Lawful Functions and Program Verification in Miranda

Laws in the Miranda programming language provide a means of implementing non-free algebraic types, by means of term rewriting. In this paper we investigate program veri cation in such a context. Speci cally, we look at how to deduce properties of functions over these `lawful' types. After examining the general problem, we look at a particular class of functions, the faithful functions. For such functions we are able, in a direct manner, to transfer properties of functions from free types to non-free types. We introduce su cient model theory to explain these transfer results, and then nd characterisations of various classes of faithful functions. Then we investigate an application of this technique to general, unfaithful, situations. In conclusion we survey Wadler's work on views and assess the utility of laws and views.