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256 Data Part of POOSL 8.7 Example: Complex Numbers In this paragraph we give an example of the calculation of the semantics of a configuration representing the addition of two complex numbers. A definition of a system Sys which contains a class Complex of complex numbers is as follows: Sys data class Complex instance variables re im instance methods init(r¥ i) add(comp) re : r; ¡ i r res ¡ 7 im : i; r : self real (comp real ); self i : self imag (comp imag ); res : new (Complex) init(r¥ i); real res re imag im Calculating the sum of complex numbers, say (3+4i) and (8+9i), can be performed by evaluating ( new (Complex) init(3¥ 4)) add( new (Complex) init(8¥ 9)) Syntactic entities 3, 4, 8, and 9 denote the direct naming of natural numbers 3, 4, 8 and 9. The evaluation of this expression is reflected by a derivation sequence, starting with configuration ( new init(3¥ (Complex) 4)) add( new init(8¥ 9))¥ ¤ ¥ ¥ ¤ ¥ Sys (Complex) In this configuration we have put brackets around expression new init(3¥ (Complex) 4), although they are not part of the abstract syntax defined in Section 8.3. Such brackets are used in ambiguous situations to explain the intended structure of expressions or statements. To ease readability we represent functions in a way explained by the following example: Assume F : A ¦£ (B ¦£ C) 7 Note that instead of self real and self imag we could have written re respectively im.
8.7 Example: Complex Numbers 257 is defined by F £ (a1¥ then we represent F as £ (b1 ¥ c1)¥ (b2 ¥ c1)¥ (b3 ¥ c2)¦ )¥ (a2 ¥ £ (b2 ¥ c3)¥ (b4¥ c1)¦ )¥ (a3 ¥ ¤ )¦ £ F a1 £ b1 ¥ c1 a1 £ b2 ¥ c1 a1 £ b3 ¥ c2 a2 £ b2 ¥ c3 a2 £ b4 ¥ c1 £ ¤ ¦ a3 For the first step of the derivation we have to find a configuration, say conf , such that ( init(3¥ new (Complex) 4)) add( init(8¥ 9))¥ ¤ ¥ ¥ ¤ ¥ Sys £ new (Complex) conf Since ( init(3¥ new (Complex) 4)) add( init(8¥ new (Complex) 9)) is of the form Ee m(Ee 1 ¥¡ ¡ ¡ ¥ Een) (choose Ee init(3¥ new (Complex) 4), m add, n 1, and Ee init(8¥ 1 new (Complex) 9)), we can apply rule (a) and deduce if conf E e ¡ add( new (Complex) init(8¥ 9))¥ ¡ ¡ ¥ s¡ ¥ ¡ ¡ ¥ Sys init(3¥ 4)¥ ¤ ¥ ¥ ¤ ¥ Sys £ e new ¡ ¥ ¡ ¡ ¥ s¡ ¥ ¡ ¥ Sys (Complex) E So, to calculate conf , we first have to calculate the latter transition. By applying rule (a) again we see that if E e ¡ ¥ ¡ ¥ s¡ ¥ ¡ ¡ ¥ Sys E e ¡ ¡ init(3¥ 4)¥ ¡ ¡ ¡ ¥ s¡ ¡ ¥ (Complex)¥ ¤ ¥ ¥ ¤ ¥ Sys £ new We can now use axiom (1) to deduce E e ¡ ¡ ¥ ¡ ¡ ¡ ¥ s¡ ¡ ¥ This implies that and thus E e ¡ ¥ ¡ ¥ s¡ ¥ conf ¡ ¡ ¡ ¡ ¥ Sys ¡ ¥ Sys ¢ 1¥ £ ¢ 1 re £ nil¥ ¢ 1 init(3¥ 4)¥ ¡ ¡ ¡ ¥ Sys E e ¡ ¡ ¥ ¡ ¡ ¡ ¥ s¡ ¡ ¥ ¢ 1 im £ nil¦ ¥ £ ¢ 1 re £ nil¥ ¡ ¡ ¡ ¥ Sys ¢ init(8¥ init(3¥ 9))¥ £ ¢ ¢ £ nil¦ £ ¥ nil¥ ( 1 4)) add( new (Complex) 1 re 1 im ¥ ¥ ¡ £ ¢ 1 £ Complex¦ ¥ Sys ¢ £ ¢ ¥ ¥ £ Complex¦ £ ¥ Sys nil¦ 1 im 1 £ ¢ 1 £ Complex¦ ¥ Sys The other transition steps of the derivation sequence are deduced in a similar way. The result of a partial derivation is as follows: £ £ ( new (Complex) init(3¥ 4)) add( new (Complex) init(8¥ 9))¥ ¤ ¥ By rules (a),(a) and axiom (1). ¦ ¥ ¤ ¥ Sys £ ¢ ¢ ¢ init(3¥ init(8¥ nil¥ nil¦ 9))¥ ¥ £ £ ¢ £ £ ¥ Complex¦ Sys ( 1 4)) add( new (Complex) 1 re 1 im 1 ¥
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Specification of Reactive Hardware/
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to Leny, Inge and our parents
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Contents Acknowledgements v 1 Intro
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CONTENTS ix 4.6.5 Aggregate Semanti
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CONTENTS xi 6 Modelling of Concurre
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CONTENTS xiii 6.6.7.2 System Specif
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CONTENTS xv 11.4.2.3 Requirements C
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List of Figures 1.1 Chapter Overvie
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LIST OF FIGURES xix 6.16 Strongly D
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Chapter 1 Introduction 1.1 Objectiv
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1.1 Objectives 3 understood and sti
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1.1 Objectives 5 Informal and Forma
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1.2 Thesis Organisation 7 Chapter 1
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1.2 Thesis Organisation 9 Recommend
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Chapter 2 On Specification of React
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2.3 Specifications, Models and View
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2.4 Specification Languages, Formal
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2.4 Specification Languages, Formal
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2.5 Modelling Concepts 23 entirety.
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2.5 Modelling Concepts 25 Tradition
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2.6 Activity Frameworks for Specifi
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2.6 Activity Frameworks for Specifi
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2.7 Summary 31 offer many guideline
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Chapter 3 Concepts for Analysis, Sp
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3.3 Concepts 35 3. creation of a sy
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3.5 Combining Compatible Concepts 3
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3.6 Practical Use of Concepts 39 3.
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3.6 Practical Use of Concepts 41 Th
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3.6 Practical Use of Concepts 43 ac
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3.6 Practical Use of Concepts 45 ac
