Understanding formal methods:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English French |
| Veröffentlicht: |
London [u.a.]
Springer
2003
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 255 - 267 |
| Beschreibung: | XV, 275 S. graph. Darst. |
| ISBN: | 1852332476 |
Internformat
MARC
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| 100 | 1 | |a Monin, Jean-François |d 1960- |e Verfasser |0 (DE-588)124266606 |4 aut | |
| 240 | 1 | 0 | |a Introduction aux méthodes formelles |
| 245 | 1 | 0 | |a Understanding formal methods |c written and transl. by Jean-François Monin |
| 264 | 1 | |a London [u.a.] |b Springer |c 2003 | |
| 300 | |a XV, 275 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. 255 - 267 | ||
| 650 | 4 | |a Softwareentwicklung - Formale Methode | |
| 650 | 4 | |a Formal methods (Computer science) | |
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Datensatz im Suchindex
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Titel: Understanding formal methods
Autor: Monin, Jean-François
Jahr: 2003
Table of Contents
1. Motivation 1
1.1 Some Industrial Applications.2
1.1.1 Specification for Re-engineering.2
1.1.2 Proving Critical Railway Software.2
1.2 What Is a Formal Method?.3
1.3 From Software Engineering to Formal Methods.4
1.3.1 Towards More Rigorous Processes .4
1.3.2 Software Development Using Formal Methods .5
1.3.3 Formal Methods for the Customer.6
1.4 On Weaknesses of Formal Methods.6
1.5 A Survey of Formal Methods.7
1.5.1 Specialized and General Approaches.8
1.5.2 Emphasizing the Specification or the Verification . 9
1.6 Aim of this Book.10
1.7 How to Read this Book .11
1.8 Notes and Suggestions for Further Reading.12
2. Introductory Exercise 15
2.1 Exposition.15
2.2 Sketch of a Formal Specification .16
2.3 Is There a Solution?.18
2.3.1 Doing Nothing.18
2.3.2 Attempting the Impossible .19
2.3.3 Weakening the Postcondition.19
2.3.4 Intermezzo: Sum of Sets.20
2.3.5 Strengthening the Precondition.22
2.4 Program Development.22
2.4.1 Prelude: Correctness of a Loop.23
2.4.2 Linear Search.25
2.4.3 Discussion: Reasoning Figures.25
2.4.4 Bounded Linear Search .27
2.4.5 Discussion.31
2.5 Summary.32
2.6 Semantics.33
2.7 Notes and Suggestions for Further Reading.33
x Understanding Formal Methods
3. A Presentation of Logical Tools ^5
3.1 Some Applications of Logic.36
3.1.1 Programming.
3.1.2 Sums and Unions.37
3.1.3 Chasing Paradoxes Away.38
9Q
3.2 Antecedents.
3.3 The Different Branches of Logic.40
3.3.1 Model Theory.40
3.3.2 Proof Theory.41
3.3.3 Axiomatic Set Theory and Type Theory.43
3.3.4 Computability Theory.44
3.4 Mathematical Reminders .45
3.4.1 Set Notations.46
3.4.2 Logical Operators .46
3.4.3 Relations and Functions.48
3.4.4 Operations.49
3.4.5 Morphisms.50
3.4.6 Numbers .50
3.4.7 Sequences.51
3.5 Well-founded Relations and Ordinals.51
3.5.1 Loop Variant and Well-founded Relation.51
3.5.2 Examples.52
3.5.3 Well-founded Induction.55
3.5.4 Well Orders and Ordinals.55
3.6 Fixed Points.57
3.7 More About Computability.58
3.7.1 Primitive Recursion.59
3.7.2 Recursion, Decidability .61
3.7.3 Partial Recursion, Semi-Decidability.62
3.7.4 A Few Words on Logical Complexity.63
3.8 Notes and Suggestions for Further Reading.64
4. Hoare Logic 65
4.1 Introducing Assertions in Programs.65
4.2 Verification Using Hoare Logic.66
4.2.1 Rules of Hoare Logic.67
4.2.2 Bounded Linear Search Program.68
4.3 Program Calculus.69
4.3.1 Calculation of a Loop.69
4.3.2 Calculation of an Assignment Statement.70
4.3.3 Weakest Precondition.72
4.4 Scope of These Techniques.73
4.5 Notes and Suggestions for Further Reading. 74
Table of Contents xi
5. Classical Logic 75
5.1 Propositional Logic.75
5.1.1 Atomic Propositions.75
5.1.2 Syntax of Propositions.76
5.1.3 Interpretation.78
5.2 First-order Predicate Logic.79
5.2.1 Syntax.80
5.2.2 Example of the Table.81
5.2.3 Interpretation.82
5.3 Significant Examples.84
5.3.1 Equational Languages.84
5.3.2 Peano Arithmetic.85
5.4 On Total Functions, Many-sorted Logics.87
