NAME
Operator::Util - A selection of array and hash functions that extend
operators
VERSION
This document describes Operator::Util version 0.02.
SYNOPSIS
use Operator::Util qw(
reduce reducewith
zip zipwith
cross crosswith
hyper hyperwith
applyop reverseop
);
WARNING
This is a pre-alpha release of Operator::Util. Not all features
described in this document are complete. Please see the "TODO" list for
details. The interface and functionality may change in the future based
on user feedback. Please make suggestions by creating an issue at
<
http://github.com/patch/operator-util-pm5/issues>.
DESCRIPTION
A pragmatic approach at providing the functionality of many of Perl 6's
meta-operators in Perl 5.
The terms "operator string" or "opstring" are used to describe a string
that represents an operator, such as the string '+' for the addition
operator or the string '.' for the concatenation operator. Except where
noted, opstrings default to binary infix operators and the short form
may be used, e.g., '*' instead of 'infix:*'. All other operator types
(prefix, postfix, circumfix, and postcircumfix) must have the type
prepended in the opstrings, e.g., "prefix:++" and "postcircumfix:{}".
When a list is passed as an argument for any of the functions, it must
be either an array reference or a scalar value that will be used as a
single-element list.
The following functions are provided but are not exported by default.
Reduction
reduce OPSTRING, LIST [, triangle => 1 ]
"reducewith" is an alias for "reduce". It may be desirable to use
"reducewith" to avoid naming conflicts or confusion with "reduce" in
List::Util.
Any infix opstring (except for non-associating operators) can be
passed to "reduce" along with an arrayref to reduce the array using
that operation:
reduce('+', [1, 2, 3]) # 1 + 2 + 3 = 6
my @a = (5, 6)
reduce('*', \@a) # 5 * 6 = 30
"reduce" associates the same way as the operator used:
reduce('-', [4, 3, 2]) # 4-3-2 = (4-3)-2 = -1
reduce('**', [4, 3, 2]) # 4**3**2 = 4**(3**2) = 262144
For comparison operators (like "<"), all reduced pairs of operands
are broken out into groups and joined with "&&" because Perl 5
doesn't support comparison operator chaining:
reduce('<', [1, 3, 5]) # 1 < 3 && 3 < 5
If fewer than two elements are given, the results will vary
depending on the operator:
reduce('+', []) # 0
reduce('+', [5]) # 5
reduce('*', []) # 1
reduce('*', [5]) # 5
If there is one element, the "reduce" returns that one element.
However, this default doesn't make sense for operators like "<" that
don't return the same type as they take, so these kinds of operators
overload the single-element case to return something more
meaningful.
You can also reduce the comma operator, although there isn't much
point in doing so. This just returns an arrayref that compares
deeply to the arrayref passed in:
[1, 2, 3]
reduce(',', [1, 2, 3]) # same thing
Operators with zero-element arrayrefs return the following values:
** # 1 (arguably nonsensical)
=~ # 1 (also for 1 arg)
!~ # 1 (also for 1 arg)
* # 1
/ # fail (reduce is nonsensical)
% # fail (reduce is nonsensical)
x # fail (reduce is nonsensical)
+ # 0
- # 0
. # ''
<< # fail (reduce is nonsensical)
>> # fail (reduce is nonsensical)
< # 1 (also for 1 arg)
> # 1 (also for 1 arg)
<= # 1 (also for 1 arg)
>= # 1 (also for 1 arg)
lt # 1 (also for 1 arg)
le # 1 (also for 1 arg)
gt # 1 (also for 1 arg)
ge # 1 (also for 1 arg)
== # 1 (also for 1 arg)
!= # 1 (also for 1 arg)
eq # 1 (also for 1 arg)
ne # 1 (also for 1 arg)
~~ # 1 (also for 1 arg)
& # -1 (from ^0, the 2's complement in arbitrary precision)
| # 0
&& # 1
|| # 0
// # 0
= # undef (same for all assignment operators)
, # []
You can say
reduce('||', [a(), b(), c(), d()])
to return the first true result, but the evaluation of the list is
controlled by the semantics of the list, not the semantics of "||".
