Relational Reasoning About Functions and Nondeterminism Basic Research in Computer Science
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Edsger W. Dijkstra: a Commemoration
Edsger W. Dijkstra: a Commemoration Krzysztof R. Apt1 and Tony Hoare2 (editors) 1 CWI, Amsterdam, The Netherlands and MIMUW, University of Warsaw, Poland 2 Department of Computer Science and Technology, University of Cambridge and Microsoft Research Ltd, Cambridge, UK Abstract This article is a multiauthored portrait of Edsger Wybe Dijkstra that consists of testimo- nials written by several friends, colleagues, and students of his. It provides unique insights into his personality, working style and habits, and his influence on other computer scientists, as a researcher, teacher, and mentor. Contents Preface 3 Tony Hoare 4 Donald Knuth 9 Christian Lengauer 11 K. Mani Chandy 13 Eric C.R. Hehner 15 Mark Scheevel 17 Krzysztof R. Apt 18 arXiv:2104.03392v1 [cs.GL] 7 Apr 2021 Niklaus Wirth 20 Lex Bijlsma 23 Manfred Broy 24 David Gries 26 Ted Herman 28 Alain J. Martin 29 J Strother Moore 31 Vladimir Lifschitz 33 Wim H. Hesselink 34 1 Hamilton Richards 36 Ken Calvert 38 David Naumann 40 David Turner 42 J.R. Rao 44 Jayadev Misra 47 Rajeev Joshi 50 Maarten van Emden 52 Two Tuesday Afternoon Clubs 54 2 Preface Edsger Dijkstra was perhaps the best known, and certainly the most discussed, computer scientist of the seventies and eighties. We both knew Dijkstra |though each of us in different ways| and we both were aware that his influence on computer science was not limited to his pioneering software projects and research articles. He interacted with his colleagues by way of numerous discussions, extensive letter correspondence, and hundreds of so-called EWD reports that he used to send to a select group of researchers. -
Massachusetts Institute of Technology Artificial Intelligence Laboratory
MASSACHUSETTS INSTITUTE OF TECHNOLOGY ARTIFICIAL INTELLIGENCE LABORATORY Working Paper 190 June 1979 A FAIR POWER DOMAIN FOR ACTOR COMPUTATIONS Will Clinger AI Laboratory Working Papers are produced for internal circulation, and may contain information that is, for example, too preliminary or too detailed for formal publication. Although some will be given a limited external distribution, it is not intended that they should be considered papers to which reference can be made in the literature. This report describes research conducted at the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for this research was provided in part by the Office of Naval Research of the Department of Defense under Contract N00014-75-C-0522. O MASSAnuTsms INSTTUTE OF TECMGoOry FM DRAFT 1 June 1979 -1- A fair power domain A FAIR POWER DOMAIN FOR ACTOR COMPUTATIONS Will Clingerl 1. Abstract Actor-based languages feature extreme concurrency, allow side effects, and specify a form of fairness which permits unbounded nondeterminism. This makes it difficult to provide a satisfactory mathematical foundation for their semantics. Due to the high degree of parallelism, an oracle semantics would be intractable. A weakest precondition semantics is out of the question because of the possibility of unbounded nondeterminism. The most attractive approach, fixed point semantics using power domains, has not been helpful because the available power domain constructions, although very general, seemed to deal inadequately with fairness. By taking advantage of the relatively complex structure of the actor computation domain C, however, a power domain P(C) can be defined which is similar to Smyth's weak power domain but richer. -
Actor Model of Computation
Published in ArXiv http://arxiv.org/abs/1008.1459 Actor Model of Computation Carl Hewitt http://carlhewitt.info This paper is dedicated to Alonzo Church and Dana Scott. The Actor model is a mathematical theory that treats “Actors” as the universal primitives of concurrent digital computation. The model has been used both as a framework for a theoretical understanding of concurrency, and as the theoretical basis for several practical implementations of concurrent systems. Unlike previous models of computation, the Actor model was inspired by physical laws. It was also influenced by the programming languages Lisp, Simula 67 and Smalltalk-72, as well as ideas for Petri Nets, capability-based systems and packet switching. The advent of massive concurrency through client- cloud computing and many-core computer architectures has galvanized interest in the Actor model. An Actor is a computational entity that, in response to a message it receives, can concurrently: send a finite number of messages to other Actors; create a finite number of new Actors; designate the behavior to be used for the next message it receives. There is no assumed order to the above actions and they could be carried out concurrently. In addition two messages sent concurrently can arrive in either order. Decoupling the sender from communications sent was a fundamental advance of the Actor model enabling asynchronous communication and control structures as patterns of passing messages. November 7, 2010 Page 1 of 25 Contents Introduction ............................................................ 3 Fundamental concepts ............................................ 3 Illustrations ............................................................ 3 Modularity thru Direct communication and asynchrony ............................................................. 3 Indeterminacy and Quasi-commutativity ............... 4 Locality and Security ............................................ -
