A self-applicable partial evaluator for the lambda calculus

Abstract

We describe theoretical and a few practical aspects of an implemented self-applicable partial evaluator for the untyped lambda calculus with constants, conditionals, and a fixed point operator. The purpose of this paper is first to announce the existence of (and to describe) a partial evaluator that is both higher-order and self-applicable; second to describe a surprisingly simple solution to the central problem of binding time analysis, and third to prove that the partial evaluator yields correct answers. While λ-mix (the name of our system) seems to have been the first higher-order self-applicable partial evaluator to run on a computer, it was developed mainly for research purposes. Two recently developed systems are much more powerful for practical use, but also much more complex: Similix[3,5] and Schism[7]. Our partial evaluator is surprisingly simple, completely automatic, and has been implemented in a side effect-free subset of Scheme. It has been used to compile, generate compilers and generate a compiler generator.