On the degeneration of program generators by program composition

One of the main discoveries in the seventies was that the concept of a generating extension covers a very wide class of apparently different program generators. Program specialization, or partial evaluation, is powerful because it provides uniform techniques for the automatic implementation of generating extensions from ordinary programs. The Futamura projections stand as the cornerstone of the development of program specialization. This paper takes the idea of the Futamura projections further. Threedegeneration projections are formulated which tell us how to achieve the reverse goal by program composition, namely turning a generating extension into an ordinary program. The fact that program composition can invert the effect of program specialization shows that these projections are dual in a sense. The degeneration projections complete a missing link between programs and generating extensions and allow for novel applications of program transformation.