overload


SYNOPSIS
           package SomeThing;

           use overload
               '+' => \&myadd,
               '-' => \&mysub;
               # etc
           ...

           package main;
           $a = SomeThing->new( 57 );
           $b = 5 + $a;
           ...
           if (overload::Overloaded $b) {...}
           ...
           $strval = overload::StrVal $b;

DESCRIPTION
       This pragma allows overloading of Perl's operators for a class.  To
       overload built-in functions, see "Overriding Built-in Functions" in
       perlsub instead.

   Fundamentals
       Declaration

       Arguments of the "use overload" directive are (key, value) pairs.  For
       the full set of legal keys, see "Overloadable Operations" below.

       Operator implementations (the values) can be subroutines, references to
       subroutines, or anonymous subroutines - in other words, anything legal
       inside a "&{ ... }" call.  Values specified as strings are interpreted
       as method names.  Thus

           package Number;
           use overload
               "-" => "minus",
               "*=" => \&muas,
               '""' => sub { ...; };

       declares that subtraction is to be implemented by method "minus()" in
       the class "Number" (or one of its base classes), and that the function
       "Number::muas()" is to be used for the assignment form of
       multiplication, "*=".  It also defines an anonymous subroutine to
       implement stringification: this is called whenever an object blessed
       into the package "Number" is used in a string context (this subroutine
       might, for example, return the number as a Roman numeral).

       Calling Conventions and Magic Autogeneration

       The following sample implementation of "minus()" (which assumes that
       "Number" objects are simply blessed references to scalars) illustrates
       the calling conventions:

       implementation - in this case, the object whose "minus()" method is
       being called.

       The second argument is the other operand, or "undef" in the case of a
       unary operator.

       The third argument is set to TRUE if (and only if) the two operands
       have been swapped. Perl may do this to ensure that the first argument
       ($self) is an object implementing the overloaded operation, in line
       with general object calling conventions.  For example, if $x and $y are
       "Number"s:

           operation   |   generates a call to
           ============|======================
           $x - $y     |   minus($x, $y, '')
           $x - 7      |   minus($x, 7, '')
           7 - $x      |   minus($x, 7, 1)

       Perl may also use "minus()" to implement other operators which have not
       been specified in the "use overload" directive, according to the rules
       for "Magic Autogeneration" described later.  For example, the "use
       overload" above declared no subroutine for any of the operators "--",
       "neg" (the overload key for unary minus), or "-=". Thus

           operation   |   generates a call to
           ============|======================
           -$x         |   minus($x, 0, 1)
           $x--        |   minus($x, 1, undef)
           $x -= 3     |   minus($x, 3, undef)

       Note the "undef"s: where autogeneration results in the method for a
       standard operator which does not change either of its operands, such as
       "-", being used to implement an operator which changes the operand
       ("mutators": here, "--" and "-="), Perl passes undef as the third
       argument.  This still evaluates as FALSE, consistent with the fact that
       the operands have not been swapped, but gives the subroutine a chance
       to alter its behaviour in these cases.

       In all the above examples, "minus()" is required only to return the
       result of the subtraction: Perl takes care of the assignment to $x.  In
       fact, such methods should not modify their operands, even if "undef" is
       passed as the third argument (see "Overloadable Operations").

       The same is not true of implementations of "++" and "--": these are
       expected to modify their operand.  An appropriate implementation of
       "--" might look like

           use overload '--' => "decr",
               # ...
           sub decr { --${$_[0]}; }

       Mathemagic, Mutators, and Copy Constructors

       The term 'mathemagic' describes the overloaded implementation of
       leaving $a and $b referring to the same object data.  One might
       therefore expect the operation "--$a" to decrement $b as well as $a.
       However, this would not be consistent with how we expect the
       mathematical operators to work.

