Ian Hayes, editor. Specification Case Studies. Prentice Hall International, second edition, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....misra cs.utexas.edu 1 Introduction An object and its associated operations may be specified in many ways. One way is to give an abstract representation of the object data structure (viz. representing a queue by a sequence) and the effects of various operations on this abstract representation [3,4,5]. Another way [2] is to leave the representation aspects unspecified but to give a set of equations that relate the effects of various operations (the equations define a congruence relation in a term algebra) The common goal of a specification, however, is to serve as a legal document that spells ....

Specification Case Studies, Ian Hayes (ed.), Prentice-Hall International, Englewood Cliffs, N.J., 1987.

.... Jon86, Jon87] 44 See, for example, proceedings of the VDM Symposia [BJMN87, BMJ88, BHL90, PT91a, PT91b] 45 A reference that has not been located is his paper which was presented at the conference whose proceedings are published as [BPT79] 46 Treatments of what Z has evolved into include [Hay86, Spi88, Spi89] 25 application to another in the form of theories. Papers such as [Dah78, Jon79] 47 hold out the hope of a real structuring of knowledge about computing ideas this knowledge should evolve in the way that mathematical theories are built up over time. In the late 80s, a ....

I. Hayes, editor. Specication Case Studies. Prentice-Hall International, 1986.

....but supporting evidence has come from the work in [6] IZ . Independently of the ideas of geometric logic, Hodges has been looking at a similarly restricted logic with no negation or implication, nor universal quantification except when bounded over finite sets. By examining the case studies in [5], he has formed the opinion that the restricted logic suffices. Even if the restrictions still allow us to write reasonable specifications, one might yet ask what is the benefit of imposing them on ourselves. Again any suggested benefit would have to be evaluated in practice, but our intention is ....

I.J. Hayes, editor. Specification Case Studies. Series in Computer Science. Prentice Hall International, 2nd edition, 1993.

....books on Z or other techniques. Also the book [WL88] is a good introduction to the use of mathematics in the speci cation of software. The book also gives a good introduction to the speci cation language Z. A collection of papers on the use of formal methods to describe computer systems is [Hay86] The book introduces the notation and has a few simple examples. It illustrates how formal methods, i.e. mathematics, can be used to de ne computer systems in a readable way. It would be worth trying the examples in VDM SL. There is also book on a modern subset of VDM SL that describes a ....

I. Hayes. Specication Case Studies. Prentice Hall International, 1986.

....Service 3.1 The Formal Language Z Z [11, 30, 33] is a formal language based on typed set theory and rst order logic with equality. It has been successfully applied, in its original form or using extensions such as Object Z [29, 31] in many case studies in formal modeling and development, e.g. [6, 7, 15, 25]. We have chosen Z for our work as the CORBA security service speci cation is heavily data oriented in that approximately half of it is focused on data, interfaces, and their functional requirements (while the remainder focuses on inter ORB communication) The Z language is well suited for such ....

I. Hayes. Specication Case Studies. Prentice-Hall International, 1993.

....Service 3.1 The Formal Language Z Z [11, 30] is a formal language based on typed set theory and rst order logic with equality. It has been successfully applied, in its original form or using extensions such as ObjectZ [29, 31] in many case studies in formal modeling and development, e.g. [6, 7, 15, 25]. We have chosen Z for our work as the CORBA security service speci cation is heavily data oriented in that approximately half of it is focused on data, interfaces, and their functional requirements (while the remainder focuses on inter ORB communication) The Z language is well suited for such ....

I. Hayes. Specication Case Studies. Prentice-Hall International, 1993.

....the efficiency of the systems in finding errors in a program. It would be a great advance in black box testing tools to be able to process already established specification languages i.e. used in other areas of software development other than testing. If languages such as VDM SL [84] or Z [85, 86] could be processed then the burden of writing specific specifications for testing purposes would be lifted thus, greater automation would, in a way, be achieved. 2.3.4 Specific Areas Softbridge, Inc. 87] has developed commercial tools for the testing of OS 2 and Windows applications graphical ....

