{"publication":"14th International Conference on Interactive Theorem Proving","department":[{"_id":"GradSch"},{"_id":"VlKo"}],"year":"2023","doi":"10.4230/LIPIcs.ITP.2023.15","abstract":[{"text":"We formalized general (i.e., type-0) grammars using the Lean 3 proof assistant. We defined basic notions of rewrite rules and of words derived by a grammar, and used grammars to show closure of the class of type-0 languages under four operations: union, reversal, concatenation, and the Kleene star. The literature mostly focuses on Turing machine arguments, which are possibly more difficult to formalize. For the Kleene star, we could not follow the literature and came up with our own grammar-based construction.","lang":"eng"}],"citation":{"mla":"Dvorak, Martin, and Jasmin Blanchette. “Closure Properties of General Grammars - Formally Verified.” <i>14th International Conference on Interactive Theorem Proving</i>, vol. 268, 15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023, doi:<a href=\"https://doi.org/10.4230/LIPIcs.ITP.2023.15\">10.4230/LIPIcs.ITP.2023.15</a>.","ista":"Dvorak M, Blanchette J. 2023. Closure properties of general grammars - formally verified. 14th International Conference on Interactive Theorem Proving. ITP: International Conference on Interactive Theorem Proving, LIPIcs, vol. 268, 15.","chicago":"Dvorak, Martin, and Jasmin Blanchette. “Closure Properties of General Grammars - Formally Verified.” In <i>14th International Conference on Interactive Theorem Proving</i>, Vol. 268. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. <a href=\"https://doi.org/10.4230/LIPIcs.ITP.2023.15\">https://doi.org/10.4230/LIPIcs.ITP.2023.15</a>.","apa":"Dvorak, M., &#38; Blanchette, J. (2023). Closure properties of general grammars - formally verified. In <i>14th International Conference on Interactive Theorem Proving</i> (Vol. 268). Bialystok, Poland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.ITP.2023.15\">https://doi.org/10.4230/LIPIcs.ITP.2023.15</a>","ieee":"M. Dvorak and J. Blanchette, “Closure properties of general grammars - formally verified,” in <i>14th International Conference on Interactive Theorem Proving</i>, Bialystok, Poland, 2023, vol. 268.","ama":"Dvorak M, Blanchette J. Closure properties of general grammars - formally verified. In: <i>14th International Conference on Interactive Theorem Proving</i>. Vol 268. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2023. doi:<a href=\"https://doi.org/10.4230/LIPIcs.ITP.2023.15\">10.4230/LIPIcs.ITP.2023.15</a>","short":"M. Dvorak, J. Blanchette, in:, 14th International Conference on Interactive Theorem Proving, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023."},"date_created":"2023-06-05T07:29:05Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"related_material":{"link":[{"url":"https://github.com/madvorak/grammars/tree/publish","relation":"software"}]},"day":"27","article_processing_charge":"No","article_number":"15","file_date_updated":"2023-08-07T11:55:43Z","scopus_import":"1","publication_status":"published","oa_version":"Published Version","type":"conference","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication_identifier":{"eissn":["1868-8969"],"isbn":["9783959772846"]},"volume":268,"acknowledgement":"Jasmin Blanchette: This research has received funding from the Netherlands Organization\r\nfor Scientific Research (NWO) under the Vidi program (project No. 016.Vidi.189.037, Lean Forward).\r\n__\r\nWe thank Vladimir Kolmogorov for making this collaboration possible. We\r\nthank Václav Končický for discussing ideas about the Kleene star construction. We thank Patrick Johnson, Floris van Doorn, and Damiano Testa for their small yet very valuable contributions to our code. We thank Eric Wieser for simplifying one of our proofs. We thank Mark Summerfield for suggesting textual improvements. We thank the anonymous reviewers for very helpful comments. Finally, we thank the Lean community for helping us with various technical issues and answering many questions. ","status":"public","external_id":{"arxiv":["2302.06420"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","conference":{"end_date":"2023-08-04","start_date":"2023-07-31","location":"Bialystok, Poland","name":"ITP: International Conference on Interactive Theorem Proving"},"alternative_title":["LIPIcs"],"month":"07","intvolume":"       268","language":[{"iso":"eng"}],"file":[{"creator":"dernst","checksum":"773a0197f05b67feaa6cb1e17ec3642d","access_level":"open_access","success":1,"relation":"main_file","date_updated":"2023-08-07T11:55:43Z","file_size":715976,"file_name":"2023_LIPIcS_Dvorak.pdf","content_type":"application/pdf","file_id":"13982","date_created":"2023-08-07T11:55:43Z"}],"quality_controlled":"1","date_updated":"2023-09-25T11:04:29Z","date_published":"2023-07-27T00:00:00Z","oa":1,"has_accepted_license":"1","_id":"13120","ddc":["000"],"title":"Closure properties of general grammars - formally verified","author":[{"first_name":"Martin","orcid":"0000-0001-5293-214X","id":"40ED02A8-C8B4-11E9-A9C0-453BE6697425","full_name":"Dvorak, Martin","last_name":"Dvorak"},{"first_name":"Jasmin","full_name":"Blanchette, Jasmin","last_name":"Blanchette"}]}