The first thing is that I'm going to be changing the callers because pp() references global data (namely $str). pp() also alters that data, so I will be returning the altered $str.

The code, upon first glance, looks slightly unfactored. But, I've taken the common element (the actual print command) and moved it out of the sub. This allows for pp() to display the actual parts that differ. For example, you have four separate paths through pp(), depending on how f1() and f2() behave. This version makes that explicit. 

{
    my ($indent, $depth) = ( "\t", 0 );

    my $_print = sub {
        print $indent x $depth, substr( $_[0], 0, $_[1] );
    };

    sub pp {
        return unless @_;
        my ($str) = @_;

        my ($pos, $first ) = f1( $str );
        if ( defined $first ) {
            if ( $first eq CONST1 ) {
                $depth++;
                $_print->( $str, ++$pos );
            }
            elsif ( defined( my $newpos = f2( $str, $first ) ) ) {
                $_print->( $str, $newpos + 2 );
            }
            else {
                $_print->( $str, $pos );
                $depth++;
            }
        }
        else {
            $_print->( $str, $pos );
        }

        $str =~ s[^.{$pos1}\s*][];
        return $str;
    }
}

[download]

Update: Upon further thought, the calls to f1() and f2() need to be refactored further. 

{
    my ($indent, $depth) = ( "\t", 0 );

    my $_print = sub {
        print $indent x $depth, substr( $_[0], 0, $_[1] );
    };

    my $_call_f1_f2 = sub {
        my $str = shift;

        my ($pos, $first) = f1( $str );
        return ($pos, 0) if !defined $first;

        if ( $first eq CONST1 ) {
            $depth--;
            return ($pos + 1, 0);
        }

        $pos = f2( $str, $first );
        return ($newpos + 2, 0) if defined $pos;

        return ($pos, 1);
    };

    sub pp {
        return unless @_;
        my ($str) = @_;

        my ($pos, $depth_mod) = $_call_f1_f2->( $str );

        $_print->( $str, $pos );

        $depth += $depth_mod;

        $str =~ s[^.{$pos1}\s*][];
        return $str;
    }
}

[download]

Update: Typo in code ($_->print -> $_print->) fixed.

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In reply to Re: Refactoring challenge. by dragonchild
in thread Refactoring challenge. by BrowserUk

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