Algebraic Approaches to Program Semantics

01.09.1986

Englisch

9780387963242

Springer US

Monographs in Computer Science

Nein

Ernest G. Manes

353

Gebundene Ausgabe

Boolean algebra, programming, proving, computer, evolution, formal languages, functional programming, control, programming language, proof, program semantics, formal language, mathematical logic, semantics

UM - Computerprogrammierung und Softwareentwicklung UYF - Rechnerarchitektur und Logik-Entwurf UYA - Theoretische Informatik UM - Computerprogrammierung und Softwareentwicklung UYQ - Künstliche Intelligenz TJFM1 - Robotik

1 Denotational Semantics of Control.- 1 An Introduction to Denotational Semantics.- 1.1 Syntax and Semantics.- 1.2 A Simple Fragment of Pascal.- 1.3 A Functional Programming Fragment.- 1.4 Multifunctions.- 1.5 A Preview of Partially Additive Semantics.- 2 An Introduction to Category Theory.- 2.1 The Definition of a Category.- 2.2 Isomorphism, Duality, and Zero Objects.- 2.3 Products and Coproducts.- 3 Partially Additive Semantics.- 3.1 Partial Addition.- 3.2 Partially Additive Categories and Iteration.- 3.3 The Boolean Algebra of Guards.- 4 Assertion Semantics.- 4.1 Assertions and Preconditions.- 4.2 Partial Correctness.- 4.3 Total Correctness.- 2 Semantics of Recursion.- 5 Recursive Specifications.- 5.1 The Kleene Sequence.- 5.2 The Pattern-of-Calls Expansion.- 5.3 Iteration Recursively.- 6 Order Semantics of Recursion.- 6.1 Domains.- 6.2 Fixed Point Theorems.- 6.3 Recursive Specification in FPF.- 6.4 Fixed Points and Formal Languages.- 7 Canonical Fixed Points.- 8 Partially Additive Semantics of Recursion.- 8.1 PAR Schemes.- 8.2 The Canonical Fixed Point for PAR Schemes.- 8.3 Additive Domains.- 8.4 Proving Correctness.- 8.5 Power Series and Products.- 9 Fixed Points in Metric Spaces.- 9.1 Contractions on Complete Metric Spaces.- 9.2 Differential Equations.- 9.3 Metrics on Trees.- 9.4 Context-Free Languages as Metric Fixed Points.- 3 Data Types.- 10 Functors.- 10.1 Data Types Lead to Functors.- 10.2 Fixed Points of Functors.- 11 Recursive Specification of Data Types.- 11.1 From Least Upper Bounds to Least Fixed Points.- 11.2 Co-continuous Functors.- 11.3 Continuous Functors and Greatest Fixed Points.- 12 Parametric Specification.- 12.1 Arrays.- 12.2 Stacks and Queues.- 12.3 A Functional Programming Fragment Revisited.- 13 Order Semantics of Data Types.- 13.1 Introduction.- 13.2 Constructions with Domains.- 13.3 Cartesian-Closed Categories.- 13.4 Solving Function Space Equations.- 14 Equational Specification.- 14.1 Initial Algebras.- 14.2 Sur-reflections.- Epilogue.- Author Index.

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