overload.pm

MSYS在windows下模拟了一个类unix的终端

  my $bar = new two_refs 3,4,5,6;
  $bar->[2] = 11;
  $bar->{two} == 11 or die 'bad hash fetch';

Note several important features of this example.  First of all, the
I<actual> type of $bar is a scalar reference, and we do not overload
the scalar dereference.  Thus we can get the I<actual> non-overloaded
contents of $bar by just using C<$$bar> (what we do in functions which
overload dereference).  Similarly, the object returned by the
TIEHASH() method is a scalar reference.

Second, we create a new tied hash each time the hash syntax is used.
This allows us not to worry about a possibility of a reference loop,
would would lead to a memory leak.

Both these problems can be cured.  Say, if we want to overload hash
dereference on a reference to an object which is I<implemented> as a
hash itself, the only problem one has to circumvent is how to access
this I<actual> hash (as opposed to the I<virtual> hash exhibited by the
overloaded dereference operator).  Here is one possible fetching routine:

  sub access_hash {
    my ($self, $key) = (shift, shift);
    my $class = ref $self;
    bless $self, 'overload::dummy'; # Disable overloading of %{}
    my $out = $self->{$key};
    bless $self, $class;	# Restore overloading
    $out;
  }

To remove creation of the tied hash on each access, one may an extra
level of indirection which allows a non-circular structure of references:

  package two_refs1;
  use overload '%{}' => sub { ${shift()}->[1] },
               '@{}' => sub { ${shift()}->[0] };
  sub new {
    my $p = shift;
    my $a = [@_];
    my %h;
    tie %h, $p, $a;
    bless \ [$a, \%h], $p;
  }
  sub gethash {
    my %h;
    my $self = shift;
    tie %h, ref $self, $self;
    \%h;
  }

  sub TIEHASH { my $p = shift; bless \ shift, $p }
  my %fields;
  my $i = 0;
  $fields{$_} = $i++ foreach qw{zero one two three};
  sub STORE {
    my $a = ${shift()};
    my $key = $fields{shift()};
    defined $key or die "Out of band access";
    $a->[$key] = shift;
  }
  sub FETCH {
    my $a = ${shift()};
    my $key = $fields{shift()};
    defined $key or die "Out of band access";
    $a->[$key];
  }

Now if $baz is overloaded like this, then C<$baz> is a reference to a
reference to the intermediate array, which keeps a reference to an
actual array, and the access hash.  The tie()ing object for the access
hash is a reference to a reference to the actual array, so

=over

=item *

There are no loops of references.

=item *

Both "objects" which are blessed into the class C<two_refs1> are
references to a reference to an array, thus references to a I<scalar>.
Thus the accessor expression C<$$foo-E<gt>[$ind]> involves no
overloaded operations.

=back

=head2 Symbolic calculator

Put this in F<symbolic.pm> in your Perl library directory:

  package symbolic;		# Primitive symbolic calculator
  use overload nomethod => \&wrap;

  sub new { shift; bless ['n', @_] }
  sub wrap {
    my ($obj, $other, $inv, $meth) = @_;
    ($obj, $other) = ($other, $obj) if $inv;
    bless [$meth, $obj, $other];
  }

This module is very unusual as overloaded modules go: it does not
provide any usual overloaded operators, instead it provides the L<Last
Resort> operator C<nomethod>.  In this example the corresponding
subroutine returns an object which encapsulates operations done over
the objects: C<new symbolic 3> contains C<['n', 3]>, C<2 + new
symbolic 3> contains C<['+', 2, ['n', 3]]>.

Here is an example of the script which "calculates" the side of
circumscribed octagon using the above package:

  require symbolic;
  my $iter = 1;			# 2**($iter+2) = 8
  my $side = new symbolic 1;
  my $cnt = $iter;

  while ($cnt--) {
    $side = (sqrt(1 + $side**2) - 1)/$side;
  }
  print "OK\n";

The value of $side is

  ['/', ['-', ['sqrt', ['+', 1, ['**', ['n', 1], 2]],
	               undef], 1], ['n', 1]]

Note that while we obtained this value using a nice little script,
there is no simple way to I<use> this value.  In fact this value may
be inspected in debugger (see L<perldebug>), but ony if
C<bareStringify> B<O>ption is set, and not via C<p> command.

