c++ - 使用 Boost::Spirit 从中缀到前缀的 n 元 bool 语法转换？

Question

我需要使用 Boost::Spirit 将如下所示的中缀表示法转换为 n 元前缀表示法，但我无法基于 https://stackoverflow.com/a/8707598/1816477 的答案进行构建等

这就是我要解析的内容:

not (xyz='a' or xyz='b' or xyz='c') and abc='s' xor (pqr ='v' and xyz='d')

这个 LISP 风格的格式是我试图提供的输出(不要介意缩进):

(xor (and (= pqr 'v') (= xyz 'd'))
     (and (= abc 's')
          (not (or (= xyz 'a')
                   (= xyz 'b')
                   (= xyz 'c')))))

因此，我尝试解析的术语由前缀表达式(not <expression>)和中缀表达式(<expression> and <expression> and ... 等)组成，即:赋值、否定和 n 元 ands、ors、xors 等，暗示运算符优先级(或 < xor < 和 < assignment < 否定)。

我不擅长的是语法正确。输出到合适的 boost::variant代表我认为我能够完成的已解析 bool 表达式。我正在考虑这样的输出结构:

struct prefixExpr;
struct infixExpr;

typedef boost::variant<
    std::string,    // identifiers, values etc.
    boost::recursive_wrapper<prefixExpr>,   // e.g. negation
    boost::recursive_wrapper<infixExpr>     // assignment, and, or, xor etc.
> expression;

struct prefixExpr {
    std::string op;    // currently only "not"
    expression expr;
};
BOOST_FUSION_ADAPT_STRUCT(prefixExpr, op, expr)

struct infixExpr {
    std::string op;    // "and", "or", "xor", "="
    std::vector<expression> exprs;
};
BOOST_FUSION_ADAPT_STRUCT(infixExpr, op, exprs)

我需要做什么才能像上面提到的那样解析表达式并将它们转换为前缀表示法？

我使用的是 boost 1.67.0(撰写本文时最新版本)和 Visual Studio 15.7.3(也是撰写本文时最新版本)。

Answer 1

代码并不完美，但应该很容易理解:

#include <boost/variant.hpp>
#include <boost/spirit/home/x3.hpp>
#include <vector>
#include <string>
#include <iostream>


struct id : std::string {};
struct value : std::string {};
struct nary_expr;

using expr = boost::variant<
    id, value,
    boost::recursive_wrapper<nary_expr>
>;


struct nary_expr
{
    std::string op;
    std::vector<expr> exprs;
};


namespace x3 = boost::spirit::x3;

auto compose_nary_expr = [](auto& ctx)
{
    //auto&& [left, tail] = x3::_attr(ctx);
    auto&& left = boost::fusion::at_c<0>(x3::_attr(ctx));
    auto&& tail = boost::fusion::at_c<1>(x3::_attr(ctx));

    if (tail.size() == 0) {
        x3::_val(ctx) = left;
        return;
    }

    // left associativity
    auto op = boost::fusion::at_c<0>(tail[0]);
    std::vector<expr> exprs = { left, boost::fusion::at_c<1>(tail[0]) };
    for (std::size_t i = 1; i < tail.size(); ++i) {
        // same priority but different operator
        auto&& next_op = boost::fusion::at_c<0>(tail[i]);
        if (op != next_op) {
            exprs = std::vector<expr>{ nary_expr{ op, std::move(exprs) } };
            op = next_op;
        }
        exprs.push_back(boost::fusion::at_c<1>(tail[i]));
    }
    x3::_val(ctx) = nary_expr{ op, std::move(exprs) };
};

x3::rule<class prec4_expr_rule, expr> const prec4_expr("prec4_expr");
x3::rule<class prec3_expr_rule, expr> const prec3_expr("prec3_expr");
x3::rule<class prec2_expr_rule, expr> const prec2_expr("prec2_expr");
x3::rule<class prec1_expr_rule, expr> const prec1_expr("prec1_expr");
x3::rule<class prec0_expr_rule, expr> const prec0_expr("prec0_expr");

auto const prec4_expr_def = prec4_expr = (
    prec3_expr
    >> *(   (x3::string("or") > prec3_expr)
        )
    )[compose_nary_expr];

