{"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/proving-soundness-of-extensional-normal-form","title":"Proving Soundness of Extensional Normal-Form Bisimilarities","arxiv_id":"1711.00113","date":"2017-10-31","proceeding":null,"authors":["Dariusz Biernacki","Serguei Lenglet","Piotr Polesiuk"],"abstract":"Normal-form bisimilarity is a simple, easy-to-use behavioral equivalence that relates terms in $\\lambda$-calculi by decomposing their normal forms into bisimilar subterms. Moreover, it typically allows for powerful up-to techniques, such as bisimulation up to context, which simplify bisimulation proofs even further. However, proving soundness of these relations becomes complicated in the presence of $\\eta$-expansion and usually relies on ad hoc proof methods which depend on the language. In this paper we propose a more systematic proof method to show that an extensional normal-form bisimilarity along with its corresponding up to context technique are sound. We illustrate our technique with three calculi: the call-by-value $\\lambda$-calculus, the call-by-value $\\lambda$-calculus with the delimited-control operators shift and reset, and the call-by-value $\\lambda$-calculus with the abortive control operators call/cc and abort. In the first two cases, there was previously no sound up to context technique validating the $\\eta$-law, whereas no theory of normal-form bisimulations for a calculus with call/cc and abort has been presented before. Our results have been fully formalized in the Coq proof assistant.","url_abs":"http://arxiv.org/abs/1711.00113v4","url_pdf":"http://arxiv.org/pdf/1711.00113v4.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"proving-soundness-of-extensional-normal-form","repo_url":"https://bitbucket.org/pl-uwr/diacritical","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}