1package overload;
2
3use strict;
4no strict 'refs';
5
6our $VERSION = '1.37';
7
8our %ops = (
9    with_assign         => "+ - * / % ** << >> x .",
10    assign              => "+= -= *= /= %= **= <<= >>= x= .=",
11    num_comparison      => "< <= >  >= == !=",
12    '3way_comparison'   => "<=> cmp",
13    str_comparison      => "lt le gt ge eq ne",
14    binary              => '& &= | |= ^ ^= &. &.= |. |.= ^. ^.=',
15    unary               => "neg ! ~ ~.",
16    mutators            => '++ --',
17    func                => "atan2 cos sin exp abs log sqrt int",
18    conversion          => 'bool "" 0+ qr',
19    iterators           => '<>',
20    filetest            => "-X",
21    dereferencing       => '${} @{} %{} &{} *{}',
22    matching            => '~~',
23    special             => 'nomethod fallback =',
24);
25
26my %ops_seen;
27@ops_seen{ map split(/ /), values %ops } = ();
28
29sub nil {}
30
31sub OVERLOAD {
32    my $package = shift;
33    my %arg = @_;
34    my $sub;
35    *{$package . "::(("} = \&nil; # Make it findable via fetchmethod.
36    for (keys %arg) {
37        if ($_ eq 'fallback') {
38            for my $sym (*{$package . "::()"}) {
39              *$sym = \&nil; # Make it findable via fetchmethod.
40              $$sym = $arg{$_};
41            }
42        } else {
43            warnings::warnif("overload arg '$_' is invalid")
44                unless exists $ops_seen{$_};
45            $sub = $arg{$_};
46            if (not ref $sub) {
47                $ {$package . "::(" . $_} = $sub;
48                $sub = \&nil;
49            }
50            #print STDERR "Setting '$ {'package'}::\cO$_' to \\&'$sub'.\n";
51            *{$package . "::(" . $_} = \&{ $sub };
52        }
53    }
54}
55
56sub import {
57    my $package = caller();
58    # *{$package . "::OVERLOAD"} = \&OVERLOAD;
59    shift;
60    $package->overload::OVERLOAD(@_);
61}
62
63sub unimport {
64    my $package = caller();
65    shift;
66    *{$package . "::(("} = \&nil;
67    for (@_) {
68        warnings::warnif("overload arg '$_' is invalid")
69            unless exists $ops_seen{$_};
70        delete $ {$package . "::"}{$_ eq 'fallback' ? '()' : "(" .$_};
71    }
72}
73
74sub Overloaded {
75    my $package = shift;
76    $package = ref $package if ref $package;
77    mycan ($package, '()') || mycan ($package, '((');
78}
79
80sub ov_method {
81    my $globref = shift;
82    return undef unless $globref;
83    my $sub = \&{*$globref};
84    no overloading;
85    return $sub if $sub != \&nil;
86    return shift->can($ {*$globref});
87}
88
89sub OverloadedStringify {
90    my $package = shift;
91    $package = ref $package if ref $package;
92    #$package->can('(""')
93    ov_method mycan($package, '(""'), $package
94        or ov_method mycan($package, '(0+'), $package
95        or ov_method mycan($package, '(bool'), $package
96        or ov_method mycan($package, '(nomethod'), $package;
97}
98
99sub Method {
100    my $package = shift;
101    if (ref $package) {
102        no warnings 'experimental::builtin';
103        $package = builtin::blessed($package);
104        return undef if !defined $package;
105    }
106    #my $meth = $package->can('(' . shift);
107    ov_method mycan($package, '(' . shift), $package;
108    #return $meth if $meth ne \&nil;
109    #return $ {*{$meth}};
110}
111
112sub AddrRef {
113    no overloading;
114    "$_[0]";
115}
116
117*StrVal = *AddrRef;
118
119sub mycan {                   # Real can would leave stubs.
120    my ($package, $meth) = @_;
121
122    local $@;
123    local $!;
124    require mro;
125
126    my $mro = mro::get_linear_isa($package);
127    foreach my $p (@$mro) {
128        my $fqmeth = $p . q{::} . $meth;
129        return \*{$fqmeth} if defined &{$fqmeth};
130    }
131
132    return undef;
133}
134
135my %constants = (
136    'integer'   =>  0x1000, # HINT_NEW_INTEGER
137    'float'     =>  0x2000, # HINT_NEW_FLOAT
138    'binary'    =>  0x4000, # HINT_NEW_BINARY
139    'q'         =>  0x8000, # HINT_NEW_STRING
140    'qr'        => 0x10000, # HINT_NEW_RE
141);
142
143use warnings::register;
144sub constant {
145    # Arguments: what, sub
146    while (@_) {
147        if (@_ == 1) {
148            warnings::warnif ("Odd number of arguments for overload::constant");
149            last;
150        }
151        elsif (!exists $constants {$_ [0]}) {
152            warnings::warnif ("'$_[0]' is not an overloadable type");
153        }
154        elsif (!ref $_ [1] || "$_[1]" !~ /(^|=)CODE\(0x[0-9a-f]+\)$/) {
155            # Can't use C<ref $_[1] eq "CODE"> above as code references can be
156            # blessed, and C<ref> would return the package the ref is blessed into.
157            if (warnings::enabled) {
158                $_ [1] = "undef" unless defined $_ [1];
159                warnings::warn ("'$_[1]' is not a code reference");
160            }
161        }
162        else {
163            $^H{$_[0]} = $_[1];
164            $^H |= $constants{$_[0]};
165        }
166        shift, shift;
167    }
168}
169
170sub remove_constant {
171    # Arguments: what, sub
172    while (@_) {
173        delete $^H{$_[0]};
174        $^H &= ~ $constants{$_[0]};
175        shift, shift;
176    }
177}
178
1791;
180
181__END__
182
183=head1 NAME
184
185overload - Package for overloading Perl operations
186
187=head1 SYNOPSIS
188
189    package SomeThing;
190
191    use overload
192        '+' => \&myadd,
193        '-' => \&mysub;
194        # etc
195    ...
196
197    package main;
198    $a = SomeThing->new( 57 );
199    $b = 5 + $a;
200    ...
201    if (overload::Overloaded $b) {...}
202    ...
203    $strval = overload::StrVal $b;
204
205=head1 DESCRIPTION
206
207This pragma allows overloading of Perl's operators for a class.
208To overload built-in functions, see L<perlsub/Overriding Built-in Functions> instead.
209
210=head2 Fundamentals
211
212=head3 Declaration
213
214Arguments of the C<use overload> directive are (key, value) pairs.
215For the full set of legal keys, see L</Overloadable Operations> below.
216
217Operator implementations (the values) can be subroutines,
218references to subroutines, or anonymous subroutines
219- in other words, anything legal inside a C<&{ ... }> call.
220Values specified as strings are interpreted as method names.
221Thus
222
223    package Number;
224    use overload
225        "-" => "minus",
226        "*=" => \&muas,
227        '""' => sub { ...; };
228
229declares that subtraction is to be implemented by method C<minus()>
230in the class C<Number> (or one of its base classes),
231and that the function C<Number::muas()> is to be used for the
232assignment form of multiplication, C<*=>.
233It also defines an anonymous subroutine to implement stringification:
234this is called whenever an object blessed into the package C<Number>
235is used in a string context (this subroutine might, for example,
236return the number as a Roman numeral).
