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NAMEoverload - Package for overloading Perl operationsSYNOPSISpackage SomeThing; use overload '+' => \&myadd, '-' => \&mysub; # etc ... package main; $a = SomeThing->new( 57 ); $b = 5 + $a; ... if (overload::Overloaded $b) {...} ... $strval = overload::StrVal $b; DESCRIPTIONThis pragma allows overloading of Perl's operators for a class. To overload built-in functions, see "Overriding Built-in Functions" in perlsub instead.FundamentalsDeclarationArguments of the "use overload" directive are (key, value) pairs. For the full set of legal keys, see "Overloadable Operations" below. Operator implementations (the values) can be subroutines, references to subroutines, or anonymous subroutines - in other words, anything legal inside a "&{ ... }" call. Values specified as strings are interpreted as method names. Thus package Number; use overload "-" => "minus", "*=" => \&muas, '""' => sub { ...; }; declares that subtraction is to be implemented by method "minus()" in the class "Number" (or one of its base classes), and that the function "Number::muas()" is to be used for the assignment form of multiplication, "*=". It also defines an anonymous subroutine to implement stringification: this is called whenever an object blessed into the package "Number" is used in a string context (this subroutine might, for example, return the number as a Roman numeral). Calling Conventions and Magic Autogeneration The following sample implementation of "minus()" (which assumes that "Number" objects are simply blessed references to scalars) illustrates the calling conventions: package Number; sub minus { my ($self, $other, $swap) = @_; my $result = $$self - $other; # * $result = -$result if $swap; ref $result ? $result : bless \$result; } # * may recurse once - see table below Three arguments are passed to all subroutines specified in the "use overload" directive (with exceptions - see below, particularly "nomethod"). The first of these is the operand providing the overloaded operator implementation - in this case, the object whose "minus()" method is being called. The second argument is the other operand, or "undef" in the case of a unary operator. The third argument is set to TRUE if (and only if) the two operands have been swapped. Perl may do this to ensure that the first argument ($self) is an object implementing the overloaded operation, in line with general object calling conventions. For example, if $x and $y are "Number"s: operation | generates a call to ============|====================== $x - $y | minus($x, $y, '') $x - 7 | minus($x, 7, '') 7 - $x | minus($x, 7, 1) Perl may also use "minus()" to implement other operators which have not been specified in the "use overload" directive, according to the rules for "Magic Autogeneration" described later. For example, the "use overload" above declared no subroutine for any of the operators "--", "neg" (the overload key for unary minus), or "-=". Thus operation | generates a call to ============|====================== -$x | minus($x, 0, 1) $x-- | minus($x, 1, undef) $x -= 3 | minus($x, 3, undef) Note the "undef"s: where autogeneration results in the method for a standard operator which does not change either of its operands, such as "-", being used to implement an operator which changes the operand ("mutators": here, "--" and "-="), Perl passes undef as the third argument. This still evaluates as FALSE, consistent with the fact that the operands have not been swapped, but gives the subroutine a chance to alter its behaviour in these cases. In all the above examples, "minus()" is required only to return the result of the subtraction: Perl takes care of the assignment to $x. In fact, such methods should not modify their operands, even if "undef" is passed as the third argument (see "Overloadable Operations"). The same is not true of implementations of "++" and "--": these are expected to modify their operand. An appropriate implementation of "--" might look like use overload '--' => "decr", # ... sub decr { --${$_[0]}; } If the "bitwise" feature is enabled (see feature), a fifth TRUE argument is passed to subroutines handling "&", "|", "^" and "~". This indicates that