 |
VOOZH | about |
|
VOOZH | about |
1995, Information and Software Technology
https://doi.org/10.1016/0950-5849(95)90001-2…
2 pages
The paper presents a glossary of terms and definitions related to Z notation, which is a formal specification language used for designing and describing computer systems. It covers various aspects of Z notation including axiomatic and generic definitions, schema operations such as schema composition, negation, projection, and quantification, as well as conventions used within the notation. This glossary serves as a reference for those engaged in formal methods and specification using Z notation.
IJID (International Journal on Informatics for Development)
This paper discusses our proposal on how to embed theorems in Z specifications. One reason behind this proposal is to ease Z users in writing theorems directly in their Z specifications. Another reason is not to overwhelm Z users in learning other language, which in this case is SAL language. In doing so, we need to inform Z2SAL programmers how to translate these embedded theorems into equivalence theorems in SAL specifications. Based on our experiments, Z2SAL is able to translate these kind of theorems and SAL model checker is also able to model check SAL specifications with theorems that are written directly in the Z specifications.
Springer monographs in mathematics, 2008
Introduction and Notation Mapping theory started in the 18th century. Beltrami, Caratheodory, Christoffel, Gauss, Hilbert, Liouville, Poincaré, Riemann, Schwarz, and so on all left their marks in this theory. Conformal mappings and their applications to potential theory, mathematical physics, Riemann surfaces, and technology played a key role in this development. During the late 1920s and early 1930s, Grötzsch, Lavrentiev, and Morrey introduced a more general and less rigid class of mappings that were later named quasiconformal. Very soon quasiconformal mappings were applied to classical problems like the covering of Riemann surfaces (Ahlfors), the moduli problem of Riemann surfaces (Teichmüller), and the classification problem for simply connected Riemann surfaces (Volkovyski). Quasiconformal mappings were later defined in higher dimensions (Lavrentiev, Gehring, Väisälä) and were further extended to quasiregular mappings (Reshetnyak, Martio, Rickman, and Väisälä). The quasiregular mappings need not be injective and in many aspects are similar to analytic functions.
Information and Software Technology, 1995
1997
Abstract Z is one of the most widely used formal speci cation languages. However, traditionally it has lacked adequate tool support for use in an industrial setting. It has grown up from a mathematically based tradition of the use of formal methods, rather than being based on any particular tool. This paper presents a tool and, in particular, its associated machine-readable syntax description of Z that could be useful as a common front-end to a number of tools to aid the production of a Z speci cation.
IJID (International Journal on Informatics for Development)
This paper describes our research on implementing a scanner and parsers for Z specifications. Rather to code them from scratch, we use tools that have specialities on creating such tasks. These tools generate several Java files which can be integrated with a main program in Java. Our research could produce a scanner and parser for Z specifications. These tools could benefit Z specifications to be studied further.
2004
The generalised disjointness operator enables one to calculate binary masks in a set-theoretic style. For example, let the sets A, B, and C be the sets we are working with. The operator calculates possible individual regions related to the combination of these sets. That is, assuming 1 as contained and 0 as not contained, the mask 101 represents all the elements of A and C but not B. The function returns this value as
Proceedings of the New Forms of Xanalogical Storage …, 2009
The focus of this paper is on particular and innovative structures for storing, linking and manipulating information: the zz-structures. In the last years, we worked at the formalization of these structures, retaining that the description of the formal aspects can provide a better understanding of them, and can also stimulate new ideas, projects and research. This work presents our contribution for a deeper discussion on zz-structures.
Springer eBooks, 2020
decision-making problems in economics, engineering, risk assessment, forecasting, manufacturing, design and process analysis are naturally determined by vagueness as well as partial reliability. Generating a formalism for dealing with Z-numbers is essential to handle these kinds of information. In this paper, the applications of Z-numbers in engineering are studied. The most current researches in the area of Z-numbers are covered in this work. Since some engineers have successfully applied Z-numbers, detailed discussions are supplied to stimulate future investigations.
2012
Práce zkoumá možnosti formalizace klasických pojmů matematické analýzy bez použití proměnných. Za tímto účelem vytváří nový matematický "jazyk", jenž je schopen popsat všechny klasické výpočty v matematické analýze (přesněji výpočty limit, konečných diferencí, jednorozměrných derivací a určitých a neurčitých integrálů) bez použití proměnných. Výpočty zapsané v tomto "jazyce" obsahují pouze symboly funkcí (a jsou tedy zcela rigorózní a nedávají prostor k vágnímu výkladu použitých symbolů). Obecně jsou také výrazně kratší a matematicky průhlednější než jejich tradiční verze (např. při výpočtech integrálů není potřeba zavádět žádné nové symboly a určitý integrál je formalizován tak, že všechna pravidla pro výpočet neurčitých integrálů (včetně "substitučních" pravidel) jsou přímo přenosná na případ určitých integrálů. Práce také formalizuje Landauovu o-notaci způsobem, díky němuž je možné provádět s ní výpočty limit zcela rigorózním způsobem.