To generate all intermediate results along with the final result,
you can set the "triangle" argument:
reduce('+', [1..5], triangle=>1) # (1, 3, 6, 10, 15)
The visual picture of a triangle is not accidental. To produce a
triangular list of lists, you can use a "triangular comma":
reduce(',', [1..5], triangle=>1)
# [1],
# [1,2],
# [1,2,3],
# [1,2,3,4],
# [1,2,3,4,5]
Zip
zip OPSTRING, LIST1, LIST2
zip LIST1, LIST2
"zipwith" is an alias for "zip".
The "zip" function may be passed any infix opstring. It applies the
operator across all groupings of its list elements.
The string concatenating form is:
zip('.', ['a','b'], [1,2]) # ('a1', 'b2')
The list concatenating form when used like this:
zip(',', ['a','b'], [1,2], ['x','y'])
produces
('a', 1, 'x', 'b', 2, 'y')
This list form is common enough to have a shortcut, calling "zip"
without an opstring as the first argument will use "," by default:
zip(['a','b'], [1,2], ['x','y'])
also produces
('a', 1, 'x', 'b', 2, 'y')
Any non-mutating infix operator may be used.
zip('*', [1,2], [3,4]) # (3, 8)
All assignment operators are considered mutating.
If the underlying operator is non-associating, so is the cross
operator, except for basic comparison operators since a chaining
workaround is provided:
zip('cmp', \@a, \@b, \@c) # ILLEGAL
zip('eq', \@a, \@b, \@c) # ok
The underlying operator is always applied with its own
associativity, just as the corresponding "reduce" operator would do.
All lists are assumed to be flat; multidimensional lists are handled
by treating the first dimension as the only dimension.
The response is a flat list by default. To return a list of
arrayrefs, unset the "flat" argument:
zip(['a','b'], [1,2], ['x','y'], flat=>0)
produces:
(['a', 1, 'x'], ['b', 2, 'y'])
Cross
cross OPSTRING, LIST1, LIST2
cross LIST1, LIST2
"crosswith" is an alias for "cross".
The "cross" function may be passed any infix opstring. It applies
the operator across all groupings of its list elements.
The string concatenating form is:
cross('.', ['a','b'], [1,2]) # ('a1', 'a2', 'b1', 'b2')
The list concatenating form when used like this:
cross(',', ['a','b'], [1,2], ['x','y'])
produces
'a', 1, 'x',
'a', 1, 'y',
'a', 2, 'x',
'a', 2, 'y',
'b', 1, 'x',
'b', 1, 'y',
'b', 2, 'x',
'b', 2, 'y'
This list form is common enough to have a shortcut, calling "cross"
without an opstring as the first argument will use "," by default:
cross(['a','b'], [1,2], ['x','y'])
Any non-mutating infix operator may be used.
cross('*', [1,2], [3,4]) # (3, 4, 6, 8)
All assignment operators are considered mutating.
If the underlying operator is non-associating, so is the cross
operator, except for basic comparison operators since a chaining
workaround is provided:
cross('cmp', \@a, \@b, \@c) # ILLEGAL
cross('eq', \@a, \@b, \@c) # ok
The underlying operator is always applied with its own
associativity, just as the corresponding "reduce" operator would do.
All lists are assumed to be flat; multidimensional lists are handled
by treating the first dimension as the only dimension.
The response is a flat list by default. To return a list of
arrayrefs, unset the "flat" argument:
cross(['a','b'], [1,2], ['x','y'], flat=>0)
produces:
['a', 1, 'x'],
['a', 1, 'y'],
['a', 2, 'x'],
['a', 2, 'y'],
['b', 1, 'x'],
['b', 1, 'y'],
['b', 2, 'x'],
['b', 2, 'y']
Hyper
hyper OPSTRING, LIST1, LIST2 [, dwim_left => 1, dwim_right => 1 ]
hyper OPSTRING, LIST
"hyperwith" is an alias for "hyper".