....strategies has yet reached a stage where full automation is achieved and the strategy trusted. Therefore, one is limited to concentrate on one strategy while hoping for further improvements in others. In the area of functional testing the development of stable specification languages such as Z [85, 86], and VDM SL [84] offers a good platform for the implementation of a multitude of supportive tools. Further, their current standardisation [97] should re enforce this development. Software testing tools should benefit from this standardisation. As detailed in the next chapter, North [11] showed ....

I. Hayes, Specification case studies. Series in computer science, Prentice Hall International, 1987.

....[54] Proofs of correctness are carried out by defining retrieve functions between successive reification steps and showing that the behavior at each state is the same as the preceding one. Some of the most used model oriented based specification languages are VDM SL(see [54] 51] Z (see [41], 24] 14] For requirements specification of the dynamic user management system, VDM SL was used. 2.2 VDM SL and IFAD VDM Toolbox 2.2.1 The language VDM SL is a model oriented specification language born in a industrial environment at the Vienna IBM laboratory. It can be used for abstract ....

Hayes. Specification Case Studies. Prentice-Hall International, 1987.

....appeared as [6] and [5] One contribution of this paper is demonstrating use of a convention for describing exceptions and error handling, and details of the approach are to be found 1 in Appendix A. An overview of Z and Object Z is beyond the scope of this paper, and the reader is directed to [12, 20] (Z) and [3, 7, 8] Object Z) for details. 1.1 A short overview of PREMO This section gives a very short overview of PREMO; for a more detailed presentation the interested reader should consult [13] or [14] Today s application developers needing to realize high level multimedia applications ....

I.J. Hayes. Specification Case Studies. Series in Computer Science. Prentice Hall International, second edition, 1992.

....design. We discuss the merits and disadvantages of each of these approaches in detail. 4.1. 1 Meta Languages as Virtual Code One common approach to expressing executable specifications or oracle constraints is to implement powerful, high level constructs, such as those found in VDM [5] or Z [3], in virtual code. The clear syntax and high level primitives of such languages allow the user to express complex requirements in a precise and abstract manner. Furthermore, a language can be designed that inherently protects the underlying program from the actions of virtual code. User training ....

....defects that had previously gone unde tected. In developing C Patrol, we evaluated alternatives for managing the assertion insertion process. Possible design alternatives concern: ffl The choice of language used to express the assertions. Choices include (1) a meta language such as Z or VDM [3, 5], 2) a restricted form of the implementation language, or (3) an unrestricted form of the implementation language. C Patrol uses unrestricted C, which maximizes user control and eases training effort. ffl The method used to insert the assertions. Assertions can be inserted manually into desired ....

I. Hayes, editor. Specification Case Studies. Prentice-Hall International, London 1987.

....the efficiency of the systems in finding errors in a program. It would be a great advance in black box testing tools to be able to process already established specification languages i.e. used in other areas of software development other than testing. If languages such as VDM SL [71] or Z [72, 73] could be processed then the burden of writing specific specifications for testing purposes would be lifted thus, greater automation would, in a way, be achieved. 23 2.2.4 Specific Areas Softbridge, Inc. 74] has developed commercial tools for the testing of OS 2 and Windows applications. These ....

....strategies has yet reach a stage where full automation is achieved and the strategy trusted. Therefore, one is limited to concentrate on one strategy while hoping for further improvement in others. In the area of functional testing the development of stable specification languages such as Z [72, 73], and VDM SL [71] offers a good platform for the imple26 mentation of a multitude of supportive tools. Further, their current standardisation [86] should re enforce this development. Software testing tools should benefit from this standardisation. As detailed in the next chapter, North [10] ....

