Huet and Lang (1978) presented a framework of automated program transformation based on lambda calculus in which programs are transformed according to a given program transformation template. They introduced a second-order matching algorithm of simply-typed lambda calculus to verify whether the input program matches the template. They also showed how to validate the correctness of the program transformation using the denotational semantics. We propose in this paper a framework of program transformation by templates based on term rewriting. In our new framework, programs are given by term rewriting systems. To automate our program transformation, we introduce a term pattern matching problem and present a sound and complete algorithm that solves this problem. We also discuss how to validate the correctness of program transformation in our framework. We introduce a notion of developed templates and a simple method to construct such templates without explicit use of induction. We then show that in any program transformation by developed templates the correctness of the transformation can be verified automatically. In our framework the correctness of the program transformation is discussed based on the operational semantics. This is a sharp contrast to Huet and Lang’s framework.

Program transformation by templates (Huet and Lang, 1978) is a technique to improve the efficiency of programs. In this technique, programs are transformed according to a given program transformation template. To enhance the variety of program transformation, it is important to introduce new transformation templates. Up to our knowledge, however, few works discuss about the construction of transformation templates. Chiba et al. (2006) proposed a framework of program transformation by template based on term rewriting and automated verification of its correctness. Based on this framework, we propose a method that automatically constructs transformation templates from similar program transformations. The key idea of our method is a second-order generalization, which is an extension of Plotkin’s firstorder generalization (1969). We give a second-order generalization algorithm and prove the soundness of the algorithm. We then report about an implementation of the generalization procedure and an experiment on the construction of transformation templates. 1.