the caller is expecting numeric behaviour. The fourth argument will be "undef", as that position ($_[3]) is reserved for use by "nomethod". Mathemagic, Mutators, and Copy Constructors The term 'mathemagic' describes the overloaded implementation of mathematical operators. Mathemagical operations raise an issue. Consider the code: $a = $b; --$a; If $a and $b are scalars then after these statements $a == $b - 1 An object, however, is a reference to blessed data, so if $a and $b are objects then the assignment "$a = $b" copies only the reference, leaving $a and $b referring to the same object data. One might therefore expect the operation "--$a" to decrement $b as well as $a. However, this would not be consistent with how we expect the mathematical operators to work. Perl resolves this dilemma by transparently calling a copy constructor before calling a method defined to implement a mutator ("--", "+=", and so on.). In the above example, when Perl reaches the decrement statement, it makes a copy of the object data in $a and assigns to $a a reference to the copied data. Only then does it call "decr()", which alters the copied data, leaving $b unchanged. Thus the object metaphor is preserved as far as possible, while mathemagical operations still work according to the arithmetic metaphor. Note: the preceding paragraph describes what happens when Perl autogenerates the copy constructor for an object based on a scalar. For other cases, see "Copy Constructor". Overloadable OperationsThe complete list of keys that can be specified in the "use overload" directive are given, separated by spaces, in the values of the hash %overload::ops:with_assign => '+ - * / % ** << >> x .', assign => '+= -= *= /= %= **= <<= >>= x= .=', num_comparison => '< <= > >= == !=', '3way_comparison'=> '<=> cmp', str_comparison => 'lt le gt ge eq ne', binary => '& &= | |= ^ ^= &. &.= |. |.= ^. ^.=', unary => 'neg ! ~ ~.', mutators => '++ --', func => 'atan2 cos sin exp abs log sqrt int', conversion => 'bool "" 0+ qr', iterators => '<>', filetest => '-X', dereferencing => '${} @{} %{} &{} *{}', matching => '~~', special => 'nomethod fallback =' Most of the overloadable operators map one-to-one to these keys. Exceptions, including additional overloadable operations not apparent from this hash, are included in the notes which follow. This list is subject to growth over time. A warning is issued if an attempt is made to register an operator not found above.
Magic AutogenerationIf a method for an operation is not found then Perl tries to autogenerate a substitute implementation from the operations that have been defined.Note: the behaviour described in this section can be disabled by setting "fallback" to FALSE (see "fallback"). In the following tables, numbers indicate priority. For example, the table below states that, if no implementation for '!' has been defined then Perl will implement it using 'bool' (that is, by inverting the value returned by the method for 'bool'); if boolean conversion is also unimplemented then Perl will use '0+' or, failing that, '""'. operator | can be autogenerated from | | 0+ "" bool . x =========|========================== 0+ | 1 2 "" | 1 2 bool | 1 2 int | 1 2 3 ! | 2 3 1 qr | 2 1 3 . | 2 1 3 x | 2 1 3 .= | 3 2 4 1 x= | 3 2 4 1 <> | 2 1 3 -X | 2 1 3 Note: The iterator ('<>') and file test ('-X') operators work as normal: if the operand is not a blessed glob or IO reference then it is converted to a string (using the method for '""', '0+', or 'bool') to be interpreted as a glob or filename. operator | can be autogenerated from | | < <=> neg -= - =========|========================== neg | 1 -= | 1 -- | 1 2 abs | a1 a2 b1 b2 [*] < | 1 <= | 1 > | 1 >= | 1 == | 1 != | 1 * one from [a1, a2] and one from [b1, b2] Just as numeric comparisons can be autogenerated from the method for '<=>', string comparisons can be autogenerated from that for 'cmp': operators | can be autogenerated from ====================|=========================== lt gt le ge eq ne | cmp Similarly, autogeneration for keys '+=' and '++' is analogous to '-=' and '--' above: operator | can be autogenerated from | | += + =========|========================== += | 1 ++ | 1 2 And other assignment variations are analogous to '+=' and '-=' (and similar to '.