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Work on the rewriting introduction

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chapters/4_rewriting.tex
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\chapter{Rewriting Constraint Modelling Languages}\label{ch:rewriting}
%************************************************
In this chapter We describe a new \textbf{systematic view
of the execution of \cmls}, and build on this to propose a new tool chain. We
show how this tool chain allows us to
Rewriting a high-level constraint model and equivalent solver-level constraint
model might often seems like a simple application of a term rewriting system. In
reality, however, eagerly rewriting the the constraints in the model will often
result in sub-optimal solver-level model and this might result in exponentially
more work for the solver. Therefore, there are many techniques that can be used
to create more efficient solver-level models such as: continuously updating
variable domains according to the constraints, correctly resolving constraint
sub-typing when variables get fixed, removing any variables and constraints that
have become unused, detecting duplicate constraints, and reusing duplicate
functional definitions.
The application of all these optimisations can, however, be time intensive
during the rewriting process. Although this was not a problem when high-level
\cmls\ were targeting \gls{cp} solvers, where the solver-level constraint model
stays relatively small, this poses a big problem for \gls{mip} and \gls{sat}
solvers, whose solver-level constraint models are significantly larger.
In this chapter, we revisit the rewriting of high-level \cmls\ into solver-level
constraint models. We describe a new \textbf{systematic view of the execution of
\minizinc{}} and build on this to propose a new tool chain. We show how this
tool chain allows us to:
\begin{itemize}
\item efficiently rewrite high-level constraint models with \textbf{minimal
overhead}.
\item easily integrate a range of \textbf{optimisation and simplification}
techniques,
\item effectively \textbf{detect and eliminate dead code} introduced by
functional definitions
\end{itemize}
The new architecture is shown in \Cref{sfig:4-newarch}. A constraint model is
first compiled to byte code (called \microzinc), independent of the data. The
@ -141,7 +167,8 @@ The translation from \minizinc\ to \microzinc\ involves the following steps:
function declaration and each call site
\item Move all top-level variable declarations and constraints into a let
expression in the body of a new function called \mzninline{main}, whose
arguments are the parameters of the model.
arguments are the parameters of the model and which returns a fresh
Boolean variable.
\end{enumerate}
\begin{example}