The revised edition contains a new chapter which provides an elegant description of the semantics. The various classes of lambda calculus models are described in a uniform manner. Some didactical improvements have been made to this edition. An example of a simple model is given and then the general theory (of categorical models) is developed. Indications are given of those parts of the book which can be used to form a coherent course.
The revised edition contains a new chapter which provides an elegant description of the semantics. The various classes of lambda calculus models are described in a uniform manner. Some didactical improvements have been made to this edition. An example of a simple model is given and then the general theory (of categorical models) is developed. Indications are given of those parts of the book which can be used to form a coherent course.
Die funktionale und applikative Programmierung nimmt seit vielen Jahren einen wichtigen Platz innerhalb der verschiedenen Programmierparadigmen ein. Das Buch bietet eine leicht verständliche Einführung – von den theoretischen Grundlagen bis hin zu Implementierungstechniken. Im Hauptteil stellt der Autor die zahlreichen Ausprägungen in den unterschiedlichen Programmiersprachen vor. Er gibt auch einen Ausblick darauf, wie sich diese Programmiersprachen auf die Entwicklung neuer Rechnerstrukturen auswirken können.
5. 2 Temporale Konjunktionen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 5. 2. 1 nachdem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 5. 2. 2 bevor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 5. 2. 3 während . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 5. 2. 4 als und wenn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 5. 2. 5 Weitere Konjunktionen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 5. 2. 5. 1 indem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 5 . 2. 5 . 2 sobald und sowie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 5. 3 Durative Konjunktionen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 5. 3. 1 Vorbemerkungen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 5. 3. 2 solange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 5. 3. 3 seit( dem) und bis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 6. Resümee und Schlußbemerkungen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 Anhang 1: Verzeichnis wichtiger Definitionen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 Anhang II: Verzeichnis wichtiger semantischer Repräsentationen . . . . . . . . . . . . 320 Literatur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 6 Vorwort Die vorliegende Untersuchung ist eine in Teilen überarbeitete und erweiterte Fasssung meiner Dissertation an der Philosophischen Fakultät der Heinrich Heine-Universität Düsseldorf mit dem Titel Semantik von Tempus, Aspekt und subordinierenden temporalen Konjunktionen, die ich im Sommer 1989 unter der Betreuung von Dieter Wunderlich fertiggestellt habe. Meine Beschäftigung mit der Temporalsemantik begann im September 1985, als ich am Seminar für Allgemeine Sprachwissenschaft der Universität Düsseldorf gemeinsam mit Sebastian Löbner für ein Jahr in einem von Dieter Wunderlich geleiteten Forschungsprojekt der Deutschen Forschungsgemeinschaft über dieses Thema gearbeitet habe. Sebastian Löbner hat während dieser Zeit meine Vorstellungen in unermüdlichen Diskussionen mit mir erörtert und so entscheidend geprägt. Dieter Wunderlich hat die Entstehung dieser Arbeit betreut und dabei viel Geduld bewiesen, wenn ich mich allzu häufig anderen Themen zugewandt habe und dadurch die Fertigstellung der Arbeit verzögert habe.
Dieses Buch vermittelt Techniken zur Formalisierung der Semantik (Bedeutungsinhalte) von Programmiersprachen. Zunächst werden unterschiedliche Formalisierungsansätze (die operationelle, denotationelle und axiomatische Semantik) vorgestellt und diskutiert. Anschließend wird die mathematische Theorie der semantischen Bereiche entwickelt, die bei der zur Zeit wichtigsten, der denotationellen Methode, Anwendung findet. Danach wird schrittweise eine umfassende, PASCAL-orientierte Programmiersprache entwickelt und die Semantik der einzelnen Sprachkonstrukte denotationell spezifiziert. Die Fortsetzungssemantik (continuation semantics) wird dabei systematisch erklärt und verwendet. Schließlich wird auf die Anwendung dieser Techniken eingegangen, insbesondere im Rahmen des Compilerbaus und als Grundlage zur Entwicklung funktionaler Programmiersprachen. Das Wissen, das in diesem Buch vermittelt wird, ermöglicht es, selbständig die Semantik neuer, unterschiedlicher Sprachkonstrukte formal zu definieren und damit umzugehen, und natürlich vorgegebene formale Beschreibungen zu verstehen. Dies ist besonders wichtig bei der Entwicklung neuer Sprachen, beim Beweisen von Programmeigenschaften und beim Compilerbau.
For over half a century, Boris (Boaz) Trakhtenbrot has made seminal contributions to virtually all of the central areas of theoretical computer science. This festschrift volume readily illustrates the profound influence he has had on the field.
The Lambda Calculus, treated in this book mainly in its untyped version, consists of a collection of expressions, called lambda terms, together with ways how to rewrite and identify these. In the parts conversion, reduction, theories, and models the view is respectively 'algebraic', computational, with more ('coinductive') identifications, and finally set-theoretic. The lambda terms are built up from variables, using application and abstraction. Applying a term F to M has as intention that F is a function, M its argument, and FM the result of the application. This is only the intention: to actually obtain the result one has to rewrite the expression FM according to the reduction rules. Abstraction provides a way to create functions according to the effect when applying them. The power of the theory comes from the fact that computations, both terminating and infinite, can be expressed by lambda terms at a 'comfortable' level of abstraction.
This volume constitutes the refereed proceedings of the 37th International Symposium on Mathematical Foundations of Computer Science, MFCS 2012, held in Bratislava, Slovakia, in August 2012. The 63 revised full papers presented together with 8 invited talks were carefully reviewed and selected from 162 submissions. Topics covered include algorithmic game theory, algorithmic learning theory, algorithms and data structures, automata, formal languages, bioinformatics, complexity, computational geometry, computer-assisted reasoning, concurrency theory, databases and knowledge-based systems, foundations of computing, logic in computer science, models of computation, semantics and verification of programs, and theoretical issues in artificial intelligence.
