R. Milner. The Polyadic p-Calculus: a Tutorial. Technical Report ECS-LFCS-91-180, LFCS, Dept. of Computer Science, Edinburgh University, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....designed to model both of these aspects within a single framework. Along with mobile computation in itself, it shows how the notions of administrative domains, their crossing, rewalls, authorizations. can be formalized in a calculus. In this sense, it is more appropriate than the calculus ([Mil91]) even if the bases are the same (for more discussion about the problems raised by mobility and computation over wide area networks, see [Car99a, Car99b] Informally, an ambient is a bounded place, with an inside and an outside, where computation happens. Many ambients can be nested so that ....

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

....present in the next section will overcome such limitations. 3. A Klailn based infrastructure language In this section we will present an infrastructure language for modeling and driving the implementation of large scale mobile 2This mechanism is reminiscent of link mobility in the N calculus [15]. systems whose structure can dynamically evolve in an unpredictable way. Our starting point will be the language presented in Section 3.1, obtained by providing KL IM with a few mechanisms for dynamically updating nodes allocation environments and with suitable notations for explicitly ....

R. Milner. The polyadic N-calculus: a tutorial. Technical Report ECS-LFCS-91-180, Dep. of Comp. Sci., Edinburgh Univ., 1991.

....explicitly employs names for message passing. As already discussed in numerous papers, the use of names greatly simplifies the modeling of object oriented systems. Examples of this are: the , calculus augmented with records (cf. 4, 5] Milner s re calculus for describing concurrent computations [11] and , calculus augmented with names, combinations and alternations [7] In [12] Oscar Nierstrasz argues that encapsulation is one of the most fundamental concepts of object orientedness, and that all object oriented mechanisms and approaches exploit this idea to various ends. For this reason, ....

....For this reason, it is useful to find out where our calculus can be situated amongst the others. Only a small set of people is currently working on OO calculi that are not based on X calculus, mostly in the area of concurrent OOPLs. For example, Robin Milner has introduced the re calculus [11], and Oscar Nierstrasz proposed an object calculus [13] Most of the current research on formal OO models consists of attempts to generalize X calculus in order to describe OO concepts more easily. All of these models however have difficulties in expressing some of the essential features of ....

R. Milner: The Poliadic r-calculus: A tutorial. Technical Report ECS-LFCS-91180, University of Edinburgh, 1991

....tag; in the case statement, the tags i (i 2 1: n) are pairwise distinct. Table 1: The syntax of the typed calculus Operational semantics. For the semantics of the calculus we adopt a labelled transition system. The advantage of a labeled semantics, compared to a reduction semantics [17, 24], is that it easily allows us to de ne labeled forms of bisimulation. Process transitions are of the form P , where is given by the following syntax: n: T ) pv j pv j j wrong The label ( n: T ) pv denotes the output of the value v on the name p. The restriction ( n: T ....

....the type environment. A subject reduction theorem guarantees us that if P is well typed and P = Q, then Q does not contain the process wrong. Some derived constructs. In the translation we shall use: Recursive de nitions, A( x) P which can be de ned the standard way from replication (c.f. [17]) polyadic inputs a(x 1 : xn ) P , de ned as a(y) let hx 1 : xn i = y in P for y 62 fn(P ) variant inputs, like p j i;j ( x i;j ) P i;j . The last abbreviation allows us to go down two levels into the structure of a variant value received in an input at p; in fact, this ....

R. Milner. The polyadic -calculus: a tutorial. Technical Report ECS{ LFCS{91-180, LFCS, Dept. of Comp. Sci., Edinburgh Univ., Oct.

....calculus what CCS is to the calculus: the former has no operator of abstraction and no instantiation of variables, while the latter does. We could not show that pure ambients were as expressive as classical mobile ambients, but we managed to encode the nite sum free synchronous calculus [Milner, 1991] in pure (safe) ambients. Such a result is also interesting: we know that the calculus is very expressive, and we show that pure ambients are at least as expressive. We give such an encoding in this paper and prove its correctness. The main problem we had to face was the simulation of ....

Milner, R. (1991). The Polyadic -Calculus: a Tutorial. Technical Report ECS-LFCS-91-180, University of Edinburgh.

