Jan Jakubův, Mikoláš Janota, Andrew Reynolds
International Workshop on Satisfiability Modulo Theories (SMT), CEUR Workshop Proceedings 2908, 2021.
pdf 
doi:10.1007/978-3-030-81097-9_5
Copyright: authors, CC BY 4.0
Abstract
We present a comparison of several online machine learning techniques for tactical learning and proving in the Coq proof assistant. This work builds on top of Tactician, a plugin for Coq that learns from proofs written by the user to synthesize new proofs. Learning happens in an online manner, meaning that Tactician’s machine learning model is updated immediately every time the user performs a step in an interactive proof. This has important advantages compared to the more studied offline learning systems: (1) it provides the user with a seamless, interactive experience with Tactician and, (2) it takes advantage of locality of proof similarity, which means that proofs similar to the current proof are likely to be found close by. We implement two online methods, namely approximate k-nearest neighbors based on locality sensitive hashing forests and random decision forests. Additionally, we conduct experiments with gradient boosted trees in an offline setting using XGBoost. We compare the relative performance of Tactician using these three learning methods on Coq’s standard library.
BibTex
@inproceedings{JJMJAR-CEURWS21, author = {Jan Jakubuv and Mikol{\'{a}}s Janota and Andrew Reynolds}, editor = {Alexander Nadel and Aina Niemetz}, title = {Characteristic Subsets of {SMT-LIB} Benchmarks}, booktitle = {Proceedings of the 19th International Workshop on Satisfiability Modulo Theories co-located with 33rd International Conference on Computer Aided Verification(CAV 2021), Online (initially located in Los Angeles, USA), July 18-19, 2021}, series = {{CEUR} Workshop Proceedings}, volume = {2908}, pages = {53--63}, publisher = {CEUR-WS.org}, year = {2021}, url = {http://ceur-ws.org/Vol-2908/paper7.pdf},}