237
238=head3 Calling Conventions and Magic Autogeneration
239
240The following sample implementation of C<minus()> (which assumes
241that C<Number> objects are simply blessed references to scalars)
242illustrates the calling conventions:
243
244    package Number;
245    sub minus {
246        my ($self, $other, $swap) = @_;
247        my $result = $$self - $other;         # *
248        $result = -$result if $swap;
249        ref $result ? $result : bless \$result;
250    }
251    # * may recurse once - see table below
252
253Three arguments are passed to all subroutines specified in the
254C<use overload> directive (with exceptions - see below, particularly
255L</nomethod>).
256
257The first of these is the operand providing the overloaded
258operator implementation -
259in this case, the object whose C<minus()> method is being called.
260
261The second argument is the other operand, or C<undef> in the
262case of a unary operator.
263
264The third argument is set to TRUE if (and only if) the two
265operands have been swapped.  Perl may do this to ensure that the
266first argument (C<$self>) is an object implementing the overloaded
267operation, in line with general object calling conventions.
268For example, if C<$x> and C<$y> are C<Number>s:
269
270    operation   |   generates a call to
271    ============|======================
272    $x - $y     |   minus($x, $y, '')
273    $x - 7      |   minus($x, 7, '')
274    7 - $x      |   minus($x, 7, 1)
275
276Perl may also use C<minus()> to implement other operators which
277have not been specified in the C<use overload> directive,
278according to the rules for L</Magic Autogeneration> described later.
279For example, the C<use overload> above declared no subroutine
280for any of the operators C<-->, C<neg> (the overload key for
281unary minus), or C<-=>.  Thus
282
283    operation   |   generates a call to
284    ============|======================
285    -$x         |   minus($x, 0, 1)
286    $x--        |   minus($x, 1, undef)
287    $x -= 3     |   minus($x, 3, undef)
288
289Note the C<undef>s:
290where autogeneration results in the method for a standard
291operator which does not change either of its operands, such
292as C<->, being used to implement an operator which changes
293the operand ("mutators": here, C<--> and C<-=>),
294Perl passes undef as the third argument.
295This still evaluates as FALSE, consistent with the fact that
296the operands have not been swapped, but gives the subroutine
297a chance to alter its behaviour in these cases.
298
299In all the above examples, C<minus()> is required
300only to return the result of the subtraction:
301Perl takes care of the assignment to $x.
302In fact, such methods should I<not> modify their operands,
303even if C<undef> is passed as the third argument
304(see L</Overloadable Operations>).
305
306The same is not true of implementations of C<++> and C<-->:
307these are expected to modify their operand.
308An appropriate implementation of C<--> might look like
309
310    use overload '--' => "decr",
311        # ...
312    sub decr { --${$_[0]}; }
313
314If the "bitwise" feature is enabled (see L<feature>), a fifth
315TRUE argument is passed to subroutines handling C<&>, C<|>, C<^> and C<~>.
316This indicates that the caller is expecting numeric behaviour.  The fourth
317argument will be C<undef>, as that position (C<$_[3]>) is reserved for use
318by L</nomethod>.
319
320=head3 Mathemagic, Mutators, and Copy Constructors
321
322The term 'mathemagic' describes the overloaded implementation
323of mathematical operators.
324Mathemagical operations raise an issue.
325Consider the code:
326
327    $a = $b;
328    --$a;
329
330If C<$a> and C<$b> are scalars then after these statements
331
332    $a == $b - 1
333
334An object, however, is a reference to blessed data, so if
335C<$a> and C<$b> are objects then the assignment C<$a = $b>
336copies only the reference, leaving C<$a> and C<$b> referring
337to the same object data.
338One might therefore expect the operation C<--$a> to decrement
339C<$b> as well as C<$a>.
340However, this would not be consistent with how we expect the
341mathematical operators to work.
342
343Perl resolves this dilemma by transparently calling a copy
344constructor before calling a method defined to implement
345a mutator (C<-->, C<+=>, and so on.).
346In the above example, when Perl reaches the decrement
347statement, it makes a copy of the object data in C<$a> and
348assigns to C<$a> a reference to the copied data.
349Only then does it call C<decr()>, which alters the copied
350data, leaving C<$b> unchanged.
351Thus the object metaphor is preserved as far as possible,
352while mathemagical operations still work according to the
353arithmetic metaphor.
354
355Note: the preceding paragraph describes what happens when
356Perl autogenerates the copy constructor for an object based
357on a scalar.
358For other cases, see L</Copy Constructor>.
359
360=head2 Overloadable Operations
361
362The complete list of keys that can be specified in the C<use overload>
363directive are given, separated by spaces, in the values of the
364hash C<%overload::ops>:
365
366    with_assign         => '+ - * / % ** << >> x .',
367    assign              => '+= -= *= /= %= **= <<= >>= x= .=',
368    num_comparison      => '< <= > >= == !=',
369    '3way_comparison'   => '<=> cmp',
370    str_comparison      => 'lt le gt ge eq ne',
371    binary              => '& &= | |= ^ ^= &. &.= |. |.= ^. ^.=',
372    unary               => 'neg ! ~ ~.',
373    mutators            => '++ --',
374    func                => 'atan2 cos sin exp abs log sqrt int',
375    conversion          => 'bool "" 0+ qr',
376    iterators           => '<>',
377    filetest            => '-X',
378    dereferencing       => '${} @{} %{} &{} *{}',
379    matching            => '~~',
380    special             => 'nomethod fallback =',
381
382Most of the overloadable operators map one-to-one to these keys.
383Exceptions, including additional overloadable operations not
384apparent from this hash, are included in the notes which follow.
385This list is subject to growth over time.
386
387A warning is issued if an attempt is made to register an operator not found
388above.
389
390=over 5
391
392=item * C<not>
393
394The operator C<not> is not a valid key for C<use overload>.
395However, if the operator C<!> is overloaded then the same
396implementation will be used for C<not>
397(since the two operators differ only in precedence).
398
399=item * C<neg>
400
401The key C<neg> is used for unary minus to disambiguate it from
402binary C<->.
403
404=item * C<++>, C<-->
405
406Assuming they are to behave analogously to Perl's C<++> and C<-->,
407overloaded implementations of these operators are required to
408mutate their operands.
409
410No distinction is made between prefix and postfix forms of the
411increment and decrement operators: these differ only in the
412point at which Perl calls the associated subroutine when
413evaluating an expression.
414
415=item * I<Assignments>
416
417    +=  -=  *=  /=  %=  **=  <<=  >>=  x=  .=
418    &=  |=  ^=  &.=  |.=  ^.=
419
420Simple assignment is not overloadable (the C<'='> key is used
421for the L</Copy Constructor>).
422Perl does have a way to make assignments to an object do whatever
423you want, but this involves using tie(), not overload -
424see L<perlfunc/tie> and the L</COOKBOOK> examples below.
425
426The subroutine for the assignment variant of an operator is
427required only to return the result of the operation.
428It is permitted to change the value of its operand
429(this is safe because Perl calls the copy constructor first),
430but this is optional since Perl assigns the returned value to
431the left-hand operand anyway.
432
433An object that overloads an assignment operator does so only in
434respect of assignments to that object.
435In other words, Perl never calls the corresponding methods with
436the third argument (the "swap" argument) set to TRUE.
