Re: Q: Junctions & send+more=money

[Rod Adams]

Markus Laire wrote:
I have two questions about this example code
(taken from http://svn.openfoundry.org/pugs/examples/sendmoremoney.p6)
I have a few issues with this code. Or at least observations of how it 
differs from the classic "SEND + MORE = MONEY" problem. see below.


#!perl6
use v6;
my $s; my $e; my $n; my $d; my $m; my $o; my $r;
my $y;
$s = any(0..10) & none(0);
$e = any(0..10);
$n = any(0..10);
$d = any(0..10);
$m = any(0..10) & none(0);
$o = any(0..10);
$r = any(0..10);
$n = any(0..10);
$y = any(0..10);

I think these should be any(0..9).
Indeed they should. I will assume they are written as such in my 
discussion below.


my $send := construct($s,$e,$n,$d);
my $more := construct($m,$o,$r,$e);
my $money := construct($m,$o,$n,$e,$y);
if ($send + $more == $money) {
    say " send = $send";
    say "+more = $more";
    say "-------------"
    say "money = $money";
}
sub foldl(Code &op, Any $initial, [EMAIL PROTECTED]) returns Any {
    if ([EMAIL PROTECTED] == 0) {
         return $initial;
    } else {
         return &op(shift @values, &?SUB(&op, $initial, @values));
    }
}
sub add(Int $x, Int $y) returns Int {
    return $x + $y;
}
sub construct([EMAIL PROTECTED]) returns Junction {
    return foldl( sub ($x, $y) { $x * 10 + $y}, 0, @values);
}

How would the if (...) {...} work if there were more than one possible 
match to this equation?
As written, this generates a rather large number of solutions. I do not 
see any test to make sure that the individual letters are different. Nor 
is there any check to see if all the "e"'s assume the same value.

So what you reach the:
   if ($send + $more == $money) {...}
stage is $send being something equivalent to  any(0000..9999) & 
none(0000..0999), only no where near as simplified. Similar values can 
be found in $more and $money. Therefore, you're asking something like: 
"Are there any two numbers between 1000 and 9999 that together total 
between 10000..99999?" The answer is yes, and then you get an error as 
you attempt to print a raw junction, if you're lucky, or 9000 "send" 
lines, followed by 9000 "more" lines, followed by 90000 "money" lines.

Junctions are _not_ the same as unbound variables in Prolog. They do not 
"widdle away" inconsistent values as those inconsistencies are found. 
Most of them (all except all()) do not have to use the same value each 
time they are evaluated.

If I'm wrong about this interpretation of this code, I apologize. But it 
certainly fits my understanding of junctions, which has grown by leaps 
and bounds over the last few weeks.

HTH,
-- Rod Adams