Common Sense for Concurrency and Strong Paraconsistency Using Unstratified Inference and Reflection
Published in ArXiv http://arxiv.org/abs/0812.4852 http://commonsense.carlhewitt.info Common sense for concurrency and strong paraconsistency using unstratified inference and reflection Carl Hewitt http://carlhewitt.info This paper is dedicated to John McCarthy. Abstract Unstratified Reflection is the Norm....................................... 11 Abstraction and Reification .............................................. 11 This paper develops a strongly paraconsistent formalism (called Direct Logic™) that incorporates the mathematics of Diagonal Argument .......................................................... 12 Computer Science and allows unstratified inference and Logical Fixed Point Theorem ........................................... 12 reflection using mathematical induction for almost all of Disadvantages of stratified metatheories ........................... 12 classical logic to be used. Direct Logic allows mutual Reification Reflection ....................................................... 13 reflection among the mutually chock full of inconsistencies Incompleteness Theorem for Theories of Direct Logic ..... 14 code, documentation, and use cases of large software systems Inconsistency Theorem for Theories of Direct Logic ........ 15 thereby overcoming the limitations of the traditional Tarskian Consequences of Logically Necessary Inconsistency ........ 16 framework of stratified metatheories. Concurrency is the Norm ...................................................... 16 Gödel first formalized and proved that it is not possible -
Fifty Years of Hoare's Logic
Fifty Years of Hoare's Logic Krzysztof R. Apt CWI, Amsterdam, The Netherlands MIMUW, University of Warsaw, Warsaw, Poland Ernst-R¨udigerOlderog University of Oldenburg, Oldenburg, Germany Contents 1 Introduction 2 2 Precursors 3 2.1 Turing . .3 2.2 Floyd . .5 3 Hoare's Contributions 6 3.1 Reasoning about while programs . .6 3.2 Reasoning about recursive procedures . .9 3.3 Reasoning about termination . 11 4 Soundness and Completeness Matters 13 4.1 Preliminaries . 13 4.2 Soundness . 14 4.3 Completeness . 15 5 Fine-tuning the Approach 18 5.1 Adaptation rules . 18 5.2 Subscripted and local variables . 20 5.3 Parameter mechanisms and procedure calls . 23 6 Reasoning about Arbitrary Procedures 25 arXiv:1904.03917v2 [cs.LO] 24 Oct 2019 6.1 Completeness results for recursive procedures . 25 6.2 Clarke's incompleteness result . 28 6.3 Clarke's language L4 ......................................... 29 6.4 The characterization problem . 30 1 7 Nondeterministic and Probabilistic Programs 32 7.1 Reasoning about nondeterminism . 32 7.2 Reasoning about fairness . 34 7.3 Probabilistic programs . 36 8 Parallel and Distributed Programs 37 8.1 Reasoning about parallel programs . 37 8.2 Reasoning about distributed programs . 42 9 Object-oriented Programs 46 9.1 Language characteristics . 46 9.2 Reasoning about object-oriented programs . 47 9.3 Advanced topics in the verification of object-oriented programs . 49 10 Alternative Approaches 51 10.1 Weakest precondition semantics and systematic program development . 51 10.2 Specifying in Hoare's logic . 53 10.3 Programming from specifications . 54 10.4 Algorithmic logic and dynamic logic . -
The Theory and Practice of Concurrency A.W. Roscoe
Contents i The Theory and Practice of Concurrency A.W. Roscoe Published 1997, revised to 2000 and lightly revised to 2005. The original version is in print in April 2005 with Prentice-Hall (Pearson). This version is made available for personal reference only. This version is copyright (c ) Pearson and Bill Roscoe. Contents Preface ix 0 Introduction 1 0.1 Background 1 0.2 Perspective 4 0.3 Tools 7 0.4 What is a communication? 8 I A FOUNDATION COURSE IN CSP 11 1 Fundamental concepts 13 1.1 Fundamental operators 14 1.2 Algebra 29 1.3 The traces model and traces refinement 35 1.4 Tools 48 2 Parallel operators 51 2.1 Synchronous parallel 51 2.2 Alphabetized parallel 55 2.3 Interleaving 65 2.4 Generalized parallel 68 iv Contents 2.5 Parallel composition as conjunction 70 2.6 Tools 74 2.7 Postscript: On alphabets 76 3 Hiding and renaming 77 3.1 Hiding 77 3.2 Renaming and alphabet transformations 86 3.3 A basic guide to failures and divergences 93 3.4 Tools 99 4 Piping and enslavement 101 4.1 Piping 101 4.2 Enslavement 107 4.3 Tools 112 5 Buffers and communication 115 5.1 Pipes and buffers 115 5.2 Buffer tolerance 127 5.3 The alternating bit protocol 130 5.4 Tools 136 5.5 Notes (2005) 137 6 Termination and sequential composition 139 6.1 What is termination? 139 6.2 Distributed termination 143 6.3 Laws 144 6.4 Effects on the traces model 147 6.5 Effects on the failures/divergences model 148 II THEORY 151 7 Operational semantics 153 7.1 A survey of semantic approaches to CSP 153 7.2 Transition systems and state machines 155 Contents v 7.3 Firing rules -