437For example, the operation
438
439    $a *= $b
440
441cannot lead to C<$b>'s implementation of C<*=> being called,
442even if C<$a> is a scalar.
443(It can, however, generate a call to C<$b>'s method for C<*>).
444
445=item * I<Non-mutators with a mutator variant>
446
447     +  -  *  /  %  **  <<  >>  x  .
448     &  |  ^  &.  |.  ^.
449
450As described L<above|"Calling Conventions and Magic Autogeneration">,
451Perl may call methods for operators like C<+> and C<&> in the course
452of implementing missing operations like C<++>, C<+=>, and C<&=>.
453While these methods may detect this usage by testing the definedness
454of the third argument, they should in all cases avoid changing their
455operands.
456This is because Perl does not call the copy constructor before
457invoking these methods.
458
459=item * C<int>
460
461Traditionally, the Perl function C<int> rounds to 0
462(see L<perlfunc/int>), and so for floating-point-like types one
463should follow the same semantic.
464
465=item * I<String, numeric, boolean, and regexp conversions>
466
467    ""  0+  bool
468
469These conversions are invoked according to context as necessary.
470For example, the subroutine for C<'""'> (stringify) may be used
471where the overloaded object is passed as an argument to C<print>,
472and that for C<'bool'> where it is tested in the condition of a flow
473control statement (like C<while>) or the ternary C<?:> operation.
474
475Of course, in contexts like, for example, C<$obj + 1>, Perl will
476invoke C<$obj>'s implementation of C<+> rather than (in this
477example) converting C<$obj> to a number using the numify method
478C<'0+'> (an exception to this is when no method has been provided
479for C<'+'> and L</fallback> is set to TRUE).
480
481The subroutines for C<'""'>, C<'0+'>, and C<'bool'> can return
482any arbitrary Perl value.
483If the corresponding operation for this value is overloaded too,
484the operation will be called again with this value.
485
486As a special case if the overload returns the object itself then it will
487be used directly.  An overloaded conversion returning the object is
488probably a bug, because you're likely to get something that looks like
489C<YourPackage=HASH(0x8172b34)>.
490
491    qr
492
493The subroutine for C<'qr'> is used wherever the object is
494interpolated into or used as a regexp, including when it
495appears on the RHS of a C<=~> or C<!~> operator.
496
497C<qr> must return a compiled regexp, or a ref to a compiled regexp
498(such as C<qr//> returns), and any further overloading on the return
499value will be ignored.
500
501=item * I<Iteration>
502
503If C<E<lt>E<gt>> is overloaded then the same implementation is used
504for both the I<read-filehandle> syntax C<E<lt>$varE<gt>> and
505I<globbing> syntax C<E<lt>${var}E<gt>>.
506
507=item * I<File tests>
508
509The key C<'-X'> is used to specify a subroutine to handle all the
510filetest operators (C<-f>, C<-x>, and so on: see L<perlfunc/-X> for
511the full list);
512it is not possible to overload any filetest operator individually.
513To distinguish them, the letter following the '-' is passed as the
514second argument (that is, in the slot that for binary operators
515is used to pass the second operand).
516
517Calling an overloaded filetest operator does not affect the stat value
518associated with the special filehandle C<_>.  It still refers to the
519result of the last C<stat>, C<lstat> or unoverloaded filetest.
520
521This overload was introduced in Perl 5.12.
522
523=item * I<Matching>
524
525The key C<"~~"> allows you to override the smart matching logic used by
526the C<~~> operator and the switch construct (C<given>/C<when>).  See
527L<perlsyn/Switch Statements> and L<feature>.
528
529Unusually, the overloaded implementation of the smart match operator
530does not get full control of the smart match behaviour.
531In particular, in the following code:
532
533    package Foo;
534    use overload '~~' => 'match';
535
536    my $obj =  Foo->new();
537    $obj ~~ [ 1,2,3 ];
538
539the smart match does I<not> invoke the method call like this:
540
541    $obj->match([1,2,3],0);
542
543rather, the smart match distributive rule takes precedence, so $obj is
544smart matched against each array element in turn until a match is found,
545so you may see between one and three of these calls instead:
546
547    $obj->match(1,0);
548    $obj->match(2,0);
549    $obj->match(3,0);
550
551Consult the match table in  L<perlop/"Smartmatch Operator"> for
552details of when overloading is invoked.
553
554=item * I<Dereferencing>
555
556    ${}  @{}  %{}  &{}  *{}
557
558If these operators are not explicitly overloaded then they
559work in the normal way, yielding the underlying scalar,
560array, or whatever stores the object data (or the appropriate
561error message if the dereference operator doesn't match it).
562Defining a catch-all C<'nomethod'> (see L<below|/nomethod>)
563makes no difference to this as the catch-all function will
564not be called to implement a missing dereference operator.
565
566If a dereference operator is overloaded then it must return a
567I<reference> of the appropriate type (for example, the
568subroutine for key C<'${}'> should return a reference to a
569scalar, not a scalar), or another object which overloads the
570operator: that is, the subroutine only determines what is
571dereferenced and the actual dereferencing is left to Perl.
572As a special case, if the subroutine returns the object itself
573then it will not be called again - avoiding infinite recursion.
574
575=item * I<Special>
576
577    nomethod  fallback  =
578
579See L</Special Keys for C<use overload>>.
580
581=back
582
583=head2 Magic Autogeneration
584
585If a method for an operation is not found then Perl tries to
586autogenerate a substitute implementation from the operations
587that have been defined.
588
589Note: the behaviour described in this section can be disabled
590by setting C<fallback> to FALSE (see L</fallback>).
591
592In the following tables, numbers indicate priority.
593For example, the table below states that,
594if no implementation for C<'!'> has been defined then Perl will
595implement it using C<'bool'> (that is, by inverting the value
596returned by the method for C<'bool'>);
597if boolean conversion is also unimplemented then Perl will
598use C<'0+'> or, failing that, C<'""'>.
599
600    operator | can be autogenerated from
601             |
602             | 0+   ""   bool   .   x
603    =========|==========================
604       0+    |       1     2
605       ""    |  1          2
606       bool  |  1    2
607       int   |  1    2     3
608       !     |  2    3     1
609       qr    |  2    1     3
610       .     |  2    1     3
611       x     |  2    1     3
612       .=    |  3    2     4    1
613       x=    |  3    2     4        1
614       <>    |  2    1     3
615       -X    |  2    1     3
616
617Note: The iterator (C<'E<lt>E<gt>'>) and file test (C<'-X'>)
618operators work as normal: if the operand is not a blessed glob or
619IO reference then it is converted to a string (using the method
620for C<'""'>, C<'0+'>, or C<'bool'>) to be interpreted as a glob
621or filename.
622
623    operator | can be autogenerated from
624             |
625             |  <   <=>   neg   -=    -
626    =========|==========================
627       neg   |                        1
628       -=    |                        1
629       --    |                   1    2
630       abs   | a1    a2    b1        b2    [*]
631       <     |        1
632       <=    |        1
633       >     |        1
634       >=    |        1
635       ==    |        1
636       !=    |        1
637
638    * one from [a1, a2] and one from [b1, b2]
639
640Just as numeric comparisons can be autogenerated from the method
641for C<< '<=>' >>, string comparisons can be autogenerated from
642that for C<'cmp'>:
643
644     operators          |  can be autogenerated from
645    ====================|===========================
646     lt gt le ge eq ne  |  cmp
647
648Similarly, autogeneration for keys C<'+='> and C<'++'> is analogous
649to C<'-='> and C<'--'> above:
650
651    operator | can be autogenerated from
652             |
653             |  +=    +
654    =========|==========================
655        +=   |        1
656        ++   |   1    2
657
658And other assignment variations are analogous to
659C<'+='> and C<'-='> (and similar to C<'.='> and C<'x='> above):
660
661              operator ||  *= /= %= **= <<= >>= &= ^= |= &.= ^.= |.=
662    -------------------||-------------------------------------------
663    autogenerated from ||  *  /  %  **  <<  >>  &  ^  |  &.  ^.  |.
