On formalised computer programs

Luckham, David C.; Park, D. M. R.; Paterson, Mike

doi:10.1016/s0022-0000(70)80022-8

Cited by 204 publications

(59 citation statements)

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“…It was given considerable impetus by the work of Luckham et al (1970) and Paterson and Hewitt (1970); see also Greibach (1975). The study of the correctness of interpreted programs goes back to the work of Turing and von Neumann, but seems to have become a well-defined area of research following Floyd (1967), Hoare (1969) and Manna (1974).…”

Section: Bibliographical Notesmentioning

confidence: 99%

First-Order Dynamic Logic

Harel¹

1979

Lecture Notes in Computer Science

424

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Section: Bibliographical Notesmentioning

confidence: 99%

First-Order Dynamic Logic

Harel¹

1979

Lecture Notes in Computer Science

424

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“…C'est pourquoi Ianov ([19]) a introduit les schémas de programme en dissociant les deux éléments sous-jacents à la notion de programme : -au niveau de la structure, le schéma de programme, qui représente intuitivement la structure de contrôle (branchements, etc..) du programme qui demeure lorsqu'on « oublie » la nature et le sens des fonctions de base et des variables et qu'on les considère comme des symboles purement formels. Nombreux sont les auteurs qui se sont penchés sur ces schémas ( [4,21,31]), leur sémantique ( [10,15]) et ses applications : équivalences de programme ( [7,29]), élimination de la récursivité ( [17,32]), vérification de programmes ( [24]), etc.. En effet, les propriétés d'un programme indépendantes de la sémantique sont de nature syntaxique et seront donc prouvées de manière plus simple et plus naturelle au niveau de la syntaxe -c'est-à-dire au niveau du schéma de programme. Elles s'appliqueront alors à tous les programmes déduits du schéma de programme au moyen d'une interprétation ( [23]).…”

Section: Schémas Et Interprétationsunclassified

“…Cela donne un moyen effectif de vérifier pratiquement que deux schémas de programme sont équivalents pour toute interprétation de #', bien que ce problème soit habituellement très complexe : c'est en particulier le cas lorsque ( €' est une famille d'interprétations où un symbole de fonction ternaire donné est toujours interprété comme un test (cf. [14,21]). Nous allons nous intéresser à ce problème dans la suite de cet article et chercher pour quelles familles # la propriété, pour un symbole de fonction donné, d'être interprété comme un test est ^-congruentielle.…”

Section: Définitionsunclassified

Les tests et leur caractérisation syntaxique

Guessarian¹

1977

RAIRO. Inform. théor.

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“…Finally, it should be noted that the fundamental paper [17] of Luckham, Park, and Paterson on flowchart schemes makes frequent use of concepts from automata and language theory as do others [16,20].…”

Section: B Program Schemesmentioning

confidence: 99%

Formal language theory and theoretical computer science

Book

1975

Lecture Notes in Computer Science

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In the last fifteen years the area of formal language theory and abstract automata has enjoyed a great deal of attention from the research community in theoretical computer science. However, in the last few years the main interest in theoretical computer science has been directed elsewhere. In these notes I shall consider the role of formal language theory in theoretical computer science by discussing some areas in which formal language theory may find applications.Behind the activities in theoretical computer science lie the major problems of understanding the nature of computation and its relationship to computing methodology.While this area is mathematical and abstract in spirit, it is not pure mathematics:indeed, theoretical computer science derives much of its motivation from the abstraction of the practical problems of computation.Abstraction for the sake of abstraction and beauty is one of the goals of modern pure mathematics [ i]. However, as part of theoretical computer science, formal language theory must speak to problems concerning the nature of computation. In Part I of these notes I point to results of language theory which stem from or lend insight to the more general study of computability and computational complexity. In Part I I I discuss several problem areas where formal language theory may find interesting and fruitful application. In this context I urge the reader to consult the paper "Programming languages, natural languages, and mathematics" by Peter Naur [ 2].# The preparation of this paper was supported in part by the National Science Foundation under Grant GJ-30409 and by the Department of Computer Science, Yale University. Part IFormal language theory is concerned with the specification and manipulation of sets of strings of symbols, i.e., languages. It is my thesis here that as an area of interest within theoretical computer science formal language theory should be closely tied to the study of computability theory and computational complexity. Computability theory is concerned with the representation of algorithms and languages, and computational complexity considers the inherent difficulty of evaluating functions and deciding predicates. Within the scope of these studies are the questions of determinism versus nondeterminism, trade-offs between measures and representations, differences in computational power stemming from different choices of atomic operations, and the existence of hierarchies.We shall explore two topics in order to illustrate how the common features and the differences between formal language theory and computability theory can interact fruitfully. In both cases it is shown that the questions and results of formal language theory take on new significance when reconsidered in terms of computability theory and computational complexity. A. Universal SetsOne of the most basic notions in computability theory is the notion of a "universal machine." This notion allows a representation of the concept of "self-reference" in terms of a class of algorithms. It is particularly...

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On formalised computer programs

Cited by 204 publications

References 2 publications

First-Order Dynamic Logic

First-Order Dynamic Logic

Les tests et leur caractérisation syntaxique

Formal language theory and theoretical computer science

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