问题
I need to build an abstract syntax tree from mathematical expression that I later need to link domain specific objects together as a calculation tree. I found the expression parser library https://github.com/hmenke/boost_matheval as an excellent starting point.
In my use case I need to have support for ternary conditional expressions condition ? true_exp : false_exp. As of now the parser is able to parse expressions such as 1 + (2 + abs(x)) or min(x,1+y). However I would need to have syntax such as this: (x > y ? 1 : 0) * (y - z).
I tried defining a rule
auto const conditional_def =
expression > '?' > expression > ':'> expression
;
and extending the start rule by conditional
auto const primary_def =
x3::double_
| ('(' > expression > ')')
| (unary_op > primary)
| binary
| unary
| conditional
| constant
| variable
;
However this does not parse correctly. The start rule consumes the condition and recursively tries to parse what is left: ? true_exp : false_exp. This does not match to anything. If I would define the condition as this
auto const conditional_def =
(x3::lit("if") > '(' > expression > ',' > expression > ','> expression > ')')
;
the parsing would work for expression such as if(x > y, x , y) - however this is not the standard ternary conditional ?:
Here is how the ast attributes and declared symbol definitions look like
namespace x3 = boost::spirit::x3;
namespace ast {
struct nil {};
struct unary_op;
struct binary_op;
struct conditional_op;
struct expression;
struct operand : x3::variant<
nil
, double
, std::string
, x3::forward_ast<unary_op>
, x3::forward_ast<binary_op>
, x3::forward_ast<conditional_op>
, x3::forward_ast<expression>
> {
using base_type::base_type;
using base_type::operator=;
};
struct unary_op {
double (*op)(double);
operand rhs;
};
struct binary_op {
double (*op)(double, double);
operand lhs;
operand rhs;
};
struct conditional_op {
operand lhs;
operand rhs_true;
operand rhs_false;
};
struct operation {
double (*op)(double, double);
operand rhs;
};
struct expression {
operand lhs;
std::list<operation> rhs;
};
} // namespace ast
struct constant_ : x3::symbols<double> {
constant_() {
add
("e" , boost::math::constants::e<double>())
("pi" , boost::math::constants::pi<double>())
;
}
} constant;
struct ufunc_ : x3::symbols<double (*)(double)> {
ufunc_() {
add
("abs" , static_cast<double (*)(double)>(&std::abs))
;
}
} ufunc;
struct bfunc_ : x3::symbols<double (*)(double, double)> {
bfunc_() {
add
("max" , static_cast<double (*)(double, double)>(&std::fmax))
;
}
} bfunc;
struct unary_op_ : x3::symbols<double (*)(double)> {
unary_op_() {
add
("+", static_cast<double (*)(double)>(&math::plus))
("-", static_cast<double (*)(double)>(&math::minus))
("!", static_cast<double (*)(double)>(&math::unary_not))
;
}
} unary_op;
struct additive_op_ : x3::symbols<double (*)(double, double)> {
additive_op_() {
add
("+", static_cast<double (*)(double, double)>(&math::plus))
("-", static_cast<double (*)(double, double)>(&math::minus))
;
}
} additive_op;
struct multiplicative_op_ : x3::symbols<double (*)(double, double)> {
multiplicative_op_() {
add
("*", static_cast<double (*)(double, double)>(&math::multiplies))
("/", static_cast<double (*)(double, double)>(&math::divides))
("%", static_cast<double (*)(double, double)>(&std::fmod))
;
}
} multiplicative_op;
struct logical_op_ : x3::symbols<double (*)(double, double)> {
logical_op_() {
add
("&&", static_cast<double (*)(double, double)>(&math::logical_and))
("||", static_cast<double (*)(double, double)>(&math::logical_or))
;
}
} logical_op;
struct relational_op_ : x3::symbols<double (*)(double, double)> {
relational_op_() {
add
("<" , static_cast<double (*)(double, double)>(&math::less))
("<=", static_cast<double (*)(double, double)>(&math::less_equals))
(">" , static_cast<double (*)(double, double)>(&math::greater))
(">=", static_cast<double (*)(double, double)>(&math::greater_equals))
;
}
} relational_op;
struct equality_op_ : x3::symbols<double (*)(double, double)> {
equality_op_() {
add
("==", static_cast<double (*)(double, double)>(&math::equals))
("!=", static_cast<double (*)(double, double)>(&math::not_equals))
;
}
} equality_op;
struct power_ : x3::symbols<double (*)(double, double)> {
power_() {
add
("**", static_cast<double (*)(double, double)>(&std::pow))
;
}
} power;
The more complete grammar and the definition of ast attributes is below. It would be highly appreciated if somebody more experienced with Boots spirit could guide me how to define the ternary conditional correctly.