I. Hayes, Specification case studies. series in computer science, Prentice Hall International, 1987.

....based on the variables used and constructed. The Z specification language is used throughout to formalise the concepts discussed, though standard syntactic conventions are relaxed or generalised on occasion in the interests of clarity and brevity. The reader unfamiliar with Z is referred to [6, 15]. In preparation, the existence of a collection of variable names [VAR] and a collection of value names is assumed. VAL] The collection of variable names is partitioned into an infinite collection of process variables VAR : ff VAR 9 p : fl VAR ffl true and a collection of logical variables ....

I. J. Hayes, editor. Specification Case Studies. Prentice Hall International, second edition, 1993.

....scope. For example 8 v ffl Q 1 Q 2 means 8 v ffl (Q 1 Q 2 ) and not (8 v ffl Q 1 ) Q 2 . The order on predicates is entailment, written Q 1 V Q 2 and true if and only if the predicate Q 1 ) Q 2 is valid. Entailment equivalence of predicates is written Q 1 j Q 2 . The Z specification language [7, 29] provides a convenient formal notation for the predicate calculus. Z schemas consist of a list of variable declarations (the signature) and a predicate that describes properties satisfied by the variables. 3 In this paper the notion of predicate is identified with that of the Z schema. Predicates ....

I. J. Hayes, editor. Specification Case Studies. Prentice Hall International, second edition, 1993.

....of the least conjunctive refinement operator for predicate transformers is presented. As an example of the use of this operator, the Z based technique of program promotion is considered in a refinement calculus setting. 1 Introduction One of the useful features of program specification in Z [3] is the concept of promotion. This technique allows the specification of operations on complex data structures through the promotion of simpler operations on components of the structure. A canonical example is the specification of an update operation on an entire file system through the promotion ....

....Utting [12] and it refers to the assumption that variables not mentioned in the frame of a specification statement will not change during the execution of the specification statement. This may be contrasted with the open world view adopted when specifying programs in the Z specification language [3, 11]. Any variables not mentioned in a Z transition schema may update to an arbitrary value. Adopting this open world view allows program conjunction to be an important and powerful tool in the development of Z specifications, whilst the closed world view adopted by the refinement calculus limits its ....

I. J. Hayes, editor. Specification Case Studies. Prentice Hall International, second edition, 1993.

.... recommendations of a Special Rapporteur s Report on Formal Description Techniques in PREMO [17] and the specification of aspects of PREMO using the Z and Object Z notations have appeared as [5] and [4] An overview of Z and Object Z is beyond the scope of this paper, and the reader is directed to [11, 18] (Z) and [2, 7, 8] Object Z) for details. One of us (G. Faconti) has explored the use of LOTOS and LOTOS tools in this endeavour in work reported elsewhere in this workshop. The next section introduces the PREMO system and the problem we are studying. 1.1 A short overview of PREMO This section ....

I.J. Hayes. Specification Case Studies. Series in Computer Science. Prentice Hall International, second edition, 1992.

....appeared as [6] and [5] One contribution of this paper is demonstrating use of a convention for describing exceptions and error handling, and details of the approach are to be found 1 in Appendix A. An overview of Z and Object Z is beyond the scope of this paper, and the reader is directed to [12, 20] (Z) and [3, 7, 8] Object Z) for details. 1.1 AshortoverviewofPREMO This section gives a very short overview of PREMO; for a more detailed presentation the interested reader should consult [13] or [14] Today s application developers needing to realize high level multimedia applications which go ....

I.J. Hayes. Specification Case Studies. Series in Computer Science. Prentice Hall International, second edition, 1992.

....status. Arrive Initail Paperwork Assessment Repair Test Final Paperwork To Users To Company Computer Company Clerk Technican Work Work Figure 5: Service Centre. 4. 2 Functional decomposition through Z The functional decomposition of the Service Centre can be handled using a Z formal specification [14, 15]. All the entities in the Service Centre such as objects and operations are identified and defined in a schema called StateSpace: StateSpace ManSt = fwork ; freeg Tech = ftech1; tech2g Clerk = fclerkg ManId = Clerk [ Tech Staff = ManId Theta ManSt MacId : PN MacSt = farrive; record ; ....

