Domain Theory, Logic and Computation

by Zhang, Guo-Qiang; Lawson, J.; Liu, Ying-Ming; Luo, M. K.; Zhang, Guo-Qiang

• ISBN13: 9781402018329
• ISBN10: 1402018320
• Format: Hardcover
• Copyright: 2004-04-01
• Publisher: Kluwer Academic Pub

Summary

Domains are mathematical structures for information and approximation; they combine order-theoretic, logical, and topological ideas and provide a natural framework for modelling and reasoning about computation. The theory of domains has proved to be a useful tool for programming languages and other areas of computer science, and for applications in mathematics. Included in this proceedings volume are selected papers of original research presented at the 2nd International Symposium on Domain Theory in Chengdu, China. With authors from France, Germany, Great Britain, Ireland, Mexico, and China, the papers cover the latest research in these sub-areas: domains and computation, topology and convergence, domains, lattices, and continuity, and representations of domains as event and logical structures. Researchers and students in theoretical computer science should find this a valuable source of reference. The survey papers at the beginning should be of particular interest to those who wish to gain an understanding of some general ideas and techniques in this area.

Table of Contents

Preface

Contributing authors

Playful, streamlike computation

Prologue: playing with Böhm trees

Introduction

Symmetric algorithms, sequential algorithms

Related works

Control

A few more remarks

Universal types and what they are good for

Universal objects

lambda-algebras

Denotational semantics

Universal types

Syntax and semantics of PCF

Examples of universal types

Conclusions and further directions

Relational representations of hyper-continuous lattices

Preliminaries

Regular representations of completely distributive lattices

Finitely regular representations of hyper-continuous lattices

Convergence classes and spaces of partial functions

Introduction

Convergence spaces and convergence classes

Convergence classes and VDM

Compactness of (X --> Y)

Conclusions and further work

On meet-continuous dcpos

Introduction

Basic properties of meet-continuous dcpos

Dcpos with the Hausdorff Lawson topology

Adjunctions between quasicontinuous domains and continuous domains

Scott-open filters

Concluding remarks

External characterizations of continuous sL-domains

Introduction

Preliminaries

Continuous sL-domains and their characterizations by function spaces

External characterizations by posets of ideals

Projectives and injectives in the category of quantales

Introduction

Regular projectives in the category of quantales

Injective objects in the category of quantales

On minimal event and concrete data structures

Introduction

Event structures, concrete data structures and their domains

Congruences on prime intervals and associated structures

Maximal and minimal structures

Conclusion

A note on strongly finite sequent structures

Introduction

Basic definitions and results

Domain constructions

Strongly finite sequent structures

Sequent structures and preorders

Constructions on preorders

Conclusion

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