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

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

by P.-L. Curien

ISBN-10: 0817636544

ISBN-13: 9780817636548

Pub. Date: 01/01/1993

Publisher: Birkhauser Verlag

Product Details

Birkhauser Verlag
Publication date:
Progress in Theoretical Computer Science Series, #9
Edition description:
2nd edition 1993
Product dimensions:
9.21(w) x 6.14(h) x 0.94(d)

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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