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

Preface to the Second Edition
Table of Dependencies
1Categorical Combinators1
1.1Introducing categorical combinators3
1.2[lambda]-calculus and untyped categorical combinatory logic23
1.3Types and cartesian closed categories79
1.4From untyped calculus to typed calculus: axiomatizing a universal type103
1.5Models of the [lambda]-calculus111
1.6Equivalence of presentations144
1.7Evaluation of categorical terms149
2Sequential Algorithms159
2.1Concrete data structures160
2.2Representation theorems171
2.3Domain equations185
2.4Sequential functions193
2.5Sequential algorithms215
2.6The category of concrete data structures and sequential algorithms230
3CDSO: The Kernel of a Functional Language251
3.1Declaring concrete data structures252
3.2The language of constants: states and sequential algorithms261
3.3The language of expressions279
3.4Operational semantics: presentation288
3.5Operational semantics: the rules of CDSO1297
3.6Full abstraction for CDSO1305
4The Full Abstraction Problem316
4.1The languages PCF, PCFP, and PCFC317
4.2Sequential algorithms and extensionality: the bicd's341
4.3Complete bicd's350
4.4Extensional algorithms and definability357
6Mathematical Prerequisites366
Index of Definitions395
Index of Symbols400

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