       Perl resolves this dilemma by transparently calling a copy constructor
       before calling a method defined to implement a mutator ("--", "+=", and
       so on.).  In the above example, when Perl reaches the decrement
       statement, it makes a copy of the object data in $a and assigns to $a a
       reference to the copied data.  Only then does it call "decr()", which
       alters the copied data, leaving $b unchanged.  Thus the object metaphor
       is preserved as far as possible, while mathemagical operations still
       work according to the arithmetic metaphor.

       Note: the preceding paragraph describes what happens when Perl
       autogenerates the copy constructor for an object based on a scalar.
       For other cases, see "Copy Constructor".

   Overloadable Operations
       The complete list of keys that can be specified in the "use overload"
       directive are given, separated by spaces, in the values of the hash
       %overload::ops:

        with_assign      => '+ - * / % ** << >> x .',
        assign           => '+= -= *= /= %= **= <<= >>= x= .=',
        num_comparison   => '< <= > >= == !=',
        '3way_comparison'=> '<=> cmp',
        str_comparison   => 'lt le gt ge eq ne',
        binary           => '& &= | |= ^ ^=',
        unary            => 'neg ! ~',
        mutators         => '++ --',
        func             => 'atan2 cos sin exp abs log sqrt int',
        conversion       => 'bool "" 0+ qr',
        iterators        => '<>',
        filetest         => '-X',
        dereferencing    => '${} @{} %{} &{} *{}',
        matching         => '~~',
        special          => 'nomethod fallback ='

       Most of the overloadable operators map one-to-one to these keys.
       Exceptions, including additional overloadable operations not apparent
       from this hash, are included in the notes which follow.

       o    "not"

            The operator "not" is not a valid key for "use overload".
            However, if the operator "!" is overloaded then the same
            implementation will be used for "not" (since the two operators
            differ only in precedence).

       o    "neg"

            The key "neg" is used for unary minus to disambiguate it from
            binary "-".

       o    Assignments

                +=  -=  *=  /=  %=  **=  <<=  >>=  x=  .=
                &=  |=  ^=

            Simple assignment is not overloadable (the '=' key is used for the
            "Copy Constructor").  Perl does have a way to make assignments to
            an object do whatever you want, but this involves using tie(), not
            overload - see "tie" in perlfunc and the "COOKBOOK" examples
            below.

            The subroutine for the assignment variant of an operator is
            required only to return the result of the operation.  It is
            permitted to change the value of its operand (this is safe because
            Perl calls the copy constructor first), but this is optional since
            Perl assigns the returned value to the left-hand operand anyway.

            An object that overloads an assignment operator does so only in
            respect of assignments to that object.  In other words, Perl never
            calls the corresponding methods with the third argument (the
            "swap" argument) set to TRUE.  For example, the operation

                $a *= $b

            cannot lead to $b's implementation of "*=" being called, even if
            $a is a scalar.  (It can, however, generate a call to $b's method
            for "*").

       o    Non-mutators with a mutator variant

                 +  -  *  /  %  **  <<  >>  x  .
                 &  |  ^

            As described above, Perl may call methods for operators like "+"
            and "&" in the course of implementing missing operations like
            "++", "+=", and "&=".  While these methods may detect this usage
            by testing the definedness of the third argument, they should in
            all cases avoid changing their operands.  This is because Perl
            does not call the copy constructor before invoking these methods.

       o    "int"

            Traditionally, the Perl function "int" rounds to 0 (see "int" in
            perlfunc), and so for floating-point-like types one should follow
            the same semantic.

       o    String, numeric, boolean, and regexp conversions

                ""  0+  bool

            These conversions are invoked according to context as necessary.
            For example, the subroutine for '""' (stringify) may be used where
            the overloaded object is passed as an argument to "print", and
            that for 'bool' where it is tested in the condition of a flow

            As a special case if the overload returns the object itself then
            it will be used directly. An overloaded conversion returning the
            object is probably a bug, because you're likely to get something
            that looks like "YourPackage=HASH(0x8172b34)".

                qr

            The subroutine for 'qr' is used wherever the object is
            interpolated into or used as a regexp, including when it appears
            on the RHS of a "=~" or "!~" operator.

