For a Better Support of Static Data Flow

This paper identiies and solves a class of problems that arise in binding time analysis and more generally in partial evaluation of programs: the approximation and loss of static information due to dynamic expressions with static subexpressions. Solving this class of problems yields substantial binding time improvements and thus dramatically better results not only in the case of partial evaluation but also for static analyses of programs | this last point actually is related to a theoretical result obtained by Nielson. Our work can also be interpreted as providing a solution to the problem of conditionally static data, the dual of partially static data. We point out which changes in the control ow of a source program may improve its static data ow. Unfortunately they require one to iterate earlier phases of partial evaluation. We show how these changes are subsumed by transforming the source program into continuation-passing style (CPS). The transformed programs get specialized more tightly by a higher-order partial evaluator, without iteration. As a consequence, static values get frozen according to the specialization strategy and not due to the structure of the source programs. Our approach makes it possible to get better results without changing our partial evaluator, by using its higher-order capabilities more thoroughly. By construction, transforming source programs into CPS makes it yield better results, even in the particular case of self-application. New problems can even be tackled such as static deforestation by partial evaluation, specialization of contexts, and conditionally static data. This development concerns applicative order, side-eeect free functional languages because we consider existing self-applicable partial evaluators. We conjecture a similar improvement for lazy functional languages, based on the normal order CPS transformation.