This volume is the proceedings of the 3rd Workshop on the Mathematical Foundations of Programming Language Semantics held at Tulane University, New Orleans, Louisiana, April 8-10, 1987. The 1st Workshop was at Kansas State University, Manhattan, Kansas in April, 1985 (see LNCS 239), and the 2nd Workshop with a limited number of participants was at Kansas State in April, 1986. It was the intention of the organizers that the 3rd Workshop survey as many areas of the Mathematical Foundations of Programming Language Semantics as reasonably possible. The Workshop attracted 49 submitted papers, from which 28 papers were chosen for presentation. The papers ranged in subject from category theory and Lambda-calculus to the structure theory of domains and power domains, to implementation issues surrounding semantics.
This volume demonstrates the viability of mathematical research into the foundations of categorial grammar, a topic at the border between logic and linguistics. A new introduction to this paperback edition updates the open research problems and records relevant results through pointers to the literature.
This monograph began life as a series of papers documenting five years of research into the logical foundations of Categorial Grammar, a grammatical paradigm which has close analogies with Lambda Calculus and Type Theory. The technical theory presented here stems from the interface between Logic and Linguistics and, in particular, the theory of generalized quantification. A categorical framework with lambda calculus-oriented semantics is a convenient vehicle for generalizing semantic insights (obtained in various corners of natural language) into one coherent theory. The book aims to demonstrate to fellow logicians that the resulting applied lambda calculus has intrinsic logical interest. In the final analysis, the idea is not just to `break the syntactic code' of natural languages but to understand the cognitive functioning of the human mind.
A compilation of papers presented at the 2001 European Summer Meeting of the Association for Symbolic Logic, Logic Colloquium '01 includes surveys and research articles from some of the world's preeminent logicians. Two long articles are based on tutorials given at the meeting and present accessible expositions of research in two active areas of logic, geometric model theory and descriptive set theory of group actions. The remaining articles cover seperate research topics in many areas of mathematical logic, including applications in Computer Science, Proof Theory, Set Theory, Model Theory, Computability Theory, and aspects of Philosophy. This collection will be of interest to philosophical logicians, historians of logic, computer scientists, formal linguists, and mathematicians in the areas of algebra, abstract analysis and topology.
This book constitutes the refereed proceedings of the 6th International Conference on Foundations of Software Science and Computation Structures, FOSSACS 2003, held in Warsaw, Poland in April 2003. The 26 revised full papers presented together with an invited paper were carefully reviewed and selected from 96 submissions. Among the topics covered are algebraic models; automata and language theory; behavioral equivalences; categorical models; computation processes over discrete and continuous data; computation structures; logics of programs; models of concurrent, reactive, distributed, and mobile systems; process algebras and calculi; semantics of programming languages; software specification and refinement; transition systems; and type systems and type theory.
These AIP Conference Proceedings contain the papers of the two invited speakers: "Systems with Emergent Dynamics" by Ian Stewart (UK), who received the CHAOS AWARD, and "The Role of Anticipation in Intelligent Systems" by George J. Klir (USA), who received the CASYS'01 AWARD. Second, all the papers of the authors who received a Best Paper Award, and, third, a selection of invited papers. The scope is the study, research, and development in the new frontier of science dealing with the paradigm of computing anticipatory systems. A computing anticipatory system is a system which computes its current states in taking into account its anticipatory states. Strong anticipation refers to an anticipation of events built by or embedded in a system. Weak anticipation refers to an anticipation of events predicted or forecast from a model of a system. Topics include Anticipatory Systems, Cybernetics and Epistemology; Mathematical System, Chaos, Anticipation and Incursion; Relativity, Quantum Physics and Quantum Computing; Intelligent Agents, Learning and Cognitive Systems; Organisation, Regulation, Management and Planning; Control Systems, Robots, Neural Nets and Agents; and Information Science Models and Anticipatory Programs.
In writing this book, our goal was to produce a text suitable for a first course in mathematical logic more attuned than the traditional textbooks to the re cent dramatic growth in the applications oflogic to computer science. Thus, our choice oftopics has been heavily influenced by such applications. Of course, we cover the basic traditional topics: syntax, semantics, soundnes5, completeness and compactness as well as a few more advanced results such as the theorems of Skolem-Lowenheim and Herbrand. Much ofour book, however, deals with other less traditional topics. Resolution theorem proving plays a major role in our treatment of logic especially in its application to Logic Programming and PRO LOG. We deal extensively with the mathematical foundations ofall three ofthese subjects. In addition, we include two chapters on nonclassical logics - modal and intuitionistic - that are becoming increasingly important in computer sci ence. We develop the basic material on the syntax and semantics (via Kripke frames) for each of these logics. In both cases, our approach to formal proofs, soundness and completeness uses modifications of the same tableau method in troduced for classical logic. We indicate how it can easily be adapted to various other special types of modal logics. A number of more advanced topics (includ ing nonmonotonic logic) are also briefly introduced both in the nonclassical logic chapters and in the material on Logic Programming and PROLOG.
This book constitutes the refereed proceedings of the 29th Conference on Current Trends in Theory and Practice of Informatics, SOFSEM 2002, held in Milovy, Czech Republic, in November 2002. The volume presents 10 invited lectures and the report on a panel discussion on GRID computing together with 11 revised full papers selected from 22 submissions. Among the topics covered are system design and testing related theory, distributed and parallel systems, type theory, multimedia, databases, computer vision, and soft computing.

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