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Softcover ISBN:  9780821851005 
Product Code:  CONM/92 
List Price:  $70.00 
MAA Member Price:  $63.00 
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Product Code:  CONM/92.E 
List Price:  $66.00 
MAA Member Price:  $59.40 
AMS Member Price:  $52.80 
Softcover ISBN:  9780821851005 
eBookISBN:  9780821876800 
Product Code:  CONM/92.B 
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Book DetailsContemporary MathematicsVolume: 92; 1989; 382 ppMSC: Primary 18; Secondary 00; 03; 68;
Category theory has had important uses in logic since the invention of topos theory in the early 1960s, and logic has always been an important component of theoretical computer science. A new development has been the increase in direct interactions between category theory and computer science. In June 1987, an AMSIMSSIAM Summer Research Conference on Categories in Computer Science and Logic was held at the University of Colorado in Boulder. The aim of the conference was to bring together researchers working on the interconnections between category theory and computer science or between computer science and logic. The conference emphasized the ways in which the general machinery developed in category theory could be applied to specific questions and be used for categorytheoretic studies of concrete problems. This volume represents the proceedings of the conference. (Some of the participants' contributions have been published elsewhere.)
The papers published here relate to three different aspects of the conference. The first concerns topics relevant to all three fields, including, for example, Horn logic, lambda calculus, normal form reductions, algebraic theories, and categorical models for computability theory. In the area of logic, topics include semantical approaches to prooftheoretical questions, internal properties of specific objects in (pre) topoi and their representations, and categorical sharpening of modeltheoretic notions. Finally, in the area of computer science, the use of category theory in formalizing aspects of computer programming and program design is discussed. 
Table of Contents

Articles

Michael Barr  Models of Horn theories [ MR 1003191 ]

Andreas Blass  Geometric invariance of existential fixedpoint logic [ MR 1003192 ]

J. R. B. Cockett  On the decidability of objects in a locos [ MR 1003193 ]

V. C. V. de Paiva  The Dialectica categories [ MR 1003194 ]

Peter Freyd  Combinators [ MR 1003195 ]

Peter Freyd  POLYNAT in PER [ MR 1003196 ]

JeanYves Girard  Towards a geometry of interaction [ MR 1003197 ]

John W. Gray  The category of sketches as a model for algebraic semantics [ MR 1003198 ]

J. Martin E. Hyland and Andrew M. Pitts  The theory of constructions: categorical semantics and topostheoretic models [ MR 1003199 ]

François Lamarche  A simple model of the theory of constructions [ MR 1003200 ]

J. Lambek  Multicategories revisited [ MR 1003201 ]

Dana May Latch  An application of minimal contextfree intersection partitions to rewrite rule consistency checking [ MR 1003202 ]

F. William Lawvere  Qualitative distinctions between some toposes of generalized graphs [ MR 1003203 ]

John C. Mitchell and Philip J. Scott  Typed lambda models and Cartesian closed categories (preliminary version) [ MR 1003204 ]

Philip S. Mulry  Some connections between models of computation [ MR 1003205 ]

Robert Paré  Some applications of categorical model theory [ MR 1003206 ]

A. J. Power  Coherence for bicategories with finite bilimits. I [ MR 1003207 ]

Leopoldo Román  On partial Cartesian closed categories [ MR 1003208 ]

Andre Scedrov  Normalization revisited [ MR 1003209 ]

R. A. G. Seely  Linear logic, $*$autonomous categories and cofree coalgebras [ MR 1003210 ]


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Category theory has had important uses in logic since the invention of topos theory in the early 1960s, and logic has always been an important component of theoretical computer science. A new development has been the increase in direct interactions between category theory and computer science. In June 1987, an AMSIMSSIAM Summer Research Conference on Categories in Computer Science and Logic was held at the University of Colorado in Boulder. The aim of the conference was to bring together researchers working on the interconnections between category theory and computer science or between computer science and logic. The conference emphasized the ways in which the general machinery developed in category theory could be applied to specific questions and be used for categorytheoretic studies of concrete problems. This volume represents the proceedings of the conference. (Some of the participants' contributions have been published elsewhere.)
The papers published here relate to three different aspects of the conference. The first concerns topics relevant to all three fields, including, for example, Horn logic, lambda calculus, normal form reductions, algebraic theories, and categorical models for computability theory. In the area of logic, topics include semantical approaches to prooftheoretical questions, internal properties of specific objects in (pre) topoi and their representations, and categorical sharpening of modeltheoretic notions. Finally, in the area of computer science, the use of category theory in formalizing aspects of computer programming and program design is discussed.

Articles

Michael Barr  Models of Horn theories [ MR 1003191 ]

Andreas Blass  Geometric invariance of existential fixedpoint logic [ MR 1003192 ]

J. R. B. Cockett  On the decidability of objects in a locos [ MR 1003193 ]

V. C. V. de Paiva  The Dialectica categories [ MR 1003194 ]

Peter Freyd  Combinators [ MR 1003195 ]

Peter Freyd  POLYNAT in PER [ MR 1003196 ]

JeanYves Girard  Towards a geometry of interaction [ MR 1003197 ]

John W. Gray  The category of sketches as a model for algebraic semantics [ MR 1003198 ]

J. Martin E. Hyland and Andrew M. Pitts  The theory of constructions: categorical semantics and topostheoretic models [ MR 1003199 ]

François Lamarche  A simple model of the theory of constructions [ MR 1003200 ]

J. Lambek  Multicategories revisited [ MR 1003201 ]

Dana May Latch  An application of minimal contextfree intersection partitions to rewrite rule consistency checking [ MR 1003202 ]

F. William Lawvere  Qualitative distinctions between some toposes of generalized graphs [ MR 1003203 ]

John C. Mitchell and Philip J. Scott  Typed lambda models and Cartesian closed categories (preliminary version) [ MR 1003204 ]

Philip S. Mulry  Some connections between models of computation [ MR 1003205 ]

Robert Paré  Some applications of categorical model theory [ MR 1003206 ]

A. J. Power  Coherence for bicategories with finite bilimits. I [ MR 1003207 ]

Leopoldo Román  On partial Cartesian closed categories [ MR 1003208 ]

Andre Scedrov  Normalization revisited [ MR 1003209 ]

R. A. G. Seely  Linear logic, $*$autonomous categories and cofree coalgebras [ MR 1003210 ]