R. Milner. The polyadic pi-calculus: a tutorial. Technical Report ECS-LFCS-91180, University of Endinburgh, 1991.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....The primitives of the if calculus are logic variables and names (which has been previously described) procedural abstractions, and cells. Cells provide an expressions of state that is fully compatible with concurrency and constraints. The if calculus is closely related to the r calculus ([8, 9, 10]) as described by Schulte in [7] The if calculus can be extended in various ways, for example with primitives providing for constraint based problem solving in the style of logic programming, and with primitives that allow for lazy evaluation and embedding of both the eager and the lazy ....

R. Milner. The polyadic pi-calculus: a tutorial, 1991.

....of their communication topology. LEDA does not support connectors. Dynamic architectures are created by using static, reconfigurable (condition based) and multiple (arrays of instances) attachments in the composed components. As a basis of a dynamic reconfiguration support LEDA uses calculus [39], a formalism related to CCS [38] targeting mobility and dynamic communication. Each component and role (similar to an interface in SOFA) is described as a calculus process, where all roles of a component form the interface (observable black box behavior) of the component. Based on the ....

R. Milner, "The Polyadic pi-Calculus: A Tutorial," in Logic and Algebra of Specification, F. L. Hamer, W. Brauer and H. Schwichtenberg (eds.), Springer-Verlag 1993.

....the #L channel, one has to use the corresponding bindings of the returned form. Similarly, the function concat(F) G) implements the polymorphic extension of the form F by G. Finally, constants like numbers or strings can be represented in the pure #L calculus using the scheme presented by Milner [Mil91] or Turner [Tur96] for the # calculus. Therefore, adding constant values to the PICCOLA language does not change the underlying semantics. However, if constant values are available, then calculations involving such values are more efficient. 1.4.2 Implementation of PICCOLA We have implemented ....

Robin Milner. The polyadic Pi-calculus: a tutorial. Technical Report ECS-LFCS-91-180, Computer Science Department, University of Edinburgh, UK, October 1991.

....recognise each others use of the word. The work in this paper may partly be seen as a comparison of notions of process from the first two of these, since in presenting a translation from the re calculus to MONSTR, both areas may be brought into contact. The re calculus [Milner et ah (1992) Milner (1993a)] arose as a generalisation of CCS [Milner (1989) to allow networks of processes to evolve dynamically. It is thus a process algebra language. MONSTR by contrast is a generalised term graph rewriting language that was used as the intermediate language for the Flagship machine. See [Banach et al. ....

....the reader is refered to [Banach (1993a) for a fuller discussion. 349 THE PI CALCULUS The re calculus first appeared in [Milner et al. 1992) and since that time has been seen in a number of minor variants. We will fix on a version of the monadic calculus, as presented in the first part of [Milner (1993a)] since it is in many ways the most economic version, and so leads to the most transparent translation. We regard as given a suitable alphabet OH of channel names, ranged over by x, y, z etc. Here is the formal syntax. Definition 3.1 The re calculus language of process expressions is given by ....

Milner R., The Polyadic Pi-Calculus: A Tutorial. in: Logic and Algebra of Specification, Bauer, Brauer, Schwichtenberg (eds.), 203-246, Springer, (1993).

....below. Because of its focus on components, Darwin is a good fit for specifications resulting from the AIC protocol information. Recall from Section 2 that, in Darwin, a component is specified in terms of the services provided and required. This representation is in the form of calculus [23]. The access names in Darwin of the provided and required services are mapped to the AIC role name indicators of the components. The service name in Darwin is mapped to a components instantiated name, when that name becomes known. name TransactionController roles TransControl in protocol ....

Milner, R. The Polyadic PI-Calculus: a Tutorial. In Bauer, F., Brauer, W., Schwichttenberg, H., eds. Logic and Algebra of Specification. Springer Verlag, 1993.

....description of calculus fundations can be found in [8] A natural extension of the monadic calculus consists in considering name tuples as the values that can be passed between processes , instead of just names : the polyadic calculus. This version of calculus, described by R. Milner in [7], allows the introduction of a rst notion of discipline on the use of names, since a reduction can be incorrect because of an arity mismatch. An other constraint on the use of names is introduced by D. Sangiorgi [9] 10] and concerns the directionality of names, that is, their ability to be used ....

