How do I get this recursive rule to work?

Question

I want to parse (in first instance, recognize only, keeping symbols) LaTeX math. Right now, I'm having trouble with the super and subscripts, in combination with curly braces (e.g. a^{bc} and combinations thereof, I've got the basic a^b working just fine). A minimal example (as short as humanly possible while keeping readability):

#include <iostream>
  using std::cout;
#include <string>
  using std::string;

#include <boost/spirit/home/x3.hpp>
  namespace x3 = boost::spirit::x3;
  using x3::space;
  using x3::char_;
  using x3::lit;
  using x3::repeat;

x3::rule<struct scripts, string> scripts = "super- and subscripts";
x3::rule<struct braced_thing, string> braced_thing = "thing optionaly surrounded by curly braces";
x3::rule<struct superscript, string> superscript = "superscript";
x3::rule<struct subscript, string> subscript = "subscript";

// main rule: any number of items with or without braces
auto const scripts_def = *braced_thing;
// second level main rule: optional braces, and any number of characters or sub/superscripts
auto const braced_thing_def = -lit('{') >> *(subscript | superscript | repeat(1)[(char_ - "_^{}")]) >> -lit('}');
// superscript: things of the form a^b where a and b can be surrounded by curly braces
auto const superscript_def = braced_thing >> '^' >> braced_thing;
// subscript: things of the form a_b where a and b can be surrounded by curly braces
auto const subscript_def = braced_thing >> '_' >> braced_thing;

BOOST_SPIRIT_DEFINE(scripts)
BOOST_SPIRIT_DEFINE(braced_thing)
BOOST_SPIRIT_DEFINE(superscript)
BOOST_SPIRIT_DEFINE(subscript)

int main()
{
  const string input = "a^{b_x y}_z {v_x}^{{x^z}_y}";
  string output; // will only contain the characters as the grammar is defined above
  auto first = input.begin();
  auto last = input.end();
  const bool result = x3::phrase_parse(first, last,
                                       scripts,
                                       space,
                                       output);
  if(first != last)
    std::cout << "partial match only:\n" << output << '\n';
  else if(!result)
    std::cout << "parse failed!\n";
  else
    std::cout << "parsing succeeded:\n" << output << '\n';
}

It's also Available on Coliru.

Problem is, this segfaults (I'm sure for obvious reasons) and I have no other way of, well, expressing this in an... expression grammar.

Answer 1

I haven't looked at the suggestion by @cv_and_he yet, instead live-debugging your grammar myself. I came up with this:

auto token        = lexeme [ +~char_("_^{} \t\r\n") ];
auto simple       = '{' >> sequence >> '}' | token;
auto expr         = lexeme [ simple % char_("_^") ];
auto sequence_def = expr % +space;

What brought me there was basically a step-by-step rethink/imagining of what the actual grammar looks like.

It took me two tries to think of the right way to get "a b" parsing (at first I "hacked" it a just another subscript operator in char_(" _^") but I got the impression that would not lead to an AST as you expect it. The clue being you used a skipper for the space).

For now, there's no AST, but we just "reap" the raw string matched using.. x3::raw[...].

Live Coliru

//#define BOOST_SPIRIT_X3_DEBUG
#include <iostream>
#include <string>

#include <boost/spirit/home/x3.hpp>
namespace x3 = boost::spirit::x3;

namespace grammar {
    using namespace x3;
    rule<struct _s> sequence { "sequence" };

    auto simple  = rule<struct _s> {"simple"} = '{' >> sequence >> '}' | lexeme [ +~char_("_^{} \t\r\n") ];
    auto expr    = rule<struct _e> {"expr"}   = lexeme [ simple % char_("_^") ];
    auto sequence_def = expr % +space;
    BOOST_SPIRIT_DEFINE(sequence)
}

int main() {
    for (const std::string input : {
            "a",
            "a^b",     "a_b",     "a b",
            "{a}^{b}", "{a}_{b}", "{a} {b}",
            "a^{b_x y}",
            "a^{b_x y}_z {v_x}^{{x^z}_y}"
        })
    {
        std::string output; // will only contain the characters as the grammar is defined above
        auto first  = input.begin(), last = input.end();
        bool result = x3::parse(first, last, x3::raw[grammar::sequence], output);

        if (result)
            std::cout << "Parse success: '" << output << "'\n";
        else
            std::cout << "parse failed!\n";

        if (last!=first)
            std::cout << "remaining unparsed: '" << std::string(first, last) << "'\n";
    }
}

