Formal specifications were first used in the description of program� ming languages because of the central role that languages and their compilers play in causing a machine to perform the computations required by a programmer. In a relatively short time, specification notations have found their place in industry and are used for the description of a wide variety of software and hardware systems. A formal method - like VDM - must offer a mathematically-based specification language. On this language rests the other key element of the formal method: the ability to reason about a specification. Proofs can be empioyed in reasoning about the potential behaviour of a system and in the process of showing that the design satisfies the specification. The existence of a formal specification is a prerequisite for the use of proofs; but this prerequisite is not in itself sufficient. Both proofs and programs are large formal texts. Would-be proofs may therefore contain errors in the same way as code. During the difficult but inevitable process of revising specifications and devel� opments, ensuring consistency is a major challenge. It is therefore evident that another requirement - for the successful use of proof techniques in the development of systems from formal descriptions - is the availability of software tools which support the manipu� lation of large bodies of formulae and help the user in the design of the proofs themselves.

Contenuti

1 Introduction.- 1.1 Background.- 1.2 How proofs arise in practice: an introductory example.- 1.3 A logical framework for proofs.- 1.4 Summary.- I A Logical Basis for Proof in VDM.- 2 Propositional LPF.- 2.1 Introduction.- 2.2 Basic axiomatisation.- 2.3 Derived rules; reasoning by cases; reasoning using contradiction.- 2.4 Using definitions: conjunction.- 2.5 Implication; definedness; further defined constructs.- 2.6 Summary.- 2.7 Exercises.- 3 Predicate LPF with Equality.- 3.1 Predicates.- 3.2 Types in predicates.- 3.3 Predicate calculus for LPF: proof strategies for quantifiers.- 3.4 Reasoning about equality: substitution and chains of equality.- 3.5 Extensions to typed predicate LPF with equality.- 3.6 Summary.- 3.7 Exercises.- 4 Basic Type Constructors.- 4.1 Introduction.- 4.2 Union types.- 4.3 Cartesian product types.- 4.4 Optional types.- 4.5 Subtypes.- 4.6 A note on composite types.- 4.7 Summary.- 4.8 Exercises.- 5 Numbers.- 5.1 Introduction.- 5.2 Axiomatising the natural numbers.- 5.3 Axiomatisation of addition and proof by induction.- 5.4 More on proof by induction.- 5.5 Using direct definitions.- 5.6 Summary.- 5.7 Exercises.- 6 Finite Sets.- 6.1 Introduction.- 6.2 Generators for sets; set membership; set induction.- 6.3 Proof using set induction.- 6.4 Quantification over sets.- 6.5 Subsets; set equality; cardinality.- 6.6 Other set constructors.- 6.7 Set comprehension.- 6.8 Reasoning about set comprehension.- 6.9 Summary.- 6.10 Exercises.- 7 Finite Maps.- 7.1 Introduction.- 7.2 Basic axiomatisation.- 7.3 Axiomatisation using generators.- 7.4 Extraction and abstraction of lemmas.- 7.5 Using subsidiary definitions.- 7.6 Polymorphic subtypes and associated induction rules.- 7.7 Map comprehension.- 7.8 Summary.- 7.9 Exercises.- 8 Finite Sequences.- 8.1 Introduction.- 8.2 Basic axiomatisation.- 8.3 Destructors.- 8.4 Equality between lists.- 8.5 Operators on lists.- 8.6 An alternative generator set.- 8.7 Summary.- 8.8 Exercises.- 9 Booleans.- 9.1 Introduction.- 9.2 Basic axiomatisation.- 9.3 Formation rules for boolean-valued operators.- 9.4 An example of a well-formedness proof obligation.- 9.5 Summary.- 9.6 Exercises.- II Proof in Practice.- 10 Proofs From Specifications.- 10.1 Introduction.- 10.2 Type definitions.- 10.3 The state.- 10.4 Functions and values.- 10.5 Operations.- 10.6 Validation proofs.- 10.7 Summary.- 10.8 Exercises.- 11 Verifying Reifications.- 11.1 Introduction.- 11.2 Data reification.- 11.3 Operation modelling.- 11.4 An example reification proof.- 11.5 Implementing functions.- 11.6 Implementation bias and unreachable states.- 11.7 Summary.- 11.8 Exercises.- 12 A Case Study in Air-Traffic Control.- 12.1 Introduction.- 12.2 The air-traffic control system.- 12.3 Formalisation of the state model.- 12.4 Top-level operations.- 12.5 First refinement step.- 12.6 Second refinement step.- 12.7 Concluding remarks.- 13 Advanced Topics.- 13.1 Introduction.- 13.2 Functions as a data type.- 13.3 Comparing elements of disjoint types.- 13.4 Recursive type definitions.- 13.5 Enumerated sets, maps and sequences.- 13.6 Patterns.- 13.7 Other expressions.- 13.8 Other types.- III Directory of Theorems.- 14 Directory of Theorems.- 14.1 Propositonal LPF.- 14.2 Predicate LPF with equality.- 14.3 Basic type constructors.- 14.4 Natural numbers.- 14.5 Finite sets.- 14.6 Finite maps.- 14.7 Finite sequences.- 14.8 Booleans.- 14.9 Specifications.- 14.10 Reifications.- 14.11 Case study I: abstract specification.- 14.12 Case study II: refinement.- Index of Symbols.- Index of Rules.

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

Descrizione libreria

Visita la pagina della libreria

Informazioni sull?azienda del venditore

WRAP Ltd
Unit 4, 119 Loverock Rd, Reading, RG30 1DZ, United Kingdom

Condizioni di vendita e spedizione

Condizioni di vendita

TBA

Diritto di recesso

Condizioni di spedizione

Shipping costs are based on books weighing 2.2 LB, or 1 KG. If your book order is heavy or oversized, we may contact you to let you know extra shipping is required.

Tariffe di spedizione da Regno Unito a U.S.A.

Tariffe di spedizione da Regno Unito a U.S.A.
Quantit� dell?ordine	Da 14 a 21 giorni lavorativi	Da 14 a 21 giorni lavorativi
Primo articolo	EUR 17.80	EUR 17.80

I tempi di consegna sono stabiliti dai venditori e variano in base al corriere e al paese. Gli ordini che devono attraversare una dogana possono subire ritardi e spetta agli acquirenti pagare eventuali tariffe o dazi associati. I venditori possono contattarti in merito ad addebiti aggiuntivi dovuti a eventuali maggiorazioni dei costi di spedizione dei tuoi articoli.