....piece of data that will be subsituted for m in its continuation P . The OUTPUT operator nm:P allows to transmit as data the name m on the chanel named n. The (n : t)P , RESTRICTION operator, restricts the visibility of the name n to its body P . P denotes an process with innite behavior (cf. [7]) We call P r I the set of processes syntactically dened this way. 2.1.2 Syntax in the COQ proof assistant The system used here is an alternative to the use of de Bruijn indices [3] The names are coded by a dioeerent constructor depending on the fact that they are in a bound position or in a ....

Robin Milner. The polyadic pi-calculus : a tutorial. Technical Report ECS-LFCS-91-180, LFCS, 1991.

....that allows one to express applications as compositions in terms of components, scripts, and glue. In order to support formal reasoning about architectural styles and concrete compositions, this language is being developed with a formal semantics based on ##,avariantofthe polyadic # calculus [21]. This chapter is organized as follows: in Section 2, we summarize the state of theart in component technology and analyze problems with existing approaches. In Section 3, we introduce a conceptual framework for software composition as an approach to overcome these problems. We present our ....

Robin Milner. The Polyadic Pi-Calculus: a Tutorial. Technical Report ECSLFCS -91-180, Computer Science Department, University of Edinburgh, UK, October 1991.

....buffer is filled, or when the end of the file has 49 been reached. Locking mechanisms are also widely used to guarantee concurrency. These techniques are attractive in the sense that the correctness of the systems employing them can often be proven with a formal calculus, such as the p calculus [36]. 3.1.2 Alternatives Agent based software engineering provides alternative solutions to some of these approaches that provide similar functionality. Use of software agents does not eliminate the need for conventional solutions entirely, especially in the area of on line mobility, but can often ....

R. Milner, "The Polyadic pi-Calculus: A Tutorial", Logic and Algebra of Specification, Springer-Verlag, 1993.

....returns a form with label aSubForm or aService, these bindings will hide the bindings that precede the invocation. The service r is invoked with the argument form count = 3. Channels. State is represented by channels. Channels have the semantics of locations in the asynchronous p calculus [16]. Using channels, we can model blackboards, locks, reference cells etc. The semantics of Piccola is given in terms of the pL calculus [13] a variant of the p calculus in which agents communicate forms instead of tuples. Agents. Agents implement the behaviour of a Piccola program. Agents ....

Robin Milner, "The Polyadic pi Calculus: a tutorial," ECS-LFCS-91-180, Computer Science Dept., University of Edinburgh, Oct. 1991.

....or channel. Parentheses ( can be used for grouping. The parallel operator binds stronger than and new . e.g. x n A B is read as x n (A B) Similar for channel and replicated agent. The reduction semantics of the pi calculus can be found in Milner s tutorial [5]. Here we consider the asynchronous pi calculus [1, 2] which has no operators of summation and matching, and output prefixes have no continuation. 3 Representation of agents For each kind of agent the frameworks provides a class to represent it. Figure 1 shows the class diagram. An application ....

Robin Milner. The polyadic Pi-calculus: a tutorial. Technical Report ECSLFCS -91-180, Computer Science Department, University of Edinburgh, UK, October 1991. 12

....of variables. This kind of encoding is called a higher order specication. It provides a concise description of the calculus, leading to simple proofs. The specication we propose for the pi calculus formalizes communication by means of function application. 1 Introduction The calculus [MPW92,Mil91] is a model of concurrent computation based upon the notion of naming. Processes receive and emit names, which denote channels. We propose here new formalizations of both evaluation and typing rules for a typed calculus, with the aim to enable machine checked proofs of various properties of ....

....variables in a term. Nor does it need denitions of notions of substitutions, which are implemented using the meta level application, i.e. application available in the Logical Framework used to implement our calculus (which in our case is the Calculus of Inductive Constructions) Robin Milner [Mil91] introduced notions of abstractions and concretions leading to a presentation of the calculus in which input processes evaluate to functions and output processes evaluate to concretions, i.e. intuitively) pairs of a value and a process. Our formalization starts from this idea, replacing ....

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Robin Milner. The polyadic pi-calculus: a tutorial. Technical Report ECS-LFCS-91-180, LFCS, Edinburgh University, October 1991.

....generic synchronization policies as an example for wrapping [LSN96, SL97, Var96] The inherent problem, however, is the limited reusability and extensibility due to position dependent parameters. We propose #L as a variant of the # calculus that is inherently extensible. In the polyadic # calculus [Mil91], sender and receiver processes need to agree on the number of communicated names and the interpretation of each of these. This schema of contracts between two components is too rigid, since it often requires the propagation of extensions of one part to the other. This propagation, however, can be ....

