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

• Published in: Bulletin of the Section of Logic Vol. 52; no. 1; pp. 39 - 58
• Main Authors: Martínez-Rivillas, Daniel O, de Queiroz, Ruy J. G. B
• Format: Journal Article
• Language: English
• Published: Wydawnictwo Uniwersytetu Łódzkiego 25.04.2023; Lodz University Press
• Subjects: higher conversion; higher lambda calculus; homotopic lambda model; homotopy type-free theory; kan complex reflexive; Logic; homotopic lambda model; Kan complex reflexive; higher conversion; higher lambda calculus; homotopy typefree theory
• ISSN: 0138-0680; 2449-836X
• DOI: 10.18778/0138-0680.2023.11

One 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.