struct expression_class;
struct logical_class;
struct equality_class;
struct relational_class;
struct additive_class;
struct multiplicative_class;
struct factor_class;
struct primary_class;
struct unary_class;
struct binary_class;
struct conditional_class;
struct variable_class;
// Rule declarations
auto const expression = x3::rule<expression_class , ast::expression >{"expression"};
auto const logical = x3::rule<logical_class , ast::expression >{"logical"};
auto const equality = x3::rule<equality_class , ast::expression >{"equality"};
auto const relational = x3::rule<relational_class , ast::expression >{"relational"};
auto const additive = x3::rule<additive_class , ast::expression >{"additive"};
auto const multiplicative = x3::rule<multiplicative_class, ast::expression >{"multiplicative"};
auto const factor = x3::rule<factor_class , ast::expression >{"factor"};
auto const primary = x3::rule<primary_class , ast::operand >{"primary"};
auto const unary = x3::rule<unary_class , ast::unary_op >{"unary"};
auto const binary = x3::rule<binary_class , ast::binary_op >{"binary"};
auto const conditional = x3::rule<conditional_class , ast::conditional_op>{"conditional"};
auto const variable = x3::rule<variable_class , std::string >{"variable"};
// Rule defintions
auto const expression_def =
logical
;
auto const logical_def =
equality >> *(logical_op > equality)
;
auto const equality_def =
relational >> *(equality_op > relational)
;
auto const relational_def =
additive >> *(relational_op > additive)
;
auto const additive_def =
multiplicative >> *(additive_op > multiplicative)
;
auto const multiplicative_def =
factor >> *(multiplicative_op > factor)
;
auto const factor_def =
primary >> *( power > factor )
;
auto const unary_def =
ufunc > '(' > expression > ')'
;
auto const binary_def =
bfunc > '(' > expression > ',' > expression > ')'
;
auto const conditional_def =
expression > '?' > expression > ':'> expression
;
auto const primary_def =
x3::double_
| ('(' > expression > ')')
| (unary_op > primary)
| binary
| unary
| conditional
| constant
| variable
;
BOOST_SPIRIT_DEFINE(
expression,
logical,
equality,
relational,
additive,
multiplicative,
factor,
primary,
unary,
binary,
conditional,
variable
)
Here is how the AST is traversed using boost static visitor to evaluate the expression with a variable symbol table
namespace ast {
// Evaluator
struct Evaluator {
using result_type = double;
explicit Evaluator(std::map<std::string, double> sym);
double operator()(nil) const;
double operator()(double n) const;
double operator()(std::string const &c) const;
double operator()(operation const &x, double lhs) const;
double operator()(unary_op const &x) const;
double operator()(binary_op const &x) const;
double operator()(conditional_op const &x) const;
double operator()(expression const &x) const;
private:
std::map<std::string, double> st;
};
Evaluator::Evaluator(std::map<std::string, double> sym)
: st(std::move(sym)) {}
double Evaluator::operator()(nil) const {
BOOST_ASSERT(0);
return 0;
}
double Evaluator::operator()(double n) const { return n; }
double Evaluator::operator()(std::string const &c) const {
auto it = st.find(c);
if (it == st.end()) {
throw std::invalid_argument("Unknown variable " + c);
}
return it->second;
}
double Evaluator::operator()(operation const &x, double lhs) const {
double rhs = boost::apply_visitor(*this, x.rhs);
return x.op(lhs, rhs);
}
double Evaluator::operator()(unary_op const &x) const {
double rhs = boost::apply_visitor(*this, x.rhs);
return x.op(rhs);
}
double Evaluator::operator()(binary_op const &x) const {
double lhs = boost::apply_visitor(*this, x.lhs);
double rhs = boost::apply_visitor(*this, x.rhs);
return x.op(lhs, rhs);
}
double Evaluator::operator()(conditional_op const &x) const {
return static_cast<bool>(boost::apply_visitor(*this, x.lhs))
? boost::apply_visitor(*this, x.rhs_true)
: boost::apply_visitor(*this, x.rhs_false);
}
double Evaluator::operator()(expression const &x) const {
double state = boost::apply_visitor(*this, x.lhs);
for (operation const &oper : x.rhs) {
state = (*this)(oper, state);
}
return state;
}
} // namespace ast
回答1:
The conditional is not a primary expression.
