I think you can employ right recursion to get what you want:
factor= expo >> -('^' >> factor [&do_power]);
I'm not sure about the desired order of evaluation; you could want something like
factor= expo [&do_power] >> -('^' >> factor);
instead.
Here's a simple test program showing it how it handles 2^(6/2)^4+1
:
Edit See it LIVE on Coliru
Type an expression...or [q or Q] to quit
2^(6/2)^4+1
push 2
push 6
push 2
divide
push 4
exp
exp
push 1
add
-------------------------
Parsing succeeded
Full Code
#define BOOST_SPIRIT_NO_PREDEFINED_TERMINALS
#define BOOST_SPIRIT_DEBUG
#include <boost/spirit/include/qi.hpp>
namespace client
{
namespace qi = boost::spirit::qi;
namespace ascii = boost::spirit::ascii;
///////////////////////////////////////////////////////////////////////////////
// Semantic actions
////////////////////////////////////////////////////////1///////////////////////
namespace
{
void do_int(int n) { std::cout << "push " << n << std::endl; }
void do_add() { std::cout << "add\n"; }
void do_subt() { std::cout << "subtract\n"; }
void do_mult() { std::cout << "mult\n"; }
void do_div() { std::cout << "divide\n"; }
void do_power() { std::cout << "exp\n"; }
void do_neg() { std::cout << "negate\n"; }
}
///////////////////////////////////////////////////////////////////////////////
// Our calculator grammar
///////////////////////////////////////////////////////////////////////////////
template <typename Iterator>
struct calculator : qi::grammar<Iterator, ascii::space_type>
{
calculator() : calculator::base_type(expression)
{
qi::uint_type uint_;
expression = term
>> *( ('+' >> term [&do_add])
| ('-' >> term [&do_subt])
)
;
term = factor
>> *( ( '*' >> factor [&do_mult])
| ('x' >> factor [&do_mult])
| ('/' >> factor [&do_div])
);
factor= expo >> -('^' >> factor [&do_power]);
expo = uint_ [&do_int]
| '(' >> expression >> ')'
| ('-' >> expo[&do_neg])
| ('+' >> expo)
;
BOOST_SPIRIT_DEBUG_NODES((expression)(term)(factor)(expo));
}
private:
qi::rule<Iterator, ascii::space_type> expression, term, factor, expo;
};
}
///////////////////////////////////////////////////////////////////////////////
// Main program
///////////////////////////////////////////////////////////////////////////////
int
main()
{
std::cout << "/////////////////////////////////////////////////////////\n\n";
std::cout << "Expression parser...\n\n";
std::cout << "/////////////////////////////////////////////////////////\n\n";
std::cout << "Type an expression...or [q or Q] to quit\n\n";
typedef std::string::const_iterator iterator_type;
typedef client::calculator<iterator_type> calculator;
boost::spirit::ascii::space_type space; // Our skipper
calculator calc; // Our grammar
std::string str;
while (std::getline(std::cin, str))
{
if (str.empty() || str[0] == 'q' || str[0] == 'Q')
break;
std::string::const_iterator iter = str.begin();
std::string::const_iterator end = str.end();
bool r = phrase_parse(iter, end, calc, space);
if (r && iter == end)
{
std::cout << "-------------------------\n";
std::cout << "Parsing succeeded\n";
std::cout << "-------------------------\n";
}
else
{
std::string rest(iter, end);
std::cout << "-------------------------\n";
std::cout << "Parsing failed\n";
std::cout << "stopped at: \" " << rest << "\"\n";
std::cout << "-------------------------\n";
}
}
std::cout << "Bye... :-) \n\n";
return 0;
}