Clarify variability of functions.

chapters/functions.tex

@@ -116,6 +116,29 @@ \subsection{Inheritance of Functions}\label{inheritance-of-functions}
 For example, it is possible to modify and extend a \lstinline!function! class to add default values for input variables.
 \end{nonnormative}
 
+A special case is defining a \lstinline!function! as a short-class definition with modifiers for inputs inside a model.
+These default values, unless overridden in the function call, will then be considered for variability similarly as if they were given in the function call.
+
+\begin{example}
+Demonstrating the variability implications.
+Note that functions cannot directly use non-constants in enclosing scopes, so we cannot write \lstinline!input Real x1=x;! directly in \lstinline!foo!.
+\begin{lstlisting}[language=modelica]
+model M
+  function foo
+    input Real x1;
+    input Real x2=2;
+    output Real y;
+  algorithm
+    y:=x1+x2;
+  end foo;
+  Real x=time;
+  function f1=foo(x1=x);
+  constant Real z=f1(x2=1); // Illegal since 'x' is seen as argument
+  constant Real z2=f1(x1=2); // Legal, since 'x1' has a new value.
+end M;
+\end{lstlisting}
+\end{example}
+
 \section{Function as a Specialized Class}\label{function-as-a-specialized-class}
 
 The function concept in Modelica is a specialized class (\cref{specialized-classes}).

chapters/interface.tex

@@ -537,6 +537,11 @@ \section{Function-Compatibility or Function-Subtyping for Functions}\label{funct
   constraining interface of the function being redeclared.
 \end{itemize}
 
+Note that function-compatibilty does currently not ensure that the function call has the correct variability, and that must then be checked after re-declaration - due the possibility of default arguments with higher variability.
+\begin{nonnormative}
+Thus any call of a function that is replaceable will need to be checked after redeclarations.
+\end{nonnormative}
+
 \begin{example}
 Demonstrating a redeclaration using a function-compatible function
 \begin{lstlisting}[language=modelica]
@@ -559,14 +564,16 @@ \section{Function-Compatibility or Function-Subtyping for Functions}\label{funct
   end UseDriveLine;
   Modelica.Mechanics.MultiBody.Interface.Frame_a frame_a;
   replaceable function gravity = GravityInterface;
+  constant Real failed[:]=gravity({1,0,0}); // May fail
 equation
   frame_a.f = gravity(frame_a.r0);
   // or gravity(position=frame_a.r0);
   frame_a.t = zeros(3);
 end Body;
 
 model PlanetSimulation
-  function sunGravity = PointMassGravity (m=2e30);
+  parameter Modelica.Units.SI.Mass mSun=2e30;
+  function sunGravity = PointMassGravity (m=mSun);
   Body planet1(redeclare function gravity = sunGravity);
   Body planet2(redeclare function gravity = PointMassGravity (m=2e30));
   $\ldots$
@@ -577,6 +584,9 @@ \section{Function-Compatibility or Function-Subtyping for Functions}\label{funct
 \lstinline!GravityInterface! (no default for \lstinline!m!), but \lstinline!sunGravity!
 inside \lstinline!PlanetSimulation! is function-compatible with
 \lstinline!GravityInterface!.
+
+The constant failed in \lstinline!planet1!, will violate variability constraints, whereas it will work in \lstinline!planet2!.
+The call \lstinline!gravity(frame_a.r0)! will work in both of them.
 \end{example}
 
 \section{Type Compatible Expressions}\label{type-compatible-expressions}

chapters/operatorsandexpressions.tex

@@ -1378,6 +1378,7 @@ \section{Variability of Expressions}\label{variability-of-expressions}
   If \lstinline!v! is a discrete-time component then \lstinline!expr! needs to be a
   discrete-time expression.
 \end{itemize}
+Note that for a function call it is also necessary to consider the variability of any used default arguments, especially if the function is redeclared, see \cref{function-compatibility}.
 
 \begin{example}
 The (underdetermined) model \lstinline!Test! below illustrates two kinds of consequences due to variability constraints.