In fact, it is an infix-notated ternary expression.
This causes the primary rule to exhibit left-recursion (it descends into expression by definition).
What you should probably do is to just treat the ternary operator as you do the other infix operators, which has the added benefit of being explicit about relative operator precedence.
Glancing at usual precendences in programming languages, I'd suggest something like:
auto const expression_def =
conditional
;
auto const conditional_def =
logical >> -('?' > expression > ':'> expression)
;
auto const logical_def =
equality >> *(logical_op > equality)
;
(and of course removing it from primary_def).
Live Demo
Live On Coliru
//#define BOOST_SPIRIT_X3_DEBUG
//#define DEBUG_SYMBOLS
#include <iostream>
#include <iomanip>
#include <boost/spirit/home/x3.hpp>
namespace x3 = boost::spirit::x3;
namespace ast {
using expression = x3::unused_type;
using unary_op = x3::unused_type;
using binary_op = x3::unused_type;
using conditional_op = x3::unused_type;
using operand = x3::unused_type;
}
namespace P {
struct ehbase {
template <typename It, typename Ctx>
x3::error_handler_result on_error(It f, It l, x3::expectation_failure<It> const& e, Ctx const& /*ctx*/) const {
std::cout << std::string(f,l) << "\n"
<< std::setw(1+std::distance(f, e.where())) << "^"
<< "-- expected: " << e.which() << "\n";
return x3::error_handler_result::fail;
}
};
struct expression_class : ehbase {};
struct logical_class : ehbase {};
struct equality_class : ehbase {};
struct relational_class : ehbase {};
struct additive_class : ehbase {};
struct multiplicative_class : ehbase {};
struct factor_class : ehbase {};
struct primary_class : ehbase {};
struct unary_class : ehbase {};
struct binary_class : ehbase {};
struct conditional_class : ehbase {};
struct variable_class : ehbase {};
// Rule declarations
auto const expression = x3::rule<expression_class , ast::expression >{"expression"};
auto const logical = x3::rule<logical_class , ast::expression >{"logical"};
auto const equality = x3::rule<equality_class , ast::expression >{"equality"};
auto const relational = x3::rule<relational_class , ast::expression >{"relational"};
auto const additive = x3::rule<additive_class , ast::expression >{"additive"};
auto const multiplicative = x3::rule<multiplicative_class, ast::expression >{"multiplicative"};
auto const factor = x3::rule<factor_class , ast::expression >{"factor"};
auto const primary = x3::rule<primary_class , ast::operand >{"primary"};
auto const unary = x3::rule<unary_class , ast::unary_op >{"unary"};
auto const binary = x3::rule<binary_class , ast::binary_op >{"binary"};
auto const conditional = x3::rule<conditional_class , ast::conditional_op>{"conditional"};
auto const variable = x3::rule<variable_class , std::string >{"variable"};
template <typename Tag>
static auto make_sym(std::initializer_list<char const*> elements) {
#ifdef DEBUG_SYMBOLS
static x3::symbols<x3::unused_type> instance;
static auto name = boost::core::demangle(typeid(Tag*).name());
for (auto el : elements)
instance += el;
return x3::rule<Tag> {name.c_str()} = instance;
#else
x3::symbols<x3::unused_type> instance;
for (auto el : elements)
instance += el;
return instance;
#endif
}
static const auto logical_op = make_sym<struct logical_op_>({"and","or","xor"});
static const auto equality_op = make_sym<struct equality_op_>({"=","!="});
static const auto relational_op = make_sym<struct relational_op_>({"<","<=",">",">="});
static const auto additive_op = make_sym<struct additive_op_>({"+","-"});
static const auto multiplicative_op = make_sym<struct multiplicative_op_>({"*","/"});
static const auto unary_op = make_sym<struct unary_op_>({"!","-","~"}); // TODO FIXME interference with binop?
