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254 Data Part of POOSL For readers with a more mathematical background it may be interesting to observe that that ¡ continuous function on ¡ ))¢¤£ . By elementary fixed point theory it then follows (Dom(¡ § that FIX(¦ ¡¤£¥ = ), FIX(¦ ¡¤£¥ where ) denotes the least fixed point ¦ ¡¤£¥ of . (Dom(¡ ))¢¤£ is a complete lattice with least element ¥ , and that each ¦ ¡¤£¥ is a We are now able to formulate a definition of function copy. Let Sys-structure. Then where copy( ¤ ¥ ¡ ¥ £ ¤ ¡ ¡ ¤ ¡ ¡ ¥ ¤ ¡ ¥ ) ¡¤£¥ (¤ n ¡ ) § n¦ 0 ¤ ¥ ¡ ¥ ¡ ¡ StrucSys be a ¨ ¡ The elements of the range of function copy are characterised by a number of interesting properties: Proposition 1 Let ¥ ¡ ¥ ¡ StrucSys and let copy( ¤ ¡ ¡ ¡ ¥ ) = ¤ ¥ ¡ ¡ ¡ ¥ ¤ ¥ (a) ¡ ¡ ¡ ¥ ¡ ¡ StrucSys. ¥ ¤ (b) copy( ¥ ¡ ¡ ¥ ¡ ) = ¤ ¡ ¡ ¡ ¡ ¥ ¤ ¥ ¡ ¡ Dom(¡ ¡ (c) proc ). ¡ . ¡ . Then The proof of Proposition 1 is given in Appendix B. ¨ According to (a) of Proposition 1, a copy of a Sys-structure is again a Sys-structure. Item (b) states that this Sys-structure is minimal in the sense that it does not contain any information about objects that are not (indirectly) known by ¤ . By item (c) we know that that implies that the Sys-structure does not contain any information about the involved process object also. Sys-structures satisfying property (b) of Proposition 16 , are called minimal Sys-structures. They will later be used extensively to describe data object passing between the various process objects. The set of all minimal Sys-structures StrucSys£ is denoted min. So, if ¡ ¡ ¥ ¤ ¥ StrucSys. Then ¡ ¡ ¡ ¥ ¡ StrucSys£ min if and only if copy( ¤ ¥ ¡ ¡ ¥ ) = ¤ ¥ ¡ ¡ ¥ ¥ ¤ Next, we define a collection of functions relabel m. These functions are used to relabel all object identifiers of a minimal Sys-structure by increasing them by m. Let ¤ ¡ ¡ ¥ ¥ ¡¢ StrucSys£ StrucSys£ £ be a minimal Sys-structure, and let m be a natural number. Then the collection of relabelling functions relabel m : min min is defined by where relabel m( ¥ ¡ ) ¤ ¡ ¥ ¡ ¡ ¡ ¥ ¡ ¥ ¡ ¤ 6 Note that if © is a Sys-structure satisfying property (b), it also satisfies properties (a) and (c).
8.6 Primitive deepCopy Messages 255 (1) Dom(¡ ¡ ) = Dom( ¡ ¡ ¡ (2) ( k m)(x) ¥ (3) ¡ ) = ¡ £¡ k ¡ m ¢ k ¡ Dom(¡ )¦ ¢ ¢ if¡ ¢ ¢ ¡ if¡ ¡ ¡ p m ( k)(x) p NDObj ( k)(x) ( k)(x) PDObj ¢ ¢ for ¡ Dom(¡ all k ) ¡ Dom(¡ and x ( k)) ¡ ¢ ¢ ( k m) ( k) ¡ Dom(¡ for all k ) ¡ This definition states that relabelling a minimal Sys-structure consists of replacing ¢ all non-primitive data object identifiers k by objects identifiers k m. All primitive objects remain unchanged. The relabelling of a minimal Sys-structure yields another minimal Sys-structure. The proof of this fact is of a similar complexity as the proof of Proposition 1. The semantics of deepCopy messages is formalised by axioms (21) and (22) of the transition system of Section A.1. Axiom (21) deals with deepCopies of primitive objects and (22) with deepCopies of non-primitive objects. (21) Primitive method deepCopy, primitive objects deepCopy()¥ ¡ ¥ s¥ ¡ ¥ Sys £ ¥ ¡ ¥ s¥ This axiom states that the deepCopy of a primitive object yields the primitive object itself. (22) Primitive method deepCopy, non-primitive objects if where copy( deepCopy()¥ ¡ ¥ s¥ ¡ ¡ ¥ Sys £ ¡ ¡ ¡ ¡ ¥ ¡ ¡ ¡ ¡ ¥ s¥ ¡ ¥ Sys ¡ ¡ ¡ ¡ ¥ Sys ¥ ¡ ¡ ¡ ¡ ¡ ¡ ¥ CDl ¡ ¡ ¡ ¡ ¡ ¡ ¡ (¡ ¡ is a Sys-structure , Sys CD1 CDj , CDj data class C MD1 MD MDl , C ) and MD deepCopy() primitive ¥ ¡ ¡ ¡ ¡ ¥ ¡ ¡ ¡ ¥ ¡ , relabel MaxId(¡ ( ¡ ¥ ) ) ¡ ¡ ¡ ¥ ¡ ¡ ¡ ¡ ¡ ¥ ¡ ¡ ¡ ¡ ¥ ¡ ¥ ¡ ¡ ¡ ¡ ¡ , ¡ ¡ ¡ ¡ ¡ ¦ ¡ ¡ ¡ ¡ ¡ ) and ¡ ¡ ¡ ¡ ¡ ¦ ¡ ¡ ¡ Axiom (22) states that a deepCopy of ¡ object is being made in three steps. In the first step a copy is made. This copy is being relabelled by adding the MaxId(¡ number ) to all its object MaxId(¡ identifiers. ) is the largest object identifier which is contained in the original ¡ state , so the newly created identifiers are all ’fresh’. As a final step, the relabelled object is added to the original state and type, and the (new) object identifier ¡ ¡ ¡ associated with ¡ is the evaluated result of the deepCopy operation. ¡ The theory of this paragraph is not just developed to describe deepCopy messages. Later, we will need the same theory to describe data object passing between process objects. ¡ ¡ ,
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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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Page 227 and 228: 6.6 Dynamic Behaviour 207 with the
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Page 235 and 236: 6.6 Dynamic Behaviour 215 A method
Page 237 and 238: 6.6 Dynamic Behaviour 217 to happen
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Page 247 and 248: 6.8 Summary 227 They can graphicall
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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 277 and 278: 8.7 Example: Complex Numbers 257 is
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 311 and 312: 9.7 The Development of POOSL 291 is
Page 313 and 314: 9.7 The Development of POOSL 293 da
Page 315 and 316: 9.7 The Development of POOSL 295 e
Page 317 and 318: 9.7 The Development of POOSL 297 Em
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Page 321 and 322: 9.8 Summary 301 To prepare the deve
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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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