regular expression with recursion in Perl - regex

Question

I'm trying to use this but can't make it work. I want to check the syntax of expressions like this: (1+2)*(3+4)
I have integers, +, * and brackets. That's it, but it can be nested to any depth.
In BNF syntax the expr can be described like this:
expr
<sum>
sum
<product>{+<product>}
product
<atom>{*<atom>}
atom
<number>|(<expr>)
number
<digit>{<digit>}
I tried to translate this to Perl like this:
$number = '\d+';
$atom = "($number|\\((?R)\\))";
$product = "$atom(\\*$atom)*";
$sum = "$product(\\+$product)*";
$expr = $sum;
if ('(1+2)*(3+4)' =~ /^$expr$/)
{
print "OK";
}
But it doesn't match! What am I doing wrong?

Answer 1

When you recurse, the ^ at the start of the pattern will fail to match.
Use (?(DEFINE)...) to define the rules instead of using (?R).
'(1+2)*(3+4)' =~ /
^ (?&expr) \z
(?(DEFINE)
# Rules.
(?<expr> (?&sum) )
(?<sum> (?&product) (?: \+ (?&product) )*+ )
(?<product> (?&atom) (?: \* (?&atom) )*+ )
(?<atom> (?&NUMBER) | \( (?&expr) \) )
# Tokens.
(?<NUMBER> \d++ )
)
/x
or die("Doesn't match.\n");
which simplifies to
'(1+2)*(3+4)' =~ /
^ (?&expr) \z
(?(DEFINE)
# Rules.
(?<expr> (?&binary_op) )
(?<binary_op> (?&atom) (?: [+*] (?&atom) )*+ )
(?<atom> (?&NUMBER) | \( (?&expr) \) )
# Tokens.
(?<NUMBER> \d++ )
)
/x
or die("Doesn't match.\n");
That's assuming you're only trying to check for validity rather than trying to parse the string. If you need to parse the string, you can build a parser using Parse::RecDescent or Marpa::R2.

Answer 2

ikegami's workaround above with the DEFINE stuff is beautiful, but it doesn't answer the question how to do it my way. A minimal change of my code to make it work? ikegami is right, the cause of no match is the ^ in /^$expr$/ . When the parser reenters the regex recursively it again checks for beginning of string, which fails. So I cannot have ^ and $ in the regex it seems. Without them my string matches. But then some invalid strings match too, like A(1+2)*(3+4)B . In the absence of ^ and $ it doesn't necessarily match the whole string. Problem.
ikegami suggested a solution to this in a comment above. I'll just write it out. I have tested it and it works:
$number = '\d+';
$atom = "($number|\\((?1)\\))";
$product = "$atom(\\*$atom)*";
$sum = "$product(\\+$product)*";
$expr = $sum;
if ('(1+2)*(3+4)' =~ /^($expr)$/)
{
print "OK";
}
Notice that I now have (?1) instead of (?R) and that I have enclosed $expr in brackets. (?1) refers to the first capture group, which is ($expr). So the recursion reenters this subex instead of the whole regex. ^ is not met again. That solves it.