{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/automatically-proving-mathematical-theorems","title":"Automatically Proving Mathematical Theorems with Evolutionary Algorithms and Proof Assistants","arxiv_id":"1602.07455","date":"2016-02-24","proceeding":null,"authors":["Li-An Yang","Jui-Pin Liu","Chao-Hong Chen","Ying-ping Chen"],"abstract":"Mathematical theorems are human knowledge able to be accumulated in the form\nof symbolic representation, and proving theorems has been considered\nintelligent behavior. Based on the BHK interpretation and the Curry-Howard\nisomorphism, proof assistants, software capable of interacting with human for\nconstructing formal proofs, have been developed in the past several decades.\nSince proofs can be considered and expressed as programs, proof assistants\nsimplify and verify a proof by computationally evaluating the program\ncorresponding to the proof. Thanks to the transformation from logic to\ncomputation, it is now possible to generate or search for formal proofs\ndirectly in the realm of computation. Evolutionary algorithms, known to be\nflexible and versatile, have been successfully applied to handle a variety of\nscientific and engineering problems in numerous disciplines for also several\ndecades. Examining the feasibility of establishing the link between\nevolutionary algorithms, as the program generator, and proof assistants, as the\nproof verifier, in order to automatically find formal proofs to a given logic\nsentence is the primary goal of this study. In the article, we describe in\ndetail our first, ad-hoc attempt to fully automatically prove theorems as well\nas the preliminary results. Ten simple theorems from various branches of\nmathematics were proven, and most of these theorems cannot be proven by using\nthe tactic auto alone in Coq, the adopted proof assistant. The implication and\npotential influence of this study are discussed, and the developed source code\nwith the obtained experimental results are released as open source.","url_abs":"http://arxiv.org/abs/1602.07455v2","url_pdf":"http://arxiv.org/pdf/1602.07455v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"automatically-proving-mathematical-theorems","repo_url":"https://github.com/nclab/nclab.github.io","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"evolutionary-algorithms","task_name":"Evolutionary Algorithms"},{"task_slug":"sentence","task_name":"Sentence"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}