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.

....the boundary p. Finally, the input (x) Q consumes the output hMi, to leave the residue a[ j b[Qfx Mg] where Qfx Mg is the outcome of replacing each occurrence of x in Q with the expression M . Two additional primitives of our calculus are replication and restriction. Just as in the calculus [Mil91], a replication P behaves the same as an infinite array of replicas of P running in parallel, and a restriction (n)P means: pick a completely fresh name, call it n, then run P . Operational Semantics We recall the syntax of the typed ambient calculus from [CG99] This is the same syntax as the ....

....structure of mobile computations. The type systems presented in this paper derive from our earlier work on exchange types for ambients [CG99] That type system tracks the types of messages that may be input or output within each ambient; it is analogous to Milner s sort system for the calculus [Mil91], which tracks the types of messages that may be input or output on each channel. Our mobility annotations govern the ways in which an ambient can be moved. The data movement types of the mobile calculus of Sekiguchi and Yonezawa [SY97] also govern movement, the movement of variables referred ....

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

....Plan In this paper we briefly present the main features of the concurrent object oriented specification language CO OPN 2 mentioned above and then we focus on the notion of refinement and sub typing. Several examples such as the mobile station example introduced by R. Milner in his calculus [Mil91] and the Russian philosophers example of Lakos [Lak94b] are detailed in order to illustrate these features. ....

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

....e : ph ei j p( y) j P : 0 j :P j P P j P jP j ( p)P j [x = n]P j [x 6= n]P j p( y) P: 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 ....

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

....the boundary p. Finally, the input (x) Q consumes the output hMi, to leave the residue a[ j b[Qfx Mg] where Qfx Mg is the outcome of replacing each occurrence of x in Q with the expression M . Two additional primitives of our calculus are replication and restriction. Just as in the calculus [Mil91], a replication P behaves the same as an infinite array of replicas of P running in parallel, and a restriction (n)P means: pick a completely fresh name, call it n, then run P . 2.2 Syntax and Operational Semantics We recall the syntax of the typed ambient calculus from [CG99] This is the ....

....scope is Net and Cro, respectively. In the phrase c(x 1 :W 1 ; x k :W k ) Th, the names x 1 , x k are bound; their scope is the phrase Th. The type system of our language controls the typing of messages on communication channels, much as in previous schemes for the calculus [Mil91]. We formalize the type system using the following five judgments: Judgments: E Pi good environment E n : W name n has type W E Net good network E Cro good crowd E Th good thread These judgments are defined by the fairly standard rules in the following tables. Good environment: ....

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

....as follows. In the next section we recall calculus. Its proved semantics is defined in Sect. 3 and it is used to derive the timed semantics in Sect. 4. Section 5 introduces our amortized preordering. An example is discussed in Sect. 6. 2 Calculus In this section we briefly recall calculus [20, 19], a model of concurrent communicating processes providing the notion of naming. Definition1. Let N be a countably infinite set of names ranged over by a; b; x; y; and let S = f 0 ; 1 ; 2 ; g be a countably infinite set of invisible actions ranged over by i , with N S ....

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

....Section 4 shows what can be achieved with the type model as well as its limitations. A comparison with related work follows in Section 5. 2 Computation Model The computation model is based on a process algebra combined with the actor model. Process calculi like those explored by Hoare [5] Milner [10, 11, 12] and others [2] provide a theoretically well founded and expressive basis for specifying the behavior of concurrent agents. The well known actor model [1] introduces active objects and designates them by unique identifiers. Each object responds to a received message according to its behavior ....

....that will be replaced with an appropriate parametric process expression. In general, parentheses are used in clarifying the structure of expressions. Round brackets in receive actions and parametric process expressions and their annotations symbolize name abstraction: As in the polyadic calculus [12] pairwise different names enclosed in parentheses represent formal parameters. They bind further occurrences of these names. Concrete parameters (enclosed in square brackets) are substituted for them when executing these actions. Type lists enclosed in triangular brackets specify the types of the ....

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Robin Milner. The polyadic ß-calculus: A tutorial. Technical Report ECS-LFCS-91180, Dept. of Comp. Sci., Edinburgh University, 1991.

....because rewriting modulo such a complex theory is not practically feasible. The fact of having two sets of rules is useful for relating fi reduction and its implementation in a single framework. 5. 3 LOTOS Similar ideas can also be applied to process algebras, for instance calculus [Mil91] where processes can exchange actual values rather than only synchronizations. The equations in E and equational rules in ER specify the structure of processes and the application of substitutions, while the only reduction rule in R specifies internal transitions of processes. A complete ....