If one attempts to print this value, then the overloaded operator
C<""> will be called, which will call C<nomethod> operator.  The
result of this operator will be stringified again, but this result is
again of type C<symbolic>, which will lead to an infinite loop.

Add a pretty-printer method to the module F<symbolic.pm>:

  sub pretty {
    my ($meth, $a, $b) = @{+shift};
    $a = 'u' unless defined $a;
    $b = 'u' unless defined $b;
    $a = $a->pretty if ref $a;
    $b = $b->pretty if ref $b;
    "[$meth $a $b]";
  }

Now one can finish the script by

  print "side = ", $side->pretty, "\n";

The method C<pretty> is doing object-to-string conversion, so it
is natural to overload the operator C<""> using this method.  However,
inside such a method it is not necessary to pretty-print the
I<components> $a and $b of an object.  In the above subroutine
C<"[$meth $a $b]"> is a catenation of some strings and components $a
and $b.  If these components use overloading, the catenation operator
will look for an overloaded operator C<.>; if not present, it will
look for an overloaded operator C<"">.  Thus it is enough to use

  use overload nomethod => \&wrap, '""' => \&str;
  sub str {
    my ($meth, $a, $b) = @{+shift};
    $a = 'u' unless defined $a;
    $b = 'u' unless defined $b;
    "[$meth $a $b]";
  }

Now one can change the last line of the script to

  print "side = $side\n";

which outputs

  side = [/ [- [sqrt [+ 1 [** [n 1 u] 2]] u] 1] [n 1 u]]

and one can inspect the value in debugger using all the possible
methods.

Something is is still amiss: consider the loop variable $cnt of the
script.  It was a number, not an object.  We cannot make this value of
type C<symbolic>, since then the loop will not terminate.

Indeed, to terminate the cycle, the $cnt should become false.
However, the operator C<bool> for checking falsity is overloaded (this
time via overloaded C<"">), and returns a long string, thus any object
of type C<symbolic> is true.  To overcome this, we need a way to
compare an object to 0.  In fact, it is easier to write a numeric
conversion routine.

Here is the text of F<symbolic.pm> with such a routine added (and
slightly modified str()):

  package symbolic;		# Primitive symbolic calculator
  use overload
    nomethod => \&wrap, '""' => \&str, '0+' => \&num;

  sub new { shift; bless ['n', @_] }
  sub wrap {
    my ($obj, $other, $inv, $meth) = @_;
    ($obj, $other) = ($other, $obj) if $inv;
    bless [$meth, $obj, $other];
  }
  sub str {
    my ($meth, $a, $b) = @{+shift};
    $a = 'u' unless defined $a;
    if (defined $b) {
      "[$meth $a $b]";
    } else {
      "[$meth $a]";
    }
  }
  my %subr = ( n => sub {$_[0]},
	       sqrt => sub {sqrt $_[0]},
	       '-' => sub {shift() - shift()},
	       '+' => sub {shift() + shift()},
	       '/' => sub {shift() / shift()},
	       '*' => sub {shift() * shift()},
	       '**' => sub {shift() ** shift()},
	     );
  sub num {
    my ($meth, $a, $b) = @{+shift};
    my $subr = $subr{$meth}
      or die "Do not know how to ($meth) in symbolic";
    $a = $a->num if ref $a eq __PACKAGE__;
    $b = $b->num if ref $b eq __PACKAGE__;
    $subr->($a,$b);
  }

All the work of numeric conversion is done in %subr and num().  Of
course, %subr is not complete, it contains only operators used in the
example below.  Here is the extra-credit question: why do we need an
explicit recursion in num()?  (Answer is at the end of this section.)

