Scoping Constructs in Logic Programming : Implementation Problems and their

This paper examines the implementation issues arising from introducing universally quantiied goals and some forms of implication goals in a logic programming language. While these constructs are useful in providing a logical approach to lexical scoping, they raise new implementation problems. Since universal and existential quantiiers may appear in mixed order in goals, the uniication operation used for solving existential goals must respect this ordering. We present a solution to this problem based on a tagging of constants and variables and the use of these tags in constraining uniication. This solution is amenable to an eecient implementation and can be easily assimilated into the machinery of the Warren Abstract Machine (WAM). Implication goals require new program clauses to be introduced dynamically for the purpose of solving speciic subgoals. A naive scheme based on asserting and retracting program clauses does not suuce to solve this problem, for two reasons: First, backtracking may require reinstating programs previously in existence and bookkeeping devices are needed for achieving this eeciently. Second, implication goals surrounded by existential quantiiers may give rise to program clauses parameterized by bindings for variables. Compilation and the sharing of compiled code require a closure based representation for program clauses to be developed. We describe methods for achieving these eeects and integrate these ideas into the WAM. We also outline extensions to the resulting machine for incorporating higher-order aspects into our language. The ideas developed here provide part of the basis for an ongoing implementation of the higher-order logic programming language Prolog. This paper has been submitted for publication. Comments on its contents are welcome and may be sent to one of the authors at the indicated addresses.