Use [*0] instead of #e, and support [*] in addition to *.

* src/ltlparse/ltlscan.ll: Recognize [*] as *, and use
[*0] instead of #e for the empty word.
* src/ltlast/binop.cc, src/ltlast/constant.cc,
src/ltlast/multop.cc, src/ltlast/multop.hh, src/ltlast/unop.cc,
src/ltlast/unop.hh, src/ltltest/consterm.test,
src/ltltest/equals.test: Adjust all occurrences of #e to [*0].
* src/tgbatest/ltl2tgba.test: Also use [*].

src/ltlast/binop.cc

@@ -261,7 +261,7 @@ namespace spot
 	case EConcatMarked:
 	  //   - 0 <>-> Exp = 0
 	  //   - 1 <>-> Exp = Exp
-	  //   - #e <>-> Exp = 0
+	  //   - [*0] <>-> Exp = 0
 	  //   - Exp <>-> 0 = 0
 	  if (first == constant::true_instance())
 	    return second;
@@ -280,7 +280,7 @@ namespace spot
 	case UConcat:
 	  //   - 0 []-> Exp = 1
 	  //   - 1 []-> Exp = Exp
-	  //   - #e []-> Exp = 1
+	  //   - [*0] []-> Exp = 1
 	  //   - Exp []-> 1 = 1
 	  if (first == constant::true_instance())
 	    return second;

src/ltlast/constant.cc

@@ -87,7 +87,7 @@ namespace spot
 	case False:
 	  return "0";
 	case EmptyWord:
-	  return "#e";
+	  return "[*0]";
 	}
       // Unreachable code.
       assert(0);

src/ltlast/multop.cc

@@ -239,9 +239,9 @@ namespace spot
 		++i;
 	      }
 	  }
-	// We have    a* & #e & 0  = 0  // already checked above
+	// We have    a* & [*0] & 0  = 0  // already checked above
-	//     but    a* & #e & c*  = #e
+	//     but    a* & [*0] & c* = [*0]
-	// So if #e has been seen, check if all term recognize the
+	// So if [*0] has been seen, check if all term recognize the
 	// empty word.
 	if (weak_abs_seen)
 	  {

src/ltlast/multop.hh

@@ -80,7 +80,7 @@ namespace spot
       /// are also taken care of.  The following rewriting are performed
       /// (the left patterns are rewritten as shown on the right):
       ///
-      /// - Concat(Exps1...,#e,Exps2...) = Concat(Exps1...,Exps2...)
+      /// - Concat(Exps1...,[*0],Exps2...) = Concat(Exps1...,Exps2...)
       /// - Concat(Exps1...,0,Exps2...) = 0
       /// - Concat(Exp) = Exp
       /// - And(Exps1...,1,Exps2...) = And(Exps1...,Exps2...)

src/ltlast/unop.cc

@@ -120,8 +120,8 @@ namespace spot
       // Some trivial simplifications.
       switch (op)
 	{
-	  // We have (0*) == (#e)
+	  // We have (0*) == ([*0])
-	  //         (#e*) == (#e)
+	  //         ([*0]*) == ([*0])
 	case Star:
 	  if (child == constant::false_instance()
 	      || child == constant::empty_word_instance())
@@ -145,7 +145,7 @@ namespace spot
 	    if (child == constant::false_instance()
 		|| child == constant::true_instance())
 	      return child;
-	    // F(#e) = G(#e) = 1
+	    // F([*0]) = G([*0]) = 1
 	    if (child == constant::empty_word_instance())
 	      return constant::true_instance();
 	  }
@@ -192,7 +192,7 @@ namespace spot
 	  if (child == constant::true_instance()
 	      || child == constant::false_instance())
 	    return child;
-	  // X(#e) = 1
+	  // X([*0]) = 1
 	  if (child == constant::empty_word_instance())
 	    return constant::true_instance();
 	  break;

