这是一个基于Boost Spirit的实现。
由于Boost Spirit基于表达式模板生成递归下降解析器,遵守“个人独特”的优先顺序规则(如其他人所提到的)相当麻烦。因此,该语法缺乏一定的优雅性。
抽象数据类型
我使用Boost Variant的递归变量支持定义了一个树形数据结构,请注意expr的定义:
struct op_or {};
struct op_and {};
struct op_xor {};
struct op_not {};
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;
语法规则
以下为(稍微枯燥的)语法定义,如前所述。
虽然我不认为这个语法是最优秀的,但它相当易读,并且我们拥有一个大约50行代码的静态编译解析器与强类型的AST数据类型。情况可能会更糟。
template <typename It, typename Skipper = qi::space_type>
struct parser : qi::grammar<It, expr(), Skipper>
{
parser() : parser::base_type(expr_)
{
using namespace qi;
expr_ = or_.alias();
not_ = ("not" > simple ) [ _val = phx::construct<unop <op_not>>(_1) ] | simple [ _val = _1 ];
#ifdef RIGHT_ASSOCIATIVE
or_ = (xor_ >> "or" >> or_ ) [ _val = phx::construct<binop<op_or >>(_1, _2) ] | xor_ [ _val = _1 ];
xor_ = (and_ >> "xor" >> xor_) [ _val = phx::construct<binop<op_xor>>(_1, _2) ] | and_ [ _val = _1 ];
and_ = (not_ >> "and" >> and_) [ _val = phx::construct<binop<op_and>>(_1, _2) ] | not_ [ _val = _1 ];
#else
or_ = xor_ [ _val = _1 ] >> *("or" >> xor_ [ _val = phx::construct<binop<op_or>> (_val, _1) ]);
xor_ = and_ [ _val = _1 ] >> *("xor" >> and_ [ _val = phx::construct<binop<op_xor>>(_val, _1) ]);
and_ = not_ [ _val = _1 ] >> *("and" >> not_ [ _val = phx::construct<binop<op_and>>(_val, _1) ]);
#endif
simple = (('(' > expr_ > ')') | var_);
var_ = qi::lexeme[ +alpha ];
}
private:
qi::rule<It, var() , Skipper> var_;
qi::rule<It, expr(), Skipper> not_, and_, xor_, or_, simple, expr_;
};
注意:我已经为参考留下了旧的规则定义,这些规则会导致二进制运算符的右结合性,但是左结合性更为自然,因此默认采用左结合性
操作语法树
显然,您希望评估表达式。现在,我决定只停留在打印上,这样我就不必为命名变量做查找表 :)
遍历递归变体可能一开始看起来很神秘,但是一旦你掌握了boost::static_visitor<>
,它就非常简单了:
struct printer : boost::static_visitor<void>
{
printer(std::ostream& os) : _os(os) {}
std::ostream& _os;
void operator()(const var& v) const { _os << v; }
void operator()(const binop<op_and>& b) const { print(" & ", b.oper1, b.oper2); }
void operator()(const binop<op_or >& b) const { print(" | ", b.oper1, b.oper2); }
void operator()(const binop<op_xor>& b) const { print(" ^ ", b.oper1, b.oper2); }
void print(const std::string& op, const expr& l, const expr& r) const
{
_os << "(";
boost::apply_visitor(*this, l);
_os << op;
boost::apply_visitor(*this, r);
_os << ")";
}
void operator()(const unop<op_not>& u) const
{
_os << "(";
_os << "!";
boost::apply_visitor(*this, u.oper1);
_os << ")";
}
};
std::ostream& operator<<(std::ostream& os, const expr& e)
{ boost::apply_visitor(printer(os), e); return os; }
测试输出:
对于代码中的测试用例,以下是输出结果,演示通过添加(冗余的)括号正确地处理优先规则:
在线预览
result: ((a & b) ^ ((c & d) | (a & b)))
result: ((a & b) ^ ((c & d) | (a & b)))
result: (a & b)
result: (a | b)
result: (a ^ b)
result: (!a)
result: ((!a) & b)
result: (!(a & b))
result: ((a | b) | c)
请注意,与 在 Coliru 上使用 -DRIGHT_ASSOCIATIVE 比较
完整代码:
在 Coliru 上实时演示
#include <boost/spirit/include/qi.hpp>
#include <boost/spirit/include/phoenix.hpp>
#include <boost/spirit/include/phoenix_operator.hpp>
#include <boost/variant/recursive_wrapper.hpp>
namespace qi = boost::spirit::qi;
namespace phx = boost::phoenix;
struct op_or {};
struct op_and {};
struct op_xor {};
struct op_not {};
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;
template <typename tag> struct binop
{
explicit binop(const expr& l, const expr& r) : oper1(l), oper2(r) { }
expr oper1, oper2;
};
template <typename tag> struct unop
{
explicit unop(const expr& o) : oper1(o) { }
expr oper1;
};
struct printer : boost::static_visitor<void>
{
printer(std::ostream& os) : _os(os) {}
std::ostream& _os;
void operator()(const var& v) const { _os << v; }
void operator()(const binop<op_and>& b) const { print(" & ", b.oper1, b.oper2); }
void operator()(const binop<op_or >& b) const { print(" | ", b.oper1, b.oper2); }
