sub P {
    # Returns strings!
    my ( $m, $n ) = @_;
    if ( $m == 1 or $n == 1 ) {
        return 1;
    }
    if ( $m < $n ) {
        return "P($m,$m)";
    }
    if ( $m == $n ) {
        return sprintf( "1 + P(%i,%i)", $m, $m - 1 );
    }
    if ( $m > $n ) {
        return sprintf( "P(%i,%i) + P(%i,%i)", $m, $n - 1, $m - $n, $n );
    }
    die "impossible!";
}

MAIN: {
    local $_ = "P($m,$n)";
    print;
    while ( /\D/ ) {
        # Put ints up front
        1 while s/^(.+\)) \+ (\d+)/$2 + $1/;
        # Add the ints
        1 while s/(\d+) \+ (\d+)/$1 + $2/eg;
        # Evaluate *one* level at a time
        s/(P\(\d+,\d+\))/$1/eeg;
        printf( "\n = %s", $_ );   
    }
}