Tactic Learning and Proving for the Coq Proof Assistant

13 pages•Published: May 27, 2020

Lasse Blaauwbroek, Josef Urban and Herman Geuvers

Abstract

We present a system that utilizes machine learning for tactic proof search in the Coq Proof Assistant. In a similar vein as the TacticToe project for HOL4, our system predicts appropriate tactics and finds proofs in the form of tactic scripts. To do this, it learns from previous tactic scripts and how they are applied to proof states. The performance of the system is evaluated on the Coq Standard Library. Currently, our predictor can identify the correct tactic to be applied to a proof state 23.4% of the time. Our proof searcher can fully automatically prove 39.3% of the lemmas. When combined with the CoqHammer system, the two systems together prove 56.7% of the library’s lemmas.

Keyphrases: coq, interactive theorem proving, machine learning, proof synthesis, tactic search

In: Elvira Albert and Laura Kovacs (editors). LPAR23. LPAR-23: 23rd International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 73, pages 138-150.

Links:	https://easychair.org/publications/paper/JLdB
	https://doi.org/10.29007/wg1q

BibTeX entry

@inproceedings{LPAR23:Tactic_Learning_Proving_Coq,
  author    = {Lasse Blaauwbroek and Josef Urban and Herman Geuvers},
  title     = {Tactic Learning and Proving for the Coq Proof Assistant},
  booktitle = {LPAR23. LPAR-23: 23rd International Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Elvira Albert and Laura Kovacs},
  series    = {EPiC Series in Computing},
  volume    = {73},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/JLdB},
  doi       = {10.29007/wg1q},
  pages     = {138-150},
  year      = {2020}}

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