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3.6 Practical Use of Concepts 47 wa
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3.6 Practical Use of Concepts 49 Ge
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3.6 Practical Use of Concepts 51 Re
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3.7 Summary and Concluding Remarks
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Chapter 4 Abstraction of a Problem
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4.1 Introduction 57 earlier phase t
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4.2 Objects 59 An object can mean t
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4.2 Objects 61 wonder what other ob
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4.3 Classes 63 A message interface
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4.3 Classes 65 Class B Attributes M
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4.4 Data Objects and Process Object
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4.5 Clusters 79 flows. Clusters ena
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4.6 Aggregates 81 Therefore a compl
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4.6 Aggregates 83 4.6.4 Clustered A
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4.6 Aggregates 85 An old philosophi
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4.7 Identity and Object Identifiers
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4.8 Properties of Composites 89 for
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4.8 Properties of Composites 91 com
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4.8 Properties of Composites 93 Whe
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4.8 Properties of Composites 95 In
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4.9 Channel Hiding 97 Servant A Sup
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4.11 Composites and Hierarchies 99
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4.12 Object Variety 101 Part class
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4.13 Object Class Models 103 Anothe
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4.13 Object Class Models 105 of obj
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4.14 Attributes and Variables 107 c
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4.14 Attributes and Variables 109 4
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4.15 Operations, Services, Methods
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4.15 Operations, Services, Methods
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4.17 Summary 115 Accidental Propert
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Chapter 5 Concepts for the Integrat
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5.2 Architecture 119 Requirements D
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5.3 Design Philosophy 121 this. The
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5.4 Essential Model and Extended Mo
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5.4 Essential Model and Extended Mo
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5.6 Architecture and Implementation
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5.7 Views 129 Management £ £ £ P
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5.7 Views 131 Behaviour Behaviour U
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5.8 Boundaries 133 5.8 Boundaries 5
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5.8 Boundaries 135 x x Object A y z
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5.8 Boundaries 137 x w w x Object A
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5.8 Boundaries 139 In Chapter 10 we
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5.9 Transformations 141 The modific
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5.10 Formalisation 143 Level 1 Leve
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5.11 Summary 145 Behaviour Requirem
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Chapter 6 Modelling of Concurrent R
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6.2 Concurrency and Synchronisation
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6.3 Communication 157 between proce
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6.3 Communication 159 or to transfo
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6.3 Communication 161 6.3.3.4 Messa
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6.3 Communication 163 Synchronous m
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6.3 Communication 165 channel-name
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6.3 Communication 167 can be descri
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6.3 Communication 169 statement aft
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6.3 Communication 171 (normalCourse
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6.3 Communication 173 ∞ client re
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6.3 Communication 175 There is a gr
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6.3 Communication 177 process A pro
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6.3 Communication 179 Clocks An int
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6.3 Communication 181 whether the s
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6.3 Communication 183 6.3.9.4 Model
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6.3 Communication 185 6.3.10.2 Desc
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6.4 Distribution 187 force to take
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6.4 Distribution 189 is that the in
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6.4 Distribution 191 links to each
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6.4 Distribution 193 6.4.6 Distribu
