MirOS Manual: overload(3p)


overload(3p)    Perl Programmers Reference Guide     overload(3p)

NAME

     overload - Package for overloading Perl operations

SYNOPSIS

         package SomeThing;

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

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

DESCRIPTION

     Declaration of overloaded functions

     The compilation directive

         package Number;
         use overload
             "+" => \&add,
             "*=" => "muas";

     declares function Number::add() for addition, and method
     muas() in the "class" "Number" (or one of its base classes)
     for the assignment form "*=" of multiplication.

     Arguments of this directive come in (key, value) pairs.
     Legal values are values legal inside a "&{ ... }" call, so
     the name of a subroutine, a reference to a subroutine, or an
     anonymous subroutine will all work.  Note that values speci-
     fied as strings are interpreted as methods, not subroutines.
     Legal keys are listed below.

     The subroutine "add" will be called to execute "$a+$b" if $a
     is a reference to an object blessed into the package
     "Number", or if $a is not an object from a package with
     defined mathemagic addition, but $b is a reference to a
     "Number".  It can also be called in other situations, like
     "$a+=7", or "$a++".  See "MAGIC AUTOGENERATION".  (Mathemag-
     ical methods refer to methods triggered by an overloaded
     mathematical operator.)

     Since overloading respects inheritance via the @ISA hierar-
     chy, the above declaration would also trigger overloading of

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     "+" and "*=" in all the packages which inherit from
     "Number".

     Calling Conventions for Binary Operations

     The functions specified in the "use overload ..." directive
     are called with three (in one particular case with four, see
     "Last Resort") arguments.  If the corresponding operation is
     binary, then the first two arguments are the two arguments
     of the operation.  However, due to general object calling
     conventions, the first argument should always be an object
     in the package, so in the situation of "7+$a", the order of
     the arguments is interchanged.  It probably does not matter
     when implementing the addition method, but whether the argu-
     ments are reversed is vital to the subtraction method.  The
     method can query this information by examining the third
     argument, which can take three different values:

     FALSE  the order of arguments is as in the current opera-
            tion.

     TRUE   the arguments are reversed.

     "undef"
            the current operation is an assignment variant (as in
            "$a+=7"), but the usual function is called instead.
            This additional information can be used to generate
            some optimizations.  Compare "Calling Conventions for
            Mutators".

     Calling Conventions for Unary Operations

     Unary operation are considered binary operations with the
     second argument being "undef".  Thus the functions that
     overloads "{"++"}" is called with arguments "($a,undef,'')"
     when $a++ is executed.

     Calling Conventions for Mutators

     Two types of mutators have different calling conventions:

     "++" and "--"
         The routines which implement these operators are
         expected to actually mutate their arguments.  So, assum-
         ing that $obj is a reference to a number,

           sub incr { my $n = $ {$_[0]}; ++$n; $_[0] = bless \$n}

         is an appropriate implementation of overloaded "++".
         Note that

           sub incr { ++$ {$_[0]} ; shift }

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         is OK if used with preincrement and with postincrement.
         (In the case of postincrement a copying will be per-
         formed, see "Copy Constructor".)

     "x=" and other assignment versions
         There is nothing special about these methods.  They may
         change the value of their arguments, and may leave it as
         is.  The result is going to be assigned to the value in
         the left-hand-side if different from this value.

         This allows for the same method to be used as overloaded
         "+=" and "+".  Note that this is allowed, but not recom-
         mended, since by the semantic of "Fallback" Perl will
         call the method for "+" anyway, if "+=" is not over-
         loaded.

     Warning.  Due to the presence of assignment versions of
     operations, routines which may be called in assignment con-
     text may create self-referential structures.  Currently Perl
     will not free self-referential structures until cycles are
     "explicitly" broken.  You may get problems when traversing
     your structures too.

     Say,

       use overload '+' => sub { bless [ \$_[0], \$_[1] ] };

     is asking for trouble, since for code "$obj += $foo" the
     subroutine is called as "$obj = add($obj, $foo, undef)", or
     "$obj = [\$obj, \$foo]".  If using such a subroutine is an
     important optimization, one can overload "+=" explicitly by
     a non-"optimized" version, or switch to non-optimized ver-
     sion if "not defined $_[2]" (see "Calling Conventions for
     Binary Operations").