=' and 'x=' above): operator || *= /= %= **= <<= >>= &= ^= |= &.= ^.= |.= -------------------||------------------------------------------- autogenerated from || * / % ** << >> & ^ | &. ^. |. Note also that the copy constructor (key '=') may be autogenerated, but only for objects based on scalars. See "Copy Constructor". Minimal Set of Overloaded Operations Since some operations can be automatically generated from others, there is a minimal set of operations that need to be overloaded in order to have the complete set of overloaded operations at one's disposal. Of course, the autogenerated operations may not do exactly what the user expects. The minimal set is: + - * / % ** << >> x <=> cmp & | ^ ~ &. |. ^. ~. atan2 cos sin exp log sqrt int "" 0+ bool ~~ Of the conversions, only one of string, boolean or numeric is needed because each can be generated from either of the other two. Special Keys for "use overload""nomethod"The 'nomethod' key is used to specify a catch-all function to be called for any operator that is not individually overloaded. The specified function will be passed four parameters. The first three arguments coincide with those that would have been passed to the corresponding method if it had been defined. The fourth argument is the "use overload" key for that missing method. If the "bitwise" feature is enabled (see feature), a fifth TRUE argument is passed to subroutines handling "&", "|", "^" and "~" to indicate that the caller is expecting numeric behaviour. For example, if $a is an object blessed into a package declaring use overload 'nomethod' => 'catch_all', # ... then the operation 3 + $a could (unless a method is specifically declared for the key '+') result in a call catch_all($a, 3, 1, '+') See "How Perl Chooses an Operator Implementation". "fallback" The value assigned to the key 'fallback' tells Perl how hard it should try to find an alternative way to implement a missing operator.
See "How Perl Chooses an Operator Implementation". Copy Constructor As mentioned above, this operation is called when a mutator is applied to a reference that shares its object with some other reference. For example, if $b is mathemagical, and '++' is overloaded with 'incr', and '=' is overloaded with 'clone', then the code $a = $b; # ... (other code which does not modify $a or $b) ... ++$b; would be executed in a manner equivalent to $a = $b; # ... $b = $b->clone(undef, ""); $b->incr(undef, ""); Note:
How Perl Chooses an Operator ImplementationWhich is checked first, "nomethod" or "fallback"? If the two operands of an operator are of different types and both overload the operator, which implementation is used? The following are the precedence rules:
Where there is only one operand (or only one operand with overloading) the checks in respect of the other operand above are skipped. There are exceptions to the above rules for dereference operations (which, if Step 1 fails, always fall back to the normal, built-in implementations - see Dereferencing), and for "~~" (which has its own set of rules - see "Matching" under "Overloadable Operations" above). Note on Step 7: some operators have a different semantic depending on the type of their operands. As there is no way to instruct Perl to treat the operands as, e.g., numbers instead of strings, the result here may not be what you expect. See "BUGS AND PITFALLS". Losing OverloadingThe restriction for the comparison operation is that even if, for example, "cmp" should return a blessed reference, the autogenerated "lt" function will produce only a standard logical value based on the numerical value of the result of "cmp". In particular, a working numeric conversion is needed in this case (possibly expressed in terms of other conversions).Similarly, ".=" and "x=" operators lose their mathemagical properties if the string conversion substitution is applied. When you chop() a mathemagical object it is promoted to a string and its mathemagical properties are lost. The same can happen with other operations as well. Inheritance and OverloadingOverloading respects inheritance via the @ISA hierarchy. Inheritance interacts with overloading in two ways.
