> > PEANO ARITHMETIC is a simple list [1[2[3[4[5]]]]]
> >
> >
> > > > ------- -------- --------
> > > > | 1| . |-----> | 2| . |------> | 3| . |---> NIL
> > > > --|----- --|------ --|-----
> > which is incomplete logic
>
>
> "Isn't what you're writing really just gibberish?"

All your logic seems to be at the level of peano arithmetic

TRY MATCHING STRINGS!

<?

$wrd1 = '[ [ a b C ] [ D e ] g ]';
$wrd2 = '[ [ A B c ] [ [ dd ddd dddd ] e ] G ]';
smatch( $wrd1 , $wrd2 );
showv();

function smatch( $wrd1 , $wrd2 )
{ global $v;

$pos1 = 0;
$pos2 = 0;
$brak1 = 0;
$brak2 = 0;
$wrd1 = 0;
$wrd2 = 0;
while ( ( $wrd1!='') & ($wrd2!='') )
{
while ($brak1 < $brak2)
{
while ($wrd1 < $wrd2)
{
$pos1 = 0;
$char1 = $wrd1[$pos1];
$char2 = $wrd2[$pos2];
if ($char1=='[')
{
$brak1++ ;
$wrd = '';

}

}

function showv()
{ global $v;

echo "****************<br>";
foreach( $v as $x => $y )
{
echo $x . ' = ' . $y . ' ';
}
echo "<br>****************<br>";
}

?>

AND THE ANSWER IS . . .

$wrd1 = '[ X [ aa BB CC ] ] [ [ [ dd ddd dddd ] e ] G ]';
$wrd2 = '[ YY [ AA BB c ] ] [ [ D e ] G ]';

STRINGS [ X [ aa BB CC ] ] [ [ [ dd ddd dddd ] e ] G ] - [ YY [ AA BB c ] ] [ [ D e ] G ]
# X [ aa BB CC ] ]# YY [ AA BB c ] ]#
UNIFY X [ aa BB CC ] ] - YY [ AA BB c ] ]
#YY#
>>> YY = X
>> X = YY
#[ AA BB c ]#
STRINGS [ aa BB CC ] - [ AA BB c ]
# aa BB CC ]# AA BB c ]#
UNIFY aa BB CC ] - AA BB c ]
#AA#
>>> AA = aa
#BB#
>>> BB = BB
>> BB = BB
#c#
>> CC = c
#]#
#]#
# [ [ dd ddd dddd ] e ] G ]# [ D e ] G ]#
UNIFY [ [ dd ddd dddd ] e ] G ] - [ D e ] G ]
#[ D e ]#
STRINGS [ [ dd ddd dddd ] e ] - [ D e ]
# [ dd ddd dddd ] e ]# D e ]#
UNIFY [ dd ddd dddd ] e ] - D e ]
#D#
>>> D = [ dd ddd dddd ]
#e#
#]#
#G#
>>> G = G
>> G = G
#]#
TRUE