664
665Note also that the copy constructor (key C<'='>) may be
666autogenerated, but only for objects based on scalars.
667See L</Copy Constructor>.
668
669=head3 Minimal Set of Overloaded Operations
670
671Since some operations can be automatically generated from others, there is
672a minimal set of operations that need to be overloaded in order to have
673the complete set of overloaded operations at one's disposal.
674Of course, the autogenerated operations may not do exactly what the user
675expects.  The minimal set is:
676
677    + - * / % ** << >> x
678    <=> cmp
679    & | ^ ~ &. |. ^. ~.
680    atan2 cos sin exp log sqrt int
681    "" 0+ bool
682    ~~
683
684Of the conversions, only one of string, boolean or numeric is
685needed because each can be generated from either of the other two.
686
687=head2 Special Keys for C<use overload>
688
689=head3 C<nomethod>
690
691The C<'nomethod'> key is used to specify a catch-all function to
692be called for any operator that is not individually overloaded.
693The specified function will be passed four parameters.
694The first three arguments coincide with those that would have been
695passed to the corresponding method if it had been defined.
696The fourth argument is the C<use overload> key for that missing
697method.  If the "bitwise" feature is enabled (see L<feature>),
698a fifth TRUE argument is passed to subroutines handling C<&>, C<|>, C<^> and C<~> to indicate that the caller is expecting numeric behaviour.
699
700For example, if C<$a> is an object blessed into a package declaring
701
702    use overload 'nomethod' => 'catch_all', # ...
703
704then the operation
705
706    3 + $a
707
708could (unless a method is specifically declared for the key
709C<'+'>) result in a call
710
711    catch_all($a, 3, 1, '+')
712
713See L</How Perl Chooses an Operator Implementation>.
714
715=head3 C<fallback>
716
717The value assigned to the key C<'fallback'> tells Perl how hard
718it should try to find an alternative way to implement a missing
719operator.
720
721=over
722
723=item * defined, but FALSE
724
725    use overload "fallback" => 0, # ... ;
726
727This disables L</Magic Autogeneration>.
728
729=item * C<undef>
730
731In the default case where no value is explicitly assigned to
732C<fallback>, magic autogeneration is enabled.
733
734=item * TRUE
735
736The same as for C<undef>, but if a missing operator cannot be
737autogenerated then, instead of issuing an error message, Perl
738is allowed to revert to what it would have done for that
739operator if there had been no C<use overload> directive.
740
741Note: in most cases, particularly the L</Copy Constructor>,
742this is unlikely to be appropriate behaviour.
743
744=back
745
746See L</How Perl Chooses an Operator Implementation>.
747
748=head3 Copy Constructor
749
750As mentioned L<above|"Mathemagic, Mutators, and Copy Constructors">,
751this operation is called when a mutator is applied to a reference
752that shares its object with some other reference.
753For example, if C<$b> is mathemagical, and C<'++'> is overloaded
754with C<'incr'>, and C<'='> is overloaded with C<'clone'>, then the
755code
756
757    $a = $b;
758    # ... (other code which does not modify $a or $b) ...
759    ++$b;
760
761would be executed in a manner equivalent to
762
763    $a = $b;
764    # ...
765    $b = $b->clone(undef, "");
766    $b->incr(undef, "");
767
768Note:
769
770=over
771
772=item *
773
774The subroutine for C<'='> does not overload the Perl assignment
775operator: it is used only to allow mutators to work as described
776here.  (See L</Assignments> above.)
777
778=item *
779
780As for other operations, the subroutine implementing '=' is passed
781three arguments, though the last two are always C<undef> and C<''>.
782
783=item *
784
785The copy constructor is called only before a call to a function
786declared to implement a mutator, for example, if C<++$b;> in the
787code above is effected via a method declared for key C<'++'>
788(or 'nomethod', passed C<'++'> as the fourth argument) or, by
789autogeneration, C<'+='>.
790It is not called if the increment operation is effected by a call
791to the method for C<'+'> since, in the equivalent code,
792
793    $a = $b;
794    $b = $b + 1;
795
796the data referred to by C<$a> is unchanged by the assignment to
797C<$b> of a reference to new object data.
798
799=item *
800
801The copy constructor is not called if Perl determines that it is
802unnecessary because there is no other reference to the data being
803modified.
804
805=item *
806
807If C<'fallback'> is undefined or TRUE then a copy constructor
808can be autogenerated, but only for objects based on scalars.
809In other cases it needs to be defined explicitly.
810Where an object's data is stored as, for example, an array of
811scalars, the following might be appropriate:
812
813    use overload '=' => sub { bless [ @{$_[0]} ] },  # ...
814
815=item *
816
817If C<'fallback'> is TRUE and no copy constructor is defined then,
818for objects not based on scalars, Perl may silently fall back on
819simple assignment - that is, assignment of the object reference.
820In effect, this disables the copy constructor mechanism since
821no new copy of the object data is created.
822This is almost certainly not what you want.
823(It is, however, consistent: for example, Perl's fallback for the
824C<++> operator is to increment the reference itself.)
825
826=back
827
828=head2 How Perl Chooses an Operator Implementation
829
830Which is checked first, C<nomethod> or C<fallback>?
831If the two operands of an operator are of different types and
832both overload the operator, which implementation is used?
833The following are the precedence rules:
834
835=over
836
837=item 1.
838
839If the first operand has declared a subroutine to overload the
840operator then use that implementation.
841
842=item 2.
843
844Otherwise, if fallback is TRUE or undefined for the
845first operand then see if the
846L<rules for autogeneration|"Magic Autogeneration">
847allows another of its operators to be used instead.
848
849=item 3.
850
851Unless the operator is an assignment (C<+=>, C<-=>, etc.),
852repeat step (1) in respect of the second operand.
853
854=item 4.
855
856Repeat Step (2) in respect of the second operand.
857
858=item 5.
859
860If the first operand has a "nomethod" method then use that.
861
862=item 6.
863
864If the second operand has a "nomethod" method then use that.
865
866=item 7.
867
868If C<fallback> is TRUE for both operands
869then perform the usual operation for the operator,
870treating the operands as numbers, strings, or booleans
871as appropriate for the operator (see note).
872
873=item 8.
874
875Nothing worked - die.
876
877=back
878
879Where there is only one operand (or only one operand with
880overloading) the checks in respect of the other operand above are
881skipped.
882
883There are exceptions to the above rules for dereference operations
884(which, if Step 1 fails, always fall back to the normal, built-in
885implementations - see Dereferencing), and for C<~~> (which has its
886own set of rules - see C<Matching> under L</Overloadable Operations>
887above).
888
889Note on Step 7: some operators have a different semantic depending
890on the type of their operands.
