Measuring the Effectiveness of Partial Evaluation

We introduce a framework for assessing the effectiveness of partial evaluators for functional logic programs. Our framework is based on properties of the rewrite system that models a functional logic program and, consequently, our assessment is independent of any specific language implementation or computing environment. We define several criteria for measuring the cost of a computation: number of steps, number of function applications, and effort for pattern matching. Most importantly, we express the cost of each criterion by means of recurrence equations over algebraic data types, which can be automatically inferred from the partial evaluation process itself. In some cases, the equations can be solved by transforming their arguments from arbitrary data types to natural numbers. In other cases, it is possible to estimate the improvement of a partial evaluation by analyzing the recurrence equations.