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

....significant extension to these earlier notations is that we permit, as an atomic event, the communication of terms representing arbitrary tuples of values, although nothing more complicated than pairs is required for our translations below. This is very nearly equivalent to the Polyadic Calculus [Mil91] although we would allow nested terms. We allow a received term to be matched to a pattern of names, or bound to a single name. Further work is required on a sort discipline for the calculus to ensure that names bound to structured values are never used as link names. We are also very interested ....

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

....reference followed by a global reference this means that the object referred to by the global reference is not found if any of the objects on the path of the relative reference don t exist. 3. 2 Formal calculus Semantics The reason for describing the semantics in terms of the calculus[MPW89, Mil91, Wal89] is that the calculus provides a convenient way of modelling aspects of concurrency and parallelism. These aspects are essential for the language. Having a well founded calculus to describe exactly these gives us the opportunity to reason about the language in terms of the calculus. This ....

....Programs in the language that use these objects thus can still be exchanged between different systems. Appendix A Background A. 1 The calculus The calculus is an elementary calculus for describing and analysing concurrent systems with evolving communication structure[MPW89, Wal91, Mil91] The following is a brief description of the version of the calculus that has been used throughout this paper. A system is a collection of independent processes which may be linked to other processes. Links have names; the name is the most primitive entity in the calculus; names have no ....

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

....and the receiver are identified in a communication, a better account can be given to structural causality. Consider the process (x) a:xy:bjc:x(z) dz) and its computation (x) a:xy:bjc:x(z) dz) c Gamma (x) a:xy:bjx(z) dz) a Gamma (x) xy:bjx(z) dz) Gamma (x) bjdz) According to Milner [17], the effect of the communication influences only dy, the residual of the receiver of y. On the contrary, b is unaffected because no flow of information is possible from c to b. Thus, we state that there is no causal relation between c and b. They are only temporally dependent. We say in this case ....

....to the residual of the receiver as well, but not vice versa. Indeed, reading a name cannot causally affect the evolution of the residual of the sender, while it may, and usually does, affect the evolution of the receiver. This reflects the effect of a communication as introduced by Milner in [17]. Link dependencies are established when an action uses as its link a name bound by another through an input or an extrusion. The next sub section defines the causal relation, while in Subsect. 4.2 we report an example that justifies the introduction of a new kind of causality. 4.1 Causal ....

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

....the causal one cross updates the causes between the partners of communications, while locality semantics completely ignores communications. In fact, the two coincide when there are no communications [14, 9] Recently a few papers [25, 2, 20, 5, 13] have begun to study this problem in calculus [16, 19]. However, many subtle aspects still have to be clarified, especially related to the explicit distinction between input and output actions and to the dependencies induced by the usage of names. In the rest of the Introduction we assume that the reader is familiar with calculus. Following ....

....7 establishes the relations between the bisimulation based equivalences of relabelled proved transition systems. Section 8 indicates how to handle higher order calculi in our framework. There is a discussion on related works in Sect. 9. 2 Calculus In this section we briefly recall calculus [19, 16], a model of concurrent communicating processes providing the notion of naming. Definition 2.1 (syntax) Let N be a countable infinite set of names ranged over by a; b; x; y; with N f g = Processes (denoted by P; Q; R; 2 P) are built from names according to the syntax P ....

R. Milner. The polyadic ß-calculus: a tutorial. Technical Report ECS-LFCS-91-180, University of Edinburgh, 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] Our semantic conditions which assure point to point communication were also inspired by the syntactic conditions given in that paper. The semantic ....

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

....the boundary p. Finally, the input (x) Q consumes the output hMi, to leave the residue a[ j b[Qfx Mg] where Qfx Mg is the outcome of replacing each occurrence of x in Q with the expression M . Two additional primitives of our calculus are replication and restriction. Just as in the calculus [Mil91], a replication P behaves the same as an infinite array of replicas of P running in parallel, and a restriction (n)P means: pick a completely fresh name, call it n, then run P . 2.2 Operational Semantics We recall the syntax of the typed ambient calculus from [CG99] This is the same syntax as ....

....structure of mobile computations. The type systems presented in this paper derive from our earlier work on exchange types for ambients [CG99] That type system tracks the types of messages that may be input or output within each ambient; it is analogous to Milner s sort system for the calculus [Mil91], which tracks the types of messages that may be input or output on each channel. Our mobility annotations govern the ways in which an ambient can be moved. The data movement types of the mobile calculus of Sekiguchi and Yonewaza [SY97] also govern movement, the movement of variables referred to ....

