一个任意更高的理论$\lambda$ -模型

Q2 Arts and Humanities

Bulletin of the Section of Logic Pub Date : 2023-04-25 DOI:10.18778/0138-0680.2023.11

Daniel Martinez, R. D. de Queiroz

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引用次数: 2

摘要

利用每一个同位\（λ\）-模型的一些基本性质（例如\外延Kan复形）来探索更高的\（β\η\）-转换，这将对应于任何外延Kan复合物的等式理论的项之间的等式的证明。此外，基于计算路径的恒等式适用于具有更高\（\lambda\）项的无类型理论，其等式规则将包含在任何$\lambda$-同宗模型的理论中。

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The Theory of an Arbitrary Higher $\lambda$-Model

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.

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