Categorical Combinators, Sequential Algorithms, and Functional Programming / Edition 1

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Editorial Reviews

A revised edition of the author's classic monograph (Pitman, 1986) that presents an approach to the design and implementation of sequential programming languages based on the relationship between lambda-calculus and category theory. For researchers in the syntax and semantics of programming languages, rewriting systems, and applications of categorical algebra. Annotation c. Book News, Inc., Portland, OR (
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Product Details

  • ISBN-13: 9780817636548
  • Publisher: Birkhauser Verlag
  • Publication date: 1/1/1993
  • Series: Progress in Theoretical Computer Science Series, #9
  • Edition description: 2nd edition 1993
  • Edition number: 1
  • Pages: 404
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.94 (d)

Table of Contents

Preface to the Second Edition
Table of Dependencies
1 Categorical Combinators 1
1.1 Introducing categorical combinators 3
1.2 [lambda]-calculus and untyped categorical combinatory logic 23
1.3 Types and cartesian closed categories 79
1.4 From untyped calculus to typed calculus: axiomatizing a universal type 103
1.5 Models of the [lambda]-calculus 111
1.6 Equivalence of presentations 144
1.7 Evaluation of categorical terms 149
2 Sequential Algorithms 159
2.1 Concrete data structures 160
2.2 Representation theorems 171
2.3 Domain equations 185
2.4 Sequential functions 193
2.5 Sequential algorithms 215
2.6 The category of concrete data structures and sequential algorithms 230
3 CDSO: The Kernel of a Functional Language 251
3.1 Declaring concrete data structures 252
3.2 The language of constants: states and sequential algorithms 261
3.3 The language of expressions 279
3.4 Operational semantics: presentation 288
3.5 Operational semantics: the rules of CDSO1 297
3.6 Full abstraction for CDSO1 305
4 The Full Abstraction Problem 316
4.1 The languages PCF, PCFP, and PCFC 317
4.2 Sequential algorithms and extensionality: the bicd's 341
4.3 Complete bicd's 350
4.4 Extensional algorithms and definability 357
5 Conclusion 365
6 Mathematical Prerequisites 366
References 381
Index of Definitions 395
Index of Symbols 400
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