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overload(3)
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 $b;
DESCRIPTION
Declaration of overloaded functions
The compilation directive
package Number;
use overload
"+" => <!>add,
"*=" => "muas";
declares function Number::add() for addition, and method muas() in the
"class" "Number" (or one of its base classes) for the assignment form "*="
of multiplication.
Arguments of this directive come in (key, value) pairs. Legal values are
values legal inside a "&{ ... }" call, so the name of a subroutine, a
reference to a subroutine, or an anonymous subroutine will all work. Note
that values specified as strings are interpreted as methods, not
subroutines. Legal keys are listed below.
The subroutine "add" will be called to execute "$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
"$a++". See "MAGIC AUTOGENERATION". (Mathemagical methods refer to
methods triggered by an overloaded mathematical operator.)
Since overloading respects inheritance via the @ISA hierarchy, the above
declaration would also trigger overloading of "+" and "*=" in all the
packages which inherit from "Number".
Calling Conventions for Binary Operations
The functions specified in the "use overload ..." directive are called with
three (in one particular case with four, see "Last Resort") arguments. If
the corresponding operation is binary, then the first two arguments are the
two arguments of the operation. However, due to general object calling
conventions, the first argument should always be an object in the package,
so in the situation of "7+$a", the order of the arguments is interchanged.
It probably does not matter when implementing the addition method, but
whether the arguments 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 operation.
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, assuming that $obj is a reference to a
number,
sub incr { my $n = $ {$_[0]}; ++$n; $_[0] = bless \$n}
is an appropriate implementation of overloaded "++". Note that
sub incr { ++$ {$_[0]} ; shift }
is OK if used with preincrement and with postincrement. (In the case of
postincrement a copying will be performed, see "Copy Constructor".)
"x=" and other assignment versions
There is nothing special about these methods. They may change the
value of their arguments, and may leave it as is. The result is going
to be assigned to the value in the left-hand-side if different from
this value.
This allows for the same method to be used as overloaded "+=" and "+".
Note that this is allowed, but not recommended, since by the semantic
of "Fallback" Perl will call the method for "+" anyway, if "+=" is not
overloaded.
Warning. Due to the presence of assignment versions of operations,
routines which may be called in assignment context may create self-
referential structures. Currently Perl will not free self-referential
structures until cycles are "explicitly" broken. You may get problems when
traversing your structures too.
Say,
use overload '+' => sub { bless [ \$_[0], \$_[1] ] };
is asking for trouble, since for code "$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 "+="
explicitly by a non-"optimized" version, or switch to non-optimized version
if "not defined $_[2]" (see "Calling Conventions for Binary Operations").
Even if no explicit assignment-variants of operators are present in the
script, they may be generated by the optimizer. Say, ",$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 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 Operations") 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 prefix 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, 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
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 stringification). 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:
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 => '${} @{} %{} &{} *{}',
special => 'nomethod fallback ='
Inheritance and overloading
Inheritance interacts with overloading in two ways.
Strings as values of "use overload" directive
If "value" in
use overload key => value;
is a string, it is interpreted as a method name.
Overloading of an operation is inherited by derived classes
Any class derived from an overloaded class is also overloaded. The set
of overloaded methods is the union of overloaded methods of all the
ancestors. If some method is overloaded in several ancestor, then which
description will be used is decided by the usual inheritance rules:
If "A" inherits from "B" and "C" (in this order), "B" overloads "+"
with "\!>D::plus_sub", and "C" overloads "+" by "plus_meth", then the
subroutine "D::plus_sub" will be called to implement operation "+" for
an object in package "A".
Note that since the value of the "fallback" key is not a subroutine, its
inheritance is not governed by the above rules. In the current
implementation, the value of "fallback" in the first overloaded ancestor is
used, but this is accidental and subject to change.
SPECIAL SYMBOLS FOR "use overload"
Three keys are recognized by Perl that are not covered by the above
description.
Last Resort
"nomethod" should be followed by a reference to a function of four
parameters. If defined, it is called when the overloading mechanism cannot
find a method for some operation. The first three arguments of this
function coincide with the arguments for the corresponding method if it
were found, the fourth argument is the symbol corresponding to the missing
method. If several methods are tried, the last one is used. Say, "1-$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 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 "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 missing, 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 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 consider 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 conversion.
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 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.
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.
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 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 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 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 propagate 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 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.
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 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 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 overloaded 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 "tie" in perlfunc). 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.
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).
Similarly, the object returned by the TIEHASH() method is a scalar
reference.
Second, we create a new tied hash each time the hash syntax is used. This
allows us not to worry about a possibility of a reference loop, which 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 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
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 "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 $side is
['/', ['-', ['sqrt', ['+', 1, ['**', ['n', 1], 2]],
undef], 1], ['n', 1]]
Note that while we obtained this value using a nice little script, there is
no simple way to use this value. In fact this value may be inspected in
debugger (see perldebug), but ony if "bareStringify" Option is set, and not
via "p" command.
If one attempts to print this value, then the overloaded operator "" will
be called, which will call "nomethod" operator. The result of this
operator will be stringified again, but this result is again of type
"symbolic", which will lead to an infinite loop.
Add a pretty-printer method to the module symbolic.pm:
sub pretty {
my ($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 $b. If these components use overloading, the
catenation operator will look for an overloaded operator "."; if not
present, it will look for an overloaded operator "". Thus it is enough to
use
use overload nomethod => <!>wrap, '""' => <!>str;
sub str {
my ($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 $b]";
} else {
"[$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 "Calling Conventions for Mutators", 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 "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 $self;
}
To make "++" and "--" work, we need to implement actual mutators, either
directly, or in "nomethod". We continue to do things inside "nomethod",
thus add
if ($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 $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 "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), $_->nop foreach @_; }
Now
my ($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 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 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.
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
immediately 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 misleading language used
in places. It would seem a total rewrite is needed.
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