R. Milner. The polyadic #-calculus: A tutorial. Technical Report 180, LFCS, University of Edinburgh, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of this paper are: We extend SAFL with synchronous channels and assignment and argue that the resulting combination of functional, concurrent and imperative styles is a powerful framework in which to describe a wide range of hardware designs. Channel passing in the style of the calculus [12] is introduced. By parameterising functions over both data and channels the SAFL fun declaration becomes a powerful abstraction mechanism unifying a range of structuring techniques treated separately by existing HDLs (Section 2.3) We show how SAFL is implemented at the circuit level (Section ....

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

....the call and wait for result interface provided by the function model is too restrictive. To address these issues we have developed a language, SAFL , which extends SAFL with process calculus features including synchronous channels and channel passing in the style of the # calculus [101]. The incorporation of channel passing allows a style of programming which strikes a balance between the flexibility of structural blocks and the analysability of functions. In Chapter 7 we describe both the SAFL language and the implementation of our SAFL compiler. We demonstrate that our ....

.... purposes, this chapter describes Soft Scheduling in the framework of SAFL, the technique is applicable to any high level HDL which allows function definitions to be treated as shared resources (e.g. HardwareC [87] Balsa [45] Tangram [139] Indeed, in Chapter 7 we extend SAFL with # calculus [101] style channels and assignment and demonstrate that the Soft Scheduling technique scales accordingly. Traditional high level synthesis packages perform scheduling using a data structure called a sequencing graph a partial ordering which makes dependencies between operations explicit. In this ....

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MILNER, R. The polyadic #-calculus: A tutorial. Tech. Rep. ECS-LFCS-91-180, University of Edinburgh, October 1991.

.... Since the calculus allows link names to be sent and received as values, it has proved to be a very expressive notation for describing the behaviour of software components in applications with changing topologies (as those that live in open systems) In particular, we use the polyadic # calculus [21], a generalized version of the basic # calculus in which tuples, and not only single names, can be sent along links. The set of behaviour expressions is formally defined as follows: E : 0 a. E (x)E [x = y] E E E a : tau x (d) x (d) The special process 0 represents ....

R. Milner. The polyadic #-calculus: a tutorial. Technical report, University of Edinburgh, Octubre 1991.

.... as is well known, the state machine approach is inherently inadequate for describing action refinement, the operation of refining atomic actions in a concurrent process, which suggests aspects of top down modular development [1, 2, 3, 10, 16, 20, 32, 39, 40, 41, 47] and changes of granularity [28, 31]. This limitation is a direct result of the identification of concurrent actions with sequential, interleaved actions. For example, the state machine representation of the concurrent process a jj b, which can concurrently perform an a and b action, is identical to the state machine representation ....

R. Milner. Action structures. Technical report, University of Edinburgh, UK, 1992.

.... concurrent programming languages and theoretical process algebras. 1 Introduction One trendintheresearch onprocessalgebrasistoextendthemwith higherorder featuressomewhatanalogoustothe higher order rolethatfunctions play infunctionallanguages.Some approachesallow passinglabelsorports, e.g.[13],whereasothersallow passingprocesses,e.g. 21,23] Sometimes thisleadstohybridcalculithatcontainthesyntaxofa processalgebraas wellasthatofthe calculus,e.g. 5,14,9] Puttingmoreemphasison the functionalfeatures,anotherapproach istoextenda realistic functional ....

.... thisleadstohybridcalculithatcontainthesyntaxofa processalgebraas wellasthatofthe calculus,e.g. 5,14,9] Puttingmoreemphasison the functionalfeatures,anotherapproach istoextenda realistic functional languagewithprimitivesforcommunication.Good examplesincludeCML [18,19,13]andFacile[7]butalsoConcurrentClean[16]may be viewedin thisway. W ereferto[10]fora m uch moredetailedsurveyofsomeofthese issues. W efollow thelatterapproach andbaseourselvesonReppy slanguageCML. ItisanextensionofStandardML withprimitivesforcommunication;among otherthings thisallows ....

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R. Milner:The Polyadic...-Calculus:A Tutorial.ReportECS-LFCS91 -180,LaboratoryforFoundationsofComputerScience,University of Edinburgh,1991.

