By Dan Craigen, Susan Gerhart, Ted Ralston (auth.), J. P. Bowen MA, J. E. Nicholls MA (eds.)

The Z notation has been built on the Programming examine crew on the Oxford college Computing Laboratory and somewhere else for over a decade. it's now utilized by as a part of the software program (and undefined) improvement procedure in either Europe and america. it really is presently present process BSI standardisation within the united kingdom, and has been proposed for ISO standardisation the world over. in recent times researchers have started to concentration more and more at the improvement of innovations and instruments to inspire the broader program of Z and different formal tools and notations. This quantity includes papers from the 7th Annual Z consumer assembly, held in London in December 1992. unlike past years the assembly centred in particular on commercial functions of Z, and a excessive percentage of the contributors got here from an commercial history. The subject is easily represented by means of the 4 invited papers. 3 of those speak about ways that formal tools are being brought, and the fourth offers a global survey of business purposes. It additionally presents a reminder of the advancements that are had to make those equipment an authorised a part of software program improvement. moreover the quantity comprises a number of submitted papers at the business use of Z, of which debate the most important region of safety-critical purposes. There also are a couple of papers concerning the recently-completed ZIP venture. The papers hide all of the major components of the venture together with tools, instruments, and the improvement of a Z common, the 1st publicly-available model of which used to be made on hand on the assembly. ultimately the quantity includes a decide on Z bibliography, and part on the best way to entry info on Z via comp.specification.z, the overseas, computer-based USENET newsgroup. Z person Workshop, London 1992 offers a big evaluation of present learn into commercial purposes of Z, and should supply important interpreting for researchers, postgraduate scholars and in addition power business clients of Z.

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Extra resources for Z User Workshop, London 1992: Proceedings of the Seventh Annual Z User Meeting, London 14–15 December 1992

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T/ i, j, k: interval • i+k>j+k~i>j If we restrict to real numbers, we get stronger laws: 't/ i, j: interval; x: R • x-x=o i+x>j+x¢::)i>j and we have the well-known properties: 't/x,y:R. 't/x,y:O· 't/ x, y: Z • -xeRJ\ -xeOJ\ -xeZJ\ x+yeRJ\ x+yeOJ\ x+yeZJ\ x-yeR x-yeO x-yeZ 28 Induction We can state a principle of induction for integer real numbers, namely: V S: III Nl I 1 E S A (V n: S • n + 1 E S) • S = Nl Multiplication and Division Multiplication and division are defined in a way similar to that used for subtraction I I _* __: interval x interval ~ interval I j _: interval x { i: interval I -, 0 within i _*_ E / E I V i, j: I i I V i, j: I i I J ~ interval intervalPairMonotonic intervalPairMonotonic interval I qbetween i "I:- 0 "I:- qbetween j • * j = outside { q: qbetween i; r: qbetween j • q qmult r J interval I qbetween i "I:- 0 "I:- qbetween j A -, 0 within j • / j = outside { q: qbetween i; r: qbetween j • q qdivide r J Laws V i, j, k: interval • i * j = j * i (i * j) * k = i * G* k) -, 0 within j * k => (i / j) / k = i / G* k) V i, j: interval; k: boundedInterval • -, 0 within k => (i * k = j * k <=> i = j) -, 0 within i => 0 within i / i k>OAi*k>j*k=>i>j (i + j) * k within i * k + j * k i * j > 0 => (i + j) * k = i * k + j * k If we restrict to real numbers, we get stronger laws: V i, j: interval; x: I • x"l:-O=>x/x=l x > 0 => (i * x > j * x <=> i > j) (i + j) * x = i * x + j * x 29 and we have the well-known properties: Vx,y:l2..

1 Free type A free type may be used as part of a library. For example, the free type may be of the form, T ::= x«X)) I y«Y)), where the sets X and Y mayor may not be generic set parameters to the library. In some cases, however, one would like the free type T to be treated like a parameter and to be equated with a subset of some existing free type which has constructors of the same type as x and y, but may also have other constructors. For example, consider the set T2 T2 ::= x2«X)) I y2«Y)) I z2«Z)), which is similar to T.

A not uncommon mistake in Z specifications is to write generic definitions of variables that are not uniquely determined by the generic sets. We would like to provide a facility for doing this correctly. Secondly, if one separates the instantiation of a library from the use of that instantiation's definitions, then there is only one instantiation and the reason for the uniqueness condition for Z generics disappears. For multiple instantiations of the same library one needs to be able to distinguish variables in one instantiation from variables in another.

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