overload(3) Perl Programmers Reference Guide overload(3)NAMEoverload - 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 $b;
DESCRIPTION
Declaration of overloaded functions
The compilation directive
package Number;
use overload
"+" => \&add,
"*=" => "muas";
declares function Number::add() for addition, and method
muas() in the "class" "Number" (or one of its base
classes) for the assignment form "*=" of multiplication.
Arguments of this directive come in (key, value) pairs.
Legal values are values legal inside a "&{ ... }" call, so
the name of a subroutine, a reference to a subroutine, or
an anonymous subroutine will all work. Note that values
specified as strings are interpreted as methods, not sub
routines. Legal keys are listed below.
The subroutine "add" will be called to execute "$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 "$a++". See the MAGIC AUTOGENERATION entry
elsewhere in this document. (Mathemagical methods refer
to methods triggered by an overloaded mathematical opera
tor.)
Since overloading respects inheritance via the @ISA hier
archy, the above declaration would also trigger overload
ing of "+" and "*=" in all the packages which inherit from
"Number".
Calling Conventions for Binary Operations
The functions specified in the "use overload ..." direc
tive are called with three (in one particular case with
four, see the Last Resort entry elsewhere in this
document) arguments. If the corresponding operation is
binary, then the first two arguments are the two arguments
of the operation. However, due to general object calling
conventions, the first argument should always be an object
in the package, so in the situation of "7+$a", the order
of the arguments is interchanged. It probably does not
matter when implementing the addition method, but whether
the arguments are reversed is vital to the subtraction
method. The method can query this information by examin
ing 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 "$a+=7"), but the usual function is called
instead. This additional information can be used
to generate some optimizations. Compare the Call
ing Conventions for Mutators entry elsewhere in
this document.
Calling Conventions for Unary Operations
Unary operation are considered binary operations with the
second argument being "undef". Thus the functions that
overloads "{"++"}" is called with arguments
"($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,
assuming that $obj is a reference to a number,
sub incr { my $n = $ {$_[0]}; ++$n; $_[0] = bless \$n}
is an appropriate implementation of overloaded "++".
Note that
sub incr { ++$ {$_[0]} ; shift }
is OK if used with preincrement and with postincre
ment. (In the case of postincrement a copying will be
performed, see the Copy Constructor entry elsewhere in
this document.)
""x="" and other assignment versions
There is nothing special about these methods. They
may change the value of their arguments, and may leave
it as is. The result is going to be assigned to the
value in the left-hand-side if different from this
value.
This allows for the same method to be used as over
loaded "+=" and "+". Note that this is allowed, but
not recommended, since by the semantic of the section
on "Fallback" Perl will call the method for "+" any
way, if "+=" is not overloaded.
Warning. Due to the presense of assignment versions of
operations, routines which may be called in assignment
context may create self-referential structures. Currently
Perl will not free self-referential structures until
cycles are "explicitly" broken. You may get problems when
traversing your structures too.
Say,
use overload '+' => sub { bless [ \$_[0], \$_[1] ] };
is asking for trouble, since for code "$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 "+=" explic
itly by a non-"optimized" version, or switch to non-opti
mized version if "not defined $_[2]" (see the Calling Con
ventions for Binary Operations entry elsewhere in this
document).
Even if no explicit assignment-variants of operators are
present in the script, they may be generated by the opti
mizer. Say, "",$obj,"" or "',' . $obj . ','" may be both
optimized 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
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 opera
tion ""-"" can be used to autogenerate missing meth
ods for unary minus or "abs".
See the section on "MAGIC AUTOGENERATION", the sec
tion on "Calling Conventions for Mutators" and the
section on "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 avail
able, 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
prefix and postfix form.
Transcendental functions
"atan2", "cos", "sin", "exp", "abs", "log", "sqrt",
If "abs" is unavailable, it can be autogenerated
using methods for "<" or "<=>" combined with either
unary minus or subtraction.
Boolean, string and numeric conversion
"bool", "\"\"", "0+",
If one or two of these operations are not overloaded,
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 corre
sponding operation 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 stringifi
cation). The same overloading happens both for the
read-filehandle syntax "<$var>" and globbing syntax
"<${var}>".
Dereferencing
'${}', '@{}', '%{}', '&{}', '*{}'.
If not overloaded, the argument will be dereferenced
as is, thus should be of correct type. These func
tions 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 explic
itly they will not be passed to "nomethod".
Special
"nomethod", "fallback", "=",
see the SPECIAL SYMBOLS FOR "use overload" entry
elsewhere in this document.
See the section on "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-sepa
rated lists of names:
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 => '${} @{} %{} &{} *{}',
special => 'nomethod fallback ='
Inheritance and overloading
Inheritance interacts with overloading in two ways.
