Here's one way to do it, using the Algorithm::Loops module:

use strict;
use Algorithm::Loops qw/ NestedLoops /;

my @arrays = (
  [qw/ a b c /],
  [qw/ d e /],
  [qw/ f g h /],
  [qw/ i /],
  [qw/ j k /],
  [qw/ l /],
  [qw/ m /],
);
NestedLoops(
  [ map [ undef, @$_ ], @arrays ],  
  sub {
    my $count = 0;
    my $string = join '', grep { defined && ++$count } @_;
    print $string if $count >= 4;
  },
);
[download]

First, this combines the 7 individually named arrays into a single array of arrays to make it easier to handle them as a set.

The first parameter to NestedLoops() constructs the sets over which to loop by taking each of the 7 arrays and including undef to represent "nothing chosen from this array".

The second parameter is the code executed for each selection, which counts the number of defined values (to make sure we have at least 4), joins those defined values into a single string, and prints them.

Note that some slight rearrangement would allow you to use this to construct an iterator which would return the next valid combination each time you call it; that would probably be the more useful approach if you want to do something other than simply print them.

Hugo

#!/usr/bin/perl -wl
use strict;

print for generate(4, 
                   [qw(a b c)], [qw(d e)], [qw(f g h)], ["i"], 
                   [qw(j k)], ["l"], ["m"]);

sub generate {
    my $min = shift;
    my @non_empty = grep @$_, @_;
    return if $min > @non_empty;
    work($min, @non_empty);
}

sub work {
    my $min = shift;
    return "" if !@_;
    my $first = shift;
    return map { 
        my $n = $_; 
        length() < $min ? () : $_, map $_.$n, @$first;
    } work($min-1, @_);
}
[download]

sub generate {
    my $min = shift;
    my @arrays = grep @$_, @_;
    $min -= @arrays;
    return if $min > 0;
    my @current = ("");
    for my $array (@arrays) {
        $min++;
        @current = map {
            my $n = $_;
            length() < $min ? () : $_, map $n.$_, @$array;
        } @current;
    }
    return @current;
}
[download]

• choose number of arrays x to draw from
• for each number of arrays, create the (7 choose x) combinations of arrays to use
• for each combination of arrays, iterate over all the elements in each array

The first two tasks could be combined by assigning an array to each bit of a binary number, and iterating over (15..127) and only accepting binary numbers with at least 4 ones in it. But this sort of strategy is not efficient for large numbers of arrays.

To iterate over the elements on each array, you can again use a counting scheme. For the selected arrays @a1,..@ak (k = 4,..,7), form the number N = @a1*...*@ak. Then count from z = 0 to N-1. This number z represents a unique combination of the element positions in your array.

• int (z/(@a2*...*@ak)) mod @a1 is the ele position in @a1
• int (z/(@a3*...*@ak)) mod @a2 is the ele position in @a2
• ...
• z mod @ak is the ele position in @ak

Here is a simple example from some preexisting code. It uses the built-in 'glob' function. It does not check against requirement 2, but it should be enough to get you started.

### <region-file_info>
    ### main:
    ###   - name     : trySimpleCombinations000.pl
    ###     sbty     : perl
    ###     desc     : generate simple combinations from separate arra
+ys
    ### </region-file_info>

### begin_: init perl
    use strict;
    use warnings;

### begin_: init vars
    my  @aColor     = qw(Red White Blue);
    my  @aAnimal    = qw(Cat Rat Dog Mouse);
    my  @aLetter    = qw(Alpha Bravo Charlie);
    my  @aDigit     = qw(0 1 2 3 4);
    my  @aResult    = ();

### begin_: generate combis
    @aResult    = glob (
        "{@{[join',',@aColor]}}"
        ."{@{[join',',@aAnimal]}}"
        ."{@{[join',',@aLetter]}}"
        ."{@{[join',',@aDigit]}}"
        );

### begin_: show the results
    print join "\n", @aResult;
    print ("\n-----------------------------------\n");

1;
__END__

RedCatAlpha0
RedCatAlpha1
RedCatAlpha2
RedCatAlpha3
RedCatAlpha4
RedCatBravo0
.
.
.
BlueMouseCharlie0
BlueMouseCharlie1
BlueMouseCharlie2
BlueMouseCharlie3
BlueMouseCharlie4
[download]

Update: make code more readable

#!/usr/bin/perl -wl
use strict;

my @data =
  (
   [qw(a b c)],
   [qw(d e)],
   [qw(f g h)],
   [qw(i)],
   [qw(j k)],
   [qw(l)],
   [qw(m)],
  );

my @pos = (0) x @data;

sub iterator {
    my $i = @pos;
    while ($i--) {
        $pos[$i] = ($pos[$i] + 1) % @{$data[$i]}
          and last;
    }
    return  scalar grep $_, @pos;
}

sub items {
    my ($n, $str) = @_;
    return if length $str < $n;
    return substr($str, 0, 1) if $n == 1;
    return $str if $n == length $str;
    my @items = items($n, substr($str, 1));
    for my $i (1 .. length($str) - 1) {
        push @items,
             map { substr($str, 0, 1) . $_ }
               items($n - 1, substr($str, $i));
    }
    return @items;
}

do {
    for (4 .. @data) {
        print
          for items($_,
                    join '',
                    map { $data[$_]->[$pos[$_]] }
                    0 .. $#data
                   );
    }
}
while iterator();
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combos n ls = filter ((>= n) . length)
            . map concat
            . sequence
            . map (([]:) . map return)
            $ ls
[download]

Examples:

> combos 1 ["abc", "def"]
["d","e","f","a","ad","ae","af","b","bd","be","bf","c","cd","ce","cf"]
[download]

Here's the (elided) answer to your example question:

> combos 4 ["abc", "de", "fgh", "i", "jk", "l", "m"]
["ijlm","iklm","fjlm","fklm","film","fijm", ...
 "cehijlm","cehik","cehikm","cehikl","cehiklm"]
[download]

Cheers,
Tom