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6.5 Scenarios 195 entities. This su
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6.5 Scenarios 197 startJob readyToA
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6.5 Scenarios 199 collection of tex
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6.6 Dynamic Behaviour 201 selection
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6.6 Dynamic Behaviour 203 processes
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Page 251 and 252: 7.2 A Brief Language Characterisati
Page 253 and 254: 7.3 The Role of Semantics 233 7.3 T
Page 255 and 256: 7.4 Mathematical Preliminaries 235
Page 257 and 258: 7.4 Mathematical Preliminaries 237
Page 259 and 260: 7.5 Concluding Remarks 239 0 ¡ Bin
Page 261 and 262: Chapter 8 Data Part of POOSL Chapte
Page 263 and 264: 8.3 Formal Syntax 243 runk, and cun
Page 265 and 266: 8.4 Context Conditions 245 Further,
Page 267 and 268: 8.5 A Computational Semantics 247 T
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Page 273 and 274: 8.6 Primitive deepCopy Messages 253
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Page 279 and 280: 8.8 Summary and Concluding Remarks
Page 281 and 282: Chapter 9 Process Part of POOSL Cha
Page 283 and 284: 9.3 Formal Syntax 263 In almost any
Page 285 and 286: 9.3 Formal Syntax 265 The fourth st
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Page 289 and 290: 9.4 Context Conditions 269 We are n
Page 291 and 292: 9.5 A Computational Interleaving Se
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Page 317 and 318: 9.7 The Development of POOSL 297 Em
Page 319 and 320: 9.7 The Development of POOSL 299 (o
Page 321 and 322: 9.8 Summary 301 To prepare the deve
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Page 325 and 326: 10.2 Instance Structure Diagrams 30
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10.2 Instance Structure Diagrams 30
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10.3 Some Properties of Transformat
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10.4 A System of Basic Transformati
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10.5 Example: The Elevator Problem
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10.7 On the Fundamental Limitations
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10.7 On the Fundamental Limitations
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10.8 Summary 331 are transformation
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Chapter 11 SHE Framework Chapter 1
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11.2 SHE Context and Phases 335 Inf
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11.2 SHE Context and Phases 337 a p
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11.2 SHE Context and Phases 339 11.
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11.3 SHE Framework 341 the system.
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11.4 Essential Specification Modell
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11.5 Extended Specification Modelli
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Chapter 12 Case Study Chapter 1 Cha
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12.2 Initial Requirements Descripti
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12.3 The Essential Specification 37
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12.4 Towards an Extended Specificat
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12.5 Concluding Remarks 399 i1 DIST
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12.5 Concluding Remarks 401 Feeder
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Chapter 13 Conclusions and Future W
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13.2 P.H.A. van der Putten’s Cont
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13.2 P.H.A. van der Putten’s Cont
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13.4 Related Results 409 The notion
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Appendix A The POOSL Transition Sys
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A.1 The Data Part of POOSL 413 (12)
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A.2 The Process Part of POOSL 415 A
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A.2 The Process Part of POOSL 417 (
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A.2 The Process Part of POOSL 419 (
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A.2 The Process Part of POOSL 421 i
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Appendix B Proofs of Propositions a
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Proofs of Propositions and Transfor
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Appendix C Glossary of Symbols This
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Glossary of Symbols 437 267 Cp ¥¡
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References [AB90] P. America and F.
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REFERENCES 441 [C [C [C 86] B. Cohe
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REFERENCES 443 [Her90] A.J.H. Herbe
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REFERENCES 445 [MV93] S. Mauw and G
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REFERENCES 447 [vE89] P. van Eijk.
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Index abort, 297 abstract action so
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INDEX 451 strong, 190, 293 subsyste
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INDEX 453 delay, 178 do-statement,
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Summary This combined thesis descri
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Samenvatting Dit gecombineerde proe
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Curricula Vitae Piet van der Putten
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