Z User Workshop, York 1991: Proceedings of the Sixth Annual Z User Meeting, York 16–17 December 1991

J. E. Nicholls (Curatore)

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, 1992

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.

• Curatore: J. E. Nicholls
• Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
• Collana: Workshops in Computing
• Anno: 1992
• Rilegatura: Paperback / softback
• Pagine: 408 p.
• Dimensioni: 242 x 170 mm
• EAN: 9783540197805

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