....1.4 and 1.5 we show how to implement a composition mechanism and some glue paradigms. We conclude with some remarks about future work and directions. 1. 2 The #L calculus In this section we introduce the #L calculus [Lum99] an o#spring of an asynchronous fragment of the (polyadic) # calculus [Mil91, MPW92]. The asynchronous sublanguage was proposed first by Boudol [Bou92] and Honda and Tokoro [HT92] Sangiorgi [San95] extended the proposal by allowing polyadic communication. 1.2.1 Syntax In the #L calculus we replace the communication of names or tuples of names by communication of so called ....

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Milner, R. The Polyadic Pi-Calculus: a Tutorial. Technical Report ECS-LFCS-91-180, Computer Science Department, University of Edinburgh, UK, October 1991.

....can easily be made concurrent and parallel. Concurrent object based programming language development, however, has long suffered from the lack of any generally accepted formal foundation for defining their semantics. Several authors have shown that the # calculus, or some of its variants [MIL 90, MIL 91, HON 92] are expressive enough for modelling standard object oriented programming language features in a convenient way and may therefore serve as a suitable semantic foundation for defining a concurrent object oriented language. For example, Walker [WAL 95] has shown that POOL [AME 86] can be ....

....gives rise to a higher order style of programming with objects, since a complete interface of one object may be manipulated as a single value. Motivated by the basic object model of Pierce and Turner [PIE 95] we have previously defined a record based object model in the polyadic # calculus [MIL 91] that incorporates known languages features of object oriented programming languages such as encapsulation, object identity, instantiation, synchronization, dynamic binding, inheritance, overriding, and class variables [LUM 96, SCH 97] In this model, classes are represented as runtime entities ....

MILNER R., "The Polyadic Pi-Calculus: a Tutorial", Technical report num. ECSLFCS -91-180, Computer Science Department, University of Edinburgh, UK, 1991.

....to [LSN96] or [SL96] We have used Pict [PT97] an experimental programming language based on the polyadic mini # calculus [San95] as an executable specification language for our modellings. We will first informally present the polyadic mini # calculus, which is a simplified polyadic # calculus [Mil91] The polyadic mini # calculus is built from the operators of inaction, input prefix, output, parallel composition, restriction, and replication. Small letters a, b, x, y, range over the infinite set of names, and P, Q, R, over the set of processes: P : 0 # # # a(x) P # # ....

Robin Milner. The Polyadic Pi-Calculus: a Tutorial. Technical Report ECS-LFCS-91-180, Computer Science Department, University of Edinburgh, UK, October 1991.

....possible to pass some kind of reference to a private channel as data along another channel. The process receiving the reference may then access the channel through the reference. Such a scheme may actually be seen as a complete substitute for channel hiding. Such a scheme is found in calculus (Milner, 1993), which is an extension of CCS. A more simplistic but readily model checkable scheme, which is closer to the object oriented scheme, is described here. In this scheme, identities of objects are passed, rather than those of channels. The pointer scheme we will adopt here is the scheme found in the ....

Milner, R. (1993). The polyadic pi-calculus: a tutorial. Springer Verlag.

....to be introduced and communicated much in the sameway that the l calculus introduces new bound names. This is needed for modelling creation of new objects with their own unique object identifiers. The basic (monadic) calculus allows only communication of channel names. The polyadic p calculus [16] supports communication of tuples, needed to model passing of complex messages. The higher order p calculus [27] supports the communication of process abstractions, which is needed for modelling software composition within the calculus itself. Interestingly, the polyadic and higher order variants ....

Robin Milner, "The Polyadic pi Calculus: a tutorial," ECS-LFCS-91-180, Computer Science Dept., University of Edinburgh, Oct. 1991.

....that is much higher than that of a cooperative editor. The search for abstractions in concurrency and distribution leads, many times, to hiding the particularities of the concrete systems, making the application of those abstractions difficult or even untreatable. As Robin Milner puts it in [18], Because the field is indeed so large, we may doubt whether a single theory [of concurrency] is possible; or, even if possible, whether it is good research strategy to seek it so early. Another more modest strategy is to seize upon some single notion which seems to be pervasive, make it the ....

Milner R., The polyadic pi-calculus: a tutorial, University of Edinburgh, Technical report ECS-LFCS-91-180, 1991. 24

....Science, Volume 936) Lalita Jategaonkar Jagadeesan Software Production Research Dept. AT T Bell Laboratories Naperville, IL 60566 (USA) lalita research.att.com Radha Jagadeesan Math. Sciences Loyola University Chicago, IL 60626 (USA) radha math.luc.edu 1 Introduction The pi calculus [18, 17] is a process algebra for describing networks of processes with dynamically evolving communication structure. The key idea underlying the pi calculus is the notion of naming: names are used to refer to channels the links between processes, and can be dynamically created or hidden. Names ....

