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