Subset Logic Programs and Their Implementation

This paper discusses the design and implementation of a set-oriented logic programming paradigm, called subset-logic programming. 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 previous research, we developed 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 enumera-tion of sets. Although the subset-logic paradigm diiers substantially from that of Prolog, we show that few additional changes are needed to the Warren Abstract Machine (WAM) 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 whose 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 has been completed, 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. We also compare this system with other closely related systems, especially XSB and CORAL.