Applications of Categories in Computer Science

Author: London Mathematical Society. Symposium
Publisher: Cambridge University Press
ISBN: 0521427266
Release Date: 1992-06-26
Genre: Mathematics

Category theory and related topics of mathematics have been increasingly applied to computer science in recent years. This book contains selected papers from the London Mathematical Society Symposium on the subject which was held at the University of Durham. Participants at the conference were leading computer scientists and mathematicians working in the area and this volume reflects the excitement and importance of the meeting. All the papers have been refereed and represent some of the most important and current ideas. Hence this book will be essential to mathematicians and computer scientists working in the applications of category theory.

Automata Languages and Programming

Author: Michele Bugliesi
Publisher: Springer Science & Business Media
ISBN: 9783540359074
Release Date: 2006-06-30
Genre: Computers

The two-volume set LNCS 4051 and LNCS 4052 constitutes the refereed proceedings of the 33rd International Colloquium on Automata, Languages and Programming, ICALP 2006, held in Venice, Italy, July 2006. In all, these volumes present more 100 papers and lectures. Volume II (4052) presents 2 invited papers and 2 additional conference tracks with 24 papers each, focusing on algorithms, automata, complexity and games as well as on security and cryptography foundation.

Theoretical Aspects of Computer Software

Author: Martin Abadi
Publisher: Springer
ISBN: UOM:39015039942597
Release Date: 1997-10-02
Genre: Computer software

This book constitutes the refereed proceedings of the Third International Symposium on Theoretical Aspects of Computer Software, TACS'97, held in Sendai, Japan, in September 1997. The book presents 20 revised full papers selected from a total of 46 submissions. Also included are seven invited papers by internationally leading scientists. Among the topics addressed are action calculi, polymorphisms, type theory, lambda calculi, refinement, finite transition systems, model checking, process algebras, logical frameworks, higher-order logics, etc.

Names and Higher order Functions

Author: Ian David Bede Stark
ISBN: UCSC:32106013459547
Release Date: 1995
Genre: Functional programming (Computer science)

Abstract: "Many functional programming languages rely on the elimination of 'impure' features: assignment to variables, exceptions and even input/output. But some of these are genuinely useful, and it is of real interest to establish how they can be reintroducted [sic] in a controlled way. This dissertation looks in detail at one example of this: the addition to a functional language of dynamically generated names. Names are created fresh, they can be compared with each other and passed around, but that is all. As a very basic example of state, they capture the graduation between private and public, local and global, by their interaction with higher-order functions. The vehicle for this study is the nu-calculus, an extension of the simply-typed lambda calculus. The nu calculus is equivalent to a certain fragment of Standard ML, omitting side- effects, exceptions, datatypes and recursion. Even without all these features, the interaction of name creation with higher-order functions can be complex and subtle. Various operational and denotational methods for reasoning about the nu-calculus are developed. These include a computational metalanguage in the style of Moggi, which distinguishes in the type system between values and computations. This leads to categorical models that use a strong monad, and examples are devised based on functor categories. The idea of logical relations is used to derive powerful reasoning methods that capture some of the distinction between private and public names. These techniques are shown to be complete for establishing contextual equivalence between first-order expressions; they are also used to construct a correspondingly abstract categorical model All the work with the nu-calculus extends cleanly to Reduced ML, a larger language that introduces integer references: mutable storage cells that are dynamically allocated. It turns out that the step up is quite simple, and both the computational metalanguage and the simple categorical models can be reused."


ISBN: 0897917707
Release Date: 1996
Genre: Functional programming languages

Author: 国立国会図書館 (Japan)
ISBN: UCLA:L0088319629
Release Date: 1900
Genre: Science

Liebe und Mathematik

Author: Edward Frenkel
Publisher: Springer-Verlag
ISBN: 9783662434215
Release Date: 2014-11-17
Genre: Mathematics

Grundlagen der Mathematik I

Author: David Hilbert
Publisher: Springer-Verlag
ISBN: 9783642868948
Release Date: 2013-03-08
Genre: Mathematics

Die Leitgedanken meiner Untersuchungen über die Grundlagen der Mathematik, die ich - anknüpfend an frühere Ansätze - seit 1917 in Besprechungen mit P. BERNAYS wieder aufgenommen habe, sind von mir an verschiedenen Stellen eingehend dargelegt worden. Diesen Untersuchungen, an denen auch W. ACKERMANN beteiligt ist, haben sich seither noch verschiedene Mathematiker angeschlossen. Der hier in seinem ersten Teil vorliegende, von BERNAYS abgefaßte und noch fortzusetzende Lehrgang bezweckt eine Darstellung der Theorie nach ihren heutigen Ergebnissen. Dieser Ergebnisstand weist zugleich die Richtung für die weitere Forschung in der Beweistheorie auf das Endziel hin, unsere üblichen Methoden der Mathematik samt und sonders als widerspruchsfrei zu erkennen. Im Hinblick auf dieses Ziel möchte ich hervorheben, daß die zeit weilig aufgekommene Meinung, aus gewissen neueren Ergebnissen von GÖDEL folge die Undurchführbarkeit meiner Beweistheorie, als irrtüm lich erwiesen ist. Jenes Ergebnis zeigt in der Tat auch nur, daß man für die weitergehenden Widerspruchsfreiheitsbeweise den finiten Stand punkt in einer schärferen Weise ausnutzen muß, als dieses bei der Be trachtung der elementaren Formallsmen erforderlich ist. Göttingen, im März 1934 HILBERT Vorwort zur ersten Auflage Eine Darstellung der Beweistheorie, welche aus dem HILBERTschen Ansatz zur Behandlung der mathematisch-logischen Grundlagenpro bleme erwachsen ist, wurde schon seit längerem von HILBERT ange kündigt.