{"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/the-scott-model-of-pcf-in-univalent-type","title":"The Scott model of PCF in univalent type theory","arxiv_id":"1904.09810","date":"2019-04-22","proceeding":null,"authors":["Tom de Jong"],"abstract":"We develop the Scott model of the programming language PCF in univalent type theory. Moreover, we work constructively and predicatively. To account for the non-termination in PCF, we use the lifting monad (also known as the partial map classifier monad) from topos theory, which has been extended to univalent type theory by Escard\\'o and Knapp. Our results show that lifting is a viable approach to partiality in univalent type theory. Moreover, we show that the Scott model can be constructed in a predicative and constructive setting. Other approaches to partiality either require some form of choice or quotient inductive-inductive types. We show that one can do without these extensions.","url_abs":"https://arxiv.org/abs/1904.09810v4","url_pdf":"https://arxiv.org/pdf/1904.09810v4.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":"the-scott-model-of-pcf-in-univalent-type","repo_url":"https://github.com/tomdjong/Scott-PCF-UniMath","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}