eBook ISBN:  9780821876800 
Product Code:  CONM/92.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821876800 
Product Code:  CONM/92.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

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 ]