[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-327326-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-327326-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","reformalization-of-the-jordan-curve-theorem","Reformalization of the Jordan Curve Theorem","","Reformalization studies a variant of autoformalization where a mathematical input proof is formal code in one proof assistant, not natural language. This work reports three reformalizations of the Jordan Curve Theorem: transferring from Mizar to Lean, from HOL Light to Lean, and from HOL Light to Agda. Results are analyzed to determine which pipeline design choices affect practical reformalization. The final formalizations are released publicly on GitHub.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/reformalization-of-the-jordan-curve-theorem/327326/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/reformalization-of-the-jordan-curve-theorem/327326.png","ImageObject",300,407,{"name":42,"@type":43},"Emma Wilson","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-29","2026-09-21",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",11,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is reformalization in this paper?","Question",{"text":63,"@type":64},"Reformalization is a variant of autoformalization where the input is a formal development in a different proof assistant rather than a natural-language proof.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Which proof assistants are used in the three reformalizations?",{"text":68,"@type":64},"The paper reports reformalizations from Mizar to Lean, from HOL Light to Lean, and from HOL Light to Agda.",{"name":70,"@type":61,"acceptedAnswer":71},"What obstacles does the paper discuss for traditional automated proof transfer?",{"text":72,"@type":64},"It discusses foundation mismatches between proof systems and the resulting translations being unnatural due to library alignment issues.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},327326,1790915778,{"code":4,"msg":82,"data":83},"success",[84,88,92,96,101,106,111,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":93,"show_sort_weight":94,"slug":95},"Exam",70,"exam",{"id":97,"doc_module":4,"doc_module_name":25,"category_name":98,"show_sort_weight":99,"slug":100},5,"Comic",60,"comic",{"id":102,"doc_module":4,"doc_module_name":25,"category_name":103,"show_sort_weight":104,"slug":105},6,"Technology",50,"technology",{"id":107,"doc_module":4,"doc_module_name":25,"category_name":108,"show_sort_weight":109,"slug":110},7,"Healthcare",40,"healthcare",{"id":112,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":113,"slug":114},8,30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":97,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":112,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":107,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":144,"read_time":145,"preview_page_count":4},3848291630094,"https://eur-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Reformalization of the Jordan Curve Theorem  \nSimon Guilloud 1 Sankalp Gambhir 1 Samuel Chassot 1  \narXiv :2607 .0 1734v 1 [ cs .AI] 2 Jul 2026  \nAbstract  \nWe present a case study in reformalization, a variant of autoformalization in which the input proof is not natural language but a formal development in a different proof assistant. Concretely, we report three reformalizations of the Jordan Curve Theorem: from Mizar to Lean, from HOL Light to Lean, and from HOL Light to Agda. We analyse the results and identify pipeline design choices that matter for practical reformalization tasks. The final formalizations are available at [https://github.com/](https://github.com/)[ ](https://github.com/)epfl-lara/jordan-curve-theorem.  \n1. Introduction  \nMuch attention has been given to the problem of autoformalization: given a mathematical text in natural language (such as a paper or textbook), produce a corresponding formalization in a proof assistant. Much less attention has been given to the simpler but still highly useful question of formalizing a mathematical theory not from an informal proof, but from a development in a different proof assistant. We call this task reformalization.  \nAutomated proof transfer, which translates proofs across proof systems, has long been a research topic in the ITP community (Kohlhase & Rabe, 2021 ; Anonymous, 1994) . Before recent progress by LLMs in formal mathematics, the main viable approach was low-level logical translation of statements and proofs. Many approaches were developed over the years, but they face two fundamental obstacles. First, a mismatch between logical foundations (for example, dependent type theory, higher-order logic, or set theory) is difficult to overcome. Even when the logical foundations are provably equivalent, existing approaches are typically  \nAll authors contributed equally. 1´Ecole Polytechnique Fdrale de Lausanne (EPFL), Lausanne, Switzerland. Correspondence to: Simon Guilloud \u003C[simon.guilloud@epfl.ch](simon.guilloud@epfl.ch) >, Sankalp Gambhir \u003C[sankalp.gambhir@epfl.ch](sankalp.gambhir@epfl.ch) >, Samuel Chassot \u003Csamuel.chassot@epfl.ch> .  \nProceedings of the 43 rd International Conference on Machine Learning, Seoul, South Korea. PMLR 306, 2026 . Copyright 2026 by the author(s) .  \nrestricted to transfers between systems with very similar foundations, transfers from a simpler system to a more complex system (for example,(Blanqui, 2024 ; Keller & Werner, 2010)), or translations with large complexity and proof-size overhead, as in (Guilloud et al., 2024) .  \nThe second obstacle is that, even when technically feasible, the resulting translation is unnatural. In particular, the translation of a concept often does not match the way that concept is defined in the target assistant. This is the problem of library alignment. For example, in a transfer of HOL Light proofs into Lean, the natural numbers N as defined in HOL Light and translated into Lean yield a definition of N that is not only different from Lean’s inductive type N, but possibly not even provably equivalent to it in Lean. The usual solution is manual alignment of concepts, which restricts the use of each translated concept to a particular API 1.  \nIn mathematical research, however, and with the exception of a few peculiar domains, it is widely understood that the particular choice of logical foundations matters little: in principle, a mathematical proof can be carried out “naturally” in any proof system with sufficient background. In that regard, the two problems above are artefacts of translations that must be deterministic, complete, and correct by construction, but that cannot preserve the spirit of the original proof. LLM-based proof transfer is the opposite: it is not deterministic, complete, or correct by construction, but it can preserve the proof idea and thereby largely avoid the two obstacles above. This is the rationale behind reformalization.  \nIn the present work, we show through a case study that ","cbCaiiWzGg9mldJT","https://ap.wps.com/l/cbCaiiWzGg9mldJT","pdf",199967,"English","# Abstract\n# Introduction\n## Autoformalization vs. reformalization\n## Obstacles in proof transfer\n## Library alignment and foundations mismatch\n# Jordan Curve Theorem background\n## Previous formalizations in HOL Light and Mizar\n## Motivation and scale of the presented case study","[{\"question\":\"What is reformalization in this paper?\",\"answer\":\"Reformalization is a variant of autoformalization where the input is a formal development in a different proof assistant rather than a natural-language proof.\"},{\"question\":\"Which proof assistants are used in the three reformalizations?\",\"answer\":\"The paper reports reformalizations from Mizar to Lean, from HOL Light to Lean, and from HOL Light to Agda.\"},{\"question\":\"What obstacles does the paper discuss for traditional automated proof transfer?\",\"answer\":\"It discusses foundation mismatches between proof systems and the resulting translations being unnatural due to library alignment issues.\"}]","Reformalization of the Jordan Curve Theorem | PDF",1789976980,18]