Note that in Perl version prior to 5.18 inheritance of the "fallback" key was not governed by the above rules. The value of "fallback" in the first overloaded ancestor was used. This was fixed in 5.18 to follow the usual rules of inheritance. Run-time OverloadingSince all "use" directives are executed at compile-time, the only way to change overloading during run-time is toeval 'use overload "+" => \&addmethod'; You can also use eval 'no overload "+", "--", "<="'; though the use of these constructs during run-time is questionable. Public FunctionsPackage "overload.pm" provides the following public functions:
Overloading ConstantsFor 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:
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)}; } IMPLEMENTATIONWhat 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. (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 a package uses overload, it carries a special flag. This flag is also set when new functions are defined or @ISA is modified. There will be a slight speed penalty on the very first operation thereafter that supports overloading, while the overload tables are updated. If there is no overloading present, the flag is turned off. Thus the only speed penalty thereafter is the checking of this flag. It is expected that arguments to methods that are not explicitly supposed to be changed are constant (but this is not enforced). COOKBOOKPlease add examples to what follows!Two-face ScalarsPut 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 = two_face->new("vii", 7); printf "seven=$seven, seven=%d, eight=%d\n", $seven, $seven+1; print "seven contains 'i'\n" if $seven =~ /i/; (The second line creates a scalar which has both a string value, and a numeric value.) This prints: seven=vii, seven=7, eight=8 seven contains 'i' Two-face ReferencesSuppose you want to create an object which is accessible as both an array reference and a hash reference.package two_refs; use overload '%{}' => \&gethash, '@{}' => sub { $ {shift()} }; sub new { my $p = shift; bless \ [@_], $p; } sub gethash { my %h; my $self = shift; tie %h, ref $self, $self; \%h; } sub TIEHASH { my $p = shift; bless \ shift, $p } my %fields; my $i = 0; $fields{$_} = $i++ foreach qw{zero one two three}; sub STORE { my $self = ${shift()}; my $key = $fields{shift()}; defined $key or die "Out of band access"; $$self->[$key] = shift; } sub FETCH { my $self = ${shift()}; my $key = $fields{shift()}; defined $key or die "Out of band access"; $$self->[$key]; } Now one can access an object using both the array and hash syntax: my $bar = two_refs->new(3,4,5,6); $bar->[2] = 11; $bar->{two} == 11 or die 'bad hash fetch'; Note several important features of this example. First of all, the actual type of $bar is a scalar reference, and we do not overload the scalar dereference. Thus we can get the actual non-overloaded contents of $bar by just using $$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 $baz is a reference to a reference to the intermediate array, which keeps a reference to an actual array, and the access hash. The tie()ing object for the access hash is a reference to a reference to the actual array, so
Symbolic CalculatorPut this in symbolic.pm in your Perl library directory:package symbolic; # Primitive symbolic calculator use overload nomethod => \&wrap; sub new { shift; bless ['n', @_] } sub wrap { my ($obj, $other, $inv, $meth) = @_; ($obj, $other) = ($other, $obj) if $inv; bless [$meth, $obj, $other]; } This module is very unusual as overloaded modules go: it does not provide any usual overloaded operators, instead it provides an implementation for "nomethod". In this example the "nomethod" subroutine returns an object which encapsulates operations done over the objects: "symbolic->new(3)" contains "['n', 3]", "2 + symbolic->new(3)" contains "['+', 2, ['n', 3]]". Here is an example of the script which "calculates" the side of circumscribed octagon using the above package: require symbolic; my $iter = 1; # 2**($iter+2) = 8 my $side = symbolic->new(1); my $cnt = $iter; while ($cnt--) { $side = (sqrt(1 + $side**2) - 1)/$side; } print "OK\n"; The value of $side is ['/', ['-', ['sqrt', ['+', 1, ['**', ['n', 1], 2]], undef], 1], ['n', 1]] Note that while we obtained this value using a nice little script, there is no simple way to use this value. In fact this value may be inspected in debugger (see