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

....mechanism. anisms. This is to avoid forwarding based on network prefix of the destination address in the IP header. This is ensured by assuming that the mobile node and the foreign agent have a connection on the same link. 3 Calculus In this section we briefly recall calculus [19, 20, 21], a model of concurrent communicating processes based on the notion of naming. Definition 3.1 (syntax) Let N be a countable infinite set of names ranged over by a; b; x; y; with N f g = We also assume a set A of agent identifiers, each with an arity, ranged over by A; B; C; ....

....prevent inputs to occur in isolation, thus ensuring the finite branching structure of our transition systems. Closed systems impose a unique naming discipline in the sense that names are uniquely borne in the system itself. Finally, closed systems are very similar to friendly systems introduced in [19]. 3.4 Specification of IP We report here the specification of the agent discovery and registration mechanisms of the IP for mobility using calculus (Fig. 1) We consider the simplified version in which any home and foreign agent serves a single mobile node. Finite parallel compositions of home ....

[Article contains additional citation context not shown here]

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

....and the receiver are identified in a communication, a better account can be given to structural causality. Consider the process (x) a:xy:bjc:x(z) dz) and its computation (x) a:xy:bjc:x(z) dz) c Gamma (x) a:xy:bjx(z) dz) a Gamma (x) xy:bjx(z) dz) Gamma (x) bjdy) According to Milner [18], the effect of the communication influences only dy, the residual of the receiver of y. On the contrary, b is unaffected because no flow of information is possible from c to b. Thus, we state that there is no causal relation between c and b. They are only temporally dependent. We say in this case ....

....to the residual of the receiver as well, but not vice versa. Indeed, reading a name cannot causally affect the evolution of the residual of the sender, while it may, and usually does, affect the evolution of the receiver. This reflects the effect of a communication as introduced by Milner in [18]. Link dependencies are established when an action uses as its link a name bound by another through an input or an extrusion. The next subsection defines the causal relation, while Subsect. 4.2 contains an example that justifies the introduction of the new kind of causality. 4.1 Causal relation ....

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

....the receiver are clearly identified in a communication, a better account can be given to structural causality. Consider the process (x) a:xy:bjc:x(z) d) and its computation (x) a:xy:bjc:x(z) d) c Gamma (x) a:xy:bjx(z) d) a Gamma (x) xy:bjx(z) d) Gamma (x) bjd) According to Milner [13], the effect of the communication influences only d, the residual of the receiver of y. On the contrary, b is unaffected because there is no flow of information from c to b. Thus, there is no causal relation between c and b. They are only temporally dependent. This shows that c has implicitly got ....

....for CCS [19] when a communication occurs, the sender transmits its causes also to the residual of the receiver, but not vice versa. Indeed, reading a value does not causally affect the evolution of the residual of the sender (see also the effect of a communication as introduced by Milner in [13]) Link dependencies are established when an action uses as link a name bound by another through an input or an extrusion. The definition of causality between the transitions of a computation is given in three steps. Roughly, the first pertains to structural dependencies. It says that a transition ....

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

....names are quite unreadable. However, they are to be used as internal names for specifications closer to efficient implementations, rather than in high level specifications, where a global space of names and global checks are acceptable. 2 Calculus In this section we briefly recall calculus [9, 7], a model of concurrent communicating processes based on the notion of naming. Definition1. Let N be a countable infinite set of names ranged over by a; b; x; y; with N f g = Processes (denoted by P; Q; R; 2 P) are built from names according to the syntax P : 0 j :P j ....

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

....a continuous time Markov chain. We also briefly recall how performance and reliability measures can be derived. Finally, Sect. 4 reports a stochastic analysis of the network of mobile telephones described in [26] 2 Stochastic Calculus We introduce a stochastic extension [28] of calculus [20, 21, 22], a model of concurrent communicating processes based on the notion of naming. Definition 2.1 Let N be a countable infinite set of names ranged over by a; b; x; y; with N f g = We also assume a set A of agent identifiers, each with an arity, ranged over by A; B; C; ....

.... is r 0 =r a (P ) Theta r 1 =r a (Q) Therefore the rate of synchronizations is R(P; a; Q; a; r 0 ; r 1 ) r 0 =r a (P ) Theta r 1 =r a (Q) Theta min(r a (P ) r a (Q) 1) In this paper we restrict ourselves to systems in which names are uniquely borne in the system itself (closed systems [20]) as it happens with our main case study on mobile telephones. The transition relation is defined in Tab. 1. The symmetric rules of Sum, Par, Com and Close are obvious. The rate of synchronizations is computed according to equation (1) The transition in the conclusion of each rule, as well as in ....

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

....techniques for untimed as well as for timed systems exist ( GS95] BDD 93] Moreover, for stream processing functions a powerful theory for compositional refinement has been developed. By using an asynchronous system model, in contrast to process algebraic approaches like the calculus [Mil91] or CCS [Mil89] we do not have to tackle synchronization issues. To take into account synchronization aspects is in our opinion an issue which is irrelevant in the early phases of system development. However, synchronization can easily be encoded in our model, for instance by using an ....

