  ${\rm CTT}_{\rm qe}$ 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 ${\rm
CTT}_{\rm uqe}$.
