unroll.tex

由matlab开发的hybrid系统的描述语言

\chapter{Unrolling the Items}
\label{unroll_c}

Some of the statements in the \hysdel{} grammar are too powerful for direct translation into an \MLD{} system. The
solution in these cases is to split the statement into two items. We call this process unrolling.

Unrolling is done by calling \method{Section}{unroll}. It modifies the original items produced by the parser and
creates new items. It does this by calling \method{Item}{unroll} for all its items. The items in turn ask their
expressions to unroll themselves by calling \method{Expr}{unroll}. Then they add their own unrolled items, if they
have one. \method{Expr}{unroll} unrolls its children (if it has any) and can then add another unrolled item, if it
wants to. The following sections discuss all possible unrolls and table~\ref{unroll_table} gives a short summary.

\begin{table}
\begin{center}
\begin{tabular}{lm{36mm}l}
location & problem & solution \\
\hline
DA & condition is complex & LOGIC: add = logic \\
Cont. OUTPUT, CONTINUOUS & affine expr. contains constant term & LINEAR: add = const\\
Logic OUTPUT, AUTOMATA & logic expr. is complex & LOGIC: add = logic\\
Expr: cast Bool to real & logic expr. is complex & LOGIC: add = logic \\
\end{tabular}
\end{center}
\caption{When and how unrolling is done} \label{unroll_table}
\end{table}


\section{Casting real to Boolean}

Using the keyword REAL, it is possible to cast a Boolean expression in a real one. If the expression being casted
is a Boolean variable, the variable can be treated just like a real variable. There is no problem when translating
into \MLD{}. If the cast is done on a complex Boolean expression (one containing Boolean
operators), this is no longer possible. The solution is to replace the Boolean expression in the
\cppclass{Cast\_log2real\_expr} with an additional Boolean variable. That variable is set in a newly created logic
item.

\section{DA converter with complex condition}

Recall the syntax of the DA converter: \\
\hspace*{1cm} \code{lhs\_var = IF cond THEN affine\_then
[mme\_then] [ELSE affine\_else [mme\_else]];} \\
The DA converter can only be translated into \MLD{} inequalities, if the condition \code{cond} is a single Boolean
variable. However, the \hysdel{} grammar allows complex Boolean expressions. In that case, \code{cond} is replaced
with an additional Boolean variable. The \cppclass{DA\_item} stores this variable in its field \code{cond\_var}.
Then, a new logic item is constructed which assigns \code{cond} to that variable.


\section{Affine term in \MLD{} equality}
\label{affine_in_eq_s}

Statements in the CONTINUOUS section and real OUTPUT statements can assign an affine function (with a constant
term $c$) to the left hand side variable. The \MLD{} equalities allow only linear assignments. Thus, the constant
part $c$ is removed and instead an additional variable is added. This variable is set by a new linear item to $c$.

An extended \MLD{} representation (see section~\ref{B5D5}) can have constants in the equalities. If that version
is used (specified by the \cmdop{5} command line option), the unrolling described in this section is not
necessary.


\section{Logic expressions in \MLD{} equality}

In the AUTOMATA section and in the Boolean OUTPUT, Boolean variables are set using the \MLD{} equalities. An
equality can only set the left hand side variable to some other Boolean variable. Complex Boolean expression, as
they are allowed in the \hysdel{} grammar, cannot be assigned. The solution is to create a new logic item that
assigns the Boolean expression to an additional variable. \cppclass{Automata\_item} and
\cppclass{Logic\_output\_item} store this variable in their field \code{upd\_var}.