It's basically the same problem as recursive algorithm for nested data structures

Update: Actually, it's a bit more different than I thought because you said you can't have both OR and AND in the same list. 

# make_parser.pl

use strict;
use warnings;

use Parse::RecDescent qw( );

my $grammar = <<'__EOI__';

    {
        use strict;
        use warnings;

        sub dequote {
            my ($s) = @_;
            $s =~ s/^"//;
            $s =~ s/"\z//;
            $s =~ s/\\(.)/$1/sg;
            return $s;
        }
    }

    parse     : list /\Z/ { $item[1] }

    list      : term list_[ $item[1] ]

    list_     : "AND" <commit> and_list
                { [ $item[1] => $arg[0], @{$item[3]} ] }

              | "OR"  <commit> or_list
                { [ $item[1] => $arg[0], @{$item[3]} ] }

              | { $arg[0] }

    and_list  : term and_list_
                { [ $item[1], @{$item[2]} ] }

    and_list_ : "AND" <commit> term and_list_
                { [ $item[3], @{$item[4]} ] }

              | { [] }

    or_list   : term or_list_
                { [ $item[1], @{$item[2]} ] }

    or_list_  : "OR" <commit> term or_list_
                { [ $item[3], @{$item[4]} ] }

              | { [] }

    term      : IDENT
              | STRING
              | '(' list ')' { $item[2] }

    IDENT     : /\w+/
    STRING    : /"(?:\\.|[^\\])*"/s { dequote($item[1]) }

__EOI__

Parse::RecDescent->Precompile($grammar, 'Parser')
    or die("Bad grammar\n");

[download]
# test.pl

use strict;
use warnings;

use Data::Dumper qw( Dumper );
use Parser       qw( );

my $text = 'dogs OR cats OR "flying fish" OR (shrimp AND squid)';

my $parser = Parser->new();

print(Dumper($parser->parse($text)));

[download]
>perl make_parser.pl

>perl test.pl
$VAR1 = [
          'OR',
          'dogs',
          'cats',
          'flying fish',
          [
            'AND',
            'shrimp',
            'squid'
          ]
        ];

[download]

Update: Small changes to grammar to eliminate backtracking.

In reply to Re: Break string into array by ikegami
in thread Break string into array by Anonymous Monk

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