How to Efficiently Parse Boolean Expressions with Boost Spirit?

Boolean Expression Parsing using Boost Spirit

Problem:

How to efficiently parse Boolean expressions (using C ) that adhere to precedence rules, including operations like AND, OR, XOR, and NOT. The goal is to construct a tree-like representation of the expression that preserves the precedence order.

Solution:

1. Abstract Data Type (ADT) of Expression Tree:

To represent the expression tree, an ADT is defined using boost::variant's recursive variant support:

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;

Where each type in the variant represents a node in the expression tree:

• var: Leaf node representing a variable
• unop: Unary operator node (e.g., NOT)
• binop: Binary operator node (e.g., AND, XOR, OR)

2. Grammar Rules:

A context-free grammar is defined to specify the syntax rules for the Boolean expressions:

struct parser : qi::grammar<It, expr(), Skipper>
{
    parser() : parser::base_type(expr_)
    {
        using namespace qi;
        expr_  = or_.alias();
        ...
    }
};

3. Parse and Construct the Tree:

Using Boost Spirit, a parser is generated based on the grammar rules. The parser consumes the input expression and constructs the corresponding expression tree.

expr result;
bool ok = qi::phrase_parse(f, l, p > ';', qi::space, result);

4. Printing the Expression Tree:

A tree print visitor is implemented to display the expression tree in a user-friendly manner:

struct tree_print : boost::static_visitor<void>
{
    void operator()(const binop<op_and>&amp; b) const { print("and ", b.oper1, b.oper2); }
    ...
};

Example Usage:

std::cout << "result: " << result << "\n";

Output:

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

This approach provides a robust and extensible framework for parsing Boolean expressions and building a structured representation for further processing or evaluation.

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