Implementation of Subset Logic

Subset-logic programs are built up of three kinds of program clauses: subset, equational, and relational clauses. Using these clauses, we can program solutions to a broad range of problems of interest in logic programming and deductive databases. In an earlier paper Jay92], we discussed the implementation of subset and equational program clauses. This paper substantially extends that work, and focuses on the more expressive paradigm of subset and relational clauses. This paradigm supports setof operations, transitive closures, monotonic aggregation as well as incremental and lazy eager enumeration of sets. Although the subset-logic paradigm diiers substantially from that of Prolog, we show that few additional changes are needed to the WAM War83] to implement the paradigm and that these changes blend well with the overall machinery of the WAM. A central feature in the implementation of subset-logic programs is that of a \monotonic memo-table," i.e., a memo-table who entries can monotonically grow or shrink in an appropriate partial order. We present in stages the paradigm of subset-logic progams, showing the eeect of each feature on the implementation. The implementation was completed in 1994, and we present performance gures to show the eeciency and costs of memoization. Our conclusion is that the monotonic memo-tables are a practical tool for implementing a set-oriented logic programming language.