[FMFP] Modelling

semester4/fmfp/parts/04_modelling/01_promela/00_syntax.tex

@@ -1,2 +1,17 @@
 \subsection{Promela}
-% p23
+Promela has \texttt{C}-like syntax, and its main objects are processes, channels, and variables.
+
+An important consideration always is the number of states there are for each model, if spin can complete executing.
+
+The number of states is given by
+\[
+    \prod_{i = 1}^N (l(p_i) \times \prod_{\texttt{var} x_i \in p_i} |\texttt{dom}(x_i)|) \times \prod_{j = 1}^{K} |\texttt{dom}(c_j)|^{\texttt{cap}(c_j)}
+\]
+where $l(p_i)$ returns the number of program locations for process $i$, $|\texttt{dom}(x_i)|$ denotes the number of values a variable can take,
+$\texttt{dom}(c_j)$ denotes the number of values each message in the channel can take and $\texttt{cap}(c_j)$ returns the capacity of the buffer fo the channel.
+
+\shade{orange}{THUS:} \hl{Keep the model as small as possible} to prevent the above, which is called \bi{state space explosion}
+
+\newpage
+
+\inputcode{promela}{code/promela/00_basics.pml}

semester4/fmfp/parts/04_modelling/01_promela/01_expressions.tex

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+\subsubsection{Expressions}
+Expressions in Promela can be:
+\begin{itemize}
+    \item Variables, constants, and literals
+    \item Structure and array accesses
+    \item Unary and binary expressions with operators. The operators correspond to the \texttt{C} operators
+    \item Function applications
+    \item Ternary operators / conditional expressions \texttt{E1 -> E2 : E3}
+\end{itemize}
+Promela has a number of built in functions, which are:
+\begin{multicols}{5}
+    \begin{itemize}
+        \item \texttt{len()}
+        \item \texttt{empty()}
+        \item \texttt{nempty()}
+        \item \texttt{full()}
+        \item \texttt{nfull()}
+        \item \texttt{run <proc>}
+        \item \texttt{eval()}
+        \item \texttt{enabled()}
+        \item \texttt{pcvalue()}
+    \end{itemize}
+\end{multicols}

semester4/fmfp/parts/04_modelling/01_promela/02_statements.tex

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+\subsubsection{Statements}
+The following statement types are supported by Promela:
+\begin{itemize}
+    \item \texttt{skip}: Does not change the state (except the location counter). Always executable
+    \item \texttt{assert(E)}: Aborts execution if \texttt{E} evaluates to zero, otherwise is equivalent to \texttt{skip}. Always executable
+    \item Assignment: \texttt{x = E} assigns value of \texttt{E} to variable \texttt{x}. For arrays, use \texttt{a[n] = E}. Always executable
+    \item \texttt{s1;s2} (Sequential composition): Executable if \texttt{s1} is executable
+    \item Expression statement: Evaluates expression \texttt{E}, executable if \texttt{E} evaluates $\neq 0$. \texttt{E} must be \bi{side effect free}.
+\end{itemize}
+
+In addition, selection statements (i.e. if / switch) and repetitions (loops) are supported:
+\begin{code}{promela}
+    if
+    :: s1 -> code;
+    :: s2 -> code;
+    :: code; // The else statement, executes if no other option executable
+    fi
+
+    do
+    :: s1 -> loop_body_1; // We can use this technique to combine if and loops
+    :: s2 -> loop_body_2;
+    :: else -> break;
+    od
+\end{code}
+
+Then, we have atomic statements, which has signature \texttt{atomic \{ s \}}, which executes \texttt{s} atomically.

semester4/fmfp/parts/04_modelling/01_promela/03_macros.tex

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+\subsubsection{Macros}
+Promela does \textit{not} support procedures. However, many of the effects (apart from recursion) can be achieved with macros.
+
+We define them using \mint{promela}|inline name(arg1, arg2) { /* body */ }|
+As is the case in \texttt{C}, they are simply replaced in the code and thus have no new variable scope, support no recursion and have no return value.