, if there is a Processor which is ready to send run, a statement waiting run can be executed immediately without unnecessary idling. Indeed our Before seems to be the same as the Before combinators of similar works [11, 14, 20, 21], in which it is used as a sequential composition between two expressions representing statements. However, our combinator is unique in representing the execution time of a statement and processor assignment. The reader may imagine a scenario where more than N processes execute concurrently ....

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Thomsen, B., Plain CHOCS: A Second Generation Calculus for Higher Order Processes, Acta Informatica, Vol.30, No.1, p1-59, 1993.

....in this paper represent a quite limited selection amongmany other altogether useful approaches to formally describe concurrent and mobile systems. Mobility is now a major focus and new formalisms stressing the notions of locality, failure and security continue to be proposed. Plain CHOCS [Thomsen 1993] is an intermediary calculus between calculus and HO in the sense that it enables processes to communicate through fixed channels. Processes are allowed to send other processes, but not names, through the channels. The configuration of processes is static (names are not allowed to be passed in ....

Thomsen, B. (1993), "Plain CHOCS. A Second Generation Calculus for Higher Order Processes," Acta Informatica 30 , 1, 1--59.

....1. Introduction 1.1. Motivation. Process calculi provide the currently best established formalisms to express and study communicating concurrent systems. The archetypal Calculus of Communicating Systems (CCS) Mil89] and its extensions Calculus of Higher Order Communicating Systems (CHOCS) [Tho93], the calculus [Mil91] and Higher Order calculus (HO) San92] form a mature theory of handshake communication over named channels. CCS is a rst order calculus; that is, the communicated data may not be processes or channel names. Precisely these extensions are allowed in CHOCS and the ....

.... R A Theta A as: 2 R ( 2 R (p 1 ; p 2 ) 2 R (p 1 ; p 2 ) 2 R (p 1 ; p 2 ) 2 R (p 1 ; p 2 ) 2 R The following denitions of bisimulation and equivalence respectively are a reformulation of Thomsen s higher order bisimulation and equivalence respectively [Tho93]: Syntax Naturals n 2 N : 0 n 1 Variables x 2 X = A countable set of names Processes p 2 P : 0 x x p p p hx p p pi pjp fflp Messages m 2 M : p Actions a 2 A : m m Syntax indexed by a set of free variables L P L = fp j p 2 P FV (p) Lg A L = f ; p ; p j p 2 P L g ....

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Bent Thomsen. Plain CHOCS: A second generation calculus for higher order processes. Acta Informatica, 30(1):159, January 1993.

....evidence for the usefulness of this approach. However, first order process calculi are limited in the sense that they assume a fixed interconnection structure between the processes involved. Recently, name passing and higher order calculi have been proposed to remedy this obvious deficiency [11, 17]. They allow processes and functions to be communicated, and thus support a powerful abstraction technique which is similar to the one found in higher order programming languages and caters for systems with changing interconnection structure. Not surprisingly, this additional expressive power ....

....processes be extended How should free channel names or variables in transmitted processes be dealt with Should a dynamic or static scoping discipline be adopted Despite these open questions, certain higher order calculi have received continued attention. One of them is Thomsen s Plain CHOCS [17], which features a static treatment of the restriction operator and a bisimulation based semantics. In [2] Amadio and Dam address the lack of specification formalisms for Plain CHOCS and propose a modal logic which extends Hennessy Milner logic and characterizes strong context bisimulation ....

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B. Thomsen. Plain CHOCS --- A Second Generation Calculus for Higher--order Processes. Acta Informatica, (30):1--59, 1993.

....an agent via the channel a; and we typically denote an output transition by p b p 00 Gamma Gamma p 0 , where p 00 is the agent or abstraction sent via a channel b. Examples for communication where only agents are transmitted are CHOCS and Plain CHOCS as they are described in [Tho89] and [Tho93]. Such calculi have an order of two. An example for the general case, where we have an order of , is Sangiorgi s HO as it is described in [San93] and subsequent papers. Because of the waiting aspect, input transitions of the form introduced above give rise to what is called late operational ....

....first order proof techniques become circular if we want to adapt them, where one of the main reasons is that communication in a higher order framework invokes substitution. Sometimes a way out is to consider the smallest congruence containing the equivalence under consideration (see, e.g. [Tho89, Tho93]) For a proof where one deals with all operators simultaneously will usually show that this relation is a strong (higher order or context) bisimulation up to its own transitive closure; by this property, in turn, the transitive closure is a strong bisimulation and the congruence result follows. ....

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B. Thomsen. Plain CHOCS - A second generation calculus for higher order processes. Acta Informatica, 30:1--59, 1993.

....as to languages with higher order features and languages incorporating both functional and concurrent features. Relevant work includes, among others, CML [16] the # calculus [14] the Join Calculus [7] and Facile [5] Languages with Higher Order features have been studied in, for example, 20] [21], 17] 10] 11] and our own [9] Languages combining functional and concurrent features have been studied in, for example, 5] 6] and [9] A significant amount of work has been published also on the # calculus. Semantic treatments of the first order # calculus have been given in [18] 12] ....