perldebug), but only if "bareStringify" Option is set, and not via "p" command. If one attempts to print this value, then the overloaded operator "" will be called, which will call "nomethod" operator. The result of this operator will be stringified again, but this result is again of type "symbolic", which will lead to an infinite loop. Add a pretty-printer method to the module symbolic.pm: sub pretty { my ($meth, $a, $b) = @{+shift}; $a = 'u' unless defined $a; $b = 'u' unless defined $b; $a = $a->pretty if ref $a; $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 $cnt should become false. However, the operator "bool" for checking falsity is overloaded (this time via overloaded ""), and returns a long string, thus any object of type "symbolic" is true. To overcome this, we need a way to compare an object to 0. In fact, it is easier to write a numeric conversion routine. Here is the text of symbolic.pm with such a routine added (and slightly modified str()): package symbolic; # Primitive symbolic calculator use overload nomethod => \&wrap, '""' => \&str, '0+' => \# sub new { shift; bless ['n', @_] } sub wrap { my ($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 = symbolic->new(2); # 16-gon my $side = symbolic->new(1); my $cnt = $iter; while ($cnt) { $cnt = $cnt - 1; # Mutator '--' not implemented $side = (sqrt(1 + $side**2) - 1)/$side; } printf "%s=%f\n", $side, $side; printf "pi=%f\n", $side*(2**($iter+2)); It prints (without so many line breaks) [/ [- [sqrt [+ 1 [** [/ [- [sqrt [+ 1 [** [n 1] 2]]] 1] [n 1]] 2]]] 1] [/ [- [sqrt [+ 1 [** [n 1] 2]]] 1] [n 1]]]=0.198912 pi=3.182598 The above module is very primitive. It does not implement mutator methods ("++", "-=" and so on), does not do deep copying (not required without mutators!), and implements only those arithmetic operations which are used in the example. To implement most arithmetic operations is easy; one should just use the tables of operations, and change the code which fills %subr to my %subr = ( 'n' => sub {$_[0]} ); foreach my $op (split " ", $overload::ops{with_assign}) { $subr{$op} = $subr{"$op="} = eval "sub {shift() $op shift()}"; } my @bins = qw(binary 3way_comparison num_comparison str_comparison); foreach my $op (split " ", "@overload::ops{ @bins }") { $subr{$op} = eval "sub {shift() $op shift()}"; } foreach my $op (split " ", "@overload::ops{qw(unary func)}") { print "defining '$op'\n"; $subr{$op} = eval "sub {$op shift()}"; } Since subroutines implementing assignment operators are not required to modify their operands (see "Overloadable Operations" above), we do not need anything special to make "+=" and friends work, besides adding these operators to %subr and defining a copy constructor (needed since Perl has no way to know that the implementation of '+=' does not mutate the argument - see "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 CalculatorOne 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 = symbolic->new(3); my $b = symbolic->new(4); my $c = sqrt($a**2 + $b**2); and the numeric value of $c becomes 5. However, after calling $a->STORE(12); $b->STORE(5); the numeric value of $c becomes 13. There is no doubt now that the module symbolic provides a symbolic calculator indeed. To hide the rough edges under the hood, provide a tie()d interface to the package "symbolic". Add methods sub TIESCALAR { my $pack = shift; $pack->new(@_) } sub FETCH { shift } sub nop { } # Around a bug (the bug, fixed in Perl 5.14, is described in "BUGS"). One can use this new interface as tie $a, 'symbolic', 3; tie $b, 'symbolic', 4; $a->nop; $b->nop; # Around a bug my $c = sqrt($a**2 + $b**2); Now numeric value of $c is 5. After "$a = 12; $b = 5" the numeric value of $c becomes 13. To insulate the user of the module add a method sub vars { my $p = shift; tie($_, $p), $_->nop foreach @_; } Now my ($a, $b); symbolic->vars($a, $b); my $c = sqrt($a**2 + $b**2); $a = 3; $b = 4; printf "c5 %s=%f\n", $c, $c; $a = 12; $b = 5; printf "c13 %s=%f\n", $c, $c; shows that the numeric value of $c follows changes to the values of $a and $b. AUTHORIlya Zakharevich <ilya@math.mps.ohio-state.edu>.SEE ALSOThe "overloading" pragma can be used to enable or disable overloaded operations within a lexical scope - see overloading.DIAGNOSTICSWhen 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:
BUGS AND PITFALLS
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