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TacticToe: Learning to Reason with HOL4 Tactics

19 pagesPublished: May 4, 2017

Abstract

Techniques combining machine learning with translation to automated reasoning have recently become an important component of formal proof assistants. Such “hammer” techniques complement traditional proof assistant automation as implemented by tactics and decision procedures. In this paper we present a unified proof assistant automation approach which attempts to automate the selection of appropriate tactics and tactic-sequences combined with an optimized small-scale hammering approach. We implement the technique as a tactic-level automation for HOL4: TacticToe. It implements a modified A*-algorithm directly in HOL4 that explores different tactic-level proof paths, guiding their selection by learning from a large number of previous tactic-level proofs. Unlike the existing hammer methods, TacticToe avoids translation to FOL, working directly on the HOL level. By combining tactic prediction and premise selection, TacticToe is able to re-prove 39% of 7902 HOL4 theorems in 5 seconds whereas the best single HOL(y)Hammer strategy solves 32% in the same amount of time.

Keyphrases: A* proof search, automated reasoning, higher-order logic, machine learning, proof automation

In: Thomas Eiter and David Sands (editors). LPAR-21. 21st International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 46, pages 125--143

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