....and dare to dream of something with the precision and completeness of the formal definition of ML. In this context, the contribution of this paper is to demonstrate that a simple compositional treatment of fairness is necessary and possible. In the future, we plan to study the issue of mobility [MPW89, Mil91, FGL 96] namely dynamic channel creation and passing. We expect that this will nicely enhance Triveni, since mobility permits a uniform semantic treatment of dynamic channels and process creation [San92] and the rudiments of object oriented programming [Wal91] Our work inherits the ....

R. Milner, J. Parrow, and D. Walker. Mobile processes. Technical report, University of Edinburgh, 1989.

....reply channel c and the reply value is returned explicitly by reply. Schematic parser interprets synchronous process invocation (f x) as (touch (future (f x) 1 . Eliminating synchronous calls enables us (1) to get direct correspondence to process calculus such as HACL [14] calculus [15], and (2) to simplify implementation and optimization very much. Venezia has ML [3] like syntax, which we define below. P (proc) P 1 P 2 parallel execution j x.P channel creation j e 1 e 2 process call j e(x) P receive j e 1 =e 2 send j if e then P 1 condition else P 2 j fix 0 in ....

R. Milner. The polyadic ß-calculus: A tutorial. Technical report, University of Edinburgh, 1991.

....17] Traces do not, however, give one the same level of abstraction that is provided by being able to think of processes as functions. Similarly, though process algebra has now reached a high degree of mathematical maturity and elegance, see, for example, the recent books by Milner and by Hennessy [7, 12], it remains essentially an operational analysis of processes. The semantic models available are constructed from the computations of terms. This research supported by NSF grant CCR 8818979 Our study of the restricted version of Boudol s calculus, henceforth called the fl calculus, is based ....

R. Milner, J. Parrow, and D. Walker. Mobile processes. Technical report, University of Edinburgh, 1989. Draft.

....of polymorphism. In fact, an agent constant can be used to instantiate processes with different name structures for the names in the instantiated process. This name structure, arising in name passing calculi by the simple fact that names carry names, is captured by the notion of types for names [2, 7, 11, 13, 14]. Then we are in presence of a case To appear in 5th Parallel Architectures and Languages Europe, LNCS. Springer Verlag, July 1994. of predicative polymorphism where names in the instantiated processes have different types, instances of a more general (polymorphic) type for the agent. The ....

....LNCS. Springer Verlag, July 1994. of predicative polymorphism where names in the instantiated processes have different types, instances of a more general (polymorphic) type for the agent. The particular formulation of the calculus we propose introduces a new syntactic category for agents (cf. [7, 12]) variables over agents (in contrast with constants) and two new constructors for processes. Agents are either processes abstracted on a sequence of names, x n ) P , for x n = x 1 Delta Delta Delta x n a sequence of names and P a process, or recursively defined agents, rec X:A, binding ....

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

....of communication channels themselves. This calculus can be used to specify dynamically configuring concurrent systems and has been used, for example, to describe the semantics of object oriented programming languages [Wal90] Further Abstraction has resulted in the field of Action Structures [Mil92, Mil93b, Mil93a] a theory to underlie concrete models of concurrency and interaction. Overlap with other Formal Method Classes There is an evident overlap with both model based approaches and algebraic approaches, since both these classes of formal method deal with data types and operations on ....

....timed process algebras and model based formalisms could never achieve this. For the communication and timing philosophies of any particular process algebra it would be relatively easy to find another process algebra whose meaning was inexpressible although abstractions like action structures [Mil92, Mil93b, Mil93a] might provide solutions to this. In addition, there are subtle semantic differences between the different model based formal methods (for instance function application [DGS67, SDG67] which would make it impossible to capture the meaning of any one of them in any other without ....

R. Milner. Action structures. Technical report, University of Edinburgh, 1992.

....between traces and labelled transition systems. Timed extensions have been proposed for CSP [RR86] There is now a tool for the mathematical analysis of CSP agents akin to the Concurrency Workbench [Ros95] Research into Process Algebra s has continued with the pi calculus [MPW89a, MPW89b, Mil91] a generalised form of CCS which allows the transmission and reception of communication channels themselves. This calculus can be used to specify dynamically configuring concurrent systems and has been used, for example, to describe the semantics of object oriented programming languages [Wal90] ....