B. Thomsen, "Plain Chocs: A Second Generation Calculus for Higher Order Processes", Acta Informatica vol 30, pp 1-59, 1993.

....to obtain models of the calculus and in [2] a very general theory for the construction of such models is developed. In [5] a logic is developed for characterising an extension of the calculus with a parallel operator while in [12, 10] the technique is extended to languages for processes, Chocs [28, 29] and Cml [23] respectively. It should be emphasised that all of these models, including that presented in the present paper, are constructed with may testing in mind and none accommodate the static scoping of channel names. Thus the major challenges are to extend the mathematical framework so that ....

B. Thomsen, "Plain Chocs: A Second Generation Calculus for Higher Order Processes", Acta Informatica vol 30, pp 1-59, 1993.

....by V bimodules [16] Among these, we find Lawvere s generalised metric spaces [18] for V = and Set I bimodules where I is the category of finite cardinals and injections. The latter is a promising setting for working out a theory of presheaf models for higher order process calculi [27, 34] with features of local name creation and name passing as in the calculus. Aiming at a general treatment of higher order concurrent process calculi, a clear next step is to extend the intensional relations of Section 7.2 to include a treatment of the intuitionistic function space ( Gamma ) ....

B. Thomsen. Plain CHOCS: A second generation calculus for higher order processes. Acta Inform., 30(1):1--59, 1993.

....to a parallel computer with N processors. We demonstrate a derivation of expressions representing three statements executed concurrently by two processors as follows: 6 Note that P Before 0 6= P and P Before ( Q Before R ) 6= P Before Q ) Before R, unlike the Before combinators developed in [11, 14, 20, 21]. Machine 2 j(P1 Before Q1 )j (P2 Before Q2 )j(P3 Before Q3 ) run) 0 idle:Processor jrun:idle:Processorj ( P1 [b=done]jb:h0; idle:Q1 i t stat ) n fbg)j (P2 Before Q2)j(P3 Before Q3) run) 0 idle:Processor jidle:Processorj ( P 1 [b=done]jb:h0; idle:Q 1 i t stat ) n fbg)j ( P2 ....

....communication must be executed as soon as it becomes executable. Consequently, if there is a Processor which is ready to send run, a statement waiting run can be executed immediately without unnecessary idling. ffl Indeed our Before seems to be the same as the Before combinators of similar works [11, 14, 20, 21], in which it is used as a sequential composition between two expressions representing statements. However, our combinator is unique in representing the execution time of a statement and processor assignment. ffl The reader may imagine a scenario where more than N processes execute concurrently ....

[Article contains additional citation context not shown here]

Thomsen, B., Plain CHOCS: A Second Generation Calculus for Higher Order Processes, Acta Informatica,

....to obtain models of the calculus and in [2] a very general theory for the construction of such models is developed. In [5] a logic is developed for characterising an extension of the calculus with a parallel operator while in [12, 10] the technique is extended to languages for processes, Chocs [28, 29] and Cml [23] respectively. It should be emphasised that all of these models, including that presented in the present paper, are constructed with may testing in mind and none accommodate the static scoping of channel names. Thus the major challenges are to extend the mathematical framework so ....

B. Thomsen, "Plain Chocs: A Second Generation Calculus for Higher Order Processes", Acta Informatica vol 30, pp 1-59, 1993.

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B. Thomsen, Plain CHOCS: A second generation calculus for higher order processes, Acta Informatica 30 (1) (1993) 1--59.

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Bent Thomsen. Plain CHOCS: A second generation calculus for higher order processes. Acta Informatica, 30(1):1--59, 1993.

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Thomsen, B., Plain CHOCS: A second generation calculus for higher order processes, Acta Informatica 30 (1993), pp. 1--59.

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Bent Thomsen. Plain CHOCS: A second generation calculus for higher order processes. Acta Informatica, 30(1):1--59, January 1993.

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Bent Thomsen. Plain CHOCS: A second generation calculus for higher order processes. Acta Informatica, 30(1):1--59, January 1993.

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B. Thomsen. Plain CHOCS: A second generation calculus for higher order processes. Acta Informatica, 1993. 6

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Bent Thomsen. Plain CHOCS: A Second Generation Calculus for Higher Order Processes. Acta Informatica, 30(1):1-59, 1993.

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Bent Thomsen. Plain CHOCS: A Second Generation Calculus for Higher Order Processes. Acta Informatica, 30(1):1-59, 1993.

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Thomsen, B., Plain CHOCS: A Second Generation Calculus for Higher Order Processes, Acta Informatica, Vol.30, No.1, p1-59, 1993.

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Thomsen, B. 1993. Plain CHOCS - A second generation calculus for higher order processes.

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