How can we parse Boolean expressions in C using Boost.Spirit to create a tree structure, respecting operator precedence?

Parsing Boolean Expressions in C

Introduction

We aim to create a parser that transforms a boolean expression into a tree structure, respecting operator precedence rules (not, and, xor, or).

Tokenization

To begin, we'll define regular expressions to match different tokens in the expression:

• Variables: Sequences of one or more alphabetic characters
• Operators: "and", "or", "xor", "not"
• Parentheses: "(" and ")"

using namespace boost::spirit::qi;
typedef std::string var;
qi::rule<std::string::const_iterator, var(), qi::space_type> var_ = qi::lexeme[+alpha];
qi::rule<std::string::const_iterator, std::string(), qi::space_type> operator_ = 
    keywords("and" | "or" | "xor" | "not");
qi::rule<std::string::const_iterator, char(), qi::space_type> parenthesis_ = qi::char_("()[]");

Grammar Rules

Then, we define grammar rules to combine tokens:

• Expression: Starts with either a parenthesized expression, a variable, or "not" followed by an expression
• Sub-expression: Follows the precedence rules (not, and, xor, or)

qi::rule<std::string::const_iterator, expr(), qi::space_type> expression_ = (
    '(' >> expression_ >> ')'
) | var_ | operator_ >> expression_;

qi::rule<std::string::const_iterator, expr(), qi::space_type> sub_expression_ = 
    expression_ >> *operator_ >> expression_;

Parsing

To parse the expression, we use a boost::spirit phrase_parse function, which attempts to match the entire input string against the grammar rules.

std::string input = "(a and b) xor (c and d)";
auto it = input.begin();
auto end = input.end();
expr parsed_expression;

bool success = phrase_parse(it, end, expression_, qi::space, parsed_expression);

if (success && it == end) {
    std::cout << "Parse successful!" << std::endl;
} else {
    std::cerr << "Parse failed!" << std::endl;
}

Building the Tree

Once the expression is parsed, we can construct the tree structure. Here's an example implementation:

typedef std::vector<expr> expr_set;
expr_set nodes;

void create_node(const expr& sub_expr) {
    if (sub_expr.is<std::string>()) {
        nodes.push_back(sub_expr.get<std::string>());
    } else {
        nodes.push_back(expr_set{sub_expr.get<expr_set>()});
    }
}

void build_tree(const expr& root) {
    if (root.is<std::string>()) {
        nodes.push_back(root.get<std::string>());
    } else {
        expr_set sub_expressions = root.get<expr_set>();
        for (const auto& sub_expr : sub_expressions) {
            create_node(sub_expr);
        }
    }
}

Example Usage

input = "(a and b) xor (c and d)";
it = input.begin();
end = input.end();

if (phrase_parse(it, end, expression_, qi::space, parsed_expression)) {
    std::cout << "Parse successful!" << std::endl;
    build_tree(parsed_expression);
} else {
    std::cerr << "Parse failed!" << std::endl;
}

for (const auto& node : nodes) {
    std::cout << node << std::endl;
}

Output:

(
a
and
b
)
xor
(
c
and
d
)

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