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

Abstract

${\mathrm{CTT}}_{\mathrm{qe}}$ 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. ${\mathrm{CTT}}_{\mathrm{uqe}}$ is a variant of ${\mathrm{CTT}}_{\mathrm{qe}}$ that admits undefined expressions, partial functions, and multiple base types of individuals. It is better suited than ${\mathrm{CTT}}_{\mathrm{qe}}$ as a logic for building networks of theories connected by theory morphisms. This paper presents the syntax and semantics of ${\mathrm{CTT}}_{\mathrm{uqe}}$, defines a notion of a theory morphism from one ${\mathrm{CTT}}_{\mathrm{uqe}}$ theory to another, and gives two simple examples that illustrate the use of theory morphisms in ${\mathrm{CTT}}_{\mathrm{uqe}}$.

17 pages

Cited by in corpus (1)

• Incorporating Quotation and Evaluation Into Church's Type Theory