....ABSTRACTION) P = Q , P POM = Q POM . 3 pi calculus This section describes the extension of the earlier treatment to the pi calculus. Most of the theory developed for CCS goes through unchanged. The only changes will be the replacement of the base domain N v by a domain T . The pi calculus [18, 17] extends CCS by allowing the passage of names along channels. Let A be a set of actions, let A = f a : a 2 Ag such that A and A are disjoint, and let Sigma = A [ A. For all actions a 2 A, a = a. The syntax of pi calculus processes is as follows, where a; x range over A: p : NILj ....

[Article contains additional citation context not shown here]

R. Milner. The polyadic pi-calculus: a tutorial. Technical Report ECS-LFCS-91180, University of Endinburgh, 1991.

....of mobile processes in which channel names can be communicated and newly introduced using rules analogous to those for the l calculus to avoid capture of names. Although the p calculus only allows for the communication of names as values, it has been shown that both a polyadic p calculus [26] (allowing the communication of tuples) and a higher order p calculus [36] allowing the communication of process abstractions as values) can be faithfully modeled by a mapping to the monadic calculus. The higher order p calculus is a close fit to our requirements and appears to be an excellent ....

Robin Milner, "The Polyadic pi Calculus: a tutorial," ECSLFCS -91-180, Computer Science Dept., University of Edinburgh, Oct. 1991.

....to [LSN96] or [SL96] We have used Pict [PT97] an experimental programming language based on the polyadic mini calculus [San95] as an executable specification language for our modellings. We will first informally present the polyadic mini calculus, which is a simplified polyadic calculus [Mil91] The polyadic mini calculus is built from the operators of inaction, input prefix, output, parallel composition, restriction, and replication. Small letters a; b; x; y; range over the infinite set of names, and P; Q; R; over the set of processes: P : 0 fi fi fi a( x) P fi fi ....

Robin Milner. The polyadic Pi-calculus: a tutorial. Technical Report ECS-LFCS-91-180, Computer Science Department, University of Edinburgh, UK, October 1991.

....that allows one to express applications as compositions in terms of components, scripts, and glue. In order to support formal reasoning about architectural styles and concrete compositions, this language is being developed with a formal semantics based on L, a variant of the polyadic calculus [21]. This article is organized as follows: in section 2, we summarize the state ofthe art in component technology and analyze problems with existing approaches. In section 3, we introduce a conceptual framework for software composition as an approach to overcome these problems. We present our ....

Robin Milner. The Polyadic Pi-Calculus: a Tutorial. Technical Report ECS-LFCS91 -180, Computer Science Department, University of Edinburgh, UK, October 1991.

....does not require disclosure of significant IPR over and above that which will be contained in a mature TINA C, and any potential commercial differentiators arising from it. Our proof of a) rests on a case study of the above access agents, which we have specified in the Pi calculus of Milner et. al [10]. The specification enabled us to show that, providing services conformed to certain simple rules of naming and event ordering, third party services would not interfere with the activities of the access agents and the retailers management system, and also that access to services would not be ....

Milner R "The polyadic pi-calculus: a tutorial" in Logic and Algebra of Specification, F Bauer et al (eds), Springer (1993)

....hardly recognise each others use of the word. The work in this paper may partly be seen as a comparison of notions of process from the first two of these, since in presenting a translation from the p calculus to MONSTR, both areas may be brought into contact. The p calculus [Milner et al. 1992) Milner (1993a)] arose as a generalisation of CCS [Milner (1989) to allow networks of processes to evolve dynamically. It is thus a process algebra language. MONSTR by contrast is a generalised term graph rewriting language that was used as the intermediate language for the Flagship machine. See [Banach et al. ....

....a fuller discussion. 2 Nil #Q[ Root[ #G[ SUCCEED Fig. 7 3 THE PI CALCULUS The p calculus first appeared in [Milner et al. 1992) and since that time has been seen in a number of minor variants. We will fix on a version of the monadic calculus, as presented in the first part of [Milner (1993a)] since it is in many ways the most economic version, and so leads to the most transparent translation. We regard as given a suitable alphabet CN of channel names, ranged over by x, y, z etc. Here is the formal syntax. Definition 3.1 The p calculus language of process expressions is given by the ....

