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310 Behaviour-Preserving Transformations (2) BSpece L¥ envs1¥ 1 Sysp ¡ ¥ Sys ¢ ( ¢ ) BSpece 1 ¡ L¥ envs¡1 ¥ Sysp ¡ ¥ Sys (3) BSpece 1 § f ¥ envs1¥ Sysp ¡ ¥ Sys ¢ ( ¢ ) BSpece 1 ¡ § f ¥ envs¡1Sysp ¨ ¡ ¥ Sys To see this, suppose that B,Sysp ¡ ¥ Sys ¢ ,Sys p C,Sys . By Proposition 4(3) we then have that d© a B§ b© c¥ , Sysp ¢ ¡ C§ b© c¥ d© a Sys , Sys p , Sys , . Then using Proposition 4(1) we obtain b© c¥ d© a ¢ B§ A , Sysp ¢ ¡ ¢ C§ b© c¥ d© a Sys , Sys A p , Sys , . And finally the result follows from Proposition 4(2). 10.4 A System of Basic Transformations In this section we will define a system of 15 basic behaviour-preserving transformations 3 . Each of the transformations is correct with respect to transformation equivalence. The correctness of the transformations is proved in Appendix B. A transformation is defined by a law of the form conf p 1 ¢ ¡ conf p 2 if condition If the condition is vacuously true, then it is omitted. The informal interpretation is that if the condition is satisfied then configuration conf p 1 may be transformed into conf p 2 (and vice versa), without effecting the external observable behaviour. The configurations before and after the transformation are transformation equivalent. If possible, we will clarify the transformations by examples and visualise them in terms of Instance Structure Diagrams. In this section the transformations are more or less explained in isolation. In the next section we will demonstrate by an example how the successive application of different basic transformations can lead to dramatic changes in system structure. Transformations are numbered from 1 till 15. We will often denote Transformation i by i. Transformation 1 e Id ¥ envs¥ p BSpec ¥ Sys § Sys ¢ ¡ BSpec e ¥ envs¥ Sys p ¥ Sys ¨ By Transformation 1 the identity channel renaming function (¡£¢ ), i.e. the function that maps each channel onto itself, may be dropped or introduced. For example, let BSpec e A ¢ B, for some process classes A and B. Further let ChSort(A¥ Sys p ) = £ a¥ b¥ c¦ and ChSort(B¥ Sys p ) = £ a¥ d¦ . Then 3 Variants of a number of transformations we define in this section are also given in [Mil89] and in [BBK87].
10.4 A System of Basic Transformations 311 Transformation 2 e BSpec ¢ 1 BSpece 2 ¥ envs1 ¥ envs2 Sysp Sys ¥ A B ¢ Transformation 3 e BSpec1 (BSpece 2 ¢ BSpece ¥ 3)¥ envs1 envs2 envs3 Sysp Sys ¥ c a a b d ¢ ¡ ¢ ¡ a A B c b d e BSpec ¢ 2 BSpece 1 ¥ envs2 ¥ envs1 Sysp Sys ¥ ¨ ¡ ¢ e (BSpec ¢ 1 BSpece ¢ 2) BSpece 3 ¥ envs1 envs2 ¥ envs3 Sysp Sys ¨ ¥ According to 2 and 3 the parallel composition operator is commutative and associative. This gives us the liberty to write BSpece 1 ¢ BSpece2 ¢ BSpece3 ¢ BSpece4 in stead of for example BSpece 3 ¢ ((BSpece1 ¢ BSpece ¢ 2) BSpece 4) without raising any confusion. In the sequel we freely make use of this liberty. Transformation 4 e BSpec ¥ envs¥ p f ¥ Sys § Sys e BSpec § f ¢ ¥ envs¥ Sys ¡ ¡ p ¥ Sys ¤ if f ChSort(BSpece ¥ Sysp ) ¡ ¤ = f ChSort(BSpece ¥ Sysp ¨ ) Here f ¤ D is the restriction of channel renaming f to domain D. 4 states that channel renaming function f may be replaced by f ¡ if both functions perform a similar renaming of the actual involved (observable) channels. Transformation 5 e § BSpec § f ¡ ¥ envs¥ f Sysp Sys ¥ e BSpec § f ¥ f ¢ ¥ envs¥ Sys ¡ ¡ p ¨ ¥ Sys By Transformation 5 two successive channel renaming functions can be reduced to a single one and vice ¥ versa. ¡ f f is the composition of functions f ¡ and f , ¥ i.e. ¡ (f f )(ch) = f (f (ch)) for each channel ¡ ch. Transformation 6 e (BSpec ¢ 1 BSpece f ¥ envs1 envs2 ¥ Sys 2)§ p Sys ¥ e BSpec § 1 ¢ f BSpece 2 § f ¥ envs1 ¥ envs2 Sysp Sys ¥ if NoComChange(BSpece 1 ¥ BSpece 2 ¥ envs1 envs2 ¥ Sys ¥ p Sys¥ f ) ¨ ¥ ¢ ¡
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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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6.6 Dynamic Behaviour 205 even for
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6.6 Dynamic Behaviour 207 with the
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6.6 Dynamic Behaviour 209 6.6.4 Sep
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6.6 Dynamic Behaviour 211 6.6.5 Mod
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6.6 Dynamic Behaviour 213 to pay at
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6.6 Dynamic Behaviour 215 A method
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6.6 Dynamic Behaviour 217 to happen
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6.6 Dynamic Behaviour 219 c a Multi
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6.6 Dynamic Behaviour 221 but not t
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6.7 Real-Time Modelling 223 claimed
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6.7 Real-Time Modelling 225 in the
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6.8 Summary 227 They can graphicall
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Chapter 7 Introduction to the Seman
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7.2 A Brief Language Characterisati
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7.3 The Role of Semantics 233 7.3 T
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7.4 Mathematical Preliminaries 235
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7.4 Mathematical Preliminaries 237
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7.5 Concluding Remarks 239 0 ¡ Bin
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Chapter 8 Data Part of POOSL Chapte
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8.3 Formal Syntax 243 runk, and cun
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8.4 Context Conditions 245 Further,
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8.5 A Computational Semantics 247 T
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8.5 A Computational Semantics 249 w
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8.5 A Computational Semantics 251 s
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8.6 Primitive deepCopy Messages 253
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8.6 Primitive deepCopy Messages 255
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8.7 Example: Complex Numbers 257 is
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Page 317 and 318: 9.7 The Development of POOSL 297 Em
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Page 351 and 352: 10.8 Summary 331 are transformation
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Page 355 and 356: 11.2 SHE Context and Phases 335 Inf
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Page 361 and 362: 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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