Use of Higher-Order Unification for Implementing Program Transformers

Source-to-source program transformers belong to the class of meta-programs that manipulate programs as objects. It has previously been argued that a higher-order extension of Prolog, such as λProlog, makes a suitable implementation language for such meta-programs. In this paper, we consider this claim in more detail. In λProlog, object-level programs and program schemata can be represented using simply typed λ-terms and higher-order (functional) variables. Unification of these λ-terms, called higher-order unification, can elegantly describe several important meta-level operations on programs. We detail some properties of higher-order unification that make it suitable for analyzing program structures. We then present (in λProlog) the specification of several simple program transformers together with a more involved partial evaluator. With the depth-first control strategy of λProlog for both clause selection and unifier selection all the above mentioned specifications can be and have been executed and tested.