Handle units of literal constants by means of rules for the empty unit

chapters/unitexpressions.tex

@@ -94,7 +94,45 @@ \section{The Syntax of Unit Expressions}\label{the-syntax-of-unit-expressions}
 \section{Unit Checking}\label{unit-checking}
 
 How to verify that units are used in compatible ways is current not fully determined by the specification.
-This section gives rules for certain situations, but in general tools are expected to reason according to standard dimensional analysis (from here on referred to as just \firstuse{dimensional analysis}).
+This section gives rules for certain situations, but in general tools are expected to reason according to standard dimensional analysis..
+
+
+\subsection{Standard Dimensional Analysis}\label{standard-dimensional-analysis}
+
+This section gives an incomplete characterization of \emph{standard dimensional analysis}, also referred to as just \firstuse{dimensional analysis}.
+What is described below applies to unit checking in Modelica -- \emph{standard dimensional analysis} could have additional meanings in other contexts.
+While Modelica has a concept of \willintroduce{empty units} (described in later sections), standard dimensional analysis only deals with non-empty units such as \lstinline!"m"!, \lstinline!"m/s"!, or \lstinline!"1"!.
+It consists of two parts:
+\begin{itemize}
+\item
+  Unit compatibility requirements.
+\item
+  Rules for deriving the unit of an expression.
+\end{itemize}
+
+Examples of unit compatibility requirements that must be met in Modelica:
+\begin{itemize}
+\item
+  The expression of a declaration equation must have the same unit as the component to which it belongs.
+\item
+  The two sides of an equation or assignment statement must have the same unit.
+\item
+  The two operands of the additive operators \lstinline!+! and \lstinline!-! must have the same unit.
+\item
+  In a function call, the unit of an argument expression must match the unit (unless empty, see below) of the corresponding function input component.
+\end{itemize}
+
+% TODO: Replace these examples by giving unit semantics where operators and built-in functions are defined in the specification,
+% and just include some likes to places where such semantics are given.
+Examples of unit derivation in Modelica:
+\begin{itemize}
+\item
+  The result of additive operators has the same unit as the operands.
+\item
+  The result of multiplication has a unit obtained by adding the exponents of the operands' units.
+\item
+  Built-in operators such as \lstinline!pre! and \lstinline!previous! preserve units, while \lstinline!der! changes the unit by dividing it by \lstinline!"s"!.
+\end{itemize}
 
 
 \subsection{Empty and Undefined Units}\label{empty-and-undefined-units}