The Second Futamura Projection for Type-Directed Partial Evaluation

Abstract

A generating extension of a program specializes the program with respect to part of the input. Applying a partial evaluator to the program trivially yields a generating extension, but specializing the partial evaluator with respect to the program often yields a more efficient one. This specialization can be carried out by the partial evaluator itselfs in this case, the process is known as the second Futamura projection. We derive an ML implementation of the second Futamura projection for Type-Directed Partial Evaluation (TDPE). Due to the differences between ‘traditional’, syntax-directed partial evaluation and TDPE, this derivation involves several conceptual and technical steps. These include a suitable formulation of the second Futamura projection and techniques for making TDPE amenable to self-application. In the context of the second Futamura projection, we also compare and relate TDPE with conventional off-line partial evaluation. We demonstrate our technique with several examples, including compiler generation for Tiny, a prototypical imperative language.