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arXiv · 1703.02117

Theory Morphisms in Church's Type Theory with Quotation and Evaluation

William M. Farmer
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Abstract

${\rm CTT}_{\rm qe}$ is a version of Church's type theory with global quotation and evaluation operators that is engineered to reason about the interplay of syntax and semantics and to formalize syntax-based mathematical algorithms. ${\rm CTT}_{\rm uqe}$ is a variant of ${\rm CTT}_{\rm qe}$ that admits undefined expressions, partial functions, and multiple base types of individuals. It is better suited than ${\rm CTT}_{\rm qe}$ as a logic for building networks of theories connected by theory morphisms. This paper presents the syntax and semantics of ${\rm CTT}_{\rm uqe}$, defines a notion of a theory morphism from one ${\rm CTT}_{\rm uqe}$ theory to another, and gives two simple examples that illustrate the use of theory morphisms in ${\rm CTT}_{\rm uqe}$.

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William M. Farmer. 2017-03-06. Theory Morphisms in Church's Type Theory with Quotation and Evaluation. https://arxiv.org/abs/1703.02117

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