891As there is no way to instruct Perl to treat the operands as, e.g.,
892numbers instead of strings, the result here may not be what you
893expect.
894See L</BUGS AND PITFALLS>.
895
896=head2 Losing Overloading
897
898The restriction for the comparison operation is that even if, for example,
899C<cmp> should return a blessed reference, the autogenerated C<lt>
900function will produce only a standard logical value based on the
901numerical value of the result of C<cmp>.  In particular, a working
902numeric conversion is needed in this case (possibly expressed in terms of
903other conversions).
904
905Similarly, C<.=>  and C<x=> operators lose their mathemagical properties
906if the string conversion substitution is applied.
907
908When you chop() a mathemagical object it is promoted to a string and its
909mathemagical properties are lost.  The same can happen with other
910operations as well.
911
912=head2 Inheritance and Overloading
913
914Overloading respects inheritance via the @ISA hierarchy.
915Inheritance interacts with overloading in two ways.
916
917=over
918
919=item Method names in the C<use overload> directive
920
921If C<value> in
922
923    use overload key => value;
924
925is a string, it is interpreted as a method name - which may
926(in the usual way) be inherited from another class.
927
928=item Overloading of an operation is inherited by derived classes
929
930Any class derived from an overloaded class is also overloaded
931and inherits its operator implementations.
932If the same operator is overloaded in more than one ancestor
933then the implementation is determined by the usual inheritance
934rules.
935
936For example, if C<A> inherits from C<B> and C<C> (in that order),
937C<B> overloads C<+> with C<\&D::plus_sub>, and C<C> overloads
938C<+> by C<"plus_meth">, then the subroutine C<D::plus_sub> will
939be called to implement operation C<+> for an object in package C<A>.
940
941=back
942
943Note that in Perl version prior to 5.18 inheritance of the C<fallback> key
944was not governed by the above rules.  The value of C<fallback> in the first
945overloaded ancestor was used.  This was fixed in 5.18 to follow the usual
946rules of inheritance.
947
948=head2 Run-time Overloading
949
950Since all C<use> directives are executed at compile-time, the only way to
951change overloading during run-time is to
952
953    eval 'use overload "+" => \&addmethod';
954
955You can also use
956
957    eval 'no overload "+", "--", "<="';
958
959though the use of these constructs during run-time is questionable.
960
961=head2 Public Functions
962
963Package C<overload.pm> provides the following public functions:
964
965=over 5
966
967=item overload::StrVal(arg)
968
969Gives the string value of C<arg> as in the
970absence of stringify overloading.  If you
971are using this to get the address of a reference (useful for checking if two
972references point to the same thing) then you may be better off using
973C<builtin::refaddr()> or C<Scalar::Util::refaddr()>, which are faster.
974
975=item overload::Overloaded(arg)
976
977Returns true if C<arg> is subject to overloading of some operations.
978
979=item overload::Method(obj,op)
980
981Returns C<undef> or a reference to the method that implements C<op>.
982
983Such a method always takes three arguments, which will be enforced if
984it is an XS method.
985
986=back
987
988=head2 Overloading Constants
989
990For some applications, the Perl parser mangles constants too much.
991It is possible to hook into this process via C<overload::constant()>
992and C<overload::remove_constant()> functions.
993
994These functions take a hash as an argument.  The recognized keys of this hash
995are:
996
997=over 8
998
999=item integer
1000
1001to overload integer constants,
1002
1003=item float
1004
1005to overload floating point constants,
1006
1007=item binary
1008
1009to overload octal and hexadecimal constants,
1010
1011=item q
1012
1013to overload C<q>-quoted strings, constant pieces of C<qq>- and C<qx>-quoted
1014strings and here-documents,
1015
1016=item qr
1017
1018to overload constant pieces of regular expressions.
1019
1020=back
1021
1022The corresponding values are references to functions which take three arguments:
1023the first one is the I<initial> string form of the constant, the second one
1024is how Perl interprets this constant, the third one is how the constant is used.
1025Note that the initial string form does not
1026contain string delimiters, and has backslashes in backslash-delimiter
1027combinations stripped (thus the value of delimiter is not relevant for
1028processing of this string).  The return value of this function is how this
1029constant is going to be interpreted by Perl.  The third argument is undefined
1030unless for overloaded C<q>- and C<qr>- constants, it is C<q> in single-quote
1031context (comes from strings, regular expressions, and single-quote HERE
1032documents), it is C<tr> for arguments of C<tr>/C<y> operators,
1033it is C<s> for right-hand side of C<s>-operator, and it is C<qq> otherwise.
1034
1035Since an expression C<"ab$cd,,"> is just a shortcut for C<'ab' . $cd . ',,'>,
1036it is expected that overloaded constant strings are equipped with reasonable
1037overloaded catenation operator, otherwise absurd results will result.
1038Similarly, negative numbers are considered as negations of positive constants.
1039
1040Note that it is probably meaningless to call the functions overload::constant()
1041and overload::remove_constant() from anywhere but import() and unimport() methods.
1042From these methods they may be called as
1043
1044    sub import {
1045        shift;
1046        return unless @_;
1047        die "unknown import: @_" unless @_ == 1 and $_[0] eq ':constant';
1048        overload::constant integer => sub {Math::BigInt->new(shift)};
1049    }
1050
1051=head1 IMPLEMENTATION
1052
1053What follows is subject to change RSN.
1054
1055The table of methods for all operations is cached in magic for the
1056symbol table hash for the package.  The cache is invalidated during
1057processing of C<use overload>, C<no overload>, new function
1058definitions, and changes in @ISA.
1059
1060(Every SVish thing has a magic queue, and magic is an entry in that
1061queue.  This is how a single variable may participate in multiple
1062forms of magic simultaneously.  For instance, environment variables
1063regularly have two forms at once: their %ENV magic and their taint
1064magic.  However, the magic which implements overloading is applied to
1065the stashes, which are rarely used directly, thus should not slow down
1066Perl.)
1067
1068If a package uses overload, it carries a special flag.  This flag is also
1069set when new functions are defined or @ISA is modified.  There will be a
1070slight speed penalty on the very first operation thereafter that supports
1071overloading, while the overload tables are updated.  If there is no
1072overloading present, the flag is turned off.  Thus the only speed penalty
1073thereafter is the checking of this flag.
1074
1075It is expected that arguments to methods that are not explicitly supposed
1076to be changed are constant (but this is not enforced).
1077
1078=head1 COOKBOOK
1079
1080Please add examples to what follows!
1081
1082=head2 Two-face Scalars
1083
1084Put this in F<two_face.pm> in your Perl library directory:
1085
1086    package two_face;             # Scalars with separate string and
1087                                  # numeric values.
1088    sub new { my $p = shift; bless [@_], $p }
1089    use overload '""' => \&str, '0+' => \&num, fallback => 1;
1090    sub num {shift->[1]}
1091    sub str {shift->[0]}
1092
1093Use it as follows:
1094
1095    require two_face;
1096    my $seven = two_face->new("vii", 7);
1097    printf "seven=$seven, seven=%d, eight=%d\n", $seven, $seven+1;
1098    print "seven contains 'i'\n" if $seven =~ /i/;
1099
1100(The second line creates a scalar which has both a string value, and a
1101numeric value.)  This prints:
1102
1103    seven=vii, seven=7, eight=8
1104    seven contains 'i'
1105
1106=head2 Two-face References
1107
1108Suppose you want to create an object which is accessible as both an
1109array reference and a hash reference.
