<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\section{Discussion}

\subsection{Related Work}
% Discuss Joey Eremondi's thesis on gradual dependent types

% Discuss Jeremy Siek's work on graduality in Agda

\subsection{Mechanization}
% Discuss Guarded Cubical Agda and mechanization efforts

\subsection{Benefits and Drawbacks of the Synthetic Approach}

\subsection{Synthetic Ordering}

A key to managing the complexity of our concrete construction is in
using a \emph{synthetic} approach to step-indexing rather than working
analytically with presheaves. This has helped immensely in our ongoing
mechanization in cubical Agda as it sidesteps the need to formalize
these constructions internally. 
%
However, there are other aspects of the model, the bisimilarity and
the monotonicity, which are treated analytically and are .
%
It may be possible to utilize further synthetic techniques to reduce
this burden as well, and have all type intrinsically carry a notion of
bisimilarity and ordering relation, and all constructions to
automatically preserve them.
%
A synthetic approach to ordering is common in (non-guarded) synthetic
domain theory and has also been used for synthetic reasoning for cost
models \cite{synthetic-domain-theory,decalf}.

\subsection{Future Work}


% Cite GrEff paper
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