Use this module like this:

  require symbolic;
  my $iter = new symbolic 2;	# 16-gon
  my $side = new symbolic 1;
  my $cnt = $iter;

  while ($cnt) {
    $cnt = $cnt - 1;		# Mutator `--' not implemented
    $side = (sqrt(1 + $side**2) - 1)/$side;
  }
  printf "%s=%f\n", $side, $side;
  printf "pi=%f\n", $side*(2**($iter+2));

It prints (without so many line breaks)

  [/ [- [sqrt [+ 1 [** [/ [- [sqrt [+ 1 [** [n 1] 2]]] 1]
			  [n 1]] 2]]] 1]
     [/ [- [sqrt [+ 1 [** [n 1] 2]]] 1] [n 1]]]=0.198912
  pi=3.182598

The above module is very primitive.  It does not implement
mutator methods (C<++>, C<-=> and so on), does not do deep copying
(not required without mutators!), and implements only those arithmetic
operations which are used in the example.

To implement most arithmetic operations is easy; one should just use
the tables of operations, and change the code which fills %subr to

  my %subr = ( 'n' => sub {$_[0]} );
  foreach my $op (split " ", $overload::ops{with_assign}) {
    $subr{$op} = $subr{"$op="} = eval "sub {shift() $op shift()}";
  }
  my @bins = qw(binary 3way_comparison num_comparison str_comparison);
  foreach my $op (split " ", "@overload::ops{ @bins }") {
    $subr{$op} = eval "sub {shift() $op shift()}";
  }
  foreach my $op (split " ", "@overload::ops{qw(unary func)}") {
    print "defining `$op'\n";
    $subr{$op} = eval "sub {$op shift()}";
  }

Due to L<Calling Conventions for Mutators>, we do not need anything
special to make C<+=> and friends work, except filling C<+=> entry of
%subr, and defining a copy constructor (needed since Perl has no
way to know that the implementation of C<'+='> does not mutate
the argument, compare L<Copy Constructor>).

To implement a copy constructor, add C<< '=' => \&cpy >> to C<use overload>
line, and code (this code assumes that mutators change things one level
deep only, so recursive copying is not needed):

  sub cpy {
    my $self = shift;
    bless [@$self], ref $self;
  }

To make C<++> and C<--> work, we need to implement actual mutators,
either directly, or in C<nomethod>.  We continue to do things inside
C<nomethod>, thus add

    if ($meth eq '++' or $meth eq '--') {
      @$obj = ($meth, (bless [@$obj]), 1); # Avoid circular reference
      return $obj;
    }

after the first line of wrap().  This is not a most effective
implementation, one may consider

  sub inc { $_[0] = bless ['++', shift, 1]; }

instead.

As a final remark, note that one can fill %subr by

  my %subr = ( 'n' => sub {$_[0]} );
  foreach my $op (split " ", $overload::ops{with_assign}) {
    $subr{$op} = $subr{"$op="} = eval "sub {shift() $op shift()}";
  }
  my @bins = qw(binary 3way_comparison num_comparison str_comparison);
  foreach my $op (split " ", "@overload::ops{ @bins }") {
    $subr{$op} = eval "sub {shift() $op shift()}";
  }
  foreach my $op (split " ", "@overload::ops{qw(unary func)}") {
    $subr{$op} = eval "sub {$op shift()}";
  }
  $subr{'++'} = $subr{'+'};
  $subr{'--'} = $subr{'-'};

This finishes implementation of a primitive symbolic calculator in
50 lines of Perl code.  Since the numeric values of subexpressions
are not cached, the calculator is very slow.

Here is the answer for the exercise: In the case of str(), we need no
explicit recursion since the overloaded C<.>-operator will fall back
to an existing overloaded operator C<"">.  Overloaded arithmetic
operators I<do not> fall back to numeric conversion if C<fallback> is
not explicitly requested.  Thus without an explicit recursion num()
would convert C<['+', $a, $b]> to C<$a + $b>, which would just rebuild
the argument of num().

If you wonder why defaults for conversion are different for str() and
num(), note how easy it was to write the symbolic calculator.  This
simplicity is due to an appropriate choice of defaults.  One extra
note: due to the explicit recursion num() is more fragile than sym():
we need to explicitly check for the type of $a and $b.  If components
$a and $b happen to be of some related type, this may lead to problems.

