<?php
$numbers = array(5, 19, 45, 6, 7, 21);
$operators = array('*', '+', '-', '*', '+');

// String bauen
$mathString = '';
foreach ($numbers as $id => $number) {
    if ($id < count($numbers)-1) {
        $mathString .= $number . $operators[$id];
    } else {
        $mathString .= $number;
    }
}
// $mathString ist nun '5*19+45-6*7+21'
##################################
function flatten($ms, $ops) {
    $list = array();
    $len = strlen($ms);
    $buf = '';

    for ($i=0;$i<$len;$i++) {
        $chr = $ms[$i];
        if (!array_key_exists($chr, $ops)) {
            $buf .= $chr;
        } else {
            $list[] = $buf;
            $list[] = $chr;
            $buf = '';
        }
    }
    $list[] = $buf;
    return $list;
}

function apply($list, $ops) {
    $o = $list[1];
    $func = $ops[$o];
    $h = $func($list[0], $list[2]);
    return $h;
}

function foldl($list, $ops, $prio) {
    if (!isset($list[2])) {
        return $list[0];
    } else {
        $o = $list[1];
        if (in_array($o, $prio)) {
            $h = apply($list, $ops);
            $t = array_slice($list, 3);
            array_unshift($t, $h);
            return foldl($t, $ops, $prio);
        } else {
            if (isset($list[3])) {
                $look = $list[3];
                if (in_array($look, $prio)) {
                    $tmp = array_slice($list, 2, 3);
                    $m = apply($tmp, $ops);
                    if (isset($list[5])) {
                        $t = array_slice($list, 5);
                    } else {
                        $t = array();
                    }
                    $li = array_unshift($t, $list[0], $list[1], $m);
                    return foldl($t, $ops, $prio);
                } else {
                    $h = apply($list, $ops);
                    $t = array_slice($list, 3);
                    array_unshift($t, $h);
                    return foldl($t, $ops, $prio);
                }
            } else {
                $h = apply($list, $ops);
                return foldl(array($h), $ops, $prio);
            }
        }
    }
}

// prio der abarbeitung
$prio = array('*');
// closures, whee
$ops = array(
    '*' => function($a,$b) { return $a * $b; },
    '+' => function($a,$b) { return $a + $b; },
    '-' => function($a,$b) { return $a - $b; },
);
$list = flatten($mathString, $ops);
echo $mathString.PHP_EOL;
var_dump($list);
$r = foldl($list, $ops, $prio, array());
echo "----\nresult: $r".PHP_EOL;