Basic Simple Type Theory

Author: J. Roger Hindley
Publisher: Cambridge University Press
ISBN: 0521465184
Release Date: 1997-07-31
Genre: Computers

Type theory is one of the most important tools in the design of higher-level programming languages, such as ML. This book introduces and teaches its techniques by focusing on one particularly neat system and studying it in detail. By concentrating on the principles that make the theory work in practice, the author covers all the key ideas without getting involved in the complications of more advanced systems. This book takes a type-assignment approach to type theory, and the system considered is the simplest polymorphic one. The author covers all the basic ideas, including the system's relation to propositional logic, and gives a careful treatment of the type-checking algorithm that lies at the heart of every such system. Also featured are two other interesting algorithms that until now have been buried in inaccessible technical literature. The mathematical presentation is rigorous but clear, making it the first book at this level that can be used as an introduction to type theory for computer scientists.

Basic Proof Theory

Author: A. S. Troelstra
Publisher: Cambridge University Press
ISBN: 0521779111
Release Date: 2000-07-27
Genre: Computers

Introduction to proof theory and its applications in mathematical logic, theoretical computer science and artificial intelligence.

Derivation and Computation

Author: H. Simmons
Publisher: Cambridge University Press
ISBN: 0521771730
Release Date: 2000-05-18
Genre: Mathematics

Introduction to simple type theory; 200 exercises with complete solutions.

Proofs and Types

Author: Jean-Yves Girard
Publisher: Cambridge University Press
ISBN: 0521371813
Release Date: 1989-03-23
Genre: Computers

This text is an outgrowth of notes prepared by J. Y. Girard for a course at the University of Paris VII. It deals with the mathematical background of the application to computer science of aspects of logic (namely the correspondence between proposition & types). Combined with the conceptual perspectives of Girard's ideas, this sheds light on both the traditional logic material & its prospective applications to computer science. The book covers a very active & exciting research area, & it will be essential reading for all those working in logic & computer science.

Topology Via Logic

Author: Steven Vickers
Publisher: Cambridge University Press
ISBN: 0521576512
Release Date: 1996-08-22
Genre: Computers

This is an advanced textbook on topology for computer scientists. It is based on a course given by the author to postgraduate students of computer science at Imperial College.

Categorical Logic and Type Theory

Author: Bart Jacobs
Publisher: Gulf Professional Publishing
ISBN: 0444508538
Release Date: 2001
Genre: Mathematics

This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.

Term Rewriting and All That

Author: Franz Baader
Publisher: Cambridge University Press
ISBN: 0521779200
Release Date: 1999-08-05
Genre: Computers

Unified and self-contained introduction to term-rewriting; suited for students or professionals.

Computer Science Logic

Author: Julian Bradfield
Publisher: Springer
ISBN: 9783540457930
Release Date: 2003-08-02
Genre: Computers

The Annual Conference of the European Association for Computer Science Logic, CSL 2002, was held in the Old College of the University of Edinburgh on 22–25 September 2002. The conference series started as a programme of Int- national Workshops on Computer Science Logic, and then in its sixth meeting became the Annual Conference of the EACSL. This conference was the sixteenth meeting and eleventh EACSL conference; it was organized by the Laboratory for Foundations of Computer Science at the University of Edinburgh. The CSL 2002 Programme Committee considered 111 submissions from 28 countries during a two week electronic discussion; each paper was refereed by at least three reviewers. The Committee selected 37 papers for presentation at the conference and publication in these proceedings. The Programme Committee invited lectures from Susumu Hayashi, Frank Neven, and Damian Niwinski; ́ the papers provided by the invited speakers appear at the front of this volume. In addition to the main conference, two tutorials – ‘Introduction to Mu- Calculi’ (Julian Brad?eld) and ‘Parametrized Complexity’ (Martin Grohe) – were given on the previous day.

