The Second Futamura Projection for Type-Directed Partial Evaluation

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 itself; 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.