Abstract Syntax and Logic Programming

When writing programs to manipulate structures such as algebraic expressions, logical formulas, proofs, and programs, it is highly desirable to take the linear, human-oriented, concrete syntax of these structures and parse them into a more computation-oriented syntax. For a wide variety of manipulations, concrete syntax contains too much useless information (e.g., keywords and white space) while important information is not explicitly represented (e.g., function-argument relations and the scope of operators). In parse trees, much of the semantically useless information is removed while other relationships, such as between function and argument, are made more explicit. Unfortunately, parse trees do not adequately address important notions of object-level syntax, such as bound and free object-variables, scopes, alphabetic changes of bound variables, and object-level substitution. I will argue here that the abstract syntax of such objects should be organized around α-equivalence classes of λ-terms instead of parse trees. Incorporating this notion of abstract syntax into programming languages is an interesting challenge. This paper briefly describes a logic programming language that directly supports this notion of syntax. An example specifications in this programming language is presented to illustrate its approach to handling object-level syntax. A model theoretic semantics for this logic programming language is also presented.