Formal Specification : Techniques and Applications

By: Nimal Nissanke

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Formal Specification is a textbook for 2nd/3rd year undergraduate and postgraduate courses in Formal Methods which offers a practical and versatile approach to constructing specifications. It covers both model-based and algebraic approaches and emphasises the range of languages and approaches which are available. Mathematical principles are explained using examples from everyday life (like card games), in order to "demystify" them and make them more comprehensible. It includes: unrivalled coverage of the topic including all important, recent advances lots of exercises with model answers case studies to guide students through the main principles margin notes to identify key points. Readers of this book do not have to be fully competent in formal specification - it is written to be accessible to any student who wants to learn about the topic.

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Non-Fiction Computing & I.T.Computer Programming & Software Development Software Engineering Computer Science Mathematical Theory of Computation Maths for Computer Scientists

Introduction	p. 1
Specification and Correctness	p. 1
Specification as a Contract	p. 2
Specification as a Design Aid	p. 3
Specification as a Human Endeavour	p. 3
Specification as Abstraction	p. 4
Modularity in Specifications	p. 6
Benefits Beyond Precision	p. 6
Formal Specification as an Emerging Technology	p. 8
Specification Techniques	p. 9
Schema Language	p. 11
Introduction	p. 11
Type Definitions in Z	p. 12
Generic Types	p. 13
Free (Enumerated) Types	p. 13
Types Defined by Schemas	p. 14
Mathematical Definitions in Z	p. 14
Schema	p. 15
Axiomatic Definitions	p. 15
Generic Definitions	p. 16
Presentation of Schemas	p. 17
Schema Manipulation	p. 18
Schema Extension	p. 19
Merging Schemas	p. 20
Schema Negation	p. 24
Significance of Schemas	p. 24
Schemas Instead of Declarations	p. 25
Schemas and Mathematical Relations	p. 25
Bindings	p. 26
Schemas as Sets	p. 26
Schemas as Types	p. 27
In Lambda Notation	p. 28
Schemas in Predicate Logic Formulae	p. 28
Some Naming Conventions	p. 29
Schema Decoration	p. 30
Explicit Renaming of Components	p. 30
Dot Notation	p. 31
Hiding and Projection of Components	p. 32
Notation for Specification of Systems	p. 34
General	p. 34
Types of Operations	p. 34
Naming Conventions	p. 35
Some Common Abbreviations	p. 36
Schema Composition	p. 39
Pre and Post Conditions	p. 41
Promotion	p. 43
Exercises	p. 47
An Approach to Specification	p. 49
Introduction	p. 49
An Initial Understanding	p. 50
Identification of the Objects of Discourse and Operations	p. 50
Abstraction and Modularisation	p. 51
Abstraction	p. 51
Modularisation	p. 52
Flight Journey	p. 53
Flight Accommodation	p. 57
Definition of Flight	p. 58
Definition of Flight State	p. 58
Initialisation of Flight State	p. 59
Operations on Flight	p. 59
Passenger Details	p. 59
An Auxiliary Definition	p. 60
Messages	p. 61
Operation of Booking a Seat	p. 61
Operation of Cancelling a Booking	p. 63
Query Operation on Seat Availability	p. 64
An Airline	p. 64
Abstract Representation	p. 64
Initialisation	p. 65
Shared Auxiliary Specifications	p. 65
Airline Operations	p. 66
Concluding Remarks	p. 66
Exercises	p. 67
Specification for Fun	p. 69
Games as Systems	p. 69
Musical Chairs	p. 69
The Problem Description	p. 69
A Mathematical Description	p. 70
Snakes and Ladders	p. 72
The Problem Description	p. 72
The Preliminaries	p. 73
Some Notes on Decomposition	p. 73
A Simple Game	p. 74
The Full Game	p. 76
An Illustration	p. 78
Exercises	p. 80
A Specification for Clocks	p. 81
Representation of Time	p. 81
Notions of Time	p. 81
Real Time	p. 82
Points and Intervals of Time	p. 82
Clock Time	p. 83
A Mathematical Definition of Clocks	p. 84
Clock Mechanism	p. 84
Clock Utilities	p. 87
Idealised Clock with Utilities	p. 88
Operations and Transitions	p. 88
Initialisation and Resetting	p. 88
Clock Advancement	p. 89
The Functioning of the Alarm	p. 90
Intervals in Real Time	p. 91
Concluding Remarks	p. 93
Exercises	p. 93
Reasoning About Specifications	p. 95
Introduction	p. 95
Kinds of Internal Consistency	p. 96
Consistency of the General State	p. 98
Initialisation Consistency	p. 100
Consistency of Operations	p. 101
Forms of Operation Inconsistency	p. 101
Proof of Operational Aspects	p. 102
Proofs Obligatory on Specification Grounds	p. 103
An Illustration	p. 106
Exercises	p. 110
Specification of a Network Protocol	p. 111
Introduction	p. 111
OSI Reference Model	p. 112
Some Preliminaries	p. 114
Application Layer	p. 115
Presentation Layer	p. 122
Refinement of the Data Type Message	p. 122
Proofs on Verification	p. 126
Session Layer	p. 126
