Z User Workshop, York 1991: Proceedings of the Sixth Annual Z User Meeting, York 16–17 December 1991 (1992) (Workshops in Computing)

Synopsis

In ordinary mathematics, an equation can be written down which is syntactically correct, but for which no solution exists. For example, consider the equation x = x + 1 defined over the real numbers; there is no value of x which satisfies it. Similarly it is possible to specify objects using the formal specification language Z [3,4], which can not possibly exist. Such specifications are called inconsistent and can arise in a number of ways. Example 1 The following Z specification of a functionf, from integers to integers "f x : ~ 1 x ~ O· fx = x + 1 (i) "f x : ~ 1 x ~ O· fx = x + 2 (ii) is inconsistent, because axiom (i) gives f 0 = 1, while axiom (ii) gives f 0 = 2. This contradicts the fact that f was declared as a function, that is, f must have a unique result when applied to an argument. Hence no suchfexists. Furthermore, iff 0 = 1 andfO = 2 then 1 = 2 can be deduced! From 1 = 2 anything can be deduced, thus showing the danger of an inconsistent specification. Note that all examples and proofs start with the word Example or Proof and end with the symbol.1.

Copyright:

1992

Book Details

Book Quality:

Publisher Quality

ISBN-13:

9781447132035

Related ISBNs:

9783540197805

Publisher:

Springer London

Date of Addition:

02/22/21

Copyrighted By:

N/A

Adult content:

No

Language:

English

Has Image Descriptions:

No

Categories:

Nonfiction, Computers and Internet, Mathematics and Statistics, Philosophy

Submitted By:

Bookshare Staff

Usage Restrictions:

This is a copyrighted book.

Edited by:

J. E. Nicholls