[show abstract][hide abstract] ABSTRACT: Recent discussions in the Z community have considered the issue of the consistency of the free type construct in Z. A key question is whether free type definitions which met the criterion for consistency given in the Z Reference Manual, are conservative over Zermelo set theory (i.e. ZF without the axiom of replacement). The main purpose of this paper is to give an introduction to the issues and to show that the answer to this question is "yes" (given the axiom of choice). A by-product of the arguments we give here is that the criterion given in the Z reference manual may be replaced by an intuitively simpler one without loss of expressive power from the theoretical or practical point of view.
Rob Arthan added a full-text to this article and 9 others.