TacticToe: Learning to Prove with Tactics

TacticToe: Learning to Prove with Tactics

We implement an automated tactical prover TacticToe on top of the HOL4 interactive theorem prover. TacticToe learns from human proofs which mathematical technique is suitable in each proof situation. This knowledge is then used in a Monte Carlo tree search algorithm to explore promising tactic-level...

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Veröffentlicht in:Journal of automated reasoning 2021-02, Vol.65 (2), p.257-286
Hauptverfasser: Gauthier, Thibault, Kaliszyk, Cezary, Urban, Josef, Kumar, Ramana, Norrish, Michael
Format: Artikel
Sprache:eng
Schlagworte:
Artificial Intelligence
Computer Science
Computer Science, Artificial Intelligence
Mathematical Logic and Formal Languages
Mathematical Logic and Foundations
Schedules
Science & Technology
Search algorithms
Symbolic and Algebraic Manipulation
Tactics
Technology
Theorem proving
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Beschreibung
Zusammenfassung:We implement an automated tactical prover TacticToe on top of the HOL4 interactive theorem prover. TacticToe learns from human proofs which mathematical technique is suitable in each proof situation. This knowledge is then used in a Monte Carlo tree search algorithm to explore promising tactic-level proof paths. On a single CPU, with a time limit of 60 s, TacticToe proves 66.4% of the 7164 theorems in HOL4’s standard library, whereas E prover with auto-schedule solves 34.5%. The success rate rises to 69.0% by combining the results of TacticToe and E prover.
ISSN:0168-7433
1573-0670
DOI:10.1007/s10817-020-09580-x