A Logic Programming Approach to Manipulating Formulas and Programs

First-order Horn clause logic can be extended to a higher-order setting in which function and predicate symbols can be variables and terms are replaced with simply typed λ-terms. For such a logic programming language to be complete in principle, it must incorporate higher-order unification. Although higher-order unification is more complex than usual first-order unification, its availability makes writing certain kinds of programs far more straightforward. In this paper, we present such programs written in a higherorder version of Prolog called λProlog. These programs manipulate structures, such as formulas and programs, which contain abstractions or bound variables. We show how a simple natural deduction theorem prover can be implemented in this language. Similarly we demonstrate how several simple program transformers for a functional programming language can be written in λProlog. These λProlog programs exploit the availability of λ-conversion and higher-order unification to elegantly deal with several of the awkward aspects inherent in these tasks. We argue that writing similar procedures in other languages would yield programs which are much less perspicuous. Submitted to the 1987 IEEE Symposium on Logic Programming. Comments are welcome. Address correspondence to Miller at address above or at “[email protected]”. This work has been supported by NSF AI Center grants NSF-MCS-83-05221, US Army Research office grant ARO-DAA29-84-9-0027, and DARPA N000-14-85-K-0018. The second author has also been supported by a Burroughs contract.