How to Parse Boolean Expressions and Construct Syntax Trees in C using Boost Spirit?

Boolean Expression Grammar Parser in C

Problem:

Parse a boolean expression given as a string and construct a tree representing the expression's syntax tree. The tree should follow the precedence rules (NOT, AND, XOR, OR).

Answer:

Using Boost Spirit:

1. Define an enum with tags representing the operators (NOT, AND, XOR, OR).

2. Define a recursive variant type (expr) to represent the tree nodes:

   • var: Variable name
   • unop: Unary operator
   • binop: Binary operator
3. Define a grammar using Boost Spirit Qi to parse the boolean expression.
4. Create a visitor class to traverse the parsed expression and print it as a tree.

Example Usage:

using namespace qi;
using namespace phoenix;

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;

struct parser : grammar<It, expr(), Skipper> {
    parser() : parser::base_type(expr_) {
        not_ = ...
        or_  = ...
        xor_ = ...
        and_ = ...

        simple = '(' > expr_ > ')' | var_;
        var_ = lexeme[+alpha];
    }
    qi::rule<It, var(), Skipper> var_;
    qi::rule<It, expr(), Skipper> not_, and_, xor_, or_, simple, expr_;
};

int main() {
    std::string input = "(a and b) xor ((c and d) or (a and b));";
    const char *f = input.c_str(), *l = f + input.size();

    expr result;
    bool ok = phrase_parse(f, l, parser() > ';', qi::space, result);
    if (ok) {
        std::cout << result << '\n';
    }
}

Result:

((a and b) xor ((c and d) or (a and b)))

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