n-ary boolean grammar conversion from infix to prefix with Boost::Spirit? - c++

Question

I need to convert infix notations like the one below to n-ary prefix notation with Boost::Spirit, but I am failing at building on the answers from https://stackoverflow.com/a/8707598/1816477 et al.
This is what I am trying to parse:
not (xyz='a' or xyz='b' or xyz='c') and abc='s' xor (pqr ='v' and xyz='d')
and this LISP-styled format is what I am trying to provide as output (do not mind the indentation):
(xor (and (= pqr 'v') (= xyz 'd'))
(and (= abc 's')
(not (or (= xyz 'a')
(= xyz 'b')
(= xyz 'c')))))
So, the terms I try to parse consist of prefixed (not <expression>) and infix expressions (<expression> and <expression> and ... etc.), i.e.: assignments, negations and n-ary ands, ors, xors etc., implying operator precedence (or < xor < and < assignment < negation).
What I am failing at is getting the grammar right. Outputting to a suitable boost::variant representing the parsed boolean expression I think I am able to accomplish. I am thinking of an output structure like this one:
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)
What do I need to do to be able to parse expressions like the one mentioned above and convert them to a prefix notation?
I am using the boost 1.67.0 (the latest at the time of writing) and Visual Studio 15.7.3 (also the latest at the time of writing).

Answer 1

The code is not perfect but should be simple to understand:
#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;
}
It prints:
(xor (and (not (or (= xyz 'a')
(= xyz 'b')
(= xyz 'c')))
(= abc 's'))
(and (= pqr 'v')
(= xyz 'd')))