Parameterized partial evaluation

Besides specializing programs with respect to concrete values, it is often necessary to specialize programs with respect to abstract values, i.e., static properties such as signs, ranges, and types. Specializing programs with respect to static properties is a natural extension of partial evaluation and significantly contributes towards adapting partial evaluation to larger varieties of applications. This idea was first investigated by Haraldsson [14] and carried out in practice with a system called Redfun in the late seventies. This system partially evaluates Interlisp programs. It manipulates symbolic values such as data types to describe the possible values of a variable and a processed expression. Although the work on Redfun certainly started in the right direction, it has some limitations: (1) the static properties cannot be defined by the user; they are fixed; (2) the approach is not formally defined: no safety condition for the definition of symbolic values, no finiteness criteria for fixpoint iteration, etc.; and (3) because Redfun is an on-line partial evaluator—the treatment of the