\item Theories have a module name, an optional \emph{meta-theory} and a body consisting of \emph{includes} of other theories
and a list of \emph{constant declarations}.
\item Constant declarations have a name and two optional term components; a \emph{type} ($[:t]$), and a \emph{definition} ($[=t]$).
\item Views $V : T_1\to T_2$ have a module name, a domain theory $T_1$, a codomain theory $T_2$ and a body consisting of assignments
$C = t$.
\item Terms are either
\begin{itemize}
\item variables $x$,
\item symbol references $T?C$ (referencing the constant $C$ in theory $T$),
\item applications $\oma{f}{a_1,\ldots,a_n}$ of a term $f$ to a list of arguments $a_1,\ldots,a_n$ or
\item binding application $\ombind{f}{x_1[:t_1][=d_1],\ldots,x_n[:t_n][=d_n]}{b}$, where $f$\emph{binds} the variables
$x_1,\ldots,x_n$ in the body $b$ (representing binders such as quantifiers, lambdas, dependent type constructors etc.).
\end{itemize}
\end{itemize}
The term components of a constant in a theory $T$ may only contain symbol references to constants declared previously in $T$, or that are declared in some theory $T'$ (recursively) included in $T$ (or its meta-theory, which we consider an \emph{include} as well).
We can eliminate all includes in a theory $T$ by simply copying over the constant declarations in the included theories; we call this process \emph{flattening}. We will often and without loss of generality assume a theory to be \emph{flat} for convenience.
An assignment in a view $V:T_1\to T_2$ is syntactically well-formed if for any assignment $C=t$ contained, $C$ is a constant declared in the flattened domain $T_1$ and $t$ is a syntactically well-formed term in the codomain $T_2$. We call a view \emph{total} if all \emph{undefined} constants in the domain have a corresponding assignment and \emph{partial} otherwise.