     Even if no explicit assignment-variants of operators are
     present in the script, they may be generated by the optim-
     izer.  Say, ",$obj," or ',' . $obj . ',' may be both optim-
     ized to

       my $tmp = ',' . $obj;    $tmp .= ',';

     Overloadable Operations

     The following symbols can be specified in "use overload"
     directive:

     * Arithmetic operations
              "+", "+=", "-", "-=", "*", "*=", "/", "/=", "%", "%=",
              "**", "**=", "<<", "<<=", ">>", ">>=", "x", "x=", ".", ".=",

          For these operations a substituted non-assignment

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          variant can be called if the assignment variant is not
          available.  Methods for operations "+", "-", "+=", and
          "-=" can be called to automatically generate increment
          and decrement methods.  The operation "-" can be used
          to autogenerate missing methods for unary minus or
          "abs".

          See "MAGIC AUTOGENERATION", "Calling Conventions for
          Mutators" and "Calling Conventions for Binary Opera-
          tions") for details of these substitutions.

     * Comparison operations
              "<",  "<=", ">",  ">=", "==", "!=", "<=>",
              "lt", "le", "gt", "ge", "eq", "ne", "cmp",

          If the corresponding "spaceship" variant is available,
          it can be used to substitute for the missing operation.
          During "sort"ing arrays, "cmp" is used to compare
          values subject to "use overload".

     * Bit operations
              "&", "^", "|", "neg", "!", "~",

          "neg" stands for unary minus.  If the method for "neg"
          is not specified, it can be autogenerated using the
          method for subtraction. If the method for "!" is not
          specified, it can be autogenerated using the methods
          for "bool", or "", or "0+".

     * Increment and decrement
              "++", "--",

          If undefined, addition and subtraction methods can be
          used instead.  These operations are called both in pre-
          fix and postfix form.

     * Transcendental functions
              "atan2", "cos", "sin", "exp", "abs", "log", "sqrt", "int"

          If "abs" is unavailable, it can be autogenerated using
          methods for "<" or "<=>" combined with either unary
          minus or subtraction.

          Note that traditionally the Perl function int rounds to
          0, thus for floating-point-like types one should follow
          the same semantic.  If "int" is unavailable, it can be
          autogenerated using the overloading of "0+".

     * Boolean, string and numeric conversion
              'bool', '""', '0+',

          If one or two of these operations are not overloaded,

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          the remaining ones can be used instead.  "bool" is used
          in the flow control operators (like "while") and for
          the ternary "?:" operation.  These functions can return
          any arbitrary Perl value.  If the corresponding opera-
          tion for this value is overloaded too, that operation
          will be called again with this value.

          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)".

     * Iteration
              "<>"

          If not overloaded, the argument will be converted to a
          filehandle or glob (which may require a stringifica-
          tion).  The same overloading happens both for 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.

     * Dereferencing
              '${}', '@{}', '%{}', '&{}', '*{}'.

          If not overloaded, the argument will be dereferenced as
          is, thus should be of correct type.  These functions
          should return a reference of correct type, or another
          object with overloaded dereferencing.

          As a special case if the overload returns the object
          itself then it will be used directly (provided it is
          the correct type).

          The dereference operators must be specified explicitly
          they will not be passed to "nomethod".

     * Special
              "nomethod", "fallback", "=",

          see "SPECIAL SYMBOLS FOR "use overload"".

     See "Fallback" for an explanation of when a missing method
     can be autogenerated.

     A computer-readable form of the above table is available in
     the hash %overload::ops, with values being space-separated
     lists of names:

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      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',
      conversion       => 'bool "" 0+',
      iterators        => '<>',
      dereferencing    => '${} @{} %{} &{} *{}',
      special          => 'nomethod fallback ='

     Inheritance and overloading

     Inheritance interacts with overloading in two ways.

     Strings as values of "use overload" directive
         If "value" in

           use overload key => value;

         is a string, it is interpreted as a method name.

     Overloading of an operation is inherited by derived classes
         Any class derived from an overloaded class is also over-
         loaded.  The set of overloaded methods is the union of
         overloaded methods of all the ancestors. If some method
         is overloaded in several ancestor, then which descrip-
         tion will be used is decided by the usual inheritance
         rules:

         If "A" inherits from "B" and "C" (in this order), "B"
         overloads "+" with "\&D::plus_sub", and "C" overloads
         "+" by "plus_meth", then the subroutine "D::plus_sub"
         will be called to implement operation "+" for an object
         in package "A".

