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The Theory of an Arbitrary Higher \(\lambda\)-Model

dc.contributor.authorMartínez-Rivillas, Daniel O.
dc.contributor.authorde Queiroz, Ruy J. G. B.
dc.date.accessioned2023-06-07T09:21:15Z
dc.date.available2023-06-07T09:21:15Z
dc.date.issued2023-04-25
dc.identifier.issn0138-0680
dc.identifier.urihttp://hdl.handle.net/11089/47236
dc.description.abstractOne takes advantage of some basic properties of every homotopic \(\lambda\)-model (e.g. extensional Kan complex) to explore the higher \(\beta\eta\)-conversions, which would correspond to proofs of equality between terms of a theory of equality of any extensional Kan complex. Besides, Identity types based on computational paths are adapted to a type-free theory with higher \(\lambda\)-terms, whose equality rules would be contained in the theory of any \(\lambda\)-homotopic model.en
dc.language.isoen
dc.publisherWydawnictwo Uniwersytetu Łódzkiegopl
dc.relation.ispartofseriesBulletin of the Section of Logic;1en
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0
dc.subjecthigher lambda calculusen
dc.subjecthomotopic lambda modelen
dc.subjectKan complex reflexiveen
dc.subjecthigher conversionen
dc.subjecthomotopy type-free theoryen
dc.titleThe Theory of an Arbitrary Higher \(\lambda\)-Modelen
dc.typeOther
dc.page.number39-58
dc.contributor.authorAffiliationMartínez-Rivillas, Daniel O. - Universidade Federal de Pernambuco, Centro de Informática, Av. Jornalista Aníbal Fernandes, s/n Recife, Pernambuco, Brazilen
dc.contributor.authorAffiliationde Queiroz, Ruy J. G. B. - Universidade Federal de Pernambuco, Centro de Informática, Av. Jornalista Aníbal Fernandes, s/n Recife, Pernambuco, Brazilen
dc.identifier.eissn2449-836X
dc.referencesR. de Queiroz, A. de Oliveira, A. Ramos, Propositional equality, identity types, and direct computational paths, South American Journal of Logic, vol. 2(2) (2016), pp. 245–296.en
dc.referencesJ. Lurie, Higher Topos Theory, Princeton University Press, Princeton and Oxford (2009), DOI: https://doi.org/10.1515/9781400830558en
dc.referencesD. Martínez-Rivillas, R. de Queiroz, Solving Homotopy Domain Equations, arXiv:2104.01195, (2021).en
dc.referencesD. Martínez-Rivillas, R. de Queiroz, The ∞-groupoid generated by an arbitrary topological λ-model, Logic Journal of the IGPL (also arXiv:1906.05729), vol. 30 (2022), pp. 465–488, URL: https://doi.org/10.1093/jigpal/jzab015en
dc.referencesD. Martínez-Rivillas, R. de Queiroz, Towards a Homotopy Domain Theory, Archive for Mathematical Logic (also arXiv 2007.15082), (2022), URL: https://doi.org/10.1007/s00153-022-00856-0en
dc.referencesC. Rezk, Introduction to Quasicategories, Lecture Notes for course at University of Illinois at Urbana-Champaign (2022), URL: https://faculty.math.illinois.edu/~{}rezk/quasicats.pdfen
dc.contributor.authorEmailMartínez-Rivillas, Daniel O. - domr@cin.ufpe.br
dc.contributor.authorEmailde Queiroz, Ruy J. G. B. - ruy@cin.ufpe.br
dc.identifier.doi10.18778/0138-0680.2023.11
dc.relation.volume52


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