            "qr" must return a compiled regexp, or a ref to a compiled regexp
            (such as "qr//" returns), and any further overloading on the
            return value will be ignored.

       o    Iteration

            If "<>" is overloaded then the same implementation is used for
            both the read-filehandle syntax "<$var>" and globbing syntax
            "<${var}>".

            BUGS Even in list context, the iterator is currently called only
            once and with scalar context.

       o    File tests

            The key '-X' is used to specify a subroutine to handle all the
            filetest operators ("-f", "-x", and so on: see "-X" in perlfunc
            for the full list); it is not possible to overload any filetest
            operator individually.  To distinguish them, the letter following
            the '-' is passed as the second argument (that is, in the slot
            that for binary operators is used to pass the second operand).

            Calling an overloaded filetest operator does not affect the stat
            value associated with the special filehandle "_". It still refers
            to the result of the last "stat", "lstat" or unoverloaded
            filetest.

            This overload was introduced in Perl 5.12.

       o    Matching

            The key "~~" allows you to override the smart matching logic used
            by the "~~" operator and the switch construct ("given"/"when").
            See "switch" in perlsyn and feature.

            Unusually, the overloaded implementation of the smart match
            operator does not get full control of the smart match behaviour.
            In particular, in the following code:

                package Foo;
                use overload '~~' => 'match';

                $obj->match(1,0);
                $obj->match(2,0);
                $obj->match(3,0);

            Consult the match table in  "Smart matching in detail" in perlsyn
            for details of when overloading is invoked.

       o    Dereferencing

                ${}  @{}  %{}  &{}  *{}

            If these operators are not explicitly overloaded then they work in
            the normal way, yielding the underlying scalar, array, or whatever
            stores the object data (or the appropriate error message if the
            dereference operator doesn't match it).  Defining a catch-all
            'nomethod' (see below) makes no difference to this as the catch-
            all function will not be called to implement a missing dereference
            operator.

            If a dereference operator is overloaded then it must return a
            reference of the appropriate type (for example, the subroutine for
            key '${}' should return a reference to a scalar, not a scalar), or
            another object which overloads the operator: that is, the
            subroutine only determines what is dereferenced and the actual
            dereferencing is left to Perl.  As a special case, if the
            subroutine returns the object itself then it will not be called
            again - avoiding infinite recursion.

       o    Special

                nomethod  fallback  =

            See "Special Keys for "use overload"".

   Magic Autogeneration
       If a method for an operation is not found then Perl tries to
       autogenerate a substitute implementation from the operations that have
       been defined.

       Note: the behaviour described in this section can be disabled by
       setting "fallback" to FALSE (see "fallback").

       In the following tables, numbers indicate priority.  For example, the
       table below states that, if no implementation for '!' has been defined
       then Perl will implement it using 'bool' (that is, by inverting the
       value returned by the method for 'bool'); if boolean conversion is also
       unimplemented then Perl will use '0+' or, failing that, '""'.

           operator | can be autogenerated from
                    |
                    | 0+   ""   bool   .   x
           =========|==========================
              0+    |       1     2
              ""    |  1          2

       normal: if the operand is not a blessed glob or IO reference then it is
       converted to a string (using the method for '""', '0+', or 'bool') to
       be interpreted as a glob or filename.

           operator | can be autogenerated from
                    |
                    |  <   <=>   neg   -=    -
           =========|==========================
              neg   |                        1
              -=    |                        1
              --    |                   1    2
              abs   | a1    a2    b1        b2    [*]
              <     |        1
              <=    |        1
              >     |        1
              >=    |        1
              ==    |        1
              !=    |        1

           * one from [a1, a2] and one from [b1, b2]

       Just as numeric comparisons can be autogenerated from the method for
       '<=>', string comparisons can be autogenerated from that for 'cmp':

            operators          |  can be autogenerated from
           ====================|===========================
            lt gt le ge eq ne  |  cmp