src/ltlast/unop.hh

@@ -57,8 +57,8 @@ namespace spot
       /// The following trivial simplifications are performed
       /// automatically (the left expression is rewritten as the right
       /// expression):
-      ///   - 0* = #e
+      ///   - 0* = [*0]
-      ///   - #e* = #e
+      ///   - [*0]* = [*0]
       ///   - Exp** = Exp*
       ///   - FF(Exp) = F(Exp)
       ///   - GG(Exp) = G(Exp)
@@ -66,17 +66,17 @@ namespace spot
       ///   - G(0) = 0
       ///   - F(1) = 1
       ///   - G(1) = 1
-      ///   - F(#e) = 1
+      ///   - F([*0]) = 1
-      ///   - G(#e) = 1
+      ///   - G([*0]) = 1
       ///   - !1 = 0
       ///   - !0 = 1
       ///   - !!Exp = Exp
       ///   - !Closure(Exp) = NegClosure(Exp)
       ///   - !NegClosure(Exp) = Closure(Exp)
-      ///   - Closure(#e) = 1
+      ///   - Closure([*0]) = 1
       ///   - Closure(1) = 1
       ///   - Closure(0) = 0
-      ///   - NegClosure(#e) = 0
+      ///   - NegClosure([*0]) = 0
       ///   - NegClosure(1) = 0
       ///   - NegClosure(0) = 1
       ///

src/ltlparse/ltlscan.ll

@@ -1,7 +1,7 @@
 /* Copyright (C) 2010, 2011, Laboratoire de Recherche et Développement de
 ** l'Epita (LRDE).
 ** Copyright (C) 2003, 2004  Laboratoire d'Informatique de Paris 6 (LIP6),
-** département Syst�mes R�partis Coop�ratifs (SRC), Université Pierre
+** département Systèmes Répartis Coopératifs (SRC), Université Pierre
 ** et Marie Curie.
 **
 ** This file is part of Spot, a model checking library.
@@ -85,7 +85,7 @@ flex_set_buffer(const char* buf, int start_tok)
   /* ~ comes from Goal, ! from everybody else */
 "!"|"~"				BEGIN(0); return token::OP_NOT;
 
-"#e"				BEGIN(0); return token::CONST_EMPTYWORD;
+"[*0]"				BEGIN(0); return token::CONST_EMPTYWORD;
 
   /* & and | come from Spin.  && and || from LTL2BA.
      /\, \/, and xor are from LBTT.
@@ -95,7 +95,7 @@ flex_set_buffer(const char* buf, int start_tok)
 "^"|"xor"			BEGIN(0); return token::OP_XOR;
 "=>"|"->"|"-->"			BEGIN(0); return token::OP_IMPLIES;
 "<=>"|"<->"|"<-->"		BEGIN(0); return token::OP_EQUIV;
-"*"				BEGIN(0); return token::OP_STAR;
+"*"|"[*]"			BEGIN(0); return token::OP_STAR;
 ";"				BEGIN(0); return token::OP_CONCAT;
 ":"				BEGIN(0); return token::OP_FUSION;
 "[]->"				BEGIN(0); return token::OP_UCONCAT;

src/ltltest/consterm.test

@@ -29,15 +29,15 @@ set -e
 run 0 ../consterm 'a'
 run 0 ../consterm '1'
 run 0 ../consterm '0'
-run 1 ../consterm '#e'
+run 1 ../consterm '[*0]'
 run 1 ../consterm 'a*'
 run 1 ../consterm '0*'
 run 0 ../consterm '((a ; b) + c)'
-run 1 ../consterm '((a ; b) + #e)'
+run 1 ../consterm '((a ; b) + [*0])'
-run 0 ../consterm '((a ; b) + #e) & e'
+run 0 ../consterm '((a ; b) + [*0]) & e'
-run 1 ../consterm '((a ; b) + #e) & #e'
+run 1 ../consterm '((a ; b) + [*0]) & [*0]'
-run 1 ../consterm '((a ; b) + #e) & (a* + b)'
+run 1 ../consterm '((a ; b) + [*0]) & (a* + b)'
-run 1 ../consterm '{{a ; b} + {#e}} & {a* + b}'  # test braces
+run 1 ../consterm '{{a ; b} + {[*0]}} & {a* + b}'  # test braces
-run 1 ../consterm '(a + #e);(b + #e);(c + #e)'
+run 1 ../consterm '(a + [*0]);(b + [*0]);(c + [*0])'
-run 0 ../consterm '(a + #e);(b + e);(c + #e)'
+run 0 ../consterm '(a + [*0]);(b + e);(c + [*0])'
-run 1 ../consterm '(a + #e);(b + e)*;(c + #e)'
+run 1 ../consterm '(a + [*0]);(b + e)*;(c + [*0])'

src/ltltest/equals.test

@@ -70,8 +70,8 @@ run 0 ../equals 'a & b ^ c | d' 'd | c ^ b & a'
 run 0 ../equals 'FFG__GFF' 'F(F(G("__GFF")))'
 
