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238 Introduction to the Semantics of POOSL A rule has zero or more premises and one conclusion. It tells us how we can construct a complex mathematical object (the conclusions) from simpler ones (the premises). A rule may have a condition which has to be fulfilled whenever the rule is to be applied. If this condition is vacuously true, it is omitted. Rules with premises that are vacuously true are called axioms. Axioms define what are considered primitive mathematical objects. Together, the axioms and rules define a collection of mathematical objects. This collection contains those and only those objects that are derivable from these axioms and rules. Inductive Proofs Axioms and rules are used to define mathematical objects. The same axioms and rules, however, can also be used to prove some property about these objects. First the property is proved for all primitive objects defined by the axioms. Then, for each rule, the property is proved for the complex objects defined by the conclusion of that rule. Such a proof uses the assumption that the property already holds for the objects used in the premises of the rule. This assumption is called the induction hypothesis. The proofs themselves are called proofs by rule induction. Mathematical Induction Mathematical induction is probably the most well-known form of induction. It is based on the collection of natural numbers. is inductively defined by one axiom and one rule: ¡£ ¡£ ¡£ ¡ To a property, say P(n), one can use rule induction. One starts by 0 n n 1 prove for each n proving P(0). Then P(n 1) is proved under the assumption that P(n) already holds. This form of induction is commonly called mathematical induction (on n). Inductive Function Definitions We will repeatedly define functions in an inductive way. As a simple example, consider the well-known faculty function fac : £ . It is defined by one axiom and one rule: fac(n) k if ¡£ n fac(0) 1 fac(n 1) k(n 1) It is however quite unusual to define functions this way. We will therefore follow the convention and use the more usual notation: fac(0) 1 and fac(n 1) (n 1)fac(n) for n ¡£ Using rule induction one is able to prove that each object fac(n) satisfies some property P. It is also possible, however, to use mathematical induction on n. Then the axiom and rule in the definition of are used as a basis for induction. The axiom and rule of the definition of fac are used as well, but they serve a different purpose. Both of these forms of induction are applied in this thesis. Backus Naur Form (BNF) As we explained in Subsection 7.4.1, we will occasionally have to define collections of syntactic elements. Consider, for instance, the collection Bin of binary representations of natural numbers. Bin is defined as
7.5 Concluding Remarks 239 0 ¡ Bin 1 ¡ Bin B ¡ Bin B0 ¡ Bin B ¡ Bin B1 ¡ Bin Here B is a syntactic meta variable ranging over Bin. The axioms and rules are commonly represented in Backus Naur Form (BNF): B :: 0 ¡ 1 ¡ B0 ¡ B1 To prove that the elements of the collection satisfy some property, one uses rule induction. In case the collection consists of syntactic elements one often speaks about structural induction. 7.5 Concluding Remarks The POOSL language is composed from a data part and a process part. The same holds for the semantics of the language. In Chapter 8 the data part of POOSL is explained in detail. Chapter 9 deals with the development of the process part of the language. In Chapter 10 the semantics is applied to define several behaviour-preserving structure transformations and to prove them correct. The proofs of all propositions, lemmas and transformations are given in Appendix B.
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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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Page 209 and 210: 6.4 Distribution 189 is that the in
Page 211 and 212: 6.4 Distribution 191 links to each
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Page 215 and 216: 6.5 Scenarios 195 entities. This su
Page 217 and 218: 6.5 Scenarios 197 startJob readyToA
Page 219 and 220: 6.5 Scenarios 199 collection of tex
Page 221 and 222: 6.6 Dynamic Behaviour 201 selection
Page 223 and 224: 6.6 Dynamic Behaviour 203 processes
Page 225 and 226: 6.6 Dynamic Behaviour 205 even for
Page 227 and 228: 6.6 Dynamic Behaviour 207 with the
Page 229 and 230: 6.6 Dynamic Behaviour 209 6.6.4 Sep
Page 231 and 232: 6.6 Dynamic Behaviour 211 6.6.5 Mod
Page 233 and 234: 6.6 Dynamic Behaviour 213 to pay at
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 241 and 242: 6.6 Dynamic Behaviour 221 but not t
Page 243 and 244: 6.7 Real-Time Modelling 223 claimed
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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
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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
Page 269 and 270: 8.5 A Computational Semantics 249 w
Page 271 and 272: 8.5 A Computational Semantics 251 s
Page 273 and 274: 8.6 Primitive deepCopy Messages 253
Page 275 and 276: 8.6 Primitive deepCopy Messages 255
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
Page 287 and 288: 9.3 Formal Syntax 267 call of the f
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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9.6 Example: A Simple Handshake Pro
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9.7 The Development of POOSL 291 is
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9.7 The Development of POOSL 293 da
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9.7 The Development of POOSL 295 e
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9.7 The Development of POOSL 297 Em
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9.7 The Development of POOSL 299 (o
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9.8 Summary 301 To prepare the deve
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Chapter 10 Behaviour-Preserving Tra
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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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