Overview

"This book is a thoroughly revised edition of a monograph that presents an approach to the design and implementation of sequential programming languages based on the relationship between lambda-calculus and category theory. The foundations of a new ""categorical"" combinatory logic are laid down. Compilation and evaluation techniques are investigated. A simple abstract machine, called the Categorical Abstract Machine, is presented: it has served as the core of the implementation of the language CAML, of the ML family, developed at INRIA-Roquencourt and Ecole Normale Superieure, and first released in 1987. The main characteristics of this approach are conceptual simplicity and compactness, with bearings on portability, efficiency, and correctness proofs. A mathematical semantics of sequentiality is proposed, in which ""sequential algorithms"" rather than functions are used to interpret procedures. The theoretical investigation has led to the development of a programming language, CDSO, in which basic and functional types are not differentiated. The evaluation framework is a demand-driven data flow network. The model of sequential algorithms is fully abstract with respect to this language: two procedures have the same denotation if and only if they have the same behaviour. Background on full abstraction is given. The new edition covers new results, and introduces new connections, as suggested by the following non-exhaustive fist of keywords: confluence properties of categorical combinators, explicit substitutions, control operations, linear logic, geometry of interaction, strong stability."

Full Product Details

Author:   P.-L. Curien
Publisher:   Birkhauser Boston Inc
Imprint:   Birkhauser Boston Inc
Edition:   2nd Revised edition
Dimensions:   Width: 15.50cm , Height: 2.30cm , Length: 23.50cm
Weight:   1.710kg
ISBN:  

9780817636548

ISBN 10:   0817636544
Pages:   404
Publication Date:   01 January 1993
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1. Categorical Combinators.- 1.1 Introducing categorical combinators.- 1.2 ?-calculus and untyped categorical combinatory logic.- 1.3 Types and cartesian closed categories.- 1.4 From untyped calculus to typed calculus: axiomatizing a universal type.- 1.5 Models of the ?-calculus.- 1.6 Equivalence of presentations.- 1.7 Evaluation of categorical terms.- 1.8 Discussion.- 2. Sequential Algorithms.- 2.1 Concrete data structures.- 2.2 Representation theorems.- 2.3 Domain equations.- 2.4 Sequential functions.- 2.5 Sequential algorithms.- 2.6 The category of concrete data structures and sequential algorithms.- 2.7 Discussion.- 3. CDSO: The Kernel of a Functional Language.- 3.1 Declaring concrete data structures.- 3.2 The language of constants: states and sequential algorithms.- 3.3 The language of expressions.- 3.4 Operational semantics: presentation.- 3.5 Operational semantics: the rules of CDSO1.- 3.6 Pull abstraction for CDS0l.- 3.7 Discussion.- 4. The Full Abstraction Problem.- 4.1 The languages PCF, PCFP, and PCFC.- 4.2 Sequential algorithms and extensionality: the bicd’s.- 4.3 Complete bicd’s.- 4.4 Extensional algorithms and definability.- 4.5 Discussion.- 5. Conclusion.- 6. Mathematical Prerequisites.- References.- Index of Definitions.- Index of Symbols.

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