Add trivial identity {b}=b and !{b}=!b for any Boolean formula b.

* src/ltlast/unop.cc: Perform the simplification.
* src/ltlast/unop.hh, doc/tl/tl.tex: Document it.
* src/ltltest/equals.test: Adjust test cases.

doc/tl/tl.tex

@@ -794,17 +794,17 @@ while $f$ is a PSL formula.
 \begin{align*}
   \sigma\vDash \ratgroup{r}\Esuffix f &\iff \exists k\ge 0, (\sigma^{0..k}\VDash r)\land(\sigma^{k..}\vDash f)\\
   \sigma\vDash \ratgroup{r}\Asuffix f &\iff \forall k\ge 0, (\sigma^{0..k}\VDash r)\limplies (\sigma^{k..}\vDash f)\\
-  \sigma\vDash \ratgroup{r} & \iff (\exists k\ge 0, \sigma^{0..k}\VDash r)\lor(\forall k\ge 0,\,\exists \pi\in(\B^\AP)^\star,\, (\sigma^{0..k}\prec \pi)\land(\pi\VDash r))\\
+  \sigma\vDash \ratgroup{r} & \iff (\exists k\ge 0, \sigma^{0..k}\VDash r)\lor(\forall k\ge 0,\,\exists\pi\in(\B^\AP)^\star,\, (\sigma^{0..k}\prec \pi)\land(\pi\VDash r))\\
-  \sigma\vDash \nratgroup{r} & \iff (\forall k\ge 0, \sigma^{0..k}\nVDash r)\land(\exists k\ge 0,\,\exists \forall\in(\B^\AP)^\star,\, (\sigma^{0..k}\prec \pi)\limplies(\pi\nVDash r))\\
+  \sigma\vDash \nratgroup{r} & \iff (\forall k\ge 0, \sigma^{0..k}\nVDash r)\land(\exists k\ge 0,\,\forall\pi\in(\B^\AP)^\star,\, (\sigma^{0..k}\prec \pi)\limplies(\pi\nVDash r))\\
 \end{align*}
 
 The $\prec$ symbol should be read as ``\emph{is a prefix of}''.  So
 the semantic for `$\sigma\vDash \ratgroup{r}$' is that either there is
-a finite prefix of $\sigma$ that is a model of $r$, or any prefix of
+a (non-empty) finite prefix of $\sigma$ that is a model of $r$, or any
-$\sigma$ can be extended into a finite sequence $\pi$ that is a model
+prefix of $\sigma$ can be extended into a finite sequence $\pi$ that
-of $r$.  An infinite sequence $\texttt{a;a;a;a;a;}\ldots$ is therefore a
+is a model of $r$.  An infinite sequence $\texttt{a;a;a;a;a;}\ldots$
-model of the formula \samp{$\ratgroup{a\PLUS{};\NOT a}$} even though
+is therefore a model of the formula \samp{$\ratgroup{a\PLUS{};\NOT
-it never sees \samp{$\NOT a$}.
+    a}$} even though it never sees \samp{$\NOT a$}.
 
 \subsection{Syntactic Sugar}
 
@@ -842,10 +842,12 @@ formula $b$, the following rewritings are systematically performed
 & \ratgroup{\eword}\Esuffix f&\equiv \0
 & \ratgroup{\eword} & \equiv \0
 & \nratgroup{\eword} & \equiv \1 \\
+  \ratgroup{b}\Asuffix f&\equiv b\IMPLIES f
+& \ratgroup{b}\Esuffix f&\equiv b\AND f
+& \ratgroup{b} &\equiv b
+& \nratgroup{b} &\equiv \NOT b\\
   \ratgroup{r}\Asuffix \1&\equiv \1
 & \ratgroup{r}\Esuffix \0&\equiv \0  \\
-  \ratgroup{b}\Asuffix f&\equiv b\IMPLIES f
-& \ratgroup{b}\Esuffix f&\equiv b\AND f  \\
 \end{align*}
 
 \chapter{Grammar}

src/ltlast/unop.cc

@@ -295,19 +295,25 @@ namespace spot
 	  break;
 
 	case Closure:
-	  if (child == constant::true_instance()
+	  // {0} = 0, {1} = 1,  {b} = b
-	      || child == constant::empty_word_instance())
+	  if (child->is_boolean())
-	    return constant::true_instance();
-	  if (child == constant::false_instance())
 	    return child;
+	  // {[*0]} = 1
+	  if (child == constant::empty_word_instance())
+	    return constant::true_instance();
 	  break;
 
 	case NegClosure:
+	  // {1} = 0,  {[*0]} = 0
 	  if (child == constant::true_instance()
 	      || child == constant::empty_word_instance())
 	    return constant::false_instance();
+	  // {0} = 1
 	  if (child == constant::false_instance())
 	    return constant::true_instance();
+	  // {b} = !b
+	  if (child->is_boolean())
+	    return unop::instance(Not, child);
 	  break;
 	}
 

src/ltlast/unop.hh

@@ -1,4 +1,4 @@
-// Copyright (C) 2009, 2010 Laboratoire de Recherche et Développement
+// Copyright (C) 2009, 2010, 2011 Laboratoire de Recherche et Développement
 // de l'Epita (LRDE).
 // Copyright (C) 2003, 2004 Laboratoire d'Informatique de Paris
 // 6 (LIP6), département Systèmes Répartis Coopératifs (SRC),
@@ -73,9 +73,11 @@ namespace spot
       ///   - Closure([*0]) = 1
       ///   - Closure(1) = 1
       ///   - Closure(0) = 0
+      ///   - Closure(b) = b
       ///   - NegClosure([*0]) = 0
       ///   - NegClosure(1) = 0
       ///   - NegClosure(0) = 1
+      ///   - NegClosure(b) = !b
       ///
       /// This rewriting implies that it is not possible to build an
       /// LTL formula object that is SYNTACTICALLY equal to one of

src/ltltest/equals.test

@@ -179,9 +179,9 @@ run 0 ../equals '{b[=0to$]}' '{*}'
 
 run 0 ../equals '{0[->10..100];b}' '0'
 run 0 ../equals '{0[->1..];b}' '0'
-run 0 ../equals '{0[->0,100];b}' '{b}'
+run 0 ../equals '{0[->0,100];b}' 'b'
-run 0 ../equals '{0[->0..$];b}' '{b}'
+run 0 ../equals '{0[->0..$];b}' 'b'
-run 0 ../equals '{1[->0];b}' '{b}'
+run 0 ../equals '!{1[->0];b}' '!b'
 run 0 ../equals '{1[->10,20];b}' '{[*10..20];b}'
 run 0 ../equals '{1[->..];b}' '{[*1..];b}'
-run 0 ../equals '{{a&!c}[->0];b}' '{b}'
+run 0 ../equals '{{a&!c}[->0];b}' 'b'