1110
1111    package two_refs;
1112    use overload '%{}' => \&gethash, '@{}' => sub { $ {shift()} };
1113    sub new {
1114        my $p = shift;
1115        bless \ [@_], $p;
1116    }
1117    sub gethash {
1118        my %h;
1119        my $self = shift;
1120        tie %h, ref $self, $self;
1121        \%h;
1122    }
1123
1124    sub TIEHASH { my $p = shift; bless \ shift, $p }
1125    my %fields;
1126    my $i = 0;
1127    $fields{$_} = $i++ foreach qw{zero one two three};
1128    sub STORE {
1129        my $self = ${shift()};
1130        my $key = $fields{shift()};
1131        defined $key or die "Out of band access";
1132        $$self->[$key] = shift;
1133    }
1134    sub FETCH {
1135        my $self = ${shift()};
1136        my $key = $fields{shift()};
1137        defined $key or die "Out of band access";
1138        $$self->[$key];
1139    }
1140
1141Now one can access an object using both the array and hash syntax:
1142
1143    my $bar = two_refs->new(3,4,5,6);
1144    $bar->[2] = 11;
1145    $bar->{two} == 11 or die 'bad hash fetch';
1146
1147Note several important features of this example.  First of all, the
1148I<actual> type of $bar is a scalar reference, and we do not overload
1149the scalar dereference.  Thus we can get the I<actual> non-overloaded
1150contents of $bar by just using C<$$bar> (what we do in functions which
1151overload dereference).  Similarly, the object returned by the
1152TIEHASH() method is a scalar reference.
1153
1154Second, we create a new tied hash each time the hash syntax is used.
1155This allows us not to worry about a possibility of a reference loop,
1156which would lead to a memory leak.
1157
1158Both these problems can be cured.  Say, if we want to overload hash
1159dereference on a reference to an object which is I<implemented> as a
1160hash itself, the only problem one has to circumvent is how to access
1161this I<actual> hash (as opposed to the I<virtual> hash exhibited by the
1162overloaded dereference operator).  Here is one possible fetching routine:
1163
1164    sub access_hash {
1165        my ($self, $key) = (shift, shift);
1166        my $class = ref $self;
1167        bless $self, 'overload::dummy'; # Disable overloading of %{}
1168        my $out = $self->{$key};
1169        bless $self, $class;            # Restore overloading
1170        $out;
1171    }
1172
1173To remove creation of the tied hash on each access, one may an extra
1174level of indirection which allows a non-circular structure of references:
1175
1176    package two_refs1;
1177    use overload
1178        '%{}' => sub { ${shift()}->[1] },
1179        '@{}' => sub { ${shift()}->[0] };
1180
1181    sub new {
1182        my $p = shift;
1183        my $a = [@_];
1184        my %h;
1185        tie %h, $p, $a;
1186        bless \ [$a, \%h], $p;
1187    }
1188    sub gethash {
1189        my %h;
1190        my $self = shift;
1191        tie %h, ref $self, $self;
1192        \%h;
1193    }
1194
1195    sub TIEHASH { my $p = shift; bless \ shift, $p }
1196    my %fields;
1197    my $i = 0;
1198    $fields{$_} = $i++ foreach qw{zero one two three};
1199    sub STORE {
1200        my $a = ${shift()};
1201        my $key = $fields{shift()};
1202        defined $key or die "Out of band access";
1203        $a->[$key] = shift;
1204    }
1205    sub FETCH {
1206        my $a = ${shift()};
1207        my $key = $fields{shift()};
1208        defined $key or die "Out of band access";
1209        $a->[$key];
1210    }
1211
1212Now if $baz is overloaded like this, then C<$baz> is a reference to a
1213reference to the intermediate array, which keeps a reference to an
1214actual array, and the access hash.  The tie()ing object for the access
1215hash is a reference to a reference to the actual array, so
1216
1217=over
1218
1219=item *
1220
1221There are no loops of references.
1222
1223=item *
1224
1225Both "objects" which are blessed into the class C<two_refs1> are
1226references to a reference to an array, thus references to a I<scalar>.
1227Thus the accessor expression C<$$foo-E<gt>[$ind]> involves no
1228overloaded operations.
1229
1230=back
1231
1232=head2 Symbolic Calculator
1233
1234Put this in F<symbolic.pm> in your Perl library directory:
1235
1236    package symbolic;           # Primitive symbolic calculator
1237    use overload nomethod => \&wrap;
1238
1239    sub new { shift; bless ['n', @_] }
1240    sub wrap {
1241        my ($obj, $other, $inv, $meth) = @_;
1242        ($obj, $other) = ($other, $obj) if $inv;
1243        bless [$meth, $obj, $other];
1244    }
1245
1246This module is very unusual as overloaded modules go: it does not
1247provide any usual overloaded operators, instead it provides an
1248implementation for C<L</nomethod>>.  In this example the C<nomethod>
1249subroutine returns an object which encapsulates operations done over
1250the objects: C<< symbolic->new(3) >> contains C<['n', 3]>, C<< 2 +
1251symbolic->new(3) >> contains C<['+', 2, ['n', 3]]>.
1252
1253Here is an example of the script which "calculates" the side of
1254circumscribed octagon using the above package:
1255
1256    require symbolic;
1257    my $iter = 1;                   # 2**($iter+2) = 8
1258    my $side = symbolic->new(1);
1259    my $cnt = $iter;
1260
1261    while ($cnt--) {
1262        $side = (sqrt(1 + $side**2) - 1)/$side;
1263    }
1264    print "OK\n";
1265
1266The value of $side is
1267
1268    ['/', ['-', ['sqrt', ['+', 1, ['**', ['n', 1], 2]],
1269                        undef], 1], ['n', 1]]
1270
1271Note that while we obtained this value using a nice little script,
1272there is no simple way to I<use> this value.  In fact this value may
1273be inspected in debugger (see L<perldebug>), but only if
1274C<bareStringify> B<O>ption is set, and not via C<p> command.
1275
1276If one attempts to print this value, then the overloaded operator
1277C<""> will be called, which will call C<nomethod> operator.  The
1278result of this operator will be stringified again, but this result is
1279again of type C<symbolic>, which will lead to an infinite loop.
1280
1281Add a pretty-printer method to the module F<symbolic.pm>:
1282
1283    sub pretty {
1284        my ($meth, $a, $b) = @{+shift};
1285        $a = 'u' unless defined $a;
1286        $b = 'u' unless defined $b;
1287        $a = $a->pretty if ref $a;
1288        $b = $b->pretty if ref $b;
1289        "[$meth $a $b]";
1290    }
1291
1292Now one can finish the script by
1293
1294    print "side = ", $side->pretty, "\n";
1295
1296The method C<pretty> is doing object-to-string conversion, so it
1297is natural to overload the operator C<""> using this method.  However,
1298inside such a method it is not necessary to pretty-print the
1299I<components> $a and $b of an object.  In the above subroutine
1300C<"[$meth $a $b]"> is a catenation of some strings and components $a
1301and $b.  If these components use overloading, the catenation operator
1302will look for an overloaded operator C<.>; if not present, it will
1303look for an overloaded operator C<"">.  Thus it is enough to use
1304
1305    use overload nomethod => \&wrap, '""' => \&str;
1306    sub str {
1307        my ($meth, $a, $b) = @{+shift};
1308        $a = 'u' unless defined $a;
1309        $b = 'u' unless defined $b;
1310        "[$meth $a $b]";
1311    }
1312
1313Now one can change the last line of the script to
1314
1315    print "side = $side\n";
1316
1317which outputs
1318
1319    side = [/ [- [sqrt [+ 1 [** [n 1 u] 2]] u] 1] [n 1 u]]
1320
1321and one can inspect the value in debugger using all the possible
1322methods.