     Note that since the value of the "fallback" key is not a
     subroutine, its inheritance is not governed by the above
     rules.  In the current implementation, the value of "fall-
     back" in the first overloaded ancestor is used, but this is
     accidental and subject to change.

SPECIAL SYMBOLS FOR "use overload"
     Three keys are recognized by Perl that are not covered by
     the above description.

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     Last Resort

     "nomethod" should be followed by a reference to a function
     of four parameters.  If defined, it is called when the over-
     loading mechanism cannot find a method for some operation.
     The first three arguments of this function coincide with the
     arguments for the corresponding method if it were found, the
     fourth argument is the symbol corresponding to the missing
     method.  If several methods are tried, the last one is used.
     Say, "1-$a" can be equivalent to

             &nomethodMethod($a,1,1,"-")

     if the pair "nomethod" => "nomethodMethod" was specified in
     the "use overload" directive.

     The "nomethod" mechanism is not used for the dereference
     operators ( ${} @{} %{} &{} *{} ).

     If some operation cannot be resolved, and there is no func-
     tion assigned to "nomethod", then an exception will be
     raised via die()-- unless "fallback" was specified as a key
     in "use overload" directive.

     Fallback

     The key "fallback" governs what to do if a method for a par-
     ticular operation is not found.  Three different cases are
     possible depending on the value of "fallback":

     * "undef"       Perl tries to use a substituted method (see
                     "MAGIC AUTOGENERATION").  If this fails, it
                     then tries to calls "nomethod" value; if
                     missing, an exception will be raised.

     * TRUE          The same as for the "undef" value, but no
                     exception is raised.  Instead, it silently
                     reverts to what it would have done were
                     there no "use overload" present.

     * defined, but FALSE
                     No autogeneration is tried.  Perl tries to
                     call "nomethod" value, and if this is miss-
                     ing, raises an exception.

     Note. "fallback" inheritance via @ISA is not carved in stone
     yet, see "Inheritance and overloading".

     Copy Constructor

     The value for "=" is a reference to a function with three
     arguments, i.e., it looks like the other values in "use

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     overload". However, it does not overload the Perl assignment
     operator. This would go against Camel hair.

     This operation is called in the situations when a mutator is
     applied to a reference that shares its object with some
     other reference, such as

             $a=$b;
             ++$a;

     To make this change $a and not change $b, a copy of $$a is
     made, and $a is assigned a reference to this new object.
     This operation is done during execution of the "++$a", and
     not during the assignment, (so before the increment $$a
     coincides with $$b).  This is only done if "++" is expressed
     via a method for '++' or '+=' (or "nomethod").  Note that if
     this operation is expressed via '+' a nonmutator, i.e., as
     in

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

     then $a does not reference a new copy of $$a, since $$a does
     not appear as lvalue when the above code is executed.

     If the copy constructor is required during the execution of
     some mutator, but a method for '=' was not specified, it can
     be autogenerated as a string copy if the object is a plain
     scalar.

     Example
          The actually executed code for

                  $a=$b;
                  Something else which does not modify $a or $b....
                  ++$a;

          may be

                  $a=$b;
                  Something else which does not modify $a or $b....
                  $a = $a->clone(undef,"");
                  $a->incr(undef,"");

          if $b was mathemagical, and '++' was overloaded with
          "\&incr", '=' was overloaded with "\&clone".

     Same behaviour is triggered by "$b = $a++", which is con-
     sider a synonym for "$b = $a; ++$a".

MAGIC AUTOGENERATION

     If a method for an operation is not found, and the value for

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     "fallback" is TRUE or undefined, Perl tries to autogenerate
     a substitute method for the missing operation based on the
     defined operations.  Autogenerated method substitutions are
     possible for the following operations:

     Assignment forms of arithmetic operations
                     "$a+=$b" can use the method for "+" if the
                     method for "+=" is not defined.

     Conversion operations
                     String, numeric, and boolean conversion are
                     calculated in terms of one another if not
                     all of them are defined.

     Increment and decrement
                     The "++$a" operation can be expressed in
                     terms of "$a+=1" or "$a+1", and "$a--" in
                     terms of "$a-=1" and "$a-1".

     "abs($a)"       can be expressed in terms of "$a<0" and
                     "-$a" (or "0-$a").

     Unary minus     can be expressed in terms of subtraction.

     Negation        "!" and "not" can be expressed in terms of
                     boolean conversion, or string or numerical
                     conversion.

