Need a start point for resolving {[()]}

[exilepanda]

Hi monks, I am working in a project in helping colleges to do logic check from batch of Excel files. Staffs will write a sort of simple syntax (still designing) within a INI file; basically the so called syntax(expression) are some and or eq etc. operators with {[()]}. , which will return a true or false.

The first problem come to me is how do I resolve those brackets, so I can determine the logic's precedence. Now I have this :

$expr = '(A&(B&C)|((C&D)|\((A EQ 1)))';
#       01234567890123456789012345678

my (@open, @close);
my @charArr = split //, $expr;
foreach my $pos ( 0..$#charArr ) {
    push @open, $pos if ( $charArr[$pos] =~ /\(/ && $charArr[$pos-1] n
+e "\\" ) ;
    push @close, $pos if ( $charArr[$pos] =~ /\)/ && $charArr[$pos-1] 
+ne "\\" ) ;
}

die "Imbalance Pair" unless @open == @close;
print "@open$/@close$/$/";

my @preced;
foreach my $firstClose ( @close ) {
    my @temp = ();    
    while ( @open ) {
        my $lastOpen = pop @open;
        if ( $lastOpen < $firstClose ) {
            push @preced, "$lastOpen - $firstClose";            
            @open = (@open, @temp);
            last 
        }        
        else {
            unshift @temp, $lastOpen;
        }
    }    
}
print $_.$/ foreach @preced;
__END__

prints:
0 3 9 10 18
7 14 25 26 27

3 - 7
10 - 14
18 - 25
9 - 26
0 - 27

The @preced carries the string positions of each open-end brackets, and their precedence order. However, it looks like a stupid algorithm, which sound unsafe and not efficient.

My questions :

1. What is the terminology of this sort of issues ? I like to look up more, but I don't know what is it called

2. Is there any module actually suits for this kind of case? What I have only a start up, implementing each block is another issue, if more operators are needed later, like >= == != boolean, string compare etc. situations. I can't foresee what's gonna happen.

Any clues for me ? Thanks in advance.