5.5 Second-order and Higher-order Logics.89
5.6 Model Theory.91
5.6.1 Definitions .92
5.6.2 Some Results of Model Theory; Limitations of
First-Order Logic.93
5.7 Notes and Suggestions for Further Reading.94
6. Set-theoretic Specifications 95
6.1 The Z Notation.95
6.1.1 Schemas.95
6.1.2 Operations.97
6.1.3 Example.98
6.1.4 Relations and Functions.99
6.1.5 Typing.100
6.1.6 Refinements.101
6.1.7 Usage.101
6.2 VDM .102
6.2.1 Origins .102
6.2.2 Typing.103
6.2.3 Operations.103
6.2.4 Functions.103
6.2.5 Three-valued Logic.104
6.2.6 Usage.104
6.3 The B Method.105
6.3.1 Example.105
6.3.2 Abstract Machines.106
6.3.3 Simple Substitutions and Generalized Substitutions . . 107
6.3.4 The B Refinement Process.109
6.3.5 Modularity.110
6.4 Notes and Suggestions for Further Reading.110
xii Understanding Formal Methods
7. Set Theory
7.1 Typical Features.
. 7.1.1 An Untyped Theory.
. 7.1.2 Functions in Set Theory.
7.1.3 Set-theoretic Operations.
7.2 Zermelo-Fraenkel Axiomatic System.
7.2.1 Axioms.
, 7.2.2 Reconstruction of Usual Set-theoretic Concepts . . . .
7.2.3 The Original System of Zermelo .
7.3 Induction.
. 7.3.1 Reconstruction of Arithmetic.
, 7.3.2 Other Inductive Definitions.
. 7.3.3 The Axiom of Separation.
. 7.3.4 Separation of a Fixed Point.
7.3.5 Ordinals.
7.4 Sets, Abstract Data Types and Polymorphism.
7.4.1 Trees, Again .
. 7.4.2 Algebraic Approach.
7.4.3 Polymorphism (or Genericity).
7.4.4 The Abstract Type of Set Operations.
7.5 Properties of ZF and ZFC.
7.6 Summary.
7.7 Notes and Suggestions for Further Reading.
125
8. Behavioral Specifications
81 Unity .,26
8.1.1 Execution of a Unity program.
8.1.2 The Table Example .*^6
8.1.3 A Protocol Example.*28
8.2 Transition Systems.^
8.2.1 Definitions and Notations.130
8.2.2 Examples.*30
8.2.3 Behavior of a Transition System.132
8.2.4 Synchronized Product of Transition Systems .132
8.2.5 Stuttering Transitions.133
8.2.6 Transition Systems for Unity.134
8.3 CCS, a Calculus of Communicating Systems.134
8.4 The Synchronous Approach on Reactive Systems.136
8.5 Temporal Logic.137
8.5.1 Temporal Logic and Regular Logic.137
8.5.2 CTL*.138
8.5.3 CTL.141
8.5.4 LTL and PLTL .141
8.5.5 The Temporal Logic of Unity.141
8.5.6 Hennessy-Milner Modalities.142
8.5.7 Mu-calculus.
111
111
111
112
112
113
113
115
116
117
117
118
119
119
120
121
121
121
122
122
123
123
124
Table of Contents xiii
8.6 TLA.144
8.7 Verification Tools.146
8.7.1 Deductive Approach.146
8.7.2 Verification by Model Checking.146
8.8 Notes and Suggestions for Further Reading.147
9. Deduction Systems 149
9.1 Hilbert Systems.150
9.2 Natural Deduction.152
9.2.1 Informed Presentation.152
9.2.2 Formal Rules.154
9.2.3 Toward Classical Logic.160
9.2.4 Natural Deduction Presented by Sequents.161
9.2.5 Natural Deduction in Practice .162
9.3 The Sequent Calculus.163
9.3.1 The Rules of the Sequent Calculus.164
9.3.2 Examples.165
9.3.3 Cut Elimination.166
9.4 Applications to Automated Theorem Proving.168
9.4.1 Sequents and Semantical Tableaux.169
9.4.2 From the Cut Rule to Resolution.170
9.4.3 Proofs in Temporal Logic.175
9.5 Beyond First-order Logic .175
9.6 Dijkstra-Scholten's System.176
9.6.1 An Algebraic Approach.176
9.6.2 Displaying the Calculations.177
9.6.3 The Role of Equivalence.178
9.6.4 Comparison with Other Systems.179
9.6.5 Choosing Between Predicates and Sets.180
9.6.6 Uses of Dijkstra-Scholten's System.181
9.7 A Word About Rewriting Systems.181
9.8 Results on Completeness and Decidability.182
9.8.1 Properties of Logics.183
9.8.2 Properties of Theories.184
9.8.3 Impact of These Results.186
9.9 Notes and Suggestions for Further Reading.187
10.Abstract Data Types and Algebraic Specification 189
10.1 Types. 189
10.2 Sets as Types. 190
10.2.1 Basic Types. 190
10.2.2 A First Glance at Dependent Types. 191
10.2.3 Type of a Function.191
10.2.4 Type Checking. 191
10.2.5 From Sets to Types . 191
10.2.6 Towards Abstract Data Types .192
xiv Understanding Formal Methods
192
10.2.7 Coercions.
10.2.8 A Simpler Approach.
10.2.9 Unions and Sums.
10-2.10 Summary.
