The effectful forcing technique allows one to show that the denotation of a closed System T term of type (ι ⇒ ι) ⇒ ι in the set-theoretical model is a continuous function (ℕ → ℕ) → 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.
@InProceedings{escardo_et_al:LIPIcs.FSCD.2025.19, author = {Escard\'{o}, Mart{\'\i}n H. and da Rocha Paiva, Bruno and Rahli, Vincent and Tosun, Ayberk}, title = {{Internal Effectful Forcing in System T}}, booktitle = {10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)}, pages = {19:1--19:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-374-4}, ISSN = {1868-8969}, year = {2025}, volume = {337}, editor = {Fern\'{a}ndez, Maribel}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.19}, URN = {urn:nbn:de:0030-drops-236344}, doi = {10.4230/LIPIcs.FSCD.2025.19}, annote = {Keywords: Effectful forcing, Continuity, System T, Constructive Mathematics} }
Feedback for Dagstuhl Publishing