R. Milner. The polyadic ß-calculus: a tutorial. Technical report, University of Edinburgh, 1991.

....moment. To that end, the c var occurring in the body and moded out is written, for example, as Y j c and Z c . We do not care of whether or not the variables moded in are c vars. 2. 2 Polyadic Calculus calculus agents (processes) exchange data through communication channels concurrently [4]. The data and the communication channels are represented by names, which are only entities in calculus. Polyadic calculus (PPC) has the syntax defined as follows: P : P i2I i :P i j P jQ j (x 1 1 1 1 x n )P j A[x 1 1 1 1 x n ] j 0 The term i is called a prefix and has two ....

....when an agent does not include recursive calls. A summation P i2I i :P i behaves like one of the P i . 3 Translation This section tells how to translate an FGHC 0 program to a PPC statements (agent definitions) 3. 1 Term Representation in Polyadic Calculus We start with the Milner s idea[4] for representing general data structures. Accordingly, the macro definitions for cons, nil, and int are given by cons[t; x; y] t( c; n; i] c[x; y] nil[t] t( c; n; i] n( int[t; v] t( c; n; i] i[v] For instance, the cons definition represents the following protocol sequence: 1) a cons ....

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

....Science (1994) Proceedings MFPS8. On the Calculus and Linear Logic G. Bellin P. J. Scott y July 20, 1994 Abstract We detail Abramsky s proofs as processes paradigm for interpreting classical linear logic (CLL) 13] into a synchronous version of the calculus recently proposed by Milner [27, 28]. The translation is given at the abstract level of proof structures. We give a detailed treatment of information flow in proof nets and show how to mirror various evaluation strategies for proof normalization. We also give Soundness and Completeness results for the process calculus translations ....

....those involving nondeterministic choice ; typically an interaction with a process P Q chooses one of the components, and the other component is immediately destroyed. The question is: to what extent can we represent logical computation within the accepted concurrency world Robin Milner [27] recently developed a version of the calculus (the synchronous calculus) purposely supporting some of the logical rewriting envisioned by Abramsky. In this paper, we analyze the Abramsky view in detail for the synchronous calculus. We shall translate proofs (and certain normalization ....

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R. Milner. The Synchronous -Calculus. Unpublished lectures, Dept. of Computer Science, University of Edinburgh, 1992.

....(1994) Proceedings MFPS8. On the Calculus and Linear Logic G. Bellin 3 P. J. Scott y July 20, 1994 Abstract We detail Abramsky s proofs as processes paradigm for interpreting classical linear logic (CLL) 13] into a synchronous version of the calculus recently proposed by Milner [27, 28]. The translation is given at the abstract level of proof structures. We give a detailed treatment of information flow in proof nets and show how to mirror various evaluation strategies for proof normalization. We also give Soundness and Completeness results for the process calculus ....

....those involving nondeterministic choice ; typically an interaction with a process P Q chooses one of the components, and the other component is immediately destroyed. The question is: to what extent can we represent logical computation within the accepted concurrency world Robin Milner [27] recently developed a version of the calculus (the synchronous calculus) purposely supporting some of the logical rewriting envisioned by Abramsky. In this paper, we analyze the Abramsky view in detail for the synchronous calculus. We shall translate proofs (and certain normalization ....

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R. Milner. The Synchronous -Calculus. Unpublished lectures, Dept. of Computer Science, University of Edinburgh, 1992.

....N (and that of the system here presented) is the notion of attributing types to names, not to terms, resulting in a scenario where a term is assigned multiple name type scheme pairs. We leave to [8] discussions on more general type structures for dyadic interactions, among which Milner s sorting [14, 15] can be regarded as a particular instance. The only primitive operation for forming types, builds from types ff 1 ; ff n the type (ff 1 1 1 1 ff n ) n , n 0, representing a property of a name carrying a sequence of names of types ff 1 ; ff n . In this setting, a term is well typed, if ....