10.3 Abstract Data Types.
10-3.1 Sorts, Signatures.
10.3.2 Axioms.
10-3.3 First-order and Beyond.
10.4 Semantics.
10.5 Example of the Table .
10.5.1 Signature of Operations.199
10-5.2 Axioms.199
10.6 Rewriting.^00
10.7 Notes and Suggestions for Further Reading.- - • 200
11.Type Systems and Constructive Logics 203
11.1 Yet Another Concept of a Type.293
11.1.1 Formulas as Types.293
11.1.2 Interpretation.29^
11.2 The Lambda-calculus.29"*
11.2.1 Syntax .293
11.2.2 The Pure A-calculus and the A-calculus with Constants 206
11.2.3 Function and Function.299
11.2.4 Representing Elementary Functions .207
11.2.5 Functionality of/?-reduction . .211
11.3 Intuitionistic Logic and Simple Typing.212
11.3.1 Constructive Logics .212
11.3.2 Intuitionistic Logic.213
11.3.3 The Simply Typed A-calculus.214
11.3.4 Curry-Howard Correspondence.215
11.4 Expressive Power of the Simply Typed A-calculus.218
11.4.1 Typing of the Natural Numbers.218
11.4.2 Typing of Booleans.219
11.4.3 Typing of the Identity Function.219
11.4.4 Typing of Pairs, Product of Types.219
11.4.5 Sum Types.220
11.4.6 Paradoxical and Fixed-point Combinators.221
11.4.7 Summary.221
11.5 Second-Order Typing: System F .222
11.5.1 Typing of Regular Structures.223
11.5.2 Systematic Construction of Types.225
11.5.3 Expressive Power and Consistency of System F.226
11.6 Dependent Types.227
11.6.1 Introduction of First-order Variables.227
11.6.2 Sums and Products.228
11.6.3 Specification Based on Dependent Types . 230
\
Table of Contents xv
11.7 Example: Defining Temporal Logic.230
11.8 Towards Linear Logic .231
11.9 Notes and Suggestions for Further Reading.232
12.Using Type Theory 233
12.1 The Calculus of Inductive Constructions.234
12.1.1 Basic Concepts.234
12.1.2 Inductive Types .235
12.1.3 The Table Example .235
12.2 More on Type Theory.237
12.2.1 System Fa;.237
12.2.2 The Calculus of Pure Constructions.238
12.2.3 Inductive Definitions.238
12.2.4 Inductive Dependent Types.239
12.2.5 Primitive Recursive Functions.239
12.2.6 Reasoning by Generalized Induction.240
12.2.7 Induction Over a Dependent Type.241
12.2.8 General Purpose Inductive Types.241
12.3 A Program Correct by Construction.243
12.3.1 Programs and Proofs.244
12.3.2 Example: Searching for an Element in a List .245
12.3.3 Searching in an Interval of Integers.246
12.3.4 Program Extraction.248
12.4 On Undefined Expressions.251
12.5 Other Proof Systems Based on Higher-order Logic.251
12.6 Notes and Suggestions for Further Reading.253
Bibliography 255
Index 269 |
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| spelling | Monin, Jean-François 1960- Verfasser (DE-588)124266606 aut Introduction aux méthodes formelles Understanding formal methods written and transl. by Jean-François Monin London [u.a.] Springer 2003 XV, 275 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 255 - 267 Softwareentwicklung - Formale Methode Formal methods (Computer science) Softwareentwicklung (DE-588)4116522-6 gnd rswk-swf Formale Methode (DE-588)4333722-3 gnd rswk-swf Formale Methode (DE-588)4333722-3 s Softwareentwicklung (DE-588)4116522-6 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010152070&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Monin, Jean-François 1960- Understanding formal methods Softwareentwicklung - Formale Methode Formal methods (Computer science) Softwareentwicklung (DE-588)4116522-6 gnd Formale Methode (DE-588)4333722-3 gnd |
| subject_GND | (DE-588)4116522-6 (DE-588)4333722-3 |
| title | Understanding formal methods |
| title_alt | Introduction aux méthodes formelles |
| title_auth | Understanding formal methods |
| title_exact_search | Understanding formal methods |
| title_full | Understanding formal methods written and transl. by Jean-François Monin |
| title_fullStr | Understanding formal methods written and transl. by Jean-François Monin |
| title_full_unstemmed | Understanding formal methods written and transl. by Jean-François Monin |
| title_short | Understanding formal methods |
| title_sort | understanding formal methods |
| topic | Softwareentwicklung - Formale Methode Formal methods (Computer science) Softwareentwicklung (DE-588)4116522-6 gnd Formale Methode (DE-588)4333722-3 gnd |
| topic_facet | Softwareentwicklung - Formale Methode Formal methods (Computer science) Softwareentwicklung Formale Methode |
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