On Free Type Definitions in Z

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, [5], are conservative over Zermelo set theory (Le. ZF without the axiom of replacement). The main purpose of this paper is to give an intro­ duction 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.