Nominal Sets

Author: Andrew M. Pitts
Publisher: Cambridge University Press
ISBN: 9781107244689
Release Date: 2013-05-30
Genre: Computers

Nominal sets provide a promising new mathematical analysis of names in formal languages based upon symmetry, with many applications to the syntax and semantics of programming language constructs that involve binding, or localising names. Part I provides an introduction to the basic theory of nominal sets. In Part II, the author surveys some of the applications that have developed in programming language semantics (both operational and denotational), functional programming and logic programming. As the first book to give a detailed account of the theory of nominal sets, it will be welcomed by researchers and graduate students in theoretical computer science.

Theoretical Aspects of Computing ICTAC 2008

Author: John S. Fitzgerald
Publisher: Springer Science & Business Media
ISBN: 9783540857617
Release Date: 2008-08-18
Genre: Computers

This book constitutes the refereed proceedings of the 5th International Colloquium on Theoretical Aspects of Computing, ICTAC 2008 held in Istanbul, Turkey in September 2008. The 27 revised full papers were carefully reviewed and selected from over 70 submissions. The aim of the colloquium is to bring together practitioners and researchers from academia, industry and government to present research results, and exchange experience, ideas, and solutions for their problems in theoretical aspects of computing such as automata theory and formal languages, principles and semantics of programming languages, software architectures and their description languages, software specification, refinement, and verification, model checking and theorem proving, real-time, embedded and hybrid systems, theory of parallel, distributed, and internet-based (grid) computing, simulation and modeling, and service-oriented development.

Toposes and Local Set Theories

Author: John L. Bell
Publisher: Courier Corporation
ISBN: 9780486462868
Release Date: 2008-01
Genre: Mathematics

This text introduces topos theory, a development in category theory that unites important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic. Topics include local set theories, fundamental properties of toposes, sheaves, local-valued sets, and natural and real numbers in local set theories. 1988 edition.

Concurrency Verification

Author: W.-P. de Roever
Publisher: Cambridge University Press
ISBN: 0521806089
Release Date: 2001-11-26
Genre: Computers

An advanced 2001 textbook on verification of concurrent programs using a semantic approach which highlights concepts clearly.

Mathematical Theory of Domains

Author: V. Stoltenberg-Hansen
Publisher: Cambridge University Press
ISBN: 0521383447
Release Date: 1994-09-22
Genre: Computers

Domain theory is an established part of theoretical computer science, used in giving semantics to programming languages and logics. In mathematics and logic it has also proved to be useful in the study of algorithms. This book is devoted to providing a unified and self-contained treatment of the subject. The theory is presented in a mathematically precise manner which nevertheless is accessible to mathematicians and computer scientists alike. The authors begin with the basic theory including domain equations, various domain representations and universal domains. They then proceed to more specialized topics such as effective and power domains, models of lambda-calculus and so on. In particular, the connections with ultrametric spaces and the Kleene–Kreisel continuous functionals are made precise. Consequently the text will be useful as an introductory textbook (earlier versions have been class-tested in Uppsala, Gothenburg, Passau, Munich and Swansea), or as a general reference for professionals in computer science and logic.

Computational Geometry in C

Author: Joseph O'Rourke
Publisher: Cambridge University Press
ISBN: 9781107268630
Release Date: 1998-10-13
Genre: Computers

This is the revised and expanded 1998 edition of a popular introduction to the design and implementation of geometry algorithms arising in areas such as computer graphics, robotics, and engineering design. The basic techniques used in computational geometry are all covered: polygon triangulations, convex hulls, Voronoi diagrams, arrangements, geometric searching, and motion planning. The self-contained treatment presumes only an elementary knowledge of mathematics, but reaches topics on the frontier of current research, making it a useful reference for practitioners at all levels. The second edition contains material on several new topics, such as randomized algorithms for polygon triangulation, planar point location, 3D convex hull construction, intersection algorithms for ray-segment and ray-triangle, and point-in-polyhedron. The code in this edition is significantly improved from the first edition (more efficient and more robust), and four new routines are included. Java versions for this new edition are also available. All code is accessible from the book's Web site ( or by anonymous ftp.

Coherence in Three Dimensional Category Theory

Author: Nick Gurski
Publisher: Cambridge University Press
ISBN: 9781107034891
Release Date: 2013-03-21
Genre: Mathematics

Serves as an introduction to higher categories as well as a reference point for many key concepts in the field.