:Z notation

{{Short description|Formal specification language used for describing and modelling computing systems}}

File:Agendacumple en Z.svg (in Spanish) using the Z notation, with named schema boxes, including declarations and predicates]]

The Z notation {{IPAc-en|ˈ|z|ɛ|d}} is a formal specification language used for describing and modelling computing systems.{{cite book| last=Bowen | first=Jonathan P. | chapter=The Z Notation: Whence the Cause and Whither the Course? | authorlink=Jonathan Bowen | title=Engineering Trustworthy Software Systems | pages=103–151 | publisher=Springer | series=Lecture Notes in Computer Science | volume=9506 | date=2016 | doi=10.1007/978-3-319-29628-9_3| isbn=978-3-319-29627-2 | chapter-url=http://researchopen.lsbu.ac.uk/395/1/setss2014.pdf }} It is targeted at the clear specification of computer programs and computer-based systems in general.

History

In 1974, Jean-Raymond Abrial published "Data Semantics".{{Citation | author-link = Jean-Raymond Abrial | first = Jean-Raymond | last = Abrial | contribution = Data Semantics | editor1-last = Klimbie | editor1-first = J. W. | editor2-last = Koffeman | editor2-first = K. L. | title = Proceedings of the IFIP Working Conference on Data Base Management | publisher = North-Holland | pages = 1–59 | year=1974 }} He used a notation that would later be taught in the University of Grenoble until the end of the 1980s. While at EDF (Électricité de France), working with Bertrand Meyer, Abrial also worked on developing Z.{{cite book| url=https://link.springer.com/content/pdf/bbm%3A978-3-642-15187-3%2F1.pdf | title=Greetings to Bertrand on the Occasion of his Sixtieth Birthday | first=Tony | last=Hoare | authorlink=Tony Hoare | date=2010 | work=The Future of Software Engineering | page=183 | isbn=978-3-642-15187-3 | publisher=Springer }} The Z notation is used in the 1980 book Méthodes de programmation.{{Citation | author1-link = Bertrand Meyer | first1 = Bertrand | last1 = Meyer | first2 = Claude | last2 = Baudoin | title = Méthodes de programmation | publisher = Eyrolles | year = 1980 | language = fr}}

Z was originally proposed by Abrial in 1977 with the help of Steve Schuman and Bertrand Meyer.{{Citation | first1 = Jean-Raymond | last1 = Abrial | first2 = Stephen A | last2 = Schuman | first3 = Bertrand | last3 = Meyer | contribution = A Specification Language | title = On the Construction of Programs | publisher = Cambridge University Press | editor1-first = A. M. | editor1-last = Macnaghten | editor2-first = R. M. | editor2-last = McKeag | year = 1980 | isbn = 0-521-23090-X}} (describes early version of the language). It was developed further at the Programming Research Group at Oxford University, where Abrial worked in the early 1980s, having arrived at Oxford in September 1979.

Abrial has said that Z is so named "Because it is the ultimate language!"{{cite web|

url=http://liacs.leidenuniv.nl/~hoogeboomhj/praatjes/formalmethods/formalmethods.pdf |

title=Formal Methods in Software Engineering | first=Hendrik Jan | last=Hoogeboom | publisher=University of Leiden | location=The Netherland | access-date=14 April 2017 }} although the name "Zermelo" is also associated with the Z notation through its use of Zermelo–Fraenkel set theory.

In 1992, the Z User Group (ZUG) was established to oversee activities concerning the Z notation, especially meetings and conferences.{{cite news| first=Jonathan | last=Bowen | authorlink=Jonathan Bowen | title=The Z User Group: Thirty Years After | work=FACS FACTS | publisher=BCS-FACS | issue=2022–2 | pages=50–56 | date=July 2022 | url=https://www.bcs.org/media/9401/facs-jul22.pdf | accessdate=3 August 2022 }}

Usage and notation

Z is based on the standard mathematical notation used in axiomatic set theory, lambda calculus, and first-order predicate logic.{{cite book| last=Spivey | first=J. Michael | authorlink=Michael Spivey | title=The Z Notation: A Reference Manual | edition=2nd | location=Hemel Hempstead | publisher=Prentice Hall | series=International Series in Computer Science | date=1992 | isbn=978-0139785290 }} All expressions in Z notation are typed, thereby avoiding some of the paradoxes of naive set theory. Z contains a standardized catalogue (called the mathematical toolkit) of commonly used mathematical functions and predicates, defined using Z itself. It is augmented with Z schema boxes, which can be combined using their own operators, based on standard logical operators, and also by including schemas within other schemas. This allows Z specifications to be built up into large specifications in a convenient manner.

Because Z notation (just like the APL language, long before it) uses many non-ASCII symbols, the specification includes suggestions for rendering the Z notation symbols in ASCII and in LaTeX. There are also Unicode encodings for all standard Z symbols.{{cite web| url=https://unicode-search.net/unicode-namesearch.pl?term=Z%20NOTATION | title=Unicode Explained: Internationalize Documents, Programs, and Web Sites | first=Jukka K. | last=Korpela | website=unicode-search.net | access-date=24 March 2020 }}

Standards

ISO completed a Z standardization effort in 2002. This standard{{cite book | title = Information Technology — Z Formal Specification Notation — Syntax, Type System and Semantics | chapter-url = http://www.iso.ch/iso/en/CatalogueDetailPage.CatalogueDetail?CSNUMBER=21573 | chapter = ISO/IEC 13568:2002 | date = 2002-07-01 | publisher = ISO | url = http://standards.iso.org/ittf/PubliclyAvailableStandards/c021573_ISO_IEC_13568_2002(E).zip | format = Zipped PDF}} 196 pp. and a technical corrigendum{{cite book | title = Information Technology — Z Formal Specification Notation — Syntax, Type System and Semantics — Technical corrigendum 1 | url = http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=46112 | chapter = ISO/IEC 13568:2002/Cor.1:2007 | publisher = ISO | date = 2007-07-15 | format = PDF}} 12 pp. are available from ISO free:

the standard is publicly available from the ISO ITTF site free of charge and, separately, available for purchase from the ISO site;
the technical corrigendum is available from the ISO site free of charge.

Award

In 1992, Oxford University Computing Laboratory and IBM were jointly awarded The Queen's Award for Technological Achievement "for the development of ... the Z notation, and its application in the IBM Customer Information Control System (CICS) product."{{cite web |url=http://web2.comlab.ox.ac.uk/oucl/about/qata92.html |title=The Queen's Award for Technological Achievement 1992 |archive-url=https://web.archive.org/web/20081202044350/http://web2.comlab.ox.ac.uk/oucl/about/qata92.html |archive-date=2 December 2008 |website= Oxford University Computing Laboratory |access-date=17 October 2021}}

:Z notation

History

Usage and notation

Standards

Award

See also

References

Further reading