auto const prec3_expr_def = prec3_expr = (
    prec2_expr
    >> *(   (x3::string("xor") > prec2_expr)
        )
    )[compose_nary_expr];

auto const prec2_expr_def = prec2_expr = (
    prec1_expr
    >> *(   (x3::string("and") > prec1_expr)
        )
    )[compose_nary_expr];


auto compose_binary_expr = [](auto& ctx)
{
    auto&& rhs = boost::fusion::at_c<0>(x3::_attr(ctx));
    auto&& tail = boost::fusion::at_c<1>(x3::_attr(ctx));
    if (tail.size() > 0) {
        auto&& op = boost::fusion::at_c<0>(tail[0]);
        auto&& lhs = boost::fusion::at_c<1>(tail[0]);
        x3::_val(ctx) = nary_expr{ op, { rhs, lhs } };
    }
    else {
        x3::_val(ctx) = rhs;
    }
};


// should use optional, but something wrong with spirit
auto const prec1_expr_def = prec1_expr = (
    prec0_expr >> *(x3::string("=") > prec0_expr)
    )[compose_binary_expr];



x3::rule<class not_expr_rule, expr> const not_expr("not_expr");

auto compose_unary_expr = [](auto& ctx)
{
    //auto&& [op, expr] = x3::_attr(ctx);
    auto&& op = boost::fusion::at_c<0>(x3::_attr(ctx));
    auto&& expr = boost::fusion::at_c<1>(x3::_attr(ctx));
    x3::_val(ctx) = nary_expr{ op, { expr } };
};

auto const not_expr_def = not_expr = (x3::string("not") > prec0_expr)[compose_unary_expr];
auto const id_term = x3::rule<class id_r, id>{} = x3::lexeme[x3::alpha >> *x3::alnum];
auto const value_term = x3::rule<class value_r, value>{} = x3::lexeme["'" > +~x3::char_('\'') >> "'"];

auto const prec0_expr_def =
      value_term
    | ( '(' > prec4_expr >> ')' )
    | not_expr
    | id_term
    ;


BOOST_SPIRIT_DEFINE(
    prec0_expr
  , prec1_expr
  , prec2_expr
  , prec3_expr
  , prec4_expr
  , not_expr
);


struct indent
{
    std::size_t cur;
};

indent operator+(indent lhs, std::size_t rhs)
{
    return { lhs.cur + rhs };
}

std::ostream& operator<<(std::ostream& os, indent const& v)
{
    for (unsigned i = 0; i < v.cur; ++i) os << ' ';
    return os;
}

struct is_simple
{
    template <typename T>
    bool operator()(T const&) const
    {
        return std::is_same<T, id>::value || std::is_same<T, value>::value;
    }
};

struct printer
{
    indent indent_;

    void operator()(id const& v)
    {
        std::cout << v;
    }

    void operator()(value const& v)
    {
        std::cout << '\'' << v << '\'';
    }

    void operator()(nary_expr const& v)
    {
        std::cout << '(' << v.op << ' ';
        printer p{ indent_ + 2 + v.op.size() };
        boost::apply_visitor(p, v.exprs[0]);
        for (std::size_t i = 1; i < v.exprs.size(); ++i) {
            if (boost::apply_visitor(is_simple{}, v.exprs[i])) {
                std::cout << ' ';
            }
            else {
                std::cout << '\n' << p.indent_;
            }
            boost::apply_visitor(p, v.exprs[i]);
        }
        std::cout << ')';
    }
};

int main()
{
    std::string s = "not (xyz='a' or xyz='b' or xyz='c') and abc='s' xor (pqr ='v' and xyz='d')";
    expr expr;
    auto iter = s.cbegin();
    if (phrase_parse(iter, s.cend(), prec4_expr_def, x3::space, expr) && iter == s.cend()) {
        boost::apply_visitor(printer{}, expr);
    }

    return 0;
}

它打印:

(xor (and (not (or (= xyz 'a')
                   (= xyz 'b')
                   (= xyz 'c')))
          (= abc 's'))
     (and (= pqr 'v')
          (= xyz 'd')))