Directed Automated Theorem Proving

Stefan Edelkamp, Peter Leven

Abstract: This paper analyzes the effect of heuristic search algorithms like A* and IDA* to accelerate proof-state based theorem provers. A functional implementation of possibly weighted A* is proposed that extends Dijkstra’s single-source shortest-path algorithm. Efficient implementation issues and possible flaws for both A* and IDA* are discussed in detail. Initial results with first and higher order logic examples in Isabelle indicate that directed automated theorem proving is superior to other known general inference mechanisms and that it can enhance other proof techniques like model elimination.