....of any name and the number of receptors and emitters in a process are bound by p, the textual representation of the process, we have that O(p 2 ) is an upper bound on the time taken to calculate the most general typing of a process. 5. Comparison to Milner s sorting program Robin Milner ([15]) introduced a different version of polyadic calculus along with the notion of sorts. In this section we prove that sorts are in a one to one correspondence with infinite regular trees; and that well sorted (normal form, located) agents in the Milner s polyadic calculus are in a one to one ....

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Robin Milner. The Polyadic ß-Calculus: a Tutorial. ECS-LFCS 91-180, University of Edinburgh, October 1991.

....The reason for the omission is that the fragment proposed here is general enough to express a fixed point operator. Theorem 1. 1 (Fix Point) For every process P there is an agent A such that, AhP i P j AhP i 1 For the extension of this note, we will write to sorts to mean the Milner s [3] or Sangiorgi s [4] approach, and types to mean our notion of types [6, 7] Proof: Take PXX def = P j q(Xhqi j qhXi:0) W def = p)p(X) PXX WW def = q(W hqi j qhW i:0) A def = P )WW Then, A is well sorted under sorting, p; q : s 7 ( ss) X : s) and, AhP i j 2 q(q(X) PXX j qhW ....

Robin Milner. The Polyadic ß-Calculus: a Tutorial. ECS-LFCS 91-180, University of Edinburgh, October 1991.

....necessarily present an input output behavior; objects usually communicate by asynchronous message passing (instead of function application) objects do maintain a state (in contrast with the stateless nature of functions) and objects may run concurrently. Inspired by Milner s polyadic calculus [4], Honda s calculus [3] and Hewitt s actor model [1] we present a basic object calculus where the notions of objects, asynchronous messages and concurrency are primitive, and introduce a type discipline along the lines of Honda [2] and Vasconcelos and Honda [7] for the (untyped) calculus, ....

....unification [5] The outline of the paper is as follows. The next section introduces the calculus and section 3 the notion of types and the typing assignment system. Sections 4 and 5 deal with principal typings and typing inference. Section 6 compares the calculus to the polyadic calculus [4] and its typing system as proposed in [7] The last section contains some concluding remarks. 2 The Calculus This section introduces the calculus to the extent needed for typing considerations. Structural congruence caters for equivalence of terms over concrete syntax and, together with normal ....

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Robin Milner. The Polyadic ß-Calculus: a Tutorial. ECS-LFCS 91-180, University of Edinburgh, October 1991.

....arbitrary sequences of names over channels, namely a straightforward generalization of the monadic calculus as presented in [9] where ordered tuples of names replace single names as the object of communications. The notion of types we introduce for this calculus is essentially Milner s sorting [10]. Thus our results extend Milner s work on sorting, with a clean type inference system together with an efficient type reconstruction algorithm. 3 In 4th International Conference on Concurrency Theory, volume 715 of LNCS, pages 524 538. Springer Verlag, August 1993. The typing system ....

....be linear (in all interesting cases) on the number of nodes in the graph, the algorithm to find the principal typing of a process is linear on the size of the textual representation of the input term. 4 Related Work and Discussions Milner s sorting Our notion of typing already appeared in Milner [10], under the name of sorting . While there is a mild difference in outlook, our terms are, as easily seen, a subset of the terms of Milner s polyadic calculus. As to sorting, 10] introduced a sort checking system for the polyadic calculus, and it is not so difficult to prove that a term is ....

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Robin Milner. The Polyadic ß-Calculus: a Tutorial. ECS-LFCS 91-180, University of Edinburgh, October 1991.

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

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Milner, R. The Polyadic #-calculus: A Tutorial. Tech. Rep. ECS-LFCS-91-180, University of Edinburgh, October 1991.

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R. Milner, J. Parrow, and D. Walker. Mobile processes. Technical report, University of Edinburgh, 1989.

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R. Milner. The polyadic -Calculus: a Tutorial, LFCS, University of Edinburgh, October 1991 38

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R. Milner. The Polyadic ß-calculus: A Tutorial. Technical Report, University of Edinburgh, 1991.

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