The Formal Semantics of Programming Languages An Introduction. Glynn Winskel. The MIT Press Cambridge, Massachusetts London, England

Transcription

1 The Formal Semantics of Programming Languages An Introduction Glynn Winskel The MIT Press Cambridge, Massachusetts London, England

2 Series foreword Preface xiii xv 1 Basic set theory Logical notation Sets Sets and properties Some important sets Constructions on sets The axiom of foundation Relations and functions Lambda notation Composing relations and functions Direct and inverse image of a relation Equivalence relations Further reading, 10 2 Introduction to operational semantics IMP a simple imperative language The evaluation of arithmetic expressions The evaluation of boolean expressions The execution of commands A simple proof Alternative semantics Further reading Some principles of induction Mathematical induction * Structural induction Well-founded induction Induction on derivations Definitions by induction 39

3 3.6 Further reading 40 4 Inductive definitions Rule induction Special rule induction Proof rules for operational semantics Rule induction for arithmetic expressions Rule induction for boolean expressions Rule induction for commands Operators and their least fixed points Further reading 54 5 The denotational semantics of IMP Motivation Denotational semantics Equivalence of the semantics Complete partial orders and continuous functions The Knaster-Tarski Theorem Further reading 75 6 The axiomatic semantics of IMP The idea The assertion language Assn Free and bound variables Substitution Semantics of assertions Proof rules for partial correctness Soundness Using the Hoare rules an example Further reading 96 7 Completeness jof the Hoare rules 99

4 7.1 Godel's Incompleteness Theorem Weakest preconditions and expressiveness Proof of Godel's Theorem Verification conditions Predicate transformers Further reading Introduction to domain theory Basic definitions Streams an example Constructions on cpo's Discrete cpo's Finite products Function space Lifting ' Sums A metalanguage Further reading Recursion equations The language REC Operational semantics of call-by-value Denotational semantics of call-by-value Equivalence of semantics for call-by-value Operational semantics of call-by-name Denotational semantics of call-by-name Equivalence of semantics for call-by-name Local declarations Further reading Techniques for recursion Bekic's Theorem

5 10.2 Fixed-point induction Well-founded induction Well-founded recursion An exercise Further reading Languages with higher types An eager language Eager operational semantics Eager denotational semantics Agreement of eager semantics A lazy language Lazy operational semantics Lazy denotational semantics Agreement of lazy semantics Fixed-point operators Observations and full abstraction Sums Further reading Information systems Recursive types Information systems Closed families and Scott predomains A cpo of information systems Constructions Lifting Sums Product Lifted function space Further reading 249

6 13 Recursive types An eager language Eager operational semantics Eager denotational semantics Adequacy of eager semantics The eager A-calculus Equational theory A fixed-point operator A lazy language Lazy operational semantics Lazy denotational semantics Adequacy of lazy semantics The lazy A-calculus Equational theory A fixed-point operator Further reading Nondeterminism and parallelism Introduction Guarded commands Communicating processes Milner's CCS Pure CCS A specification language The modal v-calculus Local model checking Further reading 335 A Incompleteness and undecidability 337 Bibliography 353 Index 357