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/ltlparse/ltlparse.yy

@@ -83,12 +83,16 @@ using namespace spot::ltl;
 %token OP_F "sometimes operator" OP_G "always operator"
 %token OP_X "next operator" OP_NOT "not operator"
 %token <str> ATOMIC_PROP "atomic proposition"
+%token OP_STAR "star operator" OP_CONCAT "concat operator"
 %token CONST_TRUE "constant true" CONST_FALSE "constant false"
-%token END_OF_INPUT "end of formula"
+%token END_OF_INPUT "end of formula" CONST_EMPTYWORD "empty word"
 %token OP_POST_NEG "negative suffix" OP_POST_POS "positive suffix"
 
 /* Priorities.  */
 
+/* Low priority regex operator. */
+%left OP_CONCAT
+
 /* Logical operators.  */
 %left OP_IMPLIES OP_EQUIV
 %left OP_OR
@@ -100,6 +104,9 @@ using namespace spot::ltl;
 %nonassoc OP_F OP_G
 %nonassoc OP_X
 
+/* High priority regex operator. */
+%nonassoc OP_STAR
+
 /* Not has the most important priority after Wring's `=0' and `=1'.  */
 %nonassoc OP_NOT
 
@@ -194,6 +201,8 @@ subformula: ATOMIC_PROP
 	      { $$ = constant::true_instance(); }
 	    | CONST_FALSE
 	      { $$ = constant::false_instance(); }
+	    | CONST_EMPTYWORD
+	      { $$ = constant::empty_word_instance(); }
 	    | PAR_OPEN subformula PAR_CLOSE
 	      { $$ = $2; }
 	    | PAR_OPEN error PAR_CLOSE
@@ -220,6 +229,10 @@ subformula: ATOMIC_PROP
 	      { $$ = multop::instance(multop::Or, $1, $3); }
 	    | subformula OP_OR error
               { missing_right_binop($$, $1, @2, "or operator"); }
+	    | subformula OP_CONCAT subformula
+	      { $$ = multop::instance(multop::Concat, $1, $3); }
+	    | subformula OP_CONCAT error
+              { missing_right_binop($$, $1, @2, "concat operator"); }
 	    | subformula OP_XOR subformula
 	      { $$ = binop::instance(binop::Xor, $1, $3); }
 	    | subformula OP_XOR error
@@ -264,6 +277,8 @@ subformula: ATOMIC_PROP
 	      { $$ = unop::instance(unop::Not, $2); }
 	    | OP_NOT error
 	      { missing_right_op($$, @1, "not operator"); }
+	    | subformula OP_STAR
+	      { $$ = unop::instance(unop::Star, $1); }
 ;
 
 %%