{"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/internal-effectful-forcing-in-system-t","title":"Internal Effectful Forcing in System T","arxiv_id":"2505.11055","date":"2025-05-16","proceeding":null,"authors":["Martin H. Escardo","Bruno da Rocha Paiva","Vincent Rahli","Ayberk Tosun"],"abstract":"The effectful forcing technique allows one to show that the denotation of a closed System T term of type $(\\iota \\to \\iota) \\to \\iota$ in the set-theoretical model is a continuous function $(\\mathbb{N} \\to \\mathbb{N}) \\to \\mathbb{N}$. For this purpose, an alternative dialogue-tree semantics is defined and related to the set-theoretical semantics by a logical relation. In this paper, we apply effectful forcing to show that the dialogue tree of a System T term is itself System T-definable, using the Church encoding of trees.","url_abs":"https://arxiv.org/abs/2505.11055v1","url_pdf":"https://arxiv.org/pdf/2505.11055v1.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":"internal-effectful-forcing-in-system-t","repo_url":"https://github.com/martinescardo/TypeTopology","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}