The "hyper" function operates on each element of its arrayref
argument (or arguments) and returns a single list of the results. In
other words, "hyper" distributes the operator over its elements as
lists.
hyper('prefix:-' [1,2,3]) # (-1,-2,-3)
hyper('+', [1,1,2,3,5], [1,2,3,5,8]) # (2,3,5,8,13)
Unary operators always produce a list of exactly the same shape as
their single argument. When infix operators are presented with two
arrays of identical shape, a result of that same shape is produced.
Otherwise the result depends on what "dwim" arguments are passed.
For an infix operator, if either argument is insufficiently
dimensioned, "hyper" "upgrades" it, but only if you tell it to
"dwim" on that side.
hyper('-', [3,8,2,9,3,8], 1, dwim_right=>1) # (2,7,1,8,2,7)
hyper('+=', \@array, 42, dwim_right=>1) # add 42 to each element
If you don't know whether one side or the other will be
under-dimensioned, you can dwim on both sides:
hyper('*', $left, $right, dwim=>1)
The upgrade never happens on the non-dwim end of a "hyper". If you
write
hyper('*', $bigger, $smaller, dwim_left=>1)
hyper('*', $smaller, $bigger, dwim_right=>1)
an exception is thrown, and if you write
hyper('*', $foo, $bar)
you are requiring the shapes to be identical, or an exception will
be thrown.
For all hyper dwimminess, if a scalar is found where the other side
expects an array, the scalar is considered to be an array of one
element.
Once we have two lists to process, we have to decide how to put the
elements into correspondence. If both sides are dwimmy, the short
list will have to be repeated as many times as necessary to make the
appropriate number of elements.
If only one side is dwimmy, then the list on that side only will be
grown or truncated to fit the list on the non-dwimmy side.
This produces an array the same length as the corresponding
dimension on the other side. The original operator is then
recursively applied to each corresponding pair of elements, in case
there are more dimensions to handle.
Here are some examples:
hyper('+', [1,2,3,4], [1,2] ) # always error
hyper('+', [1,2,3,4], [1,2], dwim=>1 ) # (2,4,4,6) rhs dwims to 1,2,1,2
hyper('+', [1,2,3], [1,2], dwim=>1 ) # (2,4,4) rhs dwims to 1,2,1
hyper('+', [1,2,3,4], [1,2], dwim_left=>1 ) # (2,4) lhs dwims to 1,2
hyper('+', [1,2,3,4], [1,2], dwim_right=>1) # (2,4,4,6) rhs dwims to 1,2,1,2
hyper('+', [1,2,3], [1,2], dwim_right=>1) # (2,4,4) rhs dwims to 1,2,1
hyper('+', [1,2,3], 1, dwim_right=>1) # (2,3,4) rhs dwims to 1,1,1
Another way to look at it is that the dwimmy array's elements are
indexed modulo its number of elements so as to produce as many or as
few elements as necessary.
Note that each element of a dwimmy list may in turn be expanded into
another dimension if necessary, so you can, for instance, add one to
all the elements of a matrix regardless of its dimensionality:
hyper('+=', \@fancy, 1, dwim_right=>1)
On the non-dwimmy side, any scalar value will be treated as an array
of one element, and for infix operators must be matched by an
equivalent one-element array on the other side. That is, "hyper" is
guaranteed to degenerate to the corresponding scalar operation when
all its arguments are non-array arguments.
When using a unary operator no dwimmery is ever needed:
@negatives = hyper('prefix:-', \@positives)
hyper('postfix:++', \@positions) # increment each
hyper('->', \@objects, 'run', dwim_right=>1) # call ->run() on each
hyper('length', ['f','oo','bar']) # (1, 2, 3)
Note that method calls are infix operators with a string used for
the method name.
Hyper operators are defined recursively on nested arrays, so:
hyper('prefix:-', [[1, 2], 3]) # ([-1, -2], -3)
Likewise the dwimminess of dwimmy infixes propagates:
hyper('+', [[1, 2], 3], [4, [5, 6]], dwim=>1) # [[5, 6], [8, 9]]
"hyper" may be applied to hashes as well as to arrays. In this case
"dwimminess" says whether to ignore keys that do not exist in the
other hash, while "non-dwimminess" says to use all keys that are in
either hash. That is,
hyper('+', \%foo, \%bar, dwim=>1)
gives you the intersection of the keys, while
hyper('+', \%foo, \%bar)
gives you the union of the keys. Asymmetrical hypers are also
useful; for instance, if you say:
hyper('+', \%outer, \%inner, dwim_right=>1)
only the %inner keys that already exist in %outer will occur in the
result. Note, however, that you want
hyper('+=', \%outer, \%inner)
in order to pass accumulated statistics up a tree, assuming you want
%outer to have the union of keys.