       Similarly, autogeneration for keys '+=' and '++' is analogous to '-='
       and '--' above:

           operator | can be autogenerated from
                    |
                    |  +=    +
           =========|==========================
               +=   |        1
               ++   |   1    2

       And other assignment variations are analogous to '+=' and '-=' (and
       similar to '.=' and 'x=' above):

                     operator ||  *= /= %= **= <<= >>= &= ^= |=
           -------------------||--------------------------------
           autogenerated from ||  *  /  %  **  <<  >>  &  ^  |

       Note also that the copy constructor (key '=') may be autogenerated, but
       only for objects based on scalars.  See "Copy Constructor".

       Minimal Set of Overloaded Operations

       Since some operations can be automatically generated from others, there
       is a minimal set of operations that need to be overloaded in order to
       have the complete set of overloaded operations at one's disposal.  Of
       course, the autogenerated operations may not do exactly what the user

   Special Keys for "use overload"
       "nomethod"

       The 'nomethod' key is used to specify a catch-all function to be called
       for any operator that is not individually overloaded.  The specified
       function will be passed four parameters.  The first three arguments
       coincide with those that would have been passed to the corresponding
       method if it had been defined.  The fourth argument is the "use
       overload" key for that missing method.

       For example, if $a is an object blessed into a package declaring

           use overload 'nomethod' => 'catch_all', # ...

       then the operation

           3 + $a

       could (unless a method is specifically declared for the key '+') result
       in a call

           catch_all($a, 3, 1, '+')

       See "How Perl Chooses an Operator Implementation".

       "fallback"

       The value assigned to the key 'fallback' tells Perl how hard it should
       try to find an alternative way to implement a missing operator.

       o   defined, but FALSE

               use overload "fallback" => 0, # ... ;

           This disables "Magic Autogeneration".

       o   "undef"

           In the default case where no value is explicitly assigned to
           "fallback", magic autogeneration is enabled.

       o   TRUE

           The same as for "undef", but if a missing operator cannot be
           autogenerated then, instead of issuing an error message, Perl is
           allowed to revert to what it would have done for that operator if
           there had been no "use overload" directive.

           Note: in most cases, particularly the "Copy Constructor", this is
           unlikely to be appropriate behaviour.

       See "How Perl Chooses an Operator Implementation".

       Copy Constructor
           $a = $b;
           # ...
           $b = $b->clone(undef, "");
           $b->incr(undef, "");

       Note:

       o   The subroutine for '=' does not overload the Perl assignment
           operator: it is used only to allow mutators to work as described
           here. (See "Assignments" above.)

       o   As for other operations, the subroutine implementing '=' is passed
           three arguments, though the last two are always "undef" and ''.

       o   The copy constructor is called only before a call to a function
           declared to implement a mutator, for example, if "++$b;" in the
           code above is effected via a method declared for key '++' (or
           'nomethod', passed '++' as the fourth argument) or, by
           autogeneration, '+='.  It is not called if the increment operation
           is effected by a call to the method for '+' since, in the
           equivalent code,

               $a = $b;
               $b = $b + 1;

           the data referred to by $a is unchanged by the assignment to $b of
           a reference to new object data.

       o   The copy constructor is not called if Perl determines that it is
           unnecessary because there is no other reference to the data being
           modified.

       o   If 'fallback' is undefined or TRUE then a copy constructor can be
           autogenerated, but only for objects based on scalars.  In other
           cases it needs to be defined explicitly.  Where an object's data is
           stored as, for example, an array of scalars, the following might be
           appropriate:

               use overload '=' => sub { bless [ @{$_[0]} ] },  # ...

       o   If 'fallback' is TRUE and no copy constructor is defined then, for
           objects not based on scalars, Perl may silently fall back on simple
           assignment - that is, assignment of the object reference.  In
           effect, this disables the copy constructor mechanism since no new
           copy of the object data is created.  This is almost certainly not
           what you want.  (It is, however, consistent: for example, Perl's
           fallback for the "++" operator is to increment the reference
           itself.)

