打印一维、二维和三维数组组合的值

我有这个多维数组的组合，但我无法在屏幕上打印出正确的值，

$parent = array(
    array(
        'function_name' => 'home',
        'screen_name' => 'Home'
        ),
    array(
        'function_name' => 'categories',
        'screen_name' => 'Categories',

        array(
            'function_name' => 'post',
            'screen_name' => 'Post',
            )
        ),
    array(
        'function_name' => 'pages',
        'screen_name' => 'Pages',

        array(
            'function_name' => 'add',
            'screen_name' => 'Add',
            array(
                'function_name' => 'manage',
                'screen_name' => 'Manage'
                )
            )
        )
);

有些数组是单独的，有些带有sub数组，有些子数组具有subsub阵列。

foreach($parent as $index => $item)
{   
    echo 'parent - '.$item['screen_name'].'<br/>';
    foreach($item as $child)
    {
        echo 'child - '.$child['screen_name'].'<br/>';
        foreach($child as $grandchild)
        {
            echo 'grandchild - '.$grandchild['screen_name'].'<br/>';
        }
    }
}

错误消息，

Warning: Invalid argument supplied for foreach() in -> foreach($child as $grandchild)

我要找的结果是这样的，

parent - Home
parent - Categories
  child - Post
parent - Pages
  child - Add
     grandchild - Manage

编辑：

我试过下面的这个测试，

foreach ($system as $inner_1) {
    if (is_array($inner_1)) 
    {
        foreach ($inner_1 as $inner_2) 
        {
             if (is_array($inner_2)) 
             {
                  foreach ($inner_2 as $inner_3) 
                  {
                     var_dump($inner_3['function_name']);
                  }
             }
        }
    }
}

但我得到了一个奇怪的结果，

string 'p' (length=1) // don't know why I get this.
string 'P' (length=1) // don't know why I get this.
string 'a' (length=1) // don't know why I get this.
string 'A' (length=1) // don't know why I get this.
string 'manage' (length=6) // correct result.