1323
1324Something is still amiss: consider the loop variable $cnt of the
1325script.  It was a number, not an object.  We cannot make this value of
1326type C<symbolic>, since then the loop will not terminate.
1327
1328Indeed, to terminate the cycle, the $cnt should become false.
1329However, the operator C<bool> for checking falsity is overloaded (this
1330time via overloaded C<"">), and returns a long string, thus any object
1331of type C<symbolic> is true.  To overcome this, we need a way to
1332compare an object to 0.  In fact, it is easier to write a numeric
1333conversion routine.
1334
1335Here is the text of F<symbolic.pm> with such a routine added (and
1336slightly modified str()):
1337
1338    package symbolic;           # Primitive symbolic calculator
1339    use overload
1340        nomethod => \&wrap, '""' => \&str, '0+' => \&num;
1341
1342    sub new { shift; bless ['n', @_] }
1343    sub wrap {
1344        my ($obj, $other, $inv, $meth) = @_;
1345        ($obj, $other) = ($other, $obj) if $inv;
1346        bless [$meth, $obj, $other];
1347    }
1348    sub str {
1349        my ($meth, $a, $b) = @{+shift};
1350        $a = 'u' unless defined $a;
1351        if (defined $b) {
1352            "[$meth $a $b]";
1353        } else {
1354            "[$meth $a]";
1355        }
1356    }
1357    my %subr = (
1358        n => sub {$_[0]},
1359        sqrt => sub {sqrt $_[0]},
1360        '-' => sub {shift() - shift()},
1361        '+' => sub {shift() + shift()},
1362        '/' => sub {shift() / shift()},
1363        '*' => sub {shift() * shift()},
1364        '**' => sub {shift() ** shift()},
1365    );
1366    sub num {
1367        my ($meth, $a, $b) = @{+shift};
1368        my $subr = $subr{$meth}
1369        or die "Do not know how to ($meth) in symbolic";
1370        $a = $a->num if ref $a eq __PACKAGE__;
1371        $b = $b->num if ref $b eq __PACKAGE__;
1372        $subr->($a,$b);
1373    }
1374
1375All the work of numeric conversion is done in %subr and num().  Of
1376course, %subr is not complete, it contains only operators used in the
1377example below.  Here is the extra-credit question: why do we need an
1378explicit recursion in num()?  (Answer is at the end of this section.)
1379
1380Use this module like this:
1381
1382    require symbolic;
1383    my $iter = symbolic->new(2);        # 16-gon
1384    my $side = symbolic->new(1);
1385    my $cnt = $iter;
1386
1387    while ($cnt) {
1388        $cnt = $cnt - 1;                # Mutator '--' not implemented
1389        $side = (sqrt(1 + $side**2) - 1)/$side;
1390    }
1391    printf "%s=%f\n", $side, $side;
1392    printf "pi=%f\n", $side*(2**($iter+2));
1393
1394It prints (without so many line breaks)
1395
1396    [/ [- [sqrt [+ 1 [** [/ [- [sqrt [+ 1 [** [n 1] 2]]] 1]
1397                            [n 1]] 2]]] 1]
1398    [/ [- [sqrt [+ 1 [** [n 1] 2]]] 1] [n 1]]]=0.198912
1399    pi=3.182598
1400
1401The above module is very primitive.  It does not implement
1402mutator methods (C<++>, C<-=> and so on), does not do deep copying
1403(not required without mutators!), and implements only those arithmetic
1404operations which are used in the example.
1405
1406To implement most arithmetic operations is easy; one should just use
1407the tables of operations, and change the code which fills %subr to
1408
1409    my %subr = ( 'n' => sub {$_[0]} );
1410    foreach my $op (split " ", $overload::ops{with_assign}) {
1411        $subr{$op} = $subr{"$op="} = eval "sub {shift() $op shift()}";
1412    }
1413    my @bins = qw(binary 3way_comparison num_comparison str_comparison);
1414    foreach my $op (split " ", "@overload::ops{ @bins }") {
1415        $subr{$op} = eval "sub {shift() $op shift()}";
1416    }
1417    foreach my $op (split " ", "@overload::ops{qw(unary func)}") {
1418        print "defining '$op'\n";
1419        $subr{$op} = eval "sub {$op shift()}";
1420    }
1421
1422Since subroutines implementing assignment operators are not required
1423to modify their operands (see L</Overloadable Operations> above),
1424we do not need anything special to make C<+=> and friends work,
1425besides adding these operators to %subr and defining a copy
1426constructor (needed since Perl has no way to know that the
1427implementation of C<'+='> does not mutate the argument -
1428see L</Copy Constructor>).
1429
1430To implement a copy constructor, add C<< '=' => \&cpy >> to C<use overload>
1431line, and code (this code assumes that mutators change things one level
1432deep only, so recursive copying is not needed):
1433
1434    sub cpy {
1435        my $self = shift;
1436        bless [@$self], ref $self;
1437    }
1438
1439To make C<++> and C<--> work, we need to implement actual mutators,
1440either directly, or in C<nomethod>.  We continue to do things inside
1441C<nomethod>, thus add
1442
1443    if ($meth eq '++' or $meth eq '--') {
1444        @$obj = ($meth, (bless [@$obj]), 1); # Avoid circular reference
1445        return $obj;
1446    }
1447
1448after the first line of wrap().  This is not a most effective
1449implementation, one may consider
1450
1451    sub inc { $_[0] = bless ['++', shift, 1]; }
1452
1453instead.
1454
1455As a final remark, note that one can fill %subr by
1456
1457    my %subr = ( 'n' => sub {$_[0]} );
1458    foreach my $op (split " ", $overload::ops{with_assign}) {
1459        $subr{$op} = $subr{"$op="} = eval "sub {shift() $op shift()}";
1460    }
1461    my @bins = qw(binary 3way_comparison num_comparison str_comparison);
1462    foreach my $op (split " ", "@overload::ops{ @bins }") {
1463        $subr{$op} = eval "sub {shift() $op shift()}";
1464    }
1465    foreach my $op (split " ", "@overload::ops{qw(unary func)}") {
1466        $subr{$op} = eval "sub {$op shift()}";
1467    }
1468    $subr{'++'} = $subr{'+'};
1469    $subr{'--'} = $subr{'-'};
1470
1471This finishes implementation of a primitive symbolic calculator in
147250 lines of Perl code.  Since the numeric values of subexpressions
1473are not cached, the calculator is very slow.
1474
1475Here is the answer for the exercise: In the case of str(), we need no
1476explicit recursion since the overloaded C<.>-operator will fall back
1477to an existing overloaded operator C<"">.  Overloaded arithmetic
1478operators I<do not> fall back to numeric conversion if C<fallback> is
1479not explicitly requested.  Thus without an explicit recursion num()
1480would convert C<['+', $a, $b]> to C<$a + $b>, which would just rebuild
1481the argument of num().
