Abstract Interpretation Based on Alexander Templates

Abstract Recently, several bottom-up query evaluation methods for logic databases, e.g., magic set, Alexander method, Magic Templates, etc., have been developed. Given a logic program and a top-level query, Alexander Templates (AT) by Seki first transforms the program and query and then evaluates the transformed program and query in the bottom-up manner. This query-evaluation method has been proved to be as powerful as the top-down evaluation methods with memo-ization, e.g., OLDT resolution, SLD-AL resolution, Extension Tables, etc. On the other hand, several unified frameworks for abstract interpretation based on those top-down methods with memo-ization have been developed as well. Given a logic program and a top-level query, this approach analyzes various run-time properties by approximately executing the query in some abstract domain using the top-down evaluation with memo-ization. Utilizing the correspondence between AT and OLDT resolution, this paper presents a framework for abstract interpretation based on AT, and, in particular, it shows the relation to Mellish's abstract interpretation.

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