Here is a minimal example of infix to postfix translation preserving the correct associativity. For the sake of simplicity I have reduced the grammar to the minus operator:

pl@nereida:~/Lperltesting$ cat calc510withactions.pl
#!/usr/local/lib/perl/5.10.1/bin//perl5.10.1
use v5.10;

# Infix to postfix translator using 5.10 regexp
# original grammar:
#  exp ->   exp '-' digits
#         | digits
#
# Applying left-recursion elimination we have:
#  exp ->   digits rest
#  rest ->   '-' rest
#          | # empty
#
my @stack;
my $regexp = qr{
    (?&exp)

    (?(DEFINE)
        (?<exp>    (?&digits) \s* (?&rest)
        )

        (?<rest>     \s* - (?&digits) \s* (?{ push @stack, '-' }) (?&r
+est)
                  |  # empty
        )

        (?<digits>  \s* (\d+)
           (?{ push @stack, $^N })
        )
    )
}xms;

my $input = <>;
chomp($input);
if ($input =~ $regexp) {
  say "matches: $&\nStack=(@stack)";
}
else {
  say "does not match";
}
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