Output:

Parse success: 'a'
Parse success: 'a^b'
Parse success: 'a_b'
Parse success: 'a b'
Parse success: '{a}^{b}'
Parse success: '{a}_{b}'
Parse success: '{a} {b}'
Parse success: 'a^{b_x y}'
Parse success: 'a^{b_x y}_z {v_x}^{{x^z}_y}'

Output with debug information enabled:

<sequence>
<try>a</try>
<expr>
    <try>a</try>
    <simple>
    <try>a</try>
    <success></success>
    </simple>
    <success></success>
</expr>
<success></success>
</sequence>
Parse success: 'a'
<sequence>
<try>a^b</try>
<expr>
    <try>a^b</try>
    <simple>
    <try>a^b</try>
    <success>^b</success>
    </simple>
    <simple>
    <try>b</try>
    <success></success>
    </simple>
    <success></success>
</expr>
<success></success>
</sequence>
Parse success: 'a^b'
<sequence>
<try>a_b</try>
<expr>
    <try>a_b</try>
    <simple>
    <try>a_b</try>
    <success>_b</success>
    </simple>
    <simple>
    <try>b</try>
    <success></success>
    </simple>
    <success></success>
</expr>
<success></success>
</sequence>
Parse success: 'a_b'
<sequence>
<try>a b</try>
<expr>
    <try>a b</try>
    <simple>
    <try>a b</try>
    <success> b</success>
    </simple>
    <success> b</success>
</expr>
<expr>
    <try>b</try>
    <simple>
    <try>b</try>
    <success></success>
    </simple>
    <success></success>
</expr>
<success></success>
</sequence>
Parse success: 'a b'
<sequence>
<try>{a}^{b}</try>
<expr>
    <try>{a}^{b}</try>
    <simple>
    <try>{a}^{b}</try>
    <sequence>
        <try>a}^{b}</try>
        <expr>
        <try>a}^{b}</try>
        <simple>
            <try>a}^{b}</try>
            <success>}^{b}</success>
        </simple>
        <success>}^{b}</success>
        </expr>
        <success>}^{b}</success>
    </sequence>
    <success>^{b}</success>
    </simple>
    <simple>
    <try>{b}</try>
    <sequence>
        <try>b}</try>
        <expr>
        <try>b}</try>
        <simple>
            <try>b}</try>
            <success>}</success>
        </simple>
        <success>}</success>
        </expr>
        <success>}</success>
    </sequence>
    <success></success>
    </simple>
    <success></success>
</expr>
<success></success>
</sequence>
Parse success: '{a}^{b}'
<sequence>
<try>{a}_{b}</try>
<expr>
    <try>{a}_{b}</try>
    <simple>
    <try>{a}_{b}</try>
    <sequence>
        <try>a}_{b}</try>
        <expr>
        <try>a}_{b}</try>
        <simple>
            <try>a}_{b}</try>
            <success>}_{b}</success>
        </simple>
        <success>}_{b}</success>
        </expr>
        <success>}_{b}</success>
    </sequence>
    <success>_{b}</success>
    </simple>
    <simple>
    <try>{b}</try>
    <sequence>
        <try>b}</try>
        <expr>
        <try>b}</try>
        <simple>
            <try>b}</try>
            <success>}</success>
        </simple>
        <success>}</success>
        </expr>
        <success>}</success>
    </sequence>
    <success></success>
    </simple>
    <success></success>
</expr>
<success></success>
</sequence>
Parse success: '{a}_{b}'
<sequence>
<try>{a} {b}</try>
<expr>
    <try>{a} {b}</try>
    <simple>
    <try>{a} {b}</try>
    <sequence>
        <try>a} {b}</try>
        <expr>
        <try>a} {b}</try>
        <simple>
            <try>a} {b}</try>
            <success>} {b}</success>
        </simple>
        <success>} {b}</success>
        </expr>
        <success>} {b}</success>
    </sequence>
    <success> {b}</success>
    </simple>
    <success> {b}</success>
</expr>
<expr>
    <try>{b}</try>
    <simple>
    <try>{b}</try>
    <sequence>
        <try>b}</try>
        <expr>
        <try>b}</try>
        <simple>
            <try>b}</try>
            <success>}</success>
        </simple>
        <success>}</success>
        </expr>
        <success>}</success>