Unary hash hypers and binary hypers that have only one hash operand
will apply the hyper operator to just the values but return a new
hash value with the same set of keys as the original hash.
hyper('prefix:-' {a => 1, b => 2, c => 3}) # (a => -1, b => -2, c => -3)
Other utils
applyop OPSTRING, OPERAND1, OPERAND2
applyop OPSTRING, OPERAND
If three arguments are provided to "applyop", apply the binary
operator OPSTRING to the operands OPERAND1 and OPERAND2. If two
arguments are provided, apply the unary operator OPSTRING to the
operand OPERAND. The unary form defaults to using prefix operators,
so 'prefix:' may be omitted, e.g., '++' instead of 'prefix:++';
applyop '.', 'foo', 'bar' # foobar
applyop '++', 5 # 6
reverseop OPSTRING, OPERAND1, OPERAND2
"reverseop" provides the same functionality as "applyop" except that
OPERAND1 and OPERAND2 are reversed.
reverseop '.', 'foo', 'bar' # barfoo
If an unary opstring is used, "reverseop" has the same functionality
as "applyop".
The optional named-argument "flat" can be passed to "reduce", "zip",
"cross", and "hyper". It defaults to 1, which causes the function to
return a flat list. When set to 0, it causes the return value from each
operator to be stored in an array ref, resulting in a "list of lists"
being returned from the function.
zip [1..3], ['a'..'c'] # 1, 'a', 2, 'b', 3, 'c'
zip [1..3], ['a'..'c'], flat => 0 # [1, 'a'], [2, 'b'], [3, 'c']
TODO
* Allow more than two arrayrefs with "zip", "cross", and "hyper"
* Support default operator with "zip" and "cross"
* Support multi-dimensional distribution with "hyper"
* Support hashes with "hyper"
* Support the "flat => 0" option
* Support chaining "reduce"
* Add special cases for zero- and one-element arrays with "reduce"
* Add "warn"ings on errors instead of simply "return"ing
* Add named unary operators such as "uc" and "lc"
* Support meta-operator literals such as "Z" and "X"
* Should the first argument optionally be a subroutine ref instead of
an operator string?
* Should the "flat => 0" option be changed to "lol => 1"?
* Convert tests to TestML
SEE ALSO
* perlop
* "pairwise" in List::MoreUtils is similar to "zip" except that its
first argument is a block instead of an operator string and the
remaining arguments are arrays instead of array refs:
pairwise { $a + $b }, @array1, @array2 # List::MoreUtils
zip '+', \@array1, \@array2 # Operator::Util
* "mesh" a.k.a. "zip" in List::MoreUtils is similar to "zip" when
using the default operator ',' except that the arguments are arrays
instead of array refs:
mesh @array1, @array2 # List::MoreUtils
zip \@array1, \@array2 # Operator::Util
* Set::CrossProduct is an object-oriented alternative to "cross" when
using the default operator ","
* The "Meta operators" section of Synopsis 3: Perl 6 Operators
(<
http://perlcabal.org/syn/S03.html#Meta_operators>) is the
inspiration for this module
AUTHOR
Nick Patch <
[email protected]>
ACKNOWLEDGEMENTS
* This module is based on the Perl 6 specification, as described in
the Synopsis and implemented in Rakudo
* Much of the documentation is taken directly from Synopsis 3: Perl 6
Operators (<
http://perlcabal.org/syn/S03.html>)
* The tests were forked from the Official Perl 6 Test Suite
(<
https://github.com/perl6/roast>)
COPYRIGHT AND LICENSE
Copyright 2010, 2011 Nick Patch
This library is free software; you can redistribute it and/or modify it
under the same terms as Perl itself.