Milner R., The Polyadic Pi-Calculus: A Tutorial. in: Logic and Algebra of Specification, Bauer, Brauer, Schwichtenberg (eds.), 203-246, Springer, (1993).

....1: Abstract object model. 3 Implementation in PICT In this section, we will describe several PICT implementations of the abstract object model. Readers not familiar with the language PICT can find an introduction in [Pie95b] or [Var96] For additional background in the calculus, please refer to [Mil89, Mil91]. Details about the implementation of PICT, especially its type system, are described in [Tur96] 3.1 Object model of Pierce and Turner In [PT95, Pie95b, Tur96] Pierce and Turner introduce a simple object model based on processes: an object is a process consisting of ffl a server process with ....

Robin Milner. The polyadic Pi-calculus: a tutorial. Technical Report ECSLFCS -91-180, Computer Science Department, University of Edinburgh, UK, October 1991.

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R. Milner. The polyadic pi-calculus: a tutorial. Technical Report ECS-LFCS-91180, University of Endinburgh, 1991.

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R. Milner. The polyadic pi-calculus: a tutorial. In F. L. Bauer, W. Brauer, and H. Schwichtenberg, editors, Logic and Algebra of Specification, pages 203--246. Springer-Verlag, 1993.

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R. Milner. The polyadic pi-calculus: a tutorial. In F. L. Bauer, W. Brauer, and H. Schwichtenberg, editors, Logic and Algebra of Specification, pages 203--246. Springer-Verlag, 1993. http://citeseer.ist.psu. edu/milner91polyadic.html.

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R. Milner. The polyadic pi-calculus: a tutorial. In F. L. Bauer, W. Brauer, and H. Schwichtenberg, editors, Logic and Algebra of Specification, pages 203--246. Springer-Verlag, 1993.

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R. Milner. The polyadic pi-calculus: a tutorial. In F. L. Bauer, W. Brauer, and H. Schwichtenberg, editors, Logic and Algebra of Specification, pages 203--246. Springer-Verlag, 1993.

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Milner R. The polyadic pi-calculus: a tutorial. In Logic and Algebra of Specification, 203--246, Springer-Verlag, 1993.

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R. Milner. The polyadic pi-calculus: a tutorial. In F. L. Bauer, W. Brauer, and H. Schwichtenberg, editors, Logic and Algebra of Specification, pages 203--246. Springer-Verlag, 1993.

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R. Milner, The polyadic pi-calculus: a tutorial, in: F. L. Bauer, W. Brauer, H. Schwichtenberg (Eds.), Logic and Algebra of Specification, Springer-Verlag, (1993) 203--246.

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R. Milner. The Polyadic pi-Calculus: a Tutorial. Technical Report, Computer Science Dept., University of Edinburgh, 1991.

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Robin Milner. The polyadic pi-calculus : a tutorial. Technical Report ECS-LFCS-91-180, LFCS, 1991.

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R. Milner. The Polyadic pi-Calculus: A Tutorial. In Logic and Algebra of Specification. 1993.

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Milner R. The polyadic pi-calculus: a tutorial. In Logic and Algebra of Specification, 203--246, Springer-Verlag, 1993.

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R. Milner. The Polyadic pi-Calculus: A Tutorial. In Logic and Algebra of Specification. 1993.

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R. Milner. The polyadic pi-calculus: a tutorial. In F. L. Bauer, W. Brauer, and H. Schwichtenberg, editors, Logic and Algebra of Specification, pages 203--246. Springer-Verlag, 1993.

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R. Milner. The polyadic pi-calculus: a tutorial. In F. L. Bauer, W. Brauer, and H. Schwichtenberg, editors, Logic and Algebra of Specification, pages 203--246. SpringerVerlag, 1993.

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R. Milner. The polyadic pi-calculus: a tutorial. In F. L. Bauer, W. Brauer, and H. Schwichtenberg, editors, Logic and Algebra of Specification, pages 203--246. Springer-Verlag, 1993.

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R. Milner. The Polyadic Pi-calculus: a tutorial. In F. L. Bauer, W. Brauer, and H. Schwichtenberg, editors, Logic and Algebra of Speci cation, pages 203-246. Springer-Verlag, 1993.

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R. Milner. The polyadic pi-calculus: a tutorial. In F. L. Bauer, W. Brauer, and H. Schwichtenberg, editors, Logic and Algebra of Specification, pages 203--246. SpringerVerlag, 1993.

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R. Milner, "The polyadic pi-calculus:a tutorial" Research Report ECS-LFCS-01-180, Laboratory for Fondations of Computer Science, Edinburgh University, 1991.

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