I. Hayes(editor), Specification Case Studies. Prentice-Hall International, 1987.

....complexity of modern software systems, which can not be handled by classical structured programming and design techniques. The ability to specify system properties in a precise and rigorous way has been invaluable in the design and implementation of many computer systems, regardless of their size [Hal90, Haye92]. Formal specifications are gaining acceptance as an important component of methods for developing high quality software [But94] A formal specification has many roles in the development process. Some examples are: ffl as a mean of precise communication between the customer and the software ....

....at the Programming Research Group at the Oxford University Computing Laboratory and elsewhere for well over a decade. Z is now used by industry as part of the software (and hardware) development process: IBM has used Z successfully in specifying parts of its CICS transaction processing system [Haye92]; Z has been used to clarify an IEEE floating point standard; It is currently undergoing BSI standardization in the UK and has been accepted for the ISO standardization process internationally. The aim of this section is to introduce the basic features of Z which will be used throughout the ....

Hayes I. Specification Case Studies. Prentice Hall International. 1992.

....language developed by the Programming Research Group at Oxford University ComputingLaboratory in the early 80 s. Since then, Z has been used to specify a wide spectrum of software systems includingdatabase systems, transaction systems, distributed computing systems, and operating systems [2]. The most notable success of Z is the specification of CICS Application Programming Interface (API) by IBM United Kingdom Laboratories at Hursley Park [3] Approximately 37,000 lines of code were produced from Z specifications and designs, and it was reported that the code has approximately 2.5 ....

I. Hayes (ed.), Specification Case Studies, Prentice Hall International, 2nd edition, 1993.

....five types, or classes, of formal methods which can be roughly characterised as follows: 1. model based approaches giving an explicit, albeit abstract, definition of system (program) state and operations which transform the state, but giving no explicit representation of concurrency eg Z [ Hay86, Spi89] and VDM [ Jon86] 2. algebraic approaches giving an implicit definition of operations by relating the behaviour of different operations withoutdefining state, again giving no explicit representation of concurrency eg OBJ [ GT79] and PLUSS [ Dau89] 3. process algebras ....

I Hayes, editor. Specification Case Studies. Prentice Hall International, 1986.

....language developed by the Programming Research Group at Oxford University Computing Laboratory in the early 80 s. Since then, Z has been used to specify a wide spectrum of software systems including database systems, transaction systems, distributed computing systems, and operating systems [2]. The most notable success of Z is the specification of the CICS Application Programming Interface (API) by IBM United Kingdom Laboratories at Hursley Park [3] Approximately 37,000 lines of code were produced from Z specifications and designs, and it was reported that the code has approximately ....

I. Hayes (ed.), Specification Case Studies, Prentice Hall International, 2nd edition, 1993.

....into data structures involving pointers. Data refinement was first formalized in [Hoare, 72] Later [Jones, 80] introduced the concepts of adequate and fully abstract representations, providing more flexible rules for data refinement. Recent interest in the mathematics of programs [Hoare and Hayes, 1987a] Back, 88] Morris, 87a] Morris, 87b] Hehner, 84] Hehner et al. 86] has rekindled interest in data refinement. A number of more general data refinement relations have been presented recently, in a variety of formalisms. 2 However, some authors present their theories as a miraculous ....

Hayes, I., ed.: Specification Case Studies, Prentice Hall International, 1987.

....the oracle is written in the concrete domain of actual structures used by the program. A full discussion of the advantages and disadvantages of using C as a virtual language appears in a later section. Checking code can also be used as a method of specification. Efforts such as VDM [Jon86] and Z [Hay87] use pre and post condition checks to specify the actions of functions. C patrol goes a step farther by providing invariants that can be applied to data structures. Objects can be linked to label identifiers, thus associating invariants to objects: int X; label X: assert(X 20) Calls ....