void operator()(const binop<op_xor>& b) const { print(" ^ ", b.oper1, b.oper2); }
void print(const std::string& op, const expr& l, const expr& r) const
{
_os << "(";
boost::apply_visitor(*this, l);
_os << op;
boost::apply_visitor(*this, r);
_os << ")";
}
void operator()(const unop<op_not>& u) const
{
_os << "(";
_os << "!";
boost::apply_visitor(*this, u.oper1);
_os << ")";
}
};
std::ostream& operator<<(std::ostream& os, const expr& e)
{ boost::apply_visitor(printer(os), e); return os; }
template <typename It, typename Skipper = qi::space_type>
struct parser : qi::grammar<It, expr(), Skipper>
{
parser() : parser::base_type(expr_)
{
using namespace qi;
expr_ = or_.alias();
not_ = ("not" > simple ) [ _val = phx::construct<unop <op_not>>(_1) ] | simple [ _val = _1 ];
#ifdef RIGHT_ASSOCIATIVE
or_ = (xor_ >> "or" >> or_ ) [ _val = phx::construct<binop<op_or >>(_1, _2) ] | xor_ [ _val = _1 ];
xor_ = (and_ >> "xor" >> xor_) [ _val = phx::construct<binop<op_xor>>(_1, _2) ] | and_ [ _val = _1 ];
and_ = (not_ >> "and" >> and_) [ _val = phx::construct<binop<op_and>>(_1, _2) ] | not_ [ _val = _1 ];
#else
or_ = xor_ [ _val = _1 ] >> *("or" >> xor_ [ _val = phx::construct<binop<op_or>> (_val, _1) ]);
xor_ = and_ [ _val = _1 ] >> *("xor" >> and_ [ _val = phx::construct<binop<op_xor>>(_val, _1) ]);
and_ = not_ [ _val = _1 ] >> *("and" >> not_ [ _val = phx::construct<binop<op_and>>(_val, _1) ]);
#endif
simple = (('(' > expr_ > ')') | var_);
var_ = qi::lexeme[ +alpha ];
BOOST_SPIRIT_DEBUG_NODE(expr_);
BOOST_SPIRIT_DEBUG_NODE(or_);
BOOST_SPIRIT_DEBUG_NODE(xor_);
BOOST_SPIRIT_DEBUG_NODE(and_);
BOOST_SPIRIT_DEBUG_NODE(not_);
BOOST_SPIRIT_DEBUG_NODE(simple);
BOOST_SPIRIT_DEBUG_NODE(var_);
}
private:
qi::rule<It, var() , Skipper> var_;
qi::rule<It, expr(), Skipper> not_, and_, xor_, or_, simple, expr_;
};
int main()
{
for (auto& input : std::list<std::string> {
"(a and b) xor ((c and d) or (a and b));",
"a and b xor (c and d or a and b);",
"a and b;",
"a or b;",
"a xor b;",
"not a;",
"not a and b;",
"not (a and b);",
"a or b or c;",
})
{
auto f(std::begin(input)), l(std::end(input));
parser<decltype(f)> p;
try
{
expr result;
bool ok = qi::phrase_parse(f,l,p > ';',qi::space,result);
if (!ok)
std::cerr << "invalid input\n";
else
std::cout << "result: " << result << "\n";
} catch (const qi::expectation_failure<decltype(f)>& e)
{
std::cerr << "expectation_failure at '" << std::string(e.first, e.last) << "'\n";
}
if (f!=l) std::cerr << "unparsed: '" << std::string(f,l) << "'\n";
}
return 0;
}
奖励:
如果想要获得和原帖中完全一样的树形结构,请参考下面的链接:
在 Coliru 上实时查看
static const char indentstep[] = " ";
struct tree_print : boost::static_visitor<void>
{
tree_print(std::ostream& os, const std::string& indent=indentstep) : _os(os), _indent(indent) {}
std::ostream& _os;
std::string _indent;
void operator()(const var& v) const { _os << _indent << v << std::endl; }
void operator()(const binop<op_and>& b) const { print("and ", b.oper1, b.oper2); }
void operator()(const binop<op_or >& b) const { print("or ", b.oper2, b.oper1); }
void operator()(const binop<op_xor>& b) const { print("xor ", b.oper2, b.oper1); }
void print(const std::string& op, const expr& l, const expr& r) const
{
boost::apply_visitor(tree_print(_os, _indent+indentstep), l);
_os << _indent << op << std::endl;
boost::apply_visitor(tree_print(_os, _indent+indentstep), r);
}
void operator()(const unop<op_not>& u) const
{
_os << _indent << "!";
boost::apply_visitor(tree_print(_os, _indent+indentstep), u.oper1);
}
};
std::ostream& operator<<(std::ostream& os, const expr& e)
{
boost::apply_visitor(tree_print(os), e); return os;
}
结果:
a
and
b
or
c
and
d
xor
a
and
b