Constructivity in Computer Science

Summer Symposium, San Antonio, TX, June 19-22, 1991. Proceedings

By: J.Paul Jr. Myers (Editor), Michael J. O'Donnell (Editor)

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Paperback | 24 June 1992

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268 Pages

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Mathematicians have long recognized the distinction between an argument showing that an interesting object exists and a procedure for actually constructing the object. Computer science adds a new dimension of interest in constructivity, since a computer program is a formal description of a constructive procedure that can be executed automatically. It has beenover a decade since a conference was devoted to constructivity, and never before has one been held specifically relating computer science to constructivity. Thus, this proceedings volume is the most concentrated offering ever produced of the diverse ways in which constructivity and computer science are related. The papers cover semantics and type theory, logic and theorem proving, real and complex analysis, topology and combinatorics, nonconstructive graph-theoretical techniques, and curriculum and pedagogic issues. The book offers a concentrated view of the many ways in which constructivity has assumed importance in computer science, and contains results available nowhere else.

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Non-Fiction Mathematics Discrete Mathematics Mathematical Foundation Mathematical Logic Computing & I.T.Computer Programming & Software Development Programming & Scripting Languages Applied Mathematics Computer Science Artificial Intelligence Computer Architecture & Logic Design

Compilers & Interpreters

Semantics
Connecting Formal Semantics to Constructive Intuitions	p. 1
Kripke Semantics for Dependent Type Theory and Realizability Interpretations	p. 22
Types
Reflective Semantics of Constructive Type Theory: Preliminary Report	p. 33
Are Subsets Necessary in Martin-Lof Type Theory?	p. 46
Development Transformation Based on Higher Order Type Theory	p. 58
Logic
Classical Proofs as Programs: How, What, and Why	p. 71
Classical Type Theory	p. 89
Axiomatization of Calculus of Constructions	p. 108
A Logical View of Assignments	p. 131
Nonconstructive Techniques
Constructivity Issues in Graph Algorithms	p. 150
Topology
Constructive Topology and Combinatorics	p. 159
Reals
Implementing Constructive Real Analysis: Preliminary Report	p. 165
Examples of Semicomputable Sets of Real and Complex Numbers	p. 179
Curriculum / Pedagogy
Bringing Mathematics Education into the Algorithmic Age	p. 199
The Type Structure of CAT	p. 218
A Simple and Powerful Approach for Studying Constructivity, Computability, and Complexity	p. 228
Author Index	p. 247
Table of Contents provided by Blackwell. All Rights Reserved.

Constructivity in Computer Science

Summer Symposium, San Antonio, TX, June 19-22, 1991. Proceedings

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Paperback

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