--- a/doc-src/TutorialI/CTL/Base.thy Thu Jul 26 18:23:38 2001 +0200
+++ b/doc-src/TutorialI/CTL/Base.thy Fri Aug 03 18:04:55 2001 +0200
@@ -10,7 +10,7 @@
(specifications) \cite{ClarkeGP-book,Huth-Ryan-book}. Its foundations are set theoretic
and this section will explore them in HOL\@. This is done in two steps. First
we consider a simple modal logic called propositional dynamic
-logic (PDL), which we then extend to the temporal logic CTL, which is
+logic (PDL)\@. We then proceed to the temporal logic CTL, which is
used in many real
model checkers. In each case we give both a traditional semantics (@{text \<Turnstile>}) and a
recursive function @{term mc} that maps a formula into the set of all states of
@@ -21,8 +21,9 @@
\underscoreon
-Our models are \emph{transition systems}, i.e.\ sets of \emph{states} with
-transitions between them, as shown in this simple example:
+Our models are \emph{transition systems}:\index{transition systems}
+sets of \emph{states} with
+transitions between them. Here is a simple example:
\begin{center}
\unitlength.5mm
\thicklines
@@ -45,21 +46,20 @@
\put(91,21){\makebox(0,0)[bl]{$s_2$}}
\end{picture}
\end{center}
-Each state has a unique name or number ($s_0,s_1,s_2$), and in each
-state certain \emph{atomic propositions} ($p,q,r$) are true.
-The aim of temporal logic is to formalize statements such as ``there is no
-path starting from $s_2$ leading to a state where $p$ or $q$
-are true'', which is true, and ``on all paths starting from $s_0$ $q$ is always true'',
-which is false.
+Each state has a unique name or number ($s_0,s_1,s_2$), and in each state
+certain \emph{atomic propositions} ($p,q,r$) hold. The aim of temporal logic
+is to formalize statements such as ``there is no path starting from $s_2$
+leading to a state where $p$ or $q$ holds,'' which is true, and ``on all paths
+starting from $s_0$, $q$ always holds,'' which is false.
-Abstracting from this concrete example, we assume there is some type of
+Abstracting from this concrete example, we assume there is a type of
states:
*}
typedecl state
text{*\noindent
-Command \isacommand{typedecl} merely declares a new type but without
+Command \commdx{typedecl} merely declares a new type but without
defining it (see \S\ref{sec:typedecl}). Thus we know nothing
about the type other than its existence. That is exactly what we need
because @{typ state} really is an implicit parameter of our model. Of