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Categorical Combinators, Sequential Algorithms, and Functional Programming

  • Pierre-Louis Curien

Part of the Progress in Theoretical Computer Science book series (PTCS)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Pierre-Louis Curien
    Pages 1-158
  3. Pierre-Louis Curien
    Pages 159-250
  4. Pierre-Louis Curien
    Pages 251-315
  5. Pierre-Louis Curien
    Pages 316-364
  6. Pierre-Louis Curien
    Pages 365-365
  7. Pierre-Louis Curien
    Pages 366-380
  8. Back Matter
    Pages 381-404

About this book

Introduction

This book is a revised edition of the monograph which appeared under the same title in the series Research Notes in Theoretical Computer Science, Pit­ man, in 1986. In addition to a general effort to improve typography, English, and presentation, the main novelty of this second edition is the integration of some new material. Part of it is mine (mostly jointly with coauthors). Here is brief guide to these additions. I have augmented the account of categorical combinatory logic with a description of the confluence properties of rewriting systems of categor­ ical combinators (Hardin, Yokouchi), and of the newly developed cal­ culi of explicit substitutions (Abadi, Cardelli, Curien, Hardin, Levy, and Rios), which are similar in spirit to the categorical combinatory logic, but are closer to the syntax of A-calculus (Section 1.2). The study of the full abstraction problem for PCF and extensions of it has been enriched with a new full abstraction result: the model of sequential algorithms is fully abstract with respect to an extension of PCF with a control operator (Cartwright, Felleisen, Curien). An order­ extensional model of error-sensitive sequential algorithms is also fully abstract for a corresponding extension of PCF with a control operator and errors (Sections 2.6 and 4.1). I suggest that sequential algorithms lend themselves to a decomposition of the function spaces that leads to models of linear logic (Lamarche, Curien), and that connects sequentiality with games (Joyal, Blass, Abramsky) (Sections 2.1 and 2.6).

Keywords

algorithm algorithms calculus data structure data structures functional programming logic programming semantics

Authors and affiliations

  • Pierre-Louis Curien
    • 1
  1. 1.Département de Mathématiques et Informatique de l’École Normale SupérieureCNRS-LIENSParis Cedex 05France

Bibliographic information