=head2 I<Really> symbolic calculator

One may wonder why we call the above calculator symbolic.  The reason
is that the actual calculation of the value of expression is postponed
until the value is I<used>.

To see it in action, add a method

  sub STORE {
    my $obj = shift;
    $#$obj = 1;
    @$obj->[0,1] = ('=', shift);
  }

to the package C<symbolic>.  After this change one can do

  my $a = new symbolic 3;
  my $b = new symbolic 4;
  my $c = sqrt($a**2 + $b**2);

and the numeric value of $c becomes 5.  However, after calling

  $a->STORE(12);  $b->STORE(5);

the numeric value of $c becomes 13.  There is no doubt now that the module
symbolic provides a I<symbolic> calculator indeed.

To hide the rough edges under the hood, provide a tie()d interface to the
package C<symbolic> (compare with L<Metaphor clash>).  Add methods

  sub TIESCALAR { my $pack = shift; $pack->new(@_) }
  sub FETCH { shift }
  sub nop {  }		# Around a bug

(the bug is described in L<"BUGS">).  One can use this new interface as

  tie $a, 'symbolic', 3;
  tie $b, 'symbolic', 4;
  $a->nop;  $b->nop;	# Around a bug

  my $c = sqrt($a**2 + $b**2);

Now numeric value of $c is 5.  After C<$a = 12; $b = 5> the numeric value
of $c becomes 13.  To insulate the user of the module add a method

  sub vars { my $p = shift; tie($_, $p), $_->nop foreach @_; }

Now

  my ($a, $b);
  symbolic->vars($a, $b);
  my $c = sqrt($a**2 + $b**2);

  $a = 3; $b = 4;
  printf "c5  %s=%f\n", $c, $c;

  $a = 12; $b = 5;
  printf "c13  %s=%f\n", $c, $c;

shows that the numeric value of $c follows changes to the values of $a
and $b.

=head1 AUTHOR

Ilya Zakharevich E<lt>F<[e-mail]>E<gt>.

=head1 DIAGNOSTICS

When Perl is run with the B<-Do> switch or its equivalent, overloading
induces diagnostic messages.

Using the C<m> command of Perl debugger (see L<perldebug>) one can
deduce which operations are overloaded (and which ancestor triggers
this overloading). Say, if C<eq> is overloaded, then the method C<(eq>
is shown by debugger. The method C<()> corresponds to the C<fallback>
key (in fact a presence of this method shows that this package has
overloading enabled, and it is what is used by the C<Overloaded>
function of module C<overload>).

The module might issue the following warnings:

=over 4

=item Odd number of arguments for overload::constant

(W) The call to overload::constant contained an odd number of arguments.
The arguments should come in pairs.

=item `%s' is not an overloadable type

(W) You tried to overload a constant type the overload package is unaware of.

=item `%s' is not a code reference

(W) The second (fourth, sixth, ...) argument of overload::constant needs
to be a code reference. Either an anonymous subroutine, or a reference
to a subroutine.

=back

=head1 BUGS

Because it is used for overloading, the per-package hash %OVERLOAD now
has a special meaning in Perl. The symbol table is filled with names
looking like line-noise.

For the purpose of inheritance every overloaded package behaves as if
C<fallback> is present (possibly undefined). This may create
interesting effects if some package is not overloaded, but inherits
from two overloaded packages.

Relation between overloading and tie()ing is broken.  Overloading is
triggered or not basing on the I<previous> class of tie()d value.

This happens because the presence of overloading is checked too early,
before any tie()d access is attempted.  If the FETCH()ed class of the
tie()d value does not change, a simple workaround is to access the value
immediately after tie()ing, so that after this call the I<previous> class
coincides with the current one.

B<Needed:> a way to fix this without a speed penalty.

Barewords are not covered by overloaded string constants.

This document is confusing.  There are grammos and misleading language
used in places.  It would seem a total rewrite is needed.

=cut