Proving the correctness of recursion-based automatic program transformations

Abstract

This paper shows how the Improvement Theorem — a semantic condition for establishing the total correctness of program transformation on higher-order functional programs — has practical value in proving the correctness of automatic techniques. To this end we develop and study a family of automatic program transformations. The root of this family is a well-known and widely studied transformation called deforestation; descendants include generalisations to richer input languages (e.g. higher-order functions), and more powerful transformations, including a source-level representation of some of the techniques known from Turchin's super compiler.