Algebraic Approaches to Program Semantics

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.