....of abstraction, however, in many cases the dynamics may no longer be explicitly visible. Another crucial issue for an information processing system and its description is the balance between statics and dynamics. In a world without types, for instance, any behavior can be encoded (see p calculus [Milner 91] Types introduce restrictions on the system behavior and this way restrict the dynamics of systems. Obviously, it is crucial to find the right balance between static aspects including types and dynamic aspects. In system development, we want to associate a number of properties, structure, and ....

....where in one step most of the net structure remains unchanged and only . one component is added or deleted, or . one channel is added to or deleted from a component or its source and or target is changed. This leads to the idea of evolving networks along the lines of the p calculus (see [Milner 91] Milner et al. 92] or the ambient calculus (see [Cardelli 95] where the steps of changes are captured by rewriting rules. In fact, in p calculus the meaning and behavior of dynamic networks is specified in a purely operational way, which does not lead to a clear notion of an interface nor to ....

] R. Milner: The polyadic p-calculus: A tutorial. Technical Report ECS-LFCS-91-180, University of Edinburgh, 1991.

....for modeling large scale mobile systems whose structure can dynamically evolve in unpredictable way. Our starting point will be the language presented in Section 3. 1, obtained by providing Klaim with a few mechanisms for 2 This mechanism is reminiscent of link mobility in the calculus [13]. 4 dynamically updating nodes allocation environments and with suitable notations for explicitly modeling node connectivity. Then, our infrastructure language, de ned in Section 3.2, will be obtained by integrating the Klaim dialect of Section 3.1 with a new category of processes, called ....

R. Milner. The polyadic -calculus: a tutorial. Technical Report ECS-LFCS-91-180, Dep. of Comp. Sci., Edinburgh Univ., 1991.

....present in the next section will overcome such limitations. 3. A Klaim based infrastructure language In this section we will present an infrastructure language for modeling and driving the implementation of large scale mobile 2 This mechanism is reminiscent of link mobility in the p calculus [15]. systems whose structure can dynamically evolve in an unpredictable way. Our starting point will be the language presented in Section 3.1, obtained by providing KLAIM with a few mechanisms for dynamically updating nodes allocation environments and with suitable notations for explicitly ....

R. Milner. The polyadic p-calculus: a tutorial. Technical Report ECS-LFCS-91-180, Dep. of Comp. Sci., Edinburgh Univ., 1991.

....[Gro94] also presents a semantic model for mobile, deterministic networks. However, that model is higher order and mobility is achieved by communicating channels and functions instead of ports. The idea of communicating names (ports) was inspired by [MPW92a, MPW92b] The action structures [Mil92] are also related to our model. The idea of associating an access right with each channel in order to control interference was taken from [SKL90] The semantic model of [SRP91] has also some similarities to our model. However, the intentions are complementary. SRP91] aims at generality. We, on ....

R. Milner. Action structures. Technical Report ECS-LFCS-92-249, University of Edinburgh, 1992.

....cords Cords are the formalism we use to represent protocols and their parts. Cords are partly an extension of the strand formalism, with explicit variable binding and substitution to allow dynamic sending of messages in protocol communication. Cords also give rise to arrows in an action category [Mil92, Pav97], providing a structure for composing protocols. Our treatment of encryption is largely based on Spi calculus [AG99] A formal de nition of cords requires several syntactical steps. 2.1 Terms The terms formalize what can be sent and received as messages. Depending on the situation one may wish ....

R. Milner. Action structures. Technical Report ECS-LFCS-92-249, University of Edinburgh, 1992.

....far as we know, this is the first such result for value passing calculi. Moreover, in our case the representatives selected are minimal w.r.t. to the length of the defining expressions. Further motivation for the study of open bisimulation might come from Robin Milner s work on action structures [Mil92a]. These are proposed as canonical algebraic structures which underly concrete models of concurrency, like Petri Nets, event structures and process calculi. It appears that in the action structures for process calculi the bisimulation relations recovered are close to open bisimulation; but the ....

R. Milner. Action structures. Technical Report ECS--LFCS--92--249, LFCS, Dept. of Comp. Sci., Edinburgh Univ., December 1992.

