Speci cation

The basic components of any speciication language include: constructs for specifying the properties of individual program components such as types and functions; structuring mechanisms for building large speciications in a modular fashion; a description of the semantics of the language; mechanisms for performing proofs of properties of speciications; a notion of reenement of speciications; and a way of relating speciications to programs written in a programming language. These topics are discussed in other chapters of this book, and in each case there are various alternatives to choose from. To take a simple example, the properties of functions may be speciied using equations or using rst-order (or even higher-order) formulas as axioms. A speciication language is a commitment to a compatible combination of these choices. It is a commitment because the syntax of a speciication language determines once and for all what can be expressed and what cannot be expressed. For example, the syntax of formulas determines how the properties of functions are speciied; similarly, a construct for hiding types and/or functions may or may not be included. The choices must be compatible in various respects. On one hand, certain combinations of choices simply make no sense; for instance, initial semantics requires the use of axioms no more complex than conditional equations. More subtly, the inclusion of certain structuring mechanisms complicates the process of proving properties of speciications and so these might be omitted or restricted in a language in which proofs are of primary importance. There is no single best combination of choices because this depends on many factors including the intended context of use and the range of applications to be addressed. Consequently, this chapter will consider the rationale for choosing between the various alternatives available. The technical details of these alternatives are given in other chapters for the most part and will not be repeated here. The next section is devoted to a brief overview of some existing speciica-tion languages. Section 8.3, which forms the bulk of the chapter, discusses the