I have a parser, which parses boolean expressions. How I should modify it to support "implied-And" e.g "A1 A2" which must be parsed as A1 and A2? I've tried to change the "and_" rule to support it, but it started to treat "xor" as a variable even if it was used as an operation. Excluding of "xor" from the rule of var with (!(" xor ") >>) still fails for simple expressions.
The source code :
#include <boost/spirit/include/qi.hpp>
#include <boost/spirit/include/phoenix.hpp>
#include <boost/spirit/include/phoenix_operator.hpp>
#include <boost/variant/recursive_wrapper.hpp>
namespace qi    = boost::spirit::qi;
namespace phx   = boost::phoenix;
struct op_or  {};
struct op_and {};
struct op_xor {};
struct op_not {};
typedef std::string var;
template <typename tag> struct binop;
template <typename tag> struct unop;
typedef boost::variant<var,
    boost::recursive_wrapper<unop <op_not> >,
    boost::recursive_wrapper<binop<op_and> >,
    boost::recursive_wrapper<binop<op_xor> >,
    boost::recursive_wrapper<binop<op_or> >
    > expr;
template <typename tag> struct binop
{
    explicit binop(const expr& l, const expr& r) : oper1(l), oper2(r) { }
    expr oper1, oper2;
};
template <typename tag> struct unop
{
    explicit unop(const expr& o) : oper1(o) { }
    expr oper1;
};
struct printer : boost::static_visitor<void>
{
    printer(std::ostream& os) : _os(os) {}
    std::ostream& _os;
    void operator()(const var& v) const { _os << v; }
    void operator()(const binop<op_and>& b) const { print(" & ", b.oper1, b.oper2); }
    void operator()(const binop<op_or >& b) const { print(" | ", b.oper1, b.oper2); }
    void operator()(const binop<op_xor>& b) const { print(" ^ ", b.oper1, b.oper2); }
    void print(const std::string& op, const expr& l, const expr& r) const
    {
        _os << "(";
        boost::apply_visitor(*this, l);
        _os << op;
        boost::apply_visitor(*this, r);
        _os << ")";
    }
    void operator()(const unop<op_not>& u) const
    {
        _os << "(";
        _os << "!";
        boost::apply_visitor(*this, u.oper1);
        _os << ")";
    }
};
std::ostream& operator<<(std::ostream& os, const expr& e)
{ boost::apply_visitor(printer(os), e); return os; }
template <typename It, typename Skipper = qi::space_type>
struct parser : qi::grammar<It, expr(), Skipper>
{
parser() : parser::base_type(expr_)
{
    using namespace qi;
    expr_  = or_.alias();
    or_  = xor_ [_val = _1] >> *(("or"  >> xor_ ) [ _val = phx::construct<binop<op_or >>(_val, _1) ]) | xor_ [ _val = _1 ];
    xor_ = and_ [_val = _1] >> *(("xor" >> and_) [ _val = phx::construct<binop<op_xor>>(_val, _1) ]) | and_   [ _val = _1 ];
    and_ = not_ [_val = _1] >> *(("and" >> not_) [ _val = phx::construct<binop<op_and>>(_val, _1) ]) | not_ [ _val = _1 ];
    not_ = ("not" > simple       ) [ _val = phx::construct<unop <op_not>>(_1)     ] | simple [ _val = _1 ];
    simple = (('(' > expr_ > ')') | var_);
    var_ = qi::lexeme[ +alpha ];
    BOOST_SPIRIT_DEBUG_NODE(expr_);
    BOOST_SPIRIT_DEBUG_NODE(or_);
    BOOST_SPIRIT_DEBUG_NODE(xor_);
    BOOST_SPIRIT_DEBUG_NODE(and_);
    BOOST_SPIRIT_DEBUG_NODE(not_);
    BOOST_SPIRIT_DEBUG_NODE(simple);
    BOOST_SPIRIT_DEBUG_NODE(var_);
}
private:
qi::rule<It, var() , Skipper> var_;
qi::rule<It, expr(), Skipper> not_, and_, xor_, or_, simple, expr_;
};
int main()
{
for (auto& input : std::list<std::string> {
        "(a and b) xor ((c and d) or (a and b));",
        "a and b xor c and d or a and b;",
        /// Simpler tests:
        "a and b;",
        "a or b;",
        "xor_in1 xor xor_in2;",
        "xorin1 xor xorin2;",
        "and1 xor xor;",
        "not a;",
        "not a and b;",
        "not (a and b);",
        "a or b or c;",
        })
{
    auto f(std::begin(input)), l(std::end(input));
    parser<decltype(f)> p;
    try
    {
        expr result;
        bool ok = qi::phrase_parse(f,l,p > ';',qi::space,result);
        if (!ok)
            std::cerr << "invalid input\n";
        else
            std::cout << "result: " << result << "\n";
    } catch (const qi::expectation_failure<decltype(f)>& e)
    {
        std::cerr << "expectation_failure at '" << std::string(e.first, e.last) << "'\n";
    }
    if (f!=l) std::cerr << "unparsed: '" << std::string(f,l) << "'\n";
    }
    return 0;
}
 
     
    