Actor Model of Computation: Scalable Robust Information Systems
Actor Model of Computation: Scalable Robust Information Systems Carl Hewitt This article is dedicated to Alonzo Church and Dana Scott. The Actor Model is a mathematical theory that treats “Actors” as the universal primitives of digital computation. Hypothesis:i All physically possible computation can be directly implemented using Actors. The model has been used both as a framework for a theoretical understanding of concurrency, and as the theoretical basis for several practical implementations of concurrent systems. The advent of massive concurrency through client-cloud computing and many-core computer architectures has galvanized interest in the Actor Model. Message passing using types is the foundation of system communication: ñ Messages are the unit of communication1 ñ Types enable secure communication with any Actor When an Actor receives a message, it can concurrently: ñ send messages to (unforgeable) addresses of Actors that it has; ñ create new Actors; ñ designate how to handle the next message it receives. The Actor Model can be used as a framework for modeling, understanding, and reasoning about, a wide range of concurrent systems. For example: ñ Electronic mail (e-mail) can be modeled as an Actor system. Mail accounts are modeled as Actors and email addresses as Actor addresses. ñ Web Services can be modeled with endpoints modeled as Actor addresses. ñ Objects with locks (e.g. as in Java and C#) can be modeled as Actors. ñ Functional and Logic programs can be implemented using Actors. Actor technology will see significant application for integrating all kinds of digital information for individuals, groups, and organizations so their information usefully links together. -
Actor Model of Computation for Scalable Robust Information Systems Carl Hewitt
Actor Model of Computation for Scalable Robust Information Systems Carl Hewitt To cite this version: Carl Hewitt. Actor Model of Computation for Scalable Robust Information Systems: One computer is no computer in IoT. Inconsistency Robustness, 2015, 978-1-84890-159-9. hal-01163534v3 HAL Id: hal-01163534 https://hal.archives-ouvertes.fr/hal-01163534v3 Submitted on 29 Sep 2015 (v3), last revised 11 Aug 2017 (v7) HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Actor Model of Computation for Scalable Robust Information Systems: One computer is no computer in IoT Carl Hewitt This article is dedicated to Alonzo Church and Dana Scott. Introduction The Actor Model is a mathematical theory that treats “Actors” as the universal conceptual primitives of digital computation. Hypothesis:i All physically possible digital computation can be directly implemented using Actors. The model has been used both as a framework for a theoretical understanding of concurrency, and as the theoretical basis for several practical implementations of concurrent systems. Actors are direct and efficient: Digital computation can be efficiently implemented without loss of processing, communication, or storage efficiency Digital computation can be directly modeled without requiring extraneous elements, e.g., channels or registers. -
Actor Model of Computation: Scalable Robust Information Systems
Actor Model of Computation: Scalable Robust Information Systems Carl Hewitt This article is dedicated to Alonzo Church and Dana Scott. The Actor Model is a mathematical theory that treats “Actors” as the universal primitives of digital computation. Hypothesis:i All physically possible computation can be directly implemented using Actors. The model has been used both as a framework for a theoretical understanding of concurrency, and as the theoretical basis for several practical implementations of concurrent systems. The advent of massive concurrency through client-cloud computing and many-core computer architectures has galvanized interest in the Actor Model. Message passing using types is the foundation of system communication: Messages are the unit of communication1 Types enable secure communication with any Actor When an Actor receives a message, it can concurrently: send messages to (unforgeable) addresses of Actors that it has; create new Actors; designate how to handle the next message it receives. The Actor Model can be used as a framework for modeling, understanding, and reasoning about, a wide range of concurrent systems. For example: Electronic mail (e-mail) can be modeled as an Actor system. Mail accounts are modeled as Actors and email addresses as Actor addresses. Web Services can be modeled with endpoints modeled as Actor addresses. Objects with locks (e.g. as in Java and C#) can be modeled as Actors. Functional and Logic programs can be implemented using Actors. Actor technology will see significant application for integrating all kinds of digital information for individuals, groups, and organizations so their information usefully links together. i This hypothesis is an update to [Church 1936] that all physically computable functions can be implemented using the lambda calculus. -