....The merits and disadvantages of each of these approaches will be discussed in detail. 4.1. 1 Meta Languages as Virtual Code One common approach to expressing executable specifications or oracle constraints is to implement powerful, high level constructs, such as those found in VDM [Jon86] or Z [Hay87], in virtual code. The clear syntax and high level primitives of such languages allow the user to express complex requirements in a clear and abstract manner. Furthermore, a language can be designed that inherently protects the underlying program from the actions of virtual code. The intent of ....

Ian Hayes, editor. Specification Case Studies. Prentice-Hall International, Cambridge, London, 1987.

....objective of testing is to identify errors in any way possible. The TTF is very flexible, allowing many different testing strategies to be incorporated. It provides a common foundation for applying testing strategies, and for classifying and comparing these strategies. The Z specification notation [Hay87, Spi92] is used as a Test Description Language (TDL) and to define the basic components of the TTF. This enables a formal description of test data, and other test information such as test oracles. The uniform use of the Z notation improves the clarity and structure of the test information. The ....

....to one testing strategy. It allows different heuristics and strategies to be used to determine interesting subdomains of the input space and to select tests for these subdomains. 1. 4 This document Familiarity with Z is assumed (tutorial references include [WL88] and the opening chapters of [Hay87, Spi92]) Familiarity with testing strategies is also assumed [Bei90] Section 2 defines the framework. Section 3 demonstrates specification based testing using the framework on an example specification. Section 4 discusses the framework and its many applications. 2 TEST TEMPLATE FRAMEWORK This ....

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I. Hayes, editor. Specification Case Studies. Series in Computer Science. Prentice Hall International, 1987.

....inwards, and is primarily aimed at producing a precise specification of a system which can then be engineered in software. Formal methods have been used in large software systems for both safety critical systems [2] involving exhaustive application of formal methods) and other systems development [10], where formal methods are progressively transformed from an axiomatic description into working specifications in some programming language. This paper considers a specification system based on a functional programming language as a formal method for modelling information systems. Similar schemes ....

I. Hayes. Specification Case Studies. Prentice-Hall International (UK), 1987.

....introduced within this paper appears as Appendix D. 2 A Generic Theory of Presentations Formal specifications of software systems rarely describe aspects of the system other than the (abstract) state and the operations that can be performed on the state. Few published case studies (see [29] and [31] for example) distinguish between the internal state of the system and what the user can perceive through the interface. One reason may be that the formal methods community perceives the user interface as an implementation detail, at a level of reification beyond that normally considered ....

I.J. Hayes. Specification Case Studies. Series in Computer Science. Prentice Hall International, 1987.

....Programming languages do not give the proper amount of abstraction, while specification languages do. 1. 2 Using Specification Languages in Industry Some of the non executable specification languages supported by well known formal methods (e.g. VDM [Jones90] Dawes91] Andrews 91] and Z [Hayes87], Spivey92] have been used as paper and pencil tools. The strength of using specification languages in this way is that it is easy to extend the notation of the specification language to suit a particular paradigm or application area 1 . There is a trade off here, because computer based ....

Ian Hayes, editor. Specification Case Studies. Prentice-Hall International, 1987.

....Research Group at Oxford University. Z is based on set theory and predicate calculus, and uses a schema calculus for defining states and operations. We assume the reader is familiar with such concepts as sets, relations, and predicate calculus. Appendix A presents excerpts from the Z glossary in [Hay93], explaining the Z notation we use that may not be familiar. Chapter 2 Specification based testing issues To discuss work related to this thesis and to define the contribution of this thesis, we present a classification of the elements of specification based software testing. This chapter ....

I. Hayes, editor. Specification Case Studies. Series in Computer Science. Prentice Hall International, second edition, 1993.