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

....calculi. 1 Introduction The specification of systems of mobile processes is gaining more and more attention, see e.g. 20, 22, 25, 29, 7, 13] Efficiency considerations suggest implementations which provide each sequential process in the system with its own local environment. In the calculus [20, 18], this amounts to saying that each process has its own space Work partially supported by ESPRIT BRA n.8130 LOMAPS. The first two authors have been also partially supported by the CNR Progetto Strategico Modelli e Metodi per la Matematica e l Ingegneria and by the MURST Progetto Tecniche ....

....myprog and the name mytimetab at address did.teachffladm.did.lectures. While communicating the two names, the address composition transforms these relative addresses to 1 For the sake of presentation, in this example we use the polyadic calculus; for its translation to the monadic version see [18]. TeacherjStud)jP teachfflstuds chanhfflmyprog; did.teachffladm.did.lectures mytimetabi:Teacher j ffls chan(a; b) printha; bi:StudjP Teacher j printhstudfflteach myprog; did.studffladm.did.lectures mytimetabi:StudjP (TeacherjStud)jP printhstudfflteach ....

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

.... which system components should exist, and how they are inter connected, and is based on principles of software architecture[GS93, PW92, GP94] Finally coordination is concerned with the interaction of the various system components, and is founded on recent paradigms such as process calculi[Mil89, MPW92, Mil91] and the notion of interaction machines[Weg96] Having to perform three paradigm shifts during the design and implementation of a system is costly, since ultimately all elements have to work together to meet the overall system specification. In addition to the difference in paradigms, each ....

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

....mapped to light weight threads, and are therefore more expensive to use than the functional features. In its pure form, Facile enhances the calculus with primitives for process spawning and channel based communication in the style of CCS [14] Using the calculus [17] and its polyadic form [16], Milner shows that a expression may be translated to a process network which simulates the expression [15] Similar work was done by Leth [11] Building on such process translations of the expression new translations were developed to map both the functional and concurrent features of ....

....reduced. The ultimate goal is to exploit the inherent concurrency of the process networks in an implementation on a parallel machine. A number of options were considered when selecting the underlying process calculus. One approach was to use process notations close to the Polyadic Calculus [16] in which communication is name or channel based. Translations such as those of Milner may be employed as reported in [5] and [4] In these models the names can be thought of as independent entities which act as brokers, arranging communications between processes. Similar ideas appear in [19] ....

R. Milner: The Polyadic ß--Calculus: A Tutorial, Technical Report ECS-LFCS-91180, Edinburgh University. (1991)

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

No context found.

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.

....This semantics is a central component of a more comprehensive operational semantics of concurrent logic programming languages currently being developed. 1 Introduction The calculus is a process algebra suitable for modelling concurrent networks with evolving communicative structures [MPW89a, MPW89b, Mil91]. The calculus is similar to Milner s earlier CCS [Mil89] except that it is embellished with channel label passing, which gives an object oriented view of concurrency. The ability to treat channels as objects greatly enriches the descriptive power of the formalism, which can be seen by its ....

....This step is necessary for preserving the soundness of unification. However, it is computationally expensive, and is normally ignored in Prolog [CM81] 2.2 The calculus The monadic calculus of [MPW89a, MPW89b] will be used. We will embellish it with some devices from a later incarnation in [Mil91], and with Comm : Delta Delta Delta x(y) P ) j ( Delta Delta Delta xz:Q) Pfz=yg j Q Par : P P 0 P jQ P 0 jQ Res : P P 0 (x)P (x)P 0 Struct : Q j P P P 0 P 0 j Q 0 Q Q 0 Figure 1: Reduction and inference rules for calculus some notational conveniences ....

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

....objects TyCO (TYped Concurrent Objects) VT93, Vas94] is an object oriented name passing calculus with asynchronous communication between concurrent objects via labelled messages carrying names. The calculus is developed along the trends of well known models of concurrency, such as the calculus [Mil91, MPW92], the calculus [HT91] and the actor model of computation [HBS73, Agh86] 2.1 Syntax Consider names u; v; x; y 2N , labels a,b,c 2L, and processes P; Q2P. Let v stand for a sequence of names, and x for a sequence of pairwise distinct names. Definition 2.1 The set P of processes is given by ....

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

No context found.

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.

No context found.

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

No context found.

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

No context found.

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.

No context found.

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

No context found.

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

No context found.

R. Milner: The Polyadic ß-Calculus: A Tutorial, Technical Report ECS-LFCS-91-180, Edinburgh University. 1991.

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