     Concatenation   can be expressed in terms of string conver-
                     sion.

     Comparison operations
                     can be expressed in terms of its "spaceship"
                     counterpart: either "<=>" or "cmp":

                         <, >, <=, >=, ==, !=        in terms of <=>
                         lt, gt, le, ge, eq, ne      in terms of cmp

     Iterator
                         <>                          in terms of builtin operations

     Dereferencing
                         ${} @{} %{} &{} *{}         in terms of builtin operations

     Copy operator   can be expressed in terms of an assignment
                     to the dereferenced value, if this value is
                     a scalar and not a reference.

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

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     standard logical value based on the numerical value of the
     result of `"cmp"'.  In particular, a working numeric conver-
     sion 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.

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 ques-
     tionable.

Public functions

     Package "overload.pm" provides the following public func-
     tions:

     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:

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     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 com-
     binations stripped (thus the value of delimiter is not
     relevant for processing of this string).  The return value
     of this function is how this constant is going to be inter-
     preted by Perl.  The third argument is undefined unless for
     overloaded "q"- and "qr"- constants, it is "q" in single-
     quote context (comes from strings, regular expressions, and
     single-quote HERE documents), it is "tr" for arguments of
     "tr"/"y" operators, it is "s" for right-hand side of
     "s"-operator, and it is "qq" otherwise.

     Since an expression "ab$cd,," is just a shortcut for 'ab' .
     $cd . ',,', it is expected that overloaded constant strings
     are equipped with reasonable overloaded catenation operator,
     otherwise absurd results will result. Similarly, negative
     numbers are considered as negations 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)};
             }

     BUGS Currently overloaded-ness of constants does not pro-
     pagate into "eval '...'".

IMPLEMENTATION

     What follows is subject to change RSN.

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     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 over-
     load", new function definitions, and changes in @ISA. How-
     ever, 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 partici-
     pate 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 arith-
     metic 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 con-
     siderable effort was made to minimize the overhead when
     overload is used in some package, but the arguments in ques-
     tion 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.

     Copying ("$a=$b") is shallow; however, a one-level-deep
     copying is carried out before any operation that can imply
     an assignment to the object $a (or $b) refers to, like
     "$a++".  You can override this behavior by defining your own
     copy constructor (see "Copy Constructor").

     It is expected that arguments to methods that are not expli-
     citly supposed to be changed are constant (but this is not
     enforced).

Metaphor clash

     One may wonder why the semantic of overloaded "=" is so

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     counter intuitive. If it looks counter intuitive to you, you
     are subject to a metaphor clash.

     Here is a Perl object metaphor:

       object is a reference to blessed data

     and an arithmetic metaphor:

       object is a thing by itself.

     The main problem of overloading "=" is the fact that these
     metaphors imply different actions on the assignment "$a =
     $b" if $a and $b are objects.  Perl-think implies that $a
     becomes a reference to whatever $b was referencing.
     Arithmetic-think implies that the value of "object" $a is
     changed to become the value of the object $b, preserving the
     fact that $a and $b are separate entities.

     The difference is not relevant in the absence of mutators.
     After a Perl-way assignment an operation which mutates the
     data referenced by $a would change the data referenced by $b
     too.  Effectively, after "$a = $b" values of $a and $b
     become indistinguishable.

     On the other hand, anyone who has used algebraic notation
     knows the expressive power of the arithmetic metaphor.
     Overloading works hard to enable this metaphor while
     preserving the Perlian way as far as possible.  Since it is
     not possible to freely mix two contradicting metaphors,
     overloading allows the arithmetic way to write things as far
     as all the mutators are called via overloaded access only.
     The way it is done is described in "Copy Constructor".

     If some mutator methods are directly applied to the over-
     loaded values, one may need to explicitly unlink other
     values which references the same value:

         $a = new Data 23;
         ...
         $b = $a;            # $b is "linked" to $a
         ...
         $a = $a->clone;     # Unlink $b from $a
         $a->increment_by(4);

     Note that overloaded access makes this transparent:

         $a = new Data 23;
         $b = $a;            # $b is "linked" to $a
         $a += 4;            # would unlink $b automagically

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     However, it would not make

         $a = new Data 23;
         $a = 4;             # Now $a is a plain 4, not 'Data'

     preserve "objectness" of $a.  But Perl has a way to make
     assignments to an object do whatever you want.  It is just
     not the overload, but tie()ing interface (see "tie" in perl-
     func).  Adding a FETCH() method which returns the object
     itself, and STORE() method which changes the value of the
     object, one can reproduce the arithmetic metaphor in its
     completeness, at least for variables which were tie()d from
     the start.