....(T ) OS Classify j class = INVALID ] CHAPTER 6. EXAMPLES AND CASE STUDIES 76 6.2 File read The second example introduces a little more complexity of specification. The specification is of a simplified read operation on files, and is based on the specification of the UNIX read operation in [Hay87]. This case study was used as a primary example of the framework in [SC93c] the specification and testing below are drawn from this work. 6.2.1 Specification Files are modelled as bounded sequences of bytes. Bytes are introduced as a generic set and not defined further. BYTE ] MaxFileSize : fl ....

I. Hayes, editor. Specification Case Studies. Series in Computer Science. Prentice Hall International, 1987. Later edition available.

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I.J.Hayes (Ed.) Specification Case Studies (Prentice-Hall International, 1987).

....and then developing a specification in terms of the theory. 1 1 The first chapter of this report is an updated version of [Hay90] and the second and third chapters are updated versions of [Hay92] The changes from the original papers are mainly to make the notation consistent with [Spi92] and [Hay93]. Contents 1 Multi sets or bags 3 1.1 Introduction : 3 1.2 Models for bags in Z : 3 1.3 Basic operations : 4 1.4 Bag ....

....develop a specification of a bill of materials system. This specification is not intended to be a specification of a real bill of materials system, but rather a realistic illustration of the utility of multi relations for specifying such systems. Throughout this paper we make use of the Z notation [Hay93, Spi92] and make extensive use of the theory and notations of multi sets developed in [Hay90] In [Hay90] the more common term bag is used where, in this paper, we use the term multi set; this is to emphasise the correspondence between multi sets and multirelations. In addition, Hay90] allows ....

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Ian Hayes, editor. Specification Case Studies. Prentice Hall International, second edition, 1993. 288 pages.

....in specification, bags provide an additional toolkit for the specifier to use in those situations where the frequency of occurrence of values in a structure is important but the order of occurrence is not. The remainder of this chapter develops a theory of bags for Z which extends those given in [Hay87, Spi89]. We begin by introducing a model of bags as a partial function from some base set to the integers (Section 1.2) and then go on to introduce bag operators and laws that they satisfy (Sections 1.3 1.9) Finally Sections 1.10 1.12 present some simple applications of bags. 1.2 Models for bags in ....

....some base set to the integers (Section 1.2) and then go on to introduce bag operators and laws that they satisfy (Sections 1.3 1.9) Finally Sections 1.10 1.12 present some simple applications of bags. 1. 2 Models for bags in Z The model used for bags, with elements taken from some set X , in [Hay87, page 47], Spi89, page 127] and [Spi92, page 124] is a function from X to the strictly positive 1 Sets, bags, sequences and trees form what is known as the Boom hierarchy. 3 natural numbers. This function is partial: it is only defined for those elements that occur in the bag with non zero frequency. ....

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I. J. Hayes, editor. Specification Case Studies. Prentice Hall International, 1987.

....study results and Appendix B includes the Prolog programs used. 2 Specification of the All du paths Criterion The software tools used in this study are specified in the SPECS specification language [19] SPECS is an abstract model specification language and is similar to VDM s meta iv [25] and Z [26]. SPECS specifications are defined as abstract data types in terms of mathematical sets, sequences, labelled tuples, integers, booleans, and operations on these primitives. A SPECS specification consists of an abstract domain specification and the specification of operations on objects in the ....

I. Hayes (editor). Specification Case Studies. Prentice-Hall International, London, 1987.

....a collection of modules from this cross reference. A further projection stage (discussed briefly in section 2.3) is required to define the signatures and pre and post conditions of the module level operations. As a case study, in Section 3 we examine the application of the techniques to a Z [8, 16] specification of a language based editor [18, 1] In the remainder of the introduction, we discuss the multiple roles of formal specifications and the concept of modularity. 1.1 Formal specifications Formal specifications are gaining acceptance as an important component of methods for ....