Actor Model of Computation for Scalable Robust Information Systems Carl Hewitt
Actor Model of Computation for Scalable Robust Information Systems Carl Hewitt To cite this version: Carl Hewitt. Actor Model of Computation for Scalable Robust Information Systems: One IoT is No IoT1. Symposium on Logic and Collaboration for Intelligent Applications„ Mar 2017, Stanford, United States. hal-01163534v7 HAL Id: hal-01163534 https://hal.archives-ouvertes.fr/hal-01163534v7 Submitted on 11 Aug 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Copyright Actor Model of Computation for Scalable Robust Information Systems One IoT is No IoT1 Carl Hewitt This article is dedicated to Alonzo Church and Dana Scott. Introduction The Actor Model is a mathematical theory that treats “Actors” as the universal conceptual primitives of digital computation. Hypothesis:i All physically possible digital computation can be directly modeled and implemented using Actors. The model has been used both as a framework for a theoretical understanding of concurrency, and as the theoretical basis for several practical implementations of concurrent systems. Actors are direct and efficient: Digital computation can be efficiently implemented without loss of processing, communication, or storage efficiency Digital computation can be directly modeled without requiring extraneous elements, e.g., channels or registers. -
Edsger W. Dijkstra: a Commemoration
Edsger W. Dijkstra: a Commemoration Krzysztof R. Apt1 and Tony Hoare2 (editors) March 30, 2021 1 CWI, Amsterdam, The Netherlands and MIMUW, University of Warsaw, Poland 2 Department of Computer Science and Technology, University of Cambridge and Microsoft Research Ltd, Cambridge, UK Abstract This article is a multiauthored portait of Edsger Wybe Dijkstra that consists of testimo- nials written by several friends, colleagues, and students of his. It provides unique insights into his personality, working style and habits, and his influence on other computer scientists, as a researcher, teacher, and mentor. Contents Preface 3 Tony Hoare 4 Donald Knuth 9 Christian Lengauer 11 K. Mani Chandy 13 Eric C.R. Hehner 15 Mark Scheevel 17 Krzysztof R. Apt 18 Niklaus Wirth 20 Lex Bijlsma 23 Manfred Broy 24 David Gries 26 Ted Herman 28 Alain J. Martin 29 J Strother Moore 31 Vladimir Lifschitz 33 1 Wim H. Hesselink 34 Hamilton Richards 36 Ken Calvert 38 David Naumann 40 David Turner 42 J.R. Rao 44 Jayadev Misra 47 Rajeev Joshi 50 Maarten van Emden 52 Two Tuesday Afternoon Clubs 54 2 Preface Edsger Dijkstra was perhaps the best known, and certainly the most discussed, computer scientist of the seventies and eighties. We both knew Dijkstra |though each of us in different ways| and we both were aware that his influence on computer science was not limited to his pioneering software projects and research articles. He interacted with his colleagues by way of numerous discussions, extensive letter correspondence, and hundreds of so-called EWD reports that he used to send to a select group of researchers. -
A Theory for Nondeterminism, Parallelism, Communication, and Concurrency *
Theoretical Computer Science 45 (1986) 1-61 North-Holland A THEORY FOR NONDETERMINISM, PARALLELISM, COMMUNICATION, AND CONCURRENCY * Manfred BROY Fakultiit J~r Mathematik und lnformatik, Universitiit Passau, 8390 Passau, Fed. Rep. Germany Communicated by M. Nivat Received January 1984 Revised January 1986 Abstract. An applicative language is introduced for representing concurrent programs and com- municating systems in the form of mutually recursive systems of nondeterministic equations for functions and streams. Mathematical semantics is defined by associating particular fixed points with such systems. These fixed points are chosen using a combination of several complete partial orderings. Operational semantics is described in the form of term rewriting rules, consistent with the mathematical semantics. It represents data-driven reduction semantics for usual expressions and data-driven data flow semantics in the case of recursive stream equations. So the language allows to treat the basic semantic notions of nondeterminism, parallelism, communication, and concurrency for multiprogramming in a completely formal, applicative framework. In particular, it provides a semantic theory for networks of loosely coupled, nondeterministic, communicating, stream processing functions. Finally, the relationship of the presented language to partial recursive functions and nonconventional computational models such as data flow and reduction machines is shown. Contents 1. Introduction .....................................................................