   How Perl Chooses an Operator Implementation
       Which is checked first, "nomethod" or "fallback"?  If the two operands
       of an operator are of different types and both overload the operator,
       which implementation is used?  The following are the precedence rules:

       5.  If the first operand has a "nomethod" method then use that.

       6.  If the second operand has a "nomethod" method then use that.

       7.  If "fallback" is TRUE for both operands then perform the usual
           operation for the operator, treating the operands as numbers,
           strings, or booleans as appropriate for the operator (see note).

       8.  Nothing worked - die.

       Where there is only one operand (or only one operand with overloading)
       the checks in respect of the other operand above are skipped.

       There are exceptions to the above rules for dereference operations
       (which, if Step 1 fails, always fall back to the normal, built-in
       implementations - see Dereferencing), and for "~~" (which has its own
       set of rules - see Matching).

       Note on Step 7: some operators have a different semantic depending on
       the type of their operands.  As there is no way to instruct Perl to
       treat the operands as, e.g., numbers instead of strings, the result
       here may not be what you expect.  See "BUGS AND PITFALLS".

   Losing Overloading
       The restriction for the comparison operation is that even if, for
       example, `"cmp"' should return a blessed reference, the autogenerated
       `"lt"' function will produce only a standard logical value based on the
       numerical value of the result of `"cmp"'.  In particular, a working
       numeric conversion is needed in this case (possibly expressed in terms
       of other conversions).

       Similarly, ".="  and "x=" operators lose their mathemagical properties
       if the string conversion substitution is applied.

       When you chop() a mathemagical object it is promoted to a string and
       its mathemagical properties are lost.  The same can happen with other
       operations as well.

   Inheritance and Overloading
       Overloading respects inheritance via the @ISA hierarchy.  Inheritance
       interacts with overloading in two ways.

       Method names in the "use overload" directive
           If "value" in

             use overload key => value;

           is a string, it is interpreted as a method name - which may (in the
           usual way) be inherited from another class.

       Overloading of an operation is inherited by derived classes
           Any class derived from an overloaded class is also overloaded and
           inherits its operator implementations.  If the same operator is
           overloaded in more than one ancestor then the implementation is

   Run-time Overloading
       Since all "use" directives are executed at compile-time, the only way
       to change overloading during run-time is to

           eval 'use overload "+" => \&addmethod';

       You can also use

           eval 'no overload "+", "--", "<="';

       though the use of these constructs during run-time is questionable.

   Public Functions
       Package "overload.pm" provides the following public functions:

       overload::StrVal(arg)
            Gives string value of "arg" as in absence of stringify
            overloading. If you are using this to get the address of a
            reference (useful for checking if two references point to the same
            thing) then you may be better off using "Scalar::Util::refaddr()",
            which is faster.

       overload::Overloaded(arg)
            Returns true if "arg" is subject to overloading of some
            operations.

       overload::Method(obj,op)
            Returns "undef" or a reference to the method that implements "op".

   Overloading Constants
       For some applications, the Perl parser mangles constants too much.  It
       is possible to hook into this process via "overload::constant()" and
       "overload::remove_constant()" functions.

       These functions take a hash as an argument.  The recognized keys of
       this hash are:

       integer to overload integer constants,

       float   to overload floating point constants,

       binary  to overload octal and hexadecimal constants,

       q       to overload "q"-quoted strings, constant pieces of "qq"- and
               "qx"-quoted strings and here-documents,

       qr      to overload constant pieces of regular expressions.

       The corresponding values are references to functions which take three
       arguments: the first one is the initial string form of the constant,
       the second one is how Perl interprets this constant, the third one is
       how the constant is used.  Note that the initial string form does not
       contain string delimiters, and has backslashes in backslash-delimiter
       combinations stripped (thus the value of delimiter is not relevant for
       of positive constants.