    </sequence>
    <success></success>
    </simple>
    <success></success>
</expr>
<success></success>
</sequence>
Parse success: '{a} {b}'
<sequence>
<try>a^{b_x y}</try>
<expr>
    <try>a^{b_x y}</try>
    <simple>
    <try>a^{b_x y}</try>
    <success>^{b_x y}</success>
    </simple>
    <simple>
    <try>{b_x y}</try>
    <sequence>
        <try>b_x y}</try>
        <expr>
        <try>b_x y}</try>
        <simple>
            <try>b_x y}</try>
            <success>_x y}</success>
        </simple>
        <simple>
            <try>x y}</try>
            <success> y}</success>
        </simple>
        <success> y}</success>
        </expr>
        <expr>
        <try>y}</try>
        <simple>
            <try>y}</try>
            <success>}</success>
        </simple>
        <success>}</success>
        </expr>
        <success>}</success>
    </sequence>
    <success></success>
    </simple>
    <success></success>
</expr>
<success></success>
</sequence>
Parse success: 'a^{b_x y}'
<sequence>
<try>a^{b_x y}_z {v_x}^{{</try>
<expr>
    <try>a^{b_x y}_z {v_x}^{{</try>
    <simple>
    <try>a^{b_x y}_z {v_x}^{{</try>
    <success>^{b_x y}_z {v_x}^{{x</success>
    </simple>
    <simple>
    <try>{b_x y}_z {v_x}^{{x^</try>
    <sequence>
        <try>b_x y}_z {v_x}^{{x^z</try>
        <expr>
        <try>b_x y}_z {v_x}^{{x^z</try>
        <simple>
            <try>b_x y}_z {v_x}^{{x^z</try>
            <success>_x y}_z {v_x}^{{x^z}</success>
        </simple>
        <simple>
            <try>x y}_z {v_x}^{{x^z}_</try>
            <success> y}_z {v_x}^{{x^z}_y</success>
        </simple>
        <success> y}_z {v_x}^{{x^z}_y</success>
        </expr>
        <expr>
        <try>y}_z {v_x}^{{x^z}_y}</try>
        <simple>
            <try>y}_z {v_x}^{{x^z}_y}</try>
            <success>}_z {v_x}^{{x^z}_y}</success>
        </simple>
        <success>}_z {v_x}^{{x^z}_y}</success>
        </expr>
        <success>}_z {v_x}^{{x^z}_y}</success>
    </sequence>
    <success>_z {v_x}^{{x^z}_y}</success>
    </simple>
    <simple>
    <try>z {v_x}^{{x^z}_y}</try>
    <success> {v_x}^{{x^z}_y}</success>
    </simple>
    <success> {v_x}^{{x^z}_y}</success>
</expr>
<expr>
    <try>{v_x}^{{x^z}_y}</try>
    <simple>
    <try>{v_x}^{{x^z}_y}</try>
    <sequence>
        <try>v_x}^{{x^z}_y}</try>
        <expr>
        <try>v_x}^{{x^z}_y}</try>
        <simple>
            <try>v_x}^{{x^z}_y}</try>
            <success>_x}^{{x^z}_y}</success>
        </simple>
        <simple>
            <try>x}^{{x^z}_y}</try>
            <success>}^{{x^z}_y}</success>
        </simple>
        <success>}^{{x^z}_y}</success>
        </expr>
        <success>}^{{x^z}_y}</success>
    </sequence>
    <success>^{{x^z}_y}</success>
    </simple>
    <simple>
    <try>{{x^z}_y}</try>
    <sequence>
        <try>{x^z}_y}</try>
        <expr>
        <try>{x^z}_y}</try>
        <simple>
            <try>{x^z}_y}</try>
            <sequence>
            <try>x^z}_y}</try>
            <expr>
                <try>x^z}_y}</try>
                <simple>
                <try>x^z}_y}</try>
                <success>^z}_y}</success>
                </simple>
                <simple>
                <try>z}_y}</try>
                <success>}_y}</success>
                </simple>
                <success>}_y}</success>
            </expr>
            <success>}_y}</success>
            </sequence>
            <success>_y}</success>
        </simple>
        <simple>
            <try>y}</try>
            <success>}</success>
        </simple>
        <success>}</success>
        </expr>
        <success>}</success>
    </sequence>
    <success></success>
    </simple>
    <success></success>
</expr>
<success></success>
</sequence>
Parse success: 'a^{b_x y}_z {v_x}^{{x^z}_y}'