Strings as values of ""use overload"" directive
If "value" in
use overload key => value;
is a string, it is interpreted as a method name.
Overloading of an operation is inherited by derived
classes
Any class derived from an overloaded class is also
overloaded. The set of overloaded methods is the
union of overloaded methods of all the ancestors. If
some method is overloaded in several ancestor, then
which description will be used is decided by the usual
inheritance rules:
If "A" inherits from "B" and "C" (in this order), "B"
overloads "+" with "\&D::plus_sub", and "C" overloads
"+" by ""plus_meth"", then the subroutine
"D::plus_sub" will be called to implement operation
"+" for an object in package "A".
Note that since the value of the "fallback" key is not a
subroutine, its inheritance is not governed by the above
rules. In the current implementation, the value of "fall
back" in the first overloaded ancestor is used, but this
is accidental and subject to change.
SPECIAL SYMBOLS FOR "use overload"
Three keys are recognized by Perl that are not covered by
the above description.
Last Resort
""nomethod"" should be followed by a reference to a func
tion of four parameters. If defined, it is called when
the overloading mechanism cannot find a method for some
operation. The first three arguments of this function
coincide with the arguments for the corresponding method
if it were found, the fourth argument is the symbol corre
sponding to the missing method. If several methods are
tried, the last one is used. Say, "1-$a" can be equiva
lent 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
function 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
particular operation is not found. Three different cases
are possible depending on the value of ""fallback"":
""undef"" Perl tries to use a substituted method
(see the MAGIC AUTOGENERATION entry else
where in this document). 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
missing, raises an exception.
Note. ""fallback"" inheritance via @ISA is not carved in
stone yet, see the section on "Inheritance and overload
ing".
Copy Constructor
The value for ""="" is a reference to a function with
three arguments, i.e., it looks like the other values in
"use 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 exe
cuted.
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 ""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 con
version.
Comparison operations
can be expressed in terms of its "space
ship" 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 refer
ence, 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 mathemagi
cal 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
questionable.
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.
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 application Perl parser mangles constants too
much. It is possible to hook into this process via over_
load::constant() and overload::remove_constant()
functions.
These functions take a hash as an argument. The recog
nized 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 expres
sions.
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 inter
prets 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-delim
iter combinations 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
interpreted 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 con
stant 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 prop
agate into "eval '...'".
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 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 addi
tional (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 car
ries 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.
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 the section on "Copy Construc
tor").
It is expected that arguments to methods that are not
explicitly supposed to be changed are constant (but this
is not enforced).
Metaphor clash
One may wonder why the semantic of overloaded "=" is so
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 pre
serving the Perlian way as far as possible. Since it is
not 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 over_
loaded access only. The way it is done is described in
the Copy Constructor entry elsewhere in this document.
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
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 the tie
entry in the perlfunc manpage). 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 the
section on "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 bet
ter than a pseudo-hash by allowing index 0 to be treated
as a normal element.
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 derefer
ence). Similarly, the object returned by the TIEHASH()
method is a scalar reference.
Second, we create a new tied hash each time the hash
syntax is used. This allows us not to worry about a pos
sibility of a reference loop, would would lead to a memory
leak.
Both these problems can be cured. Say, if we want to
overload hash dereference on a reference to an object
which is 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 over
loaded dereference operator). Here is one possible fetch
ing 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-cir
cular 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 ref
erence 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
expression "$$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 the Last Resort entry elsewhere in this
document operator "nomethod". In this example the corre
sponding subroutine returns an object which encapsulates
operations done over the objects: "new symbolic 3" con
tains "['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 $side is
['/', ['-', ['sqrt', ['+', 1, ['**', ['n', 1], 2]],
undef], 1], ['n', 1]]
Note that while we obtained this value using a nice little
script, there is no simple way to use this value. In fact
this value may be inspected in debugger (see the perldebug
manpage), but ony if "bareStringify" Option is set, and
not via "p" command.
If one attempts to print this value, then the overloaded
operator """" will be called, which will call "nomethod"
operator. The result of this operator will be stringified
again, but this result is again of type "symbolic", which
will lead to an infinite loop.
Add a pretty-printer method to the module symbolic.pm:
sub pretty {
my ($meth, $a, $b) = @{+shift};
$a = 'u' unless defined $a;
$b = 'u' unless defined $b;
$a = $a->pretty if ref $a;
$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 $b. If these compo
nents use overloading, the catenation operator will look
for an overloaded operator "."; if not present, it will
look for an overloaded operator """". Thus it is enough
to use
use overload nomethod => \&wrap, '""' => \&str;
sub str {
my ($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 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 $cnt should become
false. However, the operator "bool" for checking falsity
is overloaded (this time via overloaded """"), and returns
a long string, thus any object of type "symbolic" is true.