     (Note that a workaround for a bug may be needed, see
     "BUGS".)

Cookbook

     Please add examples to what follows!

     Two-face scalars

     Put this in two_face.pm in your Perl library directory:

       package two_face;             # Scalars with separate string and
                                     # numeric values.
       sub new { my $p = shift; bless [@_], $p }
       use overload '""' => \&str, '0+' => \&num, fallback => 1;
       sub num {shift->[1]}
       sub str {shift->[0]}

     Use it as follows:

       require two_face;
       my $seven = new two_face ("vii", 7);
       printf "seven=$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, similar to the
     pseudo-hash builtin Perl type.  Let's make it better than a
     pseudo-hash by allowing index 0 to be treated as a normal
     element.

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overload(3p)    Perl Programmers Reference Guide     overload(3p)

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

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

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

     Both these problems can be cured.  Say, if we want to over-
     load hash dereference on a reference to an object which is
     implemented as a hash itself, the only problem one has to

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overload(3p)    Perl Programmers Reference Guide     overload(3p)

     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];
       }

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overload(3p)    Perl Programmers Reference Guide     overload(3p)

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

     +   There are no loops of references.

     +   Both "objects" which are blessed into the class
         "two_refs1" are references to a reference to an array,
         thus references to a scalar. Thus the accessor expres-
         sion "$$foo->[$ind]" involves no overloaded operations.

     Symbolic calculator

     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 the "Last Resort" operator "nomethod".  In this
     example the corresponding subroutine returns an object which
     encapsulates operations done over the objects: "new symbolic
     3" contains "['n', 3]", "2 + new symbolic 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 = new symbolic 1;
       my $cnt = $iter;

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

     The value of $side is

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

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overload(3p)    Perl Programmers Reference Guide     overload(3p)

     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
     ony if "bareStringify" Option is set, and not via "p" com-
     mand.

     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;
         $b = $b->pretty if ref $b;
         "[$meth $a $b]";
       }

     Now one can finish the script by

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

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

perl v5.8.8                2005-02-05                          18

overload(3p)    Perl Programmers Reference Guide     overload(3p)

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

     and one can inspect the value in debugger using all the pos-
     sible 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;

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overload(3p)    Perl Programmers Reference Guide     overload(3p)

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

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

     Use this module like this:

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

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

perl v5.8.8                2005-02-05                          20

overload(3p)    Perl Programmers Reference Guide     overload(3p)

     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 exam-
     ple.

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

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

     Due to "Calling Conventions for Mutators", we do not need
     anything special to make "+=" and friends work, except fil-
     ling "+=" entry of %subr, and defining a copy constructor
     (needed since Perl has no way to know that the implementa-
     tion of '+=' does not mutate the argument, compare "Copy
     Constructor").

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

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

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

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overload(3p)    Perl Programmers Reference Guide     overload(3p)

         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 effec-
     tive 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 calcu-
     lator 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 opera-
     tor "".  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 $a and $b
     happen to be of some related type, this may lead to prob-
     lems.

perl v5.8.8                2005-02-05                          22

overload(3p)    Perl Programmers Reference Guide     overload(3p)

     Really symbolic calculator

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

     To see it in action, add a method

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

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

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

     and the numeric value of $c becomes 5.  However, after cal-
     ling

       $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" (compare with "Metaphor
     clash").  Add methods

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

     (the bug 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 @_; }

perl v5.8.8                2005-02-05                          23

overload(3p)    Perl Programmers Reference Guide     overload(3p)

     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

     Ilya Zakharevich <ilya@math.mps.ohio-state.edu>.

DIAGNOSTICS

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

     Using the "m" command of Perl debugger (see perldebug) one
     can deduce which operations are overloaded (and which ances-
     tor triggers this 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

     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.

perl v5.8.8                2005-02-05                          24

overload(3p)    Perl Programmers Reference Guide     overload(3p)

     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.

     Relation between overloading and tie()ing is broken.  Over-
     loading is triggered or not basing on the previous class of
     tie()d value.

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

     Needed: a way to fix this without a speed penalty.

     Barewords are not covered by overloaded string constants.

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

perl v5.8.8                2005-02-05                          25

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