Interpretation of Reference Counting The semantics presented thus far is exact, and thus evaluating a particular reference count may not terminate, any more than a program in the standard semantics would. For use by a compiler we must choose a suitable abstraction (i.e., approximation) that will guarantee termination yet still provide useful information about the true reference counts. For us a suitable abstraction is one in which the inferred reference count is at least as great as the true one; i.e., we wish to err on the side of thinking there are more pointers to an object than there actually are. In this section we methodically develop such an abstraction in which: (1) the base domains are abstracted to powersets of finite approximations, (2) the primitive functions are abstracted similarly, (3) an abstract interpretation is thus induced on R p and R, and finally (4) a collecting interpretation of expressions is developed. 4.1 Preliminaries To set up things to come, we first gi...

Program transformation has been advocated as a potentially appropriate methodology for program development. The ability to transform large programs is crucial to the practicality of such an approach. This paper describes research directed toward applying one particular transformation method to problems of increasing scale. The method adopted is that developed by Burstall and Darlington, and familiarity with their work is assumed. The problems which arise when attempting transformation of larger scale programs are discussed, and an approach to overcoming them is presented. Parts of the approach have been embodied in a machine-based system which assists a user in transforming his programs. The approach, and the use of this system, are illustrated by presenting portions of the transformation of a compiler for a "toy" language.