Ian Hayes, editor. Specification Case Studies. Prentice Hall International, second edition, 1993. 13

....systems, especially those interfacing with physical systems, one would like to enjoy the benefits of a notation that incorporates units. Units can easily be incorporated into specifications informally, but for specifications written in formal specification languages, such as VDM [Jon90] and Z [Spi92, Hay93], it is preferable that the language provide support for units. The aims of the current paper are ffl to argue that incorporation of units into a formal specification language is worthwhile in general and especially where the language is to be used to describe components involving physical ....

I. J. Hayes, editor. Specification Case Studies. Prentice Hall International, second edition, 1993. 19

....than the others considered in this paper. Finally Section 6 reviews the approach. 2 File update To demonstrate our approach the first example is typical of specifications written using formal methods, like Z and VDM [Jon90] The example is a sequential file update similar to that specified in [Hay93, p7]. A file is considered to be a mapping from keys to values (KeyValue) Abstractly, a file update operation takes as input a set d of keys to be deleted from the file and a partial mapping r to replace part of the file; it outputs the set e of keys that were to be deleted but were not in the ....

Ian Hayes, editor. Specification Case Studies. Prentice-Hall International, second edition, 1993.

....Another point about is permutation is the way it is made concise by shifting between data types (here, sequences to sets) This technique can be useful in a range of specifications. Even where a specification does not explicitly use a conjunction, the technique may be used implicitly. In both Z [Hay87, Spi89] and VDM [Jon86] data type invariants are considered to be conjoined to other properties over types using them. An example of the use of conjunction in a non trivial specification appears in work on unification: see chapters by Fitzgerald and Vadera in [JS90] 7 2.4 Negation in ....

I. J. Hayes, editor. Specification Case Studies. Prentice-Hall International, 1987.

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I.J.Hayes (Ed.) Specification Case Studies (Prentice-Hall International, 1987).

....Section 4, a dynamic environment is defined. The dynamic semantics for variables and expressions are given in Sections 4.2 and 4.3 respectively. The projection function is defined in Section 4.4 and is an important feature of the ensuing definition of assignment in Section 5. We use the Z notation [Hay93, Spi92] to present a formal semantics for a small Oberon like language in the style of [Hay94] 2 Abstract Syntax For our purposes it is sufficient to give the abstract syntax of type declarations (Section 2.1) variable references (Section 2.2) and expressions (Section 2.3) 2.1 Type declarations We ....

I. J. Hayes(editor). Specification Case Studies. Prentice Hall International, second edition, 1993.

....on topics in Distributed Computing. PRG members carrying out case studies included Carroll Morgan, Ian Hayes, Bernard Sufrin, Ib S rensen, and others. Ian Hayes, in addition to his contributions to the IBM CICS project, later collected these case studies and published them in the first book on Z [Hay93]. One of the most extensive case studies has been the use of Z for defining CICS, a transaction processing system developed by IBM. The collaboration between the PRG and the Hursley development laboratory, starting in 1982 and still continuing, has been a valuable source of information and ....

....in the PRG and locally distributed. The complete language description, The Z Handbook by B. A. Sufrin [Suf88] was given only a limited circulation, and in fact the first account of the notation published in book form was in the 1987 edition of the collection of Case Studies (second edition [Hay93]) mentioned above. Theoretical work on the foundations of Z continued in the PRG and elsewhere, and an important contribution was provided by the D.Phil. thesis of Mike Spivey, subsequently published as a book [Spi88] With a growing number of industrial users of Z, requests for standardisation ....

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Ian Hayes, editor. Specification Case Studies. Prentice Hall International, second edition, 1993.

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Ian Hayes, editor. Specification Case Studies. Prentice Hall International, second edition, 1993.

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I. Hayes, editor. Specification Case Studies. Prentice-Hall International, 1986.

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I. Hayes, editor. Specification Case Studies. Prentice-Hall International, New Jersey, second edition, 1993.

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Ian Hayes, editor. Specification Case Studies. Prentice-Hall International (UK) Ltd., Hemel Hempstead, UK, 1987.

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I. Hayes, Specification Case Studies, Prentice-Hall International, London (1987).

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