 # Trivial simplifications
-run 0 ../equals '{0*}<>->a' '{#e}<>->a'
+run 0 ../equals '{0*}<>->a' '{[*0]}<>->a'
-run 0 ../equals '{#e*}<>->a' '{#e}<>->a'
+run 0 ../equals '{[*0]*}<>->a' '{[*0]}<>->a'
 run 0 ../equals '{Exp**}<>->a' '{Exp*}<>->a'
 run 0 ../equals 'FF(Exp)' 'F(Exp)'
 run 0 ../equals 'GG(Exp)' 'G(Exp)'
@@ -79,8 +79,8 @@ run 0 ../equals 'F(0)' '0'
 run 0 ../equals 'G(0)' '0'
 run 0 ../equals 'F(1)' '1'
 run 0 ../equals 'G(1)' '1'
-run 0 ../equals 'F({#e}<>->1)' 'F({#e}<>->1)'
+run 0 ../equals 'F({[*0]}<>->1)' 'F({[*0]}<>->1)'
-run 0 ../equals 'G({#e}<>->1)' 'G({#e}<>->1)'
+run 0 ../equals 'G({[*0]}<>->1)' 'G({[*0]}<>->1)'
 run 0 ../equals 'F({1}<>->1)' '1'
 run 0 ../equals 'G({1}<>->1)' '1'
 run 0 ../equals '!1' '0'
@@ -107,15 +107,15 @@ run 0 ../equals GGx Gx
 run 0 ../equals GGGGGx Gx
 run 0 ../equals '!!x' x
 run 0 ../equals '!!!!!x' '!x'
-run 0 ../equals '{#e;x}<>->1' '{x}<>->1'
+run 0 ../equals '{[*0];x}<>->1' '{x}<>->1'
-run 0 ../equals '{x;#e}<>->1' '{x}<>-> 1'
+run 0 ../equals '{x;[*0]}<>->1' '{x}<>-> 1'
-run 0 ../equals '{#e;x;#e;#e}<>->1' '{x}<>->1'
+run 0 ../equals '{[*0];x;[*0];[*0]}<>->1' '{x}<>->1'
-run 0 ../equals '{#e;x;#e;x;#e}<>->1' '{x;x}<>->1'
+run 0 ../equals '{[*0];x;[*0];x;[*0]}<>->1' '{x;x}<>->1'
-run 0 ../equals '{x;x;x;#e;x;x}<>->1' '{x;x;x;x;x}<>->1'
+run 0 ../equals '{x;x;x;[*0];x;x}<>->1' '{x;x;x;x;x}<>->1'
 run 0 ../equals '{x;0;x;x;x}<>->1' '0'
 run 0 ../equals '{x;0;x;x;x}[]->1' '1'
 run 0 ../equals '{0*;1}<>->x' 'x'
-run 0 ../equals '{#e*;1}<>->x' 'x'
+run 0 ../equals '{[*0]*;1}<>->x' 'x'
 run 0 ../equals '{x;x}<>->FF(0)' '0'
 run 0 ../equals '{x;x}<>->GX(1)' '{x;x}<>->1'
 run 0 ../equals '{x;x}[]->GX(1)' '1'

src/tgbatest/ltl2tgba.test

@@ -67,7 +67,7 @@ check_psl '{(g;y;r)*}<>->x'
 check_psl 'G({(g;y;r)*}<>->x)'
 check_psl 'G({(a;b)*}<>->x)&G({(c;d)*}<>->y)'
 check_psl 'G({{a;b}*}[]->x)&G({{c;d}*}[]->y)' # try sub-braces
-check_psl '{(#e + a):c*:(#e + b)}<>->d'
+check_psl '{([*0] + a):c*:([*0] + b)}<>->d'
 check_psl '{a;e;f:(g*);h}<>->d'
 check_psl '{(a:b)* & (c*:d)}<>->e'
 check_psl '{(a:b)*}'
@@ -76,10 +76,9 @@ check_psl '{a;b}'
 check_psl '{(a;b)*}'
 check_psl 'G{(a;b)*}'
 check_psl '{a*}[]->{b*}'
-
 # Example from "Beyond Hardware Verification" by Glazberg, Moulin, Orni,
 # Ruah, Zarpas (2007).
-check_psl '{1*;req;ack;1}[]->{start;busy*;done}'
+check_psl '{1[*];req;ack;1}[]->{start;busy[*];done}'
 
 # Make sure 'a U (b U c)' has 3 states and 6 transitions,
 # before and after degeneralization.