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README
NAME
    Operator::Util - A selection of array and hash functions that extend
    operators

VERSION
    This document describes Operator::Util version 0.05.

SYNOPSIS
        use Operator::Util qw(
            reduce reducewith
            zip zipwith
            cross crosswith
            hyper hyperwith
            applyop reverseop
        );

DESCRIPTION
    Warning: This is an early release of Operator::Util. Not all features
    described in this document are complete. Please see the "TODO" list for
    details.

    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. 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
            ^     # 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
    zipwith OPSTRING, LIST1, LIST2
    zip LIST1, LIST2
        The "zipwith" function may be passed any infix opstring. It applies
        the operator across all groupings of its list elements.

        The string concatenating form is:

            zipwith('.', ['a','b'], [1,2])  # ('a1', 'b2')

        The list concatenating form when used like this:

            zipwith(',', ['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.

            zipwith('*', [1,2], [3,4])  # (3, 8)

        All assignment operators are considered mutating.

        If the underlying operator is non-associating, so is "zipwith",
        except for basic comparison operators since a chaining workaround is
        provided:

            zipwith('cmp', \@a, \@b, \@c)  # ILLEGAL
            zipwith('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
    crosswith OPSTRING, LIST1, LIST2
    cross LIST1, LIST2
        The "crosswith" function may be passed any infix opstring. It
        applies the operator across all groupings of its list elements.

        The string concatenating form is:

            crosswith('.', ['a','b'], [1,2])  # ('a1', 'a2', 'b1', 'b2')

        The list concatenating form when used like this:

            crosswith(',', ['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.

            crosswith('*', [1,2], [3,4])  # (3, 4, 6, 8)

        All assignment operators are considered mutating.

        If the underlying operator is non-associating, so is "crosswith",
        except for basic comparison operators since a chaining workaround is
        provided:

            crosswith('cmp', \@a, \@b, \@c)  # ILLEGAL
            crosswith('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)

  Flat list vs. "list of lists"
    The optional named-argument "flat" can be passed to any of the above
    functions. 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']

  Other utils
    applyop OPSTRING, OPERAND1, OPERAND2
    applyop OPSTRING, OPERAND
        Apply the operator OPSTRING to the operands OPERAND1 and OPERAND2.
        If an unary opstring is provided, only the first operand will be
        used.

            applyop('.', 'foo', 'bar')  # foobar
            applyop('prefix:++', 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".

TODO
    *   Allow more than two arrayrefs with "zipwith", "crosswith", and
        "hyper"

    *   Support multi-dimensional binary operator distribution with "hyper"

    *   Support the "flat => 0" option

    *   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" in "applyop"

    *   Add "evalop" for "eval"ing strings including meta-operator literals

    *   Should the first argument optionally be a subroutine ref instead of
        an operator string?

    *   Should the "flat => 0" option be changed to "lol => 1"?

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" 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"

    *   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 <patch@cpan.org>

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.

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