Transport Layer	p. 130
Selected Proofs	p. 136
Proof of Reflexivity	p. 137
Proof of Symmetry	p. 138
Proof of Transitivity	p. 138
Bibliographical Notes	p. 139
Exercises	p. 140
Object Oriented Specification	p. 141
Object Orientation in the Narrow Sense	p. 141
Object Orientation in the Wider Sense	p. 145
What are Objects?	p. 146
Some Object Oriented Concepts	p. 147
Software Reuse	p. 147
Inheritance	p. 147
Overloading, Genericity and Polymorphism	p. 148
Abstract Data Types and Classes	p. 148
Representation of Classes	p. 149
Object Oriented Specification Languages	p. 150
An Object Oriented Syntax in Z Style	p. 150
Object Oriented Version of Sequences	p. 152
Text Processing	p. 156
A Character Set	p. 156
Textual Objects	p. 156
Text as Scripts	p. 157
Text as Documents	p. 159
Text as Dialogue	p. 160
Text Windows	p. 161
Exercises	p. 162
Specification of Safety	p. 163
Introduction	p. 163
Specification Framework	p. 165
Changes in States as Time Histories	p. 165
Representation of Equipments	p. 167
A Classification of Safety Requirements	p. 168
Specification of Safety Requirements	p. 169
Description of System State and Behaviour	p. 170
Tracks	p. 170
Signals	p. 172
Points	p. 173
Subroutes	p. 173
Routes	p. 174
System Behaviour in the Presence of Failures	p. 176
Behavioural Specification of Sensors	p. 177
Behavioural Specification of the Controller	p. 178
Behavioural Specification of Signals	p. 178
Behavioural Specification of Points	p. 180
Behavioural Specification of Tracks	p. 182
Preventing and Averting Failures	p. 183
Low to High Risk State Transitions	p. 183
High to Low Risk State Transitions	p. 185
Concluding Remarks	p. 186
Exercises	p. 186
An Overview of VDM	p. 189
Standard Mathematical Notation	p. 189
A General Comment	p. 189
Logic	p. 190
Types	p. 190
Sets and Relations	p. 191
Mathematical Functions	p. 191
Specification of State Based Systems	p. 194
Specification Structure	p. 194
A Comparison with Z	p. 195
Composite Objects	p. 195
Musical Chairs - An Example	p. 199
State Model	p. 199
Initialization	p. 200
Other Operations	p. 200
Execution Order of Operations	p. 201
VDM Specification of Musical Chairs	p. 202
An Indexed Filing System - A Case Study	p. 204
An Informal Description of Requirements	p. 204
System Organization	p. 205
Model of Individual Files	p. 205
VDM Specification of Indexed Files	p. 206
Model of the Module Interface	p. 208
Model of the Filing System	p. 209
VDM Specification of the Indexed Filing System	p. 210
Exercises	p. 212
Algebraic Approach to Specification	p. 213
Introduction	p. 213
A Preliminary Comparison	p. 214
Model Oriented Approach	p. 215
Algebraic Approach	p. 215
Algebraic Notions	p. 216
Some Basic Algebras	p. 216
Homogeneous Algebras	p. 217
Heterogeneous Algebras	p. 218
Type Algebras	p. 219
Many-sorted Algebra	p. 220
Signatures	p. 221
Signature Associated Algebra	p. 222
Subalgebras	p. 223
Homomorphisms	p. 223
Characterisation of Homomorphism	p. 226
Term Algebras	p. 227
Well Formed Terms	p. 228
Natural Numbers as a Homogeneous Data Type	p. 228
Heterogeneous (Many-Sorted) Abstract Data Types	p. 229
Equations	p. 230
Variables	p. 231
Algebras and Equations	p. 232
Other Related Terminology	p. 233
Equational Deduction	p. 233
Initial Algebras	p. 235
The Motivation for Initial Algebras	p. 235
The Definition of Initiality	p. 236
Terminal Algebras	p. 237
The Motivation for Terminal Algebras	p. 237
Reasoning About Inequalities	p. 238
Bibliographical Notes	p. 239
Algebraic Specification in CLEAR	p. 241
Data Types and Systems	p. 241
Views of Specifications	p. 242
An Introduction to CLEAR	p. 242
Sorts, Operators, Terms and Equations	p. 243
Simple Theories	p. 245
Complex Theories	p. 247
Parameterised Theories	p. 247
Meta Theories	p. 248
Base Theories	p. 249
Specifications	p. 252
A Case Study: A Filing System	p. 252
Some Basic Specifications	p. 252
A General Specification for Various Kinds of Object	p. 253
Maps	p. 254
Sequences	p. 256
Indexed Files	p. 257
Sequential Files	p. 258
File System	p. 260
Bibliographical Notes	p. 263
Exercises	p. 263
Exercises on Reading Formal Specifications	p. 265
Exercise - A Simple Text Editor	p. 265
Let's Play A Game of Cards	p. 269
Unix Filing System	p. 278
Exercises on Writing Formal Specifications	p. 279
A Catalogue Shop	p. 279
Know Your Place if You Succeed in Politics!	p. 280
Traffic Lights	p. 282
A Vending Machine	p. 282
A Bank	p. 282
A Flight Reservation Service for an Airline	p. 283
A Hospital Register	p. 284
The Mathematical Notation	p. 285
References	p. 289
Index	p. 293
Table of Contents provided by Syndetics. All Rights Reserved.

Formal Specification : Techniques and Applications

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Paperback

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