The Second Futamura Projection for Type-Directed Partial Evaluation

A generating extension of a program specializes it with respect to some specified part of the input. A generating extension of a program can be formed trivially by applying a partial evaluator to the program; the second Futamura projection describes the automatic generation of non-trivial generating extensions by applying a partial evaluator to itself with respect to the programs. 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 offline partial evaluation. We demonstrate our technique with several examples, including compiler generation for Tiny, a prototypical imperative language.