Introduce rational operators and trivial simplification rules.

Trivial simplifications rules (such as "FFa=Fa" or "x&1=x")
are performed any time a formule is instanciated.

* src/ltlast/constant.hh, src/ltlast/constant.cc
(true_instance, true_instance_): Declare the true_instance_ as a
static member, and move true_instance() into the .hh so it gets
inlined.  Have true_instance_ as a class variable will ensure that
it is the first formula instantiated.  Binop simplifications rely
on this to order arguments.
(false_instance, false_instance_): Likewise.
(empty_word_instance, empty_word_instance_): New method and static
member.
* src/ltlast/formula.hh (formula::formula): If max_count_ ever
loops, skip the first three values so that constants always have
smaller hash codes.
* src/ltlast/binop.hh, src/ltlast/binop.cc (instance): Add
simplifications and document them.
* src/ltlast/multop.hh (multop::Concat): New operator.
* src/ltlast/multop.cc (op_name): Handle Concat.
(instance): Inline Concat arguments without reordering.  Handle
absorbent and neutral elements for all operators.
* src/ltlast/unop.hh (unop::Star): New operator.
* src/ltlast/unop.cc (op_name): Handle Star.
(instance): Handle Star, and add trivial simplifications for
other unary operators.
* src/ltlparse/ltlparse.yy (OP_CONCAT, OP_STAR, CONST_EMPTYWORD):
Declare these new operators and add rules for them.
* src/ltlparse/ltlscan.ll (OP_CONCAT, OP_STAR, CONST_EMPTYWORD):
Output these new operators.
* src/ltltest/equals.test: New tests.
* src/ltltest/parse.test: Remove redundant test.
* src/ltltest/tunabbrev.test, src/tgbatest/emptchk.test: Adjust tests.
* src/ltlvisit/basicreduce.cc, src/ltlvisit/contain.cc,
src/ltlvisit/nenoform.cc, src/ltlvisit/reduce.cc,
src/ltlvisit/syntimpl.cc, src/ltlvisit/tostring.cc,
src/ltlvisit/tunabbrev.cc: Complete visitors to handle new
operators.
* src/ltltest/nenoform.test: More tests.
* src/ltlvisit/lunabbrev.cc (unabbreviate_logic_visitor::visit):
Clone formulae before instance() function actually have a chance
to destroy them.
* src/tgba/formula2bdd.cc, src/tgbaalgos/eltl2tgba_lacim.cc,
src/tgbaalgos/ltl2taa.cc, src/tgbaalgos/ltl2tgba_fm.cc,
src/tgbaalgos/ltl2tgba_lacim.cc: Adjust switches to assert on new
operators.

src/ltlast/binop.cc

@@ -24,6 +24,8 @@
 #include <cassert>
 #include <utility>
 #include "binop.hh"
+#include "unop.hh"
+#include "constant.hh"
 #include "visitor.hh"
 #include <iostream>
 
@@ -127,25 +129,127 @@ namespace spot
 
     binop::map binop::instances;
 
-    binop*
+    formula*
     binop::instance(type op, formula* first, formula* second)
     {
       // Sort the operands of commutative operators, so that for
       // example the formula instance for 'a xor b' is the same as
       // that for 'b xor a'.
+
+      /// Trivial identities:
       switch (op)
 	{
 	case Xor:
+	  {
+	    // Xor is commutative: sort operands.
+	    formula_ptr_less_than cmp;
+	    if (cmp(second, first) > 0)
+	      std::swap(first, second);
+	  }
+	  //   - (1 ^ Exp) = !Exp
+	  //   - (0 ^ Exp) = Exp
+	  if (first == constant::true_instance())
+	    return unop::instance(unop::Not, second);
+	  if (first == constant::false_instance())
+	    return second;
+	  // We expect constants to appear first, because they are
+	  // instantiated first.
+	  assert(second != constant::false_instance());
+	  assert(second != constant::true_instance());
+	  break;
 	case Equiv:
-	  if (second < first)
-	    std::swap(first, second);
+	  {
+	    // Equiv is commutative: sort operands.
+	    formula_ptr_less_than cmp;
+	    if (cmp(second, first) > 0)
+	      std::swap(first, second);
+	  }
+	  //   - (0 <=> Exp) = !Exp
+	  //   - (1 <=> Exp) = Exp
+	  if (first == constant::false_instance())
+	    return unop::instance(unop::Not, second);
+	  if (first == constant::true_instance())
+	    return second;
+	  // We expect constants to appear first, because they are
+	  // instantiated first.
+	  assert(second != constant::false_instance());
+	  assert(second != constant::true_instance());
 	  break;
 	case Implies:
+	  ///   - (1 => Exp) = Exp
+	  ///   - (0 => Exp) = 0
+	  ///   - (Exp => 1) = 1
+	  ///   - (Exp => 0) = !Exp
+	  if (first == constant::true_instance())
+	    return second;
+	  if (first == constant::false_instance())
+	    {
+	      second->destroy();
+	      return first;
+	    }
+	  if (second == constant::true_instance())
+	    {
+	      first->destroy();
+	      return second;
+	    }
+	  if (second == constant::false_instance())
+	    return unop::instance(unop::Not, first);
+	  break;
 	case U:
-	case R:
+	  ///   - (Exp U 1) = 1
+	  ///   - (Exp U 0) = 0
+	  ///   - (0 U Exp) = Exp
+	  if (second == constant::true_instance()
+	      || second == constant::false_instance()
+	      || first == constant::false_instance())
+	    {
+	      first->destroy();
+	      return second;
+	    }
+	  break;
 	case W:
+	  ///   - (Exp W 1) = 1
+	  ///   - (0 W Exp) = Exp
+	  ///   - (1 W Exp) = 1
+	  if (second == constant::true_instance()
+	      || first == constant::false_instance())
+	    {
+	      first->destroy();
+	      return second;
+	    }
+	  if (first == constant::true_instance())
+	    {
+	      second->destroy();
+	      return first;
+	    }
+	  break;
+	case R:
+	  ///   - (Exp R 1) = 1
+	  ///   - (Exp R 0) = 0
+	  ///   - (1 R Exp) = Exp
+	  if (second == constant::true_instance()
+	      || second == constant::false_instance()
+	      || first == constant::true_instance())
+	    {
+	      first->destroy();
+	      return second;
+	    }
+	  break;
 	case M:
-	  // Non commutative operators.
+	  ///   - (Exp M 0) = 0
+	  ///   - (1 M Exp) = Exp
+	  ///   - (0 M Exp) = 0
+	  if (second == constant::false_instance()
+	      || first == constant::true_instance())
+	    {
+	      first->destroy();
+	      return second;
+	    }
+	  if (first == constant::false_instance())
+	    {
+	      second->destroy();
+	      return first;
+	    }
 	  break;
 	}