       Note that it is probably meaningless to call the functions
       overload::constant() and overload::remove_constant() from anywhere but
       import() and unimport() methods.  From these methods they may be called
       as

               sub import {
                 shift;
                 return unless @_;
                 die "unknown import: @_" unless @_ == 1 and $_[0] eq ':constant';
                 overload::constant integer => sub {Math::BigInt->new(shift)};
               }

IMPLEMENTATION
       What follows is subject to change RSN.

       The table of methods for all operations is cached in magic for the
       symbol table hash for the package.  The cache is invalidated during
       processing of "use overload", "no overload", new function definitions,
       and changes in @ISA. However, this invalidation remains unprocessed
       until the next "bless"ing into the package. Hence if you want to change
       overloading structure dynamically, you'll need an additional (fake)
       "bless"ing to update the table.

       (Every SVish thing has a magic queue, and magic is an entry in that
       queue.  This is how a single variable may participate in multiple forms
       of magic simultaneously.  For instance, environment variables regularly
       have two forms at once: their %ENV magic and their taint magic.
       However, the magic which implements overloading is applied to the
       stashes, which are rarely used directly, thus should not slow down
       Perl.)

       If an object belongs to a package using overload, it carries a special
       flag.  Thus the only speed penalty during arithmetic operations without
       overloading is the checking of this flag.

       In fact, if "use overload" is not present, there is almost no overhead
       for overloadable operations, so most programs should not suffer
       measurable performance penalties.  A considerable effort was made to
       minimize the overhead when overload is used in some package, but the
       arguments in question do not belong to packages using overload.  When
       in doubt, test your speed with "use overload" and without it.  So far
       there have been no reports of substantial speed degradation if Perl is
       compiled with optimization turned on.

       There is no size penalty for data if overload is not used. The only
       size penalty if overload is used in some package is that all the
       packages acquire a magic during the next "bless"ing into the package.
       This magic is three-words-long for packages without overloading, and
       carries the cache table if the package is overloaded.

       It is expected that arguments to methods that are not explicitly
       supposed to be changed are constant (but this is not enforced).
         sub str {shift->[0]}

       Use it as follows:

         require two_face;
         my $seven = two_face->new("vii", 7);
         printf "seven=$seven, seven=%d, eight=%d\n", $seven, $seven+1;
         print "seven contains `i'\n" if $seven =~ /i/;

       (The second line creates a scalar which has both a string value, and a
       numeric value.)  This prints:

         seven=vii, seven=7, eight=8
         seven contains `i'

   Two-face References
       Suppose you want to create an object which is accessible as both an
       array reference and a hash reference.

         package two_refs;
         use overload '%{}' => \&gethash, '@{}' => sub { $ {shift()} };
         sub new {
           my $p = shift;
           bless \ [@_], $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 $self = ${shift()};
           my $key = $fields{shift()};
           defined $key or die "Out of band access";
           $$self->[$key] = shift;
         }
         sub FETCH {
           my $self = ${shift()};
           my $key = $fields{shift()};
           defined $key or die "Out of band access";
           $$self->[$key];
         }

       Now one can access an object using both the array and hash syntax:

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

       Both these problems can be cured.  Say, if we want to overload hash
       dereference on a reference to an object which is implemented as a hash
       itself, the only problem one has to circumvent is how to access this
       actual hash (as opposed to the 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 $baz is a reference to a
       Put this in 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 an
       implementation for "nomethod".  In this example the "nomethod"
       subroutine returns an object which encapsulates operations done over
       the objects: "symbolic->new(3)" contains "['n', 3]", "2 +
       symbolic->new(3)" contains "['+', 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 = symbolic->new(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 use this value.  In fact this value may be
       inspected in debugger (see perldebug), but only if "bareStringify"
       Option is set, and not via "p" command.

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

       Add a pretty-printer method to the module 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;

       catenation of some strings and components $a and $b.  If these
       components use overloading, the catenation operator will look for an
       overloaded operator "."; if not present, it will look for an overloaded
       operator "".  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 still amiss: consider the loop variable $cnt of the
       script.  It was a number, not an object.  We cannot make this value of
       type "symbolic", since then the loop will not terminate.