....compared using their encodings into observation equivalence presented here and in [San94b] The concluding section mentions directions for possible future research. 2 The polyadic calculus We start by reviewing the standard syntax and the interleaving semantics of the polyadic calculus, as in [Mil91]. 2.1 Syntax of standard processes Definition 2.1 (Standard processes) Consider an infinite countable set N of names s.t. N f g = The class of the polyadic standard processes over names N , written P(N ) is built from the operators of inaction, input prefix, output prefix, silent ....

....the ordinary interleaving bisimilarity also works well for causal bisimulation) and is easier to handle algebraically. 2.2 Sorting Virtually all calculus processes described in the literature obey some discipline in the use of names. The introduction of sorts and sortings into the calculus [Mil91] intends to make this name discipline explicit. In the polyadic calculus, sorts are also essential to avoid disagreement in the arities of tuples carried by a given name, or applied to a given constant. Below, we review the definition of sorting and of well sorted process. Names are partitioned ....

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R. Milner. The polyadic ß-calculus: a tutorial. Technical Report ECS--LFCS--91--180, LFCS, Dept. of Comp. Sci., Edinburgh Univ., October 1991.

....child, waits for replying, receives a value, and then forks a right one. On the other hand, the former waits after forking two children. Chapter 6 The Intermediate Language This section explains the intermediate language Venezia. 6. 1 Background Concurrent calculi, such as HACL[11] and calculus[14], have been drawing much attention and some languages have been designed based on them. The goal is to identify the core language which express various computation patterns by a small number of fundamental primitives. In their simplest form, both HACL and calculus are based on channels ....

Milner, R., The polyadic ß-calculus: A tutorial, Technical Report ECS-LFCS-91-180, University of Edinburgh, 1991.

....ph ei j p( y) j Prefix R : 0 j :R j R R j RjR j ( p)R j [x = n]R j [x 6= n]R j p( y) P Processes: A process is closed if it does not contain free variables. Otherwise it is open. For the semantics of the calculus we adopt a labelled transition system. In contrast to reduction semantics [Mil91], this allows us to use labelled forms of bisimulation and to use the associated proof techniques [MS92] Process transitions (in the early style) are of the form P Gamma P 0 , where is given by : b)ah vi j ah vi j : b)ah vi denotes the output of the values v on the ....

....the processes [AKH92] 4 Interpreting CIA in the calculus The calculus interpretation of CIA is given by the rules in Tables 2 and 3 at the end of this paper. The storage is modelled by registers of the form (in the calculus, recursive process definitions are derivable from replication [Mil91]) Reg [v] def = get hvi:Reg [v] put (w) Reg [w] Processes in the scope of fn def = fget ; put g are allowed to read and modify the content of Reg . Configurations hC; oei, with Gamma (oe) f i g i , translate to [ hC; oei] p def = fn 1 ; fn n ) Y ....

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

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R. Milner. The Polyadic #-Calculus: A Tutorial. Technical Report ECS-LFCS-91-180, LFCS, U. of Edinburgh, 1991.

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R. Milner. The Poliadic -calculus: A tutorial. Technical Report ECS-LFCS-91180, University of Edinburgh, 1991

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

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R. Milner. The Polyadic p-Calculus: a Tutorial. Technical Report ECS-LFCS-91-180, LFCS, Dept. of Computer Science, Edinburgh University, 1991.

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R. Milner. The polyadic p-calculus: a tutorial. Technical Report ECS-LFCS-91-180, Dep. of Comp. Sci., Edinburgh Univ., 1991.

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Milner, R. (1991). The Polyadic -Calculus: a Tutorial. Technical Report ECS-LFCS-91-180, University of Edinburgh.

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R. Milner: The Poliadic -calculus: A tutorial. Technical Report ECS-LFCS-91180, University of Edinburgh, 1991

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R. Milner. Action structures. Technical Report ECS-LFCS-92-249, LFCS, Dec 1992.

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R. Milner. Action structures. Technical Report ECS-LFCS-92-249, Universityof Edinburgh, 1992.

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R. Milner. The polyadic #-calculus: a tutorial. Technical Report ECS--LFCS--91--180, LFCS, Dept. of Comp. Sci., Edinburgh Univ., October 1991.

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R. Milner. The Poliadic 2r-calculus: A tutorial. Technical Report ECS-LFCS-91180, University of Edinburgh, 1991

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