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${\rm \small CTT}_{\rm qe}$ is a version of Church's type theory thatincludes quotation and evaluation operators that are similar to quote and evalin the Lisp programming language. With quotation and evaluation it is possibleto reason in ${\rm \small CTT}_{\rm qe}$ about the interplay of the syntax andsemantics of expressions and, as a result, to formalize syntax-basedmathematical algorithms. We present the syntax and semantics of ${\rm \smallCTT}_{\rm qe}$ and give several examples that illustrate the usefulness ofhaving quotation and evaluation in ${\rm \small CTT}_{\rm qe}$. We do not givea proof system for ${\rm \small CTT}_{\rm qe}$, but we do sketch what a proofsystem could look like.

Incorporating Quotation and Evaluation into Church's Type Theory: Syntax and Semantics