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.
Lecture Notes in Computer Science, 2016
The Z notation for the formal specification of computer-based systems has been in existence since the early 1980s. Since then, an international Z community has emerged, academic and industrial courses have been developed, an ISO standard has been adopted, and Z has been used on a number of significant software development projects, especially where safety and security have been important. This chapter traces the history of the Z notation and presents issues in teaching Z, with examples. A specific example of an industrial course is presented. Although subsequent notations have been developed, with better tool support, Z is still an excellent choice for general purpose specification and is especially useful in directing software testing to ensure good coverage.
Z Users Conference, 1991
During 1990 and 1991 we carried out a survey of Z users in the UK; in this paper we present the results. Z is being used by a wide variety of companies for many different applications. Many institutions use Z because they choose to, rather than because it is mandated by a defence or security related client. Half of the
ZUM'98: The Z Formal Specification Notation, 1998
In a number of recent presentations – most notably at FME’961 – one of the foremost scientists in the field of formal methods, C.A.R. Hoare, has highlighted the fact that formal methods are not the only technique for producing reliable software. This seems to have caused some controversy, not least amongst formal methods practitioners. How can one of the founding fathers of formal methods seemingly denounce the field of research after over a quarter of a century of support? This is a question that has been posed recently by some formal methods sceptics. However, Prof. Hoare has not abandoned formal methods. He is reiterating, albeit more radically, his 1987 view that more than one tool and notation will be required in the practical, industrial development of large-scale complex computer systems; and not all of these tools and notations will be, or even need be, formal in nature. Formal methods are not a solution, but rather one of a selection of techniques that have proven to be useful in the development of reliable complex systems, and to result in hardware and software systems that can be produced on-time and within a budget, while satisfying the stated requirements. After almost three decades, the time has come to view formal methods in the context of overall industrial-scale system development, and their relationship to other techniques and methods. We should no longer consider the issue of whether we are “pro-formal” or “anti-formal”, but rather the degree of formality (if any) that we need to support in system development. This is a goal of ZUM’98, the 11th International Conference of Z Users, held for the first time within continental Europe in the city of Berlin, Germany.
This monograph, which presents a grammar and an a.bstract syntax {or the Z specification language, is produced as part of a joint project between IBM United Kingdom Labo. ratories Limited a.t Hursley, England and the Programming Research Group of Oxford University Computing Laboratory, into the application of formal software specification techniques to industrial problems. The work WM sopported by a research contract be tween IBM and Oxford University and is published by pennission of the Company. [Abrial 811 provided the starting point in the development of the Z notation. The syntax for definitions, predicates and terms presented here was developed from Jea.n•Ra.ymond Abrial's paper. The notation has been further developed and described in [Sufrin 86]. The type roles and the semantics oCZ have been described in [Spivey 85]. The commen tary in this paper on the mea.ning of the language constructs is an informal description of what is formally described in [Spivey 85]. The schema concept is an extension to conventional set theory and preliminary descrip tions can be found in [Sumn 81], [Sfilirensen 82] and [Morgan 84]. A tutorial introduction to the present sta.te of the schema notation can be found in [Woodcock 88] Version 2.0 It is the authors' expectation (e.nd hope!) that this will be the 'final' version o{ this document, at least in its present form. It is presented 8.8 part of the PRG's (and IBM's) work towards the standardisation of Z. As such, it has two major aims: to capture the present state of the language, particularly those parts o{ the la.nguage whose syntax has become stable, and to snggest possible solutions to several problems which ha.ve to be resolved as part of the standardisation process. In this second category come such topics as the syntax for theoreIIUI (which is dependent, to some extent, on agreement on a logic for Z), mnemonic names {or the many non-ASCII symbOls used in Z, and the whole question of how to nse one Z document within another (ie imports, document qualifiers, versions etc). This last item can only be resolved when case studies ~ been completed, using {or instance a library o{ specifications. To repea.t: in these cases, what is presented in this document is merely a suggested solution-the definitive a.ns~r can only appear in due time!! 14 2.5 Predicates 15 2.6 Terms .. 18 2.7 Schema terms 24 Terminal symbols 29 3.1 Document punctuation. 29 3.2 Identifier lists and identifier symbols 29 3.3 Definitions and declarations 30 3.4 Theorem symbols. 30 3.5 Predicate symbols 31 3.6 Term symbols. . 31 3.7 Schema notation .
Citeseer, 1997
This is the reference manual for the SZ speci cation notation. SZ is a combination of statecharts and Z for the speci cation of safety-critical control systems. It combines statecharts' expressive power for the description of reactive behavior with Z's ability to describe data and data transformation. Additionally, Z is extended for the speci cation of abstract temporal properties and means to structure the speci cation in components are introduced. This manual covers a complete presentation of the language, including its visible syntax, a rst glance at a SZ library, the L A T E X input syntax, and support for Statemate speci cations.