static const auto ufunc = make_sym<struct ufunc_>({"gamma","factorial","abs"});
static const auto bfunc = make_sym<struct bfunc_>({"pow","min","max"});
static const auto constant = make_sym<struct constant_>({"pi","e","tau"});
static const auto variable_def = make_sym<struct variable_def_>({"a","b","c","d","x","y","z"});
// Rule defintions
auto const expression_def =
conditional
;
auto const conditional_def =
logical >> -('?' > expression > ':' > expression)
;
auto const logical_def =
equality >> *(logical_op > equality)
;
auto const equality_def =
relational >> *(equality_op > relational)
;
auto const relational_def =
additive >> *(relational_op > additive)
;
auto const additive_def =
multiplicative >> *(additive_op > multiplicative)
;
auto const multiplicative_def =
factor >> *(multiplicative_op > factor)
;
auto const factor_def =
primary >> *( '^' > factor )
;
auto const unary_def =
ufunc > '(' > expression > ')'
;
auto const binary_def =
bfunc > '(' > expression > ',' > expression > ')'
;
auto const primary_def =
x3::double_
| ('(' > expression > ')')
| (unary_op > primary)
| binary
| unary
| constant
| variable
;
BOOST_SPIRIT_DEFINE(
expression,
logical,
equality,
relational,
additive,
multiplicative,
factor,
primary,
unary,
binary,
conditional,
variable
)
}
int main() {
for (std::string const input : {
"x+(3^pow(2,8))",
"1 + (2 + abs(x))",
"min(x,1+y)",
"(x > y ? 1 : 0) * (y - z)",
"min(3^4,7))",
"3^^4",
"(3,4)",
})
{
std::cout << " ===== " << std::quoted(input) << " =====\n";
auto f = begin(input), l = end(input);
ast::expression out;
if (phrase_parse(f, l, P::expression, x3::space, out)) {
std::cout << "Success\n";
} else {
std::cout << "Failed\n";
}
if (f!=l) {
std::cout << "Unparsed: " << std::quoted(std::string(f,l)) << "\n";
}
}
}
Prints
===== "x+(3^pow(2,8))" =====
Success
===== "1 + (2 + abs(x))" =====
Success
===== "min(x,1+y)" =====
Success
===== "(x > y ? 1 : 0) * (y - z)" =====
Success
===== "min(3^4,7))" =====
Success
Unparsed: ")"
===== "3^^4" =====
3^^4
^-- expected: factor
Failed
Unparsed: "3^^4"
===== "(3,4)" =====
(3,4)
^-- expected: ')'
Failed
Unparsed: "(3,4)"
NOTES
I think your grammar has relatively many expectation points. That might be ok, just an observation.
Also, your grammar has a couple of domains for names. You should probably take precautions to match partial names (e.g., if aa exists, you don't want to a variable a prematurely).
来源：https://stackoverflow.com/questions/59808321/boost-spirit-x3-conditional-ternary-operator-parser