Clarify discrete and remove odd statement about Pantelides. (modelica…

…#2887)

* Clarify discrete and remove odd statement about Pantelides.
Resolves parts of modelica#2835
Co-authored-by: Henrik Tidefelt <henrikt@wolfram.com>

chapters/classes.tex

@@ -383,14 +383,33 @@ \subsection{Component Variability Prefixes discrete, parameter, constant}\label{
 definition equations is given in \cref{variability-of-expressions}.
 
 \begin{nonnormative}
-A discrete-time variable is a piecewise constant signal which
-changes its values only at event instants during simulation. Such types
-of variables are needed in order that special algorithms, such as the
-algorithm of Pantelides for index reduction, can be applied (it must be
-known that the time derivative of these variables is identical to zero).
-Furthermore, memory requirements can be reduced in the simulation
-environment, if it is known that a component can only change at event
-instants.
+For \lstinline!Real! variables we can distinguish two subtly different categories: discrete-time and piecewise constant, where the discrete-time variables are a subset of all piecewise constant variables.
+The \lstinline!Real! variables declared with the prefix \lstinline!discrete! is a subset of the discrete-time \lstinline!Real! variables.
+For a \lstinline!Real! variable, being discrete-time is equivalent to being assigned in a when-clause.
+A variable used as argument to \lstinline!pre! outside a when-clause must be discrete-time.
+
+\begin{lstlisting}[language=modelica]
+model PiecewiseConstantReals
+  discrete Real xd1 "Must be assigned in a when-clause, discrete-time";
+  Real xd2 "Assigned in a when-clause (below) and thus discrete-time";
+  Real xc3 "Not discrete-time, but piecewise constant";
+  Real x4 "Piecewise constant, but changes between events";
+equation
+  when sample(1, 1) then
+    xd1 = pre(xd1) + 1;
+    xd2 = pre(xd2) + 1;
+  end when;
+  // It is legal to use pre for a discrete-time variable outside of when
+  xc3 = xd1 + pre(xd2);
+  // But pre(xc3) would not be legal
+  x4 = if noEvent(cos(time) > 0.5) then 1.0 else -1.0;
+end PiecewiseConstantReals;
+\end{lstlisting}
+
+Tools may optimize code to only compute and store discrete-time variables at events.
+Tools may extend that optimization to piece-wise constant variables that only change at events (in the example above \lstinline!xc3!).
+As shown above variables can be piecewise constant, but change at times that are not events (in the example above \lstinline!x4!).
+It is not clear how a tool could detect and optimize the latter case.
 
 A \lstinline!parameter! variable is constant during simulation.  This prefix gives the library designer the possibility to express that the physical equations in a library are only valid if some of the used components are constant during simulation.  The same also holds for discrete-time and constant variables.  Additionally, the \lstinline!parameter! prefix allows a convenient graphical user interface in an experiment environment, to support quick changes of the most important constants of a compiled model.  In combination with an if-clause, a \lstinline!parameter! prefix allows removing parts of a model before the symbolic processing of a model takes place in order to avoid variable causalities in the model (similar to \lstinline!#ifdef! in C).  Class parameters can be sometimes used as an alternative.