To overcome this, we need a way to compare an object to 0.
In fact, it is easier to write a numeric conversion rou
tine.
Here is the text of symbolic.pm with such a routine added
(and slightly modified str()):
package symbolic; # Primitive symbolic calculator
use overload
nomethod => \&wrap, '""' => \&str, '0+' => \#
sub new { shift; bless ['n', @_] }
sub wrap {
my ($obj, $other, $inv, $meth) = @_;
($obj, $other) = ($other, $obj) if $inv;
bless [$meth, $obj, $other];
}
sub str {
my ($meth, $a, $b) = @{+shift};
$a = 'u' unless defined $a;
if (defined $b) {
"[$meth $a $b]";
} else {
"[$meth $a]";
}
}
my %subr = ( n => sub {$_[0]},
sqrt => sub {sqrt $_[0]},
'-' => sub {shift() - shift()},
'+' => sub {shift() + shift()},
'/' => sub {shift() / shift()},
'*' => sub {shift() * shift()},
'**' => sub {shift() ** shift()},
);
sub num {
my ($meth, $a, $b) = @{+shift};
my $subr = $subr{$meth}
or die "Do not know how to ($meth) in symbolic";
$a = $a->num if ref $a eq __PACKAGE__;
$b = $b->num if ref $b eq __PACKAGE__;
$subr->($a,$b);
}
All the work of numeric conversion is done in %subr and
num(). Of course, %subr is not complete, it contains only
operators used in the example below. Here is the extra-
credit question: why do we need an explicit recursion in
num()? (Answer is at the end of this section.)
Use this module like this:
require symbolic;
my $iter = new symbolic 2; # 16-gon
my $side = new symbolic 1;
my $cnt = $iter;
while ($cnt) {
$cnt = $cnt - 1; # Mutator `--' not implemented
$side = (sqrt(1 + $side**2) - 1)/$side;
}
printf "%s=%f\n", $side, $side;
printf "pi=%f\n", $side*(2**($iter+2));
It prints (without so many line breaks)
[/ [- [sqrt [+ 1 [** [/ [- [sqrt [+ 1 [** [n 1] 2]]] 1]
[n 1]] 2]]] 1]
[/ [- [sqrt [+ 1 [** [n 1] 2]]] 1] [n 1]]]=0.198912
pi=3.182598
The above module is very primitive. It does not implement
mutator methods ("++", "-=" and so on), does not do deep
copying (not required without mutators!), and implements
only those arithmetic operations which are used in the
example.
To implement most arithmetic operations is easy; one
should just use the tables of operations, and change the
code which fills %subr to
my %subr = ( 'n' => sub {$_[0]} );
foreach my $op (split " ", $overload::ops{with_assign}) {
$subr{$op} = $subr{"$op="} = eval "sub {shift() $op shift()}";
}
my @bins = qw(binary 3way_comparison num_comparison str_comparison);
foreach my $op (split " ", "@overload::ops{ @bins }") {
$subr{$op} = eval "sub {shift() $op shift()}";
}
foreach my $op (split " ", "@overload::ops{qw(unary func)}") {
print "defining `$op'\n";
$subr{$op} = eval "sub {$op shift()}";
}
Due to the Calling Conventions for Mutators entry else
where in this document, we do not need anything special to
make "+=" and friends work, except filling "+=" entry of
%subr, and defining a copy constructor (needed since Perl
has no way to know that the implementation of "'+='" does
not mutate the argument, compare the Copy Constructor
entry elsewhere in this document).
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 $self;
}
To make "++" and "--" work, we need to implement actual
mutators, either directly, or in "nomethod". We continue
to do things inside "nomethod", thus add
if ($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 cal
culator in 50 lines of Perl code. Since the numeric val
ues 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 appro
priate choice of defaults. One extra note: due to the
explicit recursion num() is more fragile than sym(): we
need to explicitly check for the type of $a and $b. If
components $a and $b happen to be of some related type,
this may lead to problems.
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
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" (compare with the
Metaphor clash entry elsewhere in this document). Add
methods
sub TIESCALAR { my $pack = shift; $pack->new(@_) }
sub FETCH { shift }
sub nop { } # Around a bug
(the bug is described in the section on "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
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 the perldebug
manpage) one can deduce which operations are overloaded
(and which ancestor 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 over
load::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.
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.
Overloading 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 simple workaround is to access the value immedi
ately after tie()ing, so that after this call the previous
class coincides 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 mis
leading language used in places. It would seem a total
rewrite is needed.
2001-03-18 perl v5.6.1 overload(3)