       Indeed, to terminate the cycle, the $cnt should become false.  However,
       the operator "bool" for checking falsity is overloaded (this time via
       overloaded ""), and returns a long string, thus any object of type
       "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 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 $b]";
           } else {
           my ($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 = symbolic->new(2);  # 16-gon
         my $side = symbolic->new(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 ("++", "-=" 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()}";
         }
         sub cpy {
           my $self = shift;
           bless [@$self], ref $self;
         }

       To make "++" and "--" work, we need to implement actual mutators,
       either directly, or in "nomethod".  We continue to do things inside
       "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 "."-operator will fall back to
       an existing overloaded operator "".  Overloaded arithmetic operators do
       not fall back to numeric conversion if "fallback" is not explicitly
       requested.  Thus without an explicit recursion num() would convert
       "['+', $a, $b]" to "$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 $b.  If components
           @$obj->[0,1] = ('=', shift);
         }

       to the package "symbolic".  After this change one can do

         my $a = symbolic->new(3);
         my $b = symbolic->new(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 symbolic calculator indeed.

       To hide the rough edges under the hood, provide a tie()d interface to
       the package "symbolic".  Add methods

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

       (the bug, fixed in Perl 5.14, is described in "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 $c is 5.  After "$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.

AUTHOR
       overloading). Say, if "eq" is overloaded, then the method "(eq" is
       shown by debugger. The method "()" corresponds to the "fallback" key
       (in fact a presence of this method shows that this package has
       overloading enabled, and it is what is used by the "Overloaded"
       function of module "overload").

       The module might issue the following warnings:

       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.

       `%s' is not an overloadable type
           (W) You tried to overload a constant type the overload package is
           unaware of.

       `%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.

BUGS AND PITFALLS
       o   No warning is issued for invalid "use overload" keys.  Such errors
           are not always obvious:

                   use overload "+0" => sub { ...; },   # should be "0+"
                       "not" => sub { ...; };           # should be "!"

           (Bug #74098)

       o   A pitfall when fallback is TRUE and Perl resorts to a built-in
           implementation of an operator is that some operators have more than
           one semantic, for example "|":

                   use overload '0+' => sub { $_[0]->{n}; },
                       fallback => 1;
                   my $x = bless { n => 4 }, "main";
                   my $y = bless { n => 8 }, "main";
                   print $x | $y, "\n";

           You might expect this to output "12".  In fact, it prints "<": the
           ASCII result of treating "|" as a bitwise string operator - that
           is, the result of treating the operands as the strings "4" and "8"
           rather than numbers.  The fact that numify ("0+") is implemented
           but stringify ("") isn't makes no difference since the latter is
           simply autogenerated from the former.

           The only way to change this is to provide your own subroutine for
           '|'.

       o   Magic autogeneration increases the potential for inadvertently
           creating self-referential structures.  Currently Perl will not free
           self-referential structures until cycles are explicitly broken.
           For example,
           with the same result as

               $obj = [\$obj, \$foo];

           Even if no explicit assignment-variants of operators are present in
           the script, they may be generated by the optimizer.  For example,

               "obj = $obj\n"

           may be optimized to

               my $tmp = 'obj = ' . $obj;  $tmp .= "\n";

       o   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.

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

       o   Before Perl 5.14, the relation between overloading and tie()ing was
           broken.  Overloading is triggered or not basing on the previous
           class of the tie()d variable.

           This happened because the presence of overloading was checked too
           early, before any tie()d access was attempted.  If the class of the
           value FETCH()ed from the tied variable does not change, a simple
           workaround for code that is to run on older Perl versions is to
           access the value (via "() = $foo" or some such) immediately after
           tie()ing, so that after this call the previous class coincides with
           the current one.

       o   Barewords are not covered by overloaded string constants.



perl v5.14.2                      2011-09-26                   overload(3perl)
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