1482
1483If you wonder why defaults for conversion are different for str() and
1484num(), note how easy it was to write the symbolic calculator.  This
1485simplicity is due to an appropriate choice of defaults.  One extra
1486note: due to the explicit recursion num() is more fragile than sym():
1487we need to explicitly check for the type of $a and $b.  If components
1488$a and $b happen to be of some related type, this may lead to problems.
1489
1490=head2 I<Really> Symbolic Calculator
1491
1492One may wonder why we call the above calculator symbolic.  The reason
1493is that the actual calculation of the value of expression is postponed
1494until the value is I<used>.
1495
1496To see it in action, add a method
1497
1498    sub STORE {
1499        my $obj = shift;
1500        $#$obj = 1;
1501        @$obj->[0,1] = ('=', shift);
1502    }
1503
1504to the package C<symbolic>.  After this change one can do
1505
1506    my $a = symbolic->new(3);
1507    my $b = symbolic->new(4);
1508    my $c = sqrt($a**2 + $b**2);
1509
1510and the numeric value of $c becomes 5.  However, after calling
1511
1512    $a->STORE(12);  $b->STORE(5);
1513
1514the numeric value of $c becomes 13.  There is no doubt now that the module
1515symbolic provides a I<symbolic> calculator indeed.
1516
1517To hide the rough edges under the hood, provide a tie()d interface to the
1518package C<symbolic>.  Add methods
1519
1520    sub TIESCALAR { my $pack = shift; $pack->new(@_) }
1521    sub FETCH { shift }
1522    sub nop {  }                # Around a bug
1523
1524(the bug, fixed in Perl 5.14, is described in L<"BUGS">).  One can use this
1525new interface as
1526
1527    tie $a, 'symbolic', 3;
1528    tie $b, 'symbolic', 4;
1529    $a->nop;  $b->nop;          # Around a bug
1530
1531    my $c = sqrt($a**2 + $b**2);
1532
1533Now numeric value of $c is 5.  After C<$a = 12; $b = 5> the numeric value
1534of $c becomes 13.  To insulate the user of the module add a method
1535
1536    sub vars { my $p = shift; tie($_, $p), $_->nop foreach @_; }
1537
1538Now
1539
1540    my ($a, $b);
1541    symbolic->vars($a, $b);
1542    my $c = sqrt($a**2 + $b**2);
1543
1544    $a = 3; $b = 4;
1545    printf "c5  %s=%f\n", $c, $c;
1546
1547    $a = 12; $b = 5;
1548    printf "c13  %s=%f\n", $c, $c;
1549
1550shows that the numeric value of $c follows changes to the values of $a
1551and $b.
1552
1553=head1 AUTHOR
1554
1555Ilya Zakharevich E<lt>F<ilya@math.mps.ohio-state.edu>E<gt>.
1556
1557=head1 SEE ALSO
1558
1559The C<overloading> pragma can be used to enable or disable overloaded
1560operations within a lexical scope - see L<overloading>.
1561
1562=head1 DIAGNOSTICS
1563
1564When Perl is run with the B<-Do> switch or its equivalent, overloading
1565induces diagnostic messages.
1566
1567Using the C<m> command of Perl debugger (see L<perldebug>) one can
1568deduce which operations are overloaded (and which ancestor triggers
1569this overloading).  Say, if C<eq> is overloaded, then the method C<(eq>
1570is shown by debugger.  The method C<()> corresponds to the C<fallback>
1571key (in fact a presence of this method shows that this package has
1572overloading enabled, and it is what is used by the C<Overloaded>
1573function of module C<overload>).
1574
1575The module might issue the following warnings:
1576
1577=over 4
1578
1579=item Odd number of arguments for overload::constant
1580
1581(W) The call to overload::constant contained an odd number of arguments.
1582The arguments should come in pairs.
1583
1584=item '%s' is not an overloadable type
1585
1586(W) You tried to overload a constant type the overload package is unaware of.
1587
1588=item '%s' is not a code reference
1589
1590(W) The second (fourth, sixth, ...) argument of overload::constant needs
1591to be a code reference.  Either an anonymous subroutine, or a reference
1592to a subroutine.
1593
1594=item overload arg '%s' is invalid
1595
1596(W) C<use overload> was passed an argument it did not
1597recognize.  Did you mistype an operator?
1598
1599=back
1600
1601=head1 BUGS AND PITFALLS
1602
1603=over
1604
1605=item *
1606
1607A pitfall when fallback is TRUE and Perl resorts to a built-in
1608implementation of an operator is that some operators have more
1609than one semantic, for example C<|>:
1610
1611    use overload '0+' => sub { $_[0]->{n}; },
1612        fallback => 1;
1613    my $x = bless { n => 4 }, "main";
1614    my $y = bless { n => 8 }, "main";
1615    print $x | $y, "\n";
1616
1617You might expect this to output "12".
1618In fact, it prints "<": the ASCII result of treating "|"
1619as a bitwise string operator - that is, the result of treating
1620the operands as the strings "4" and "8" rather than numbers.
1621The fact that numify (C<0+>) is implemented but stringify
1622(C<"">) isn't makes no difference since the latter is simply
1623autogenerated from the former.
1624
1625The only way to change this is to provide your own subroutine
1626for C<'|'>.
1627
1628=item *
1629
1630Magic autogeneration increases the potential for inadvertently
1631creating self-referential structures.
1632Currently Perl will not free self-referential
1633structures until cycles are explicitly broken.
1634For example,
1635
1636    use overload '+' => 'add';
1637    sub add { bless [ \$_[0], \$_[1] ] };
1638
1639is asking for trouble, since
1640
1641    $obj += $y;
1642
1643will effectively become
1644
1645    $obj = add($obj, $y, undef);
1646
1647with the same result as
1648
1649    $obj = [\$obj, \$foo];
1650
1651Even if no I<explicit> assignment-variants of operators are present in
1652the script, they may be generated by the optimizer.
1653For example,
1654
1655    "obj = $obj\n"
1656
1657may be optimized to
1658
1659    my $tmp = 'obj = ' . $obj;  $tmp .= "\n";
1660
1661=item *
1662
1663The symbol table is filled with names looking like line-noise.
1664
1665=item *
1666
1667This bug was fixed in Perl 5.18, but may still trip you up if you are using
1668older versions:
1669
1670For the purpose of inheritance every overloaded package behaves as if
1671C<fallback> is present (possibly undefined).  This may create
1672interesting effects if some package is not overloaded, but inherits
1673from two overloaded packages.
1674
1675=item *
1676
1677Before Perl 5.14, the relation between overloading and tie()ing was broken.
1678Overloading was triggered or not based on the I<previous> class of the
1679tie()d variable.
1680
1681This happened because the presence of overloading was checked
1682too early, before any tie()d access was attempted.  If the
1683class of the value FETCH()ed from the tied variable does not
1684change, a simple workaround for code that is to run on older Perl
1685versions is to access the value (via C<() = $foo> or some such)
1686immediately after tie()ing, so that after this call the I<previous> class
1687coincides with the current one.
1688
1689=item *
1690
1691Barewords are not covered by overloaded string constants.
1692
1693=item *
1694
1695The range operator C<..> cannot be overloaded.
1696
1697=back
1698
1699=cut
1700
1701# ex: set ts=8 sts=4 sw=4 et:
1702