Re: Using overload to parse arithmetic terms

[japhy]

If you want to output a properly parenthesized mathematical expression, you'll have to do so on the fly, examining the tree that I assume you have in your Arithmetic object. For example, if you have $x = ($a + $b) * $c;, then you probably have a tree like:

Arithmetic::Multiply(
  Arithmetic::Add(
    Variable('a'),
    Variable('b')
  ),
  Variable('c')
)

When you're walking that tree, when you get to a Multiply or Divide node, you have to check to see if its children are Add or Subtract nodes; if they are, those child nodes need to be surrounded by parentheses when output.

[blokhead]

To expand (and generalize) on this a bit, let each type of operation have a precedence. Then as you walk the expression tree, you need to parenthesize operations that have a lower precedence than the expression they appear within.

A good way to do this is via OO, representing your operation types as subclasses:

package Op;
sub new {
    my $pkg = shift;
    bless [@_], $pkg;
}
sub children { @{ $_[0] } }
sub display {
    my ($self, $precedence) = @_;
    $precedence = 0 if not defined $precedence;
    my $s = join $self->op,
            map { $_->display($self->precedence) } $self->children;
    $s = "($s)" if $precedence > $self->precedence;
    return $s;
}

package Op::Addition;
@ISA = qw[Op];
sub precedence { 10 }
sub op { " + " }

package Op::Multiplication;
@ISA = qw[Op];
sub precedence { 20 }
sub op { " * " }

# ...

package Op::Term;
@ISA = qw[Op];
sub precedence { 100 }
sub display { $_[0][0] }

Then you just call the display method on an Op tree. For example,

Op::Multiplication->new(
  Op::Term->new(5),
  Op::Addition->new(
    Op::Term->new(6),
    Op::Term->new(7)
  )
)->display;
# 5 * (6 + 7)

Op::Addition->new(
  Op::Term->new(5),
  Op::Multiplication->new(
    Op::Term->new(6),
    Op::Term->new(7)
  )
)->display;
# 5 + 6 * 7

And you can see how easy it would be to add new types of operations, due to the beauty of subclassing.

[japhy]

That is a beautiful approach and technique. ++ well deserved.

[esskar]

perfect ... thanks.