访问具有谓词属性的XML元素，该属性在PHP中动态更新

Newbie here.Trouble with xpath() function in PHP.

XML file (data.xml):

<?xml version="1.0" ?> 
<menu>
<food type="Pizza">

    <item>
            <name>  Tomato &amp; Cheese  </name>
            <small price="5.50"/>
            <large price="9.75"/>

    </item>

    <item>
            <name>   Onions </name>
            <small price="6.85"/>
            <large price="10.85"/>

    </item>
</food>
</menu>

PHP code:

   <?php 
   $xml = simplexml_load_file("data.xml");
   $types = $xml->xpath("/menu/food/@type");
   foreach($types as $type){
      echo("<h1>$type</h1>");
      $menu = $xml->xpath("/menu/food[@type=$type]");     
      echo("<ul>");
      foreach($menu as $submenu){
         echo ("<li>$submenu</li>");
      }
      echo("</ul>");
   } 
   ?>

I have many types of food. I would like to access them and their subtypes in order. There is something wrong with my approach above. I can't seem to find it. Below is my intended output. How do I arrive at that with xpath()?

Intended Output:

PIZZA

=>Tomato & Cheese

=> Onions

=>

FOO

=> BAR

You need only a single xpath query, like this:

$xml = simplexml_load_file("data.xml");

// Get food items and iterate over them
$foods = $xml->xpath("/menu/food");
foreach($foods as $food){

    // print type attribute
    echo("<h1>{$food["type"]}</h1>");

    // Iterate over food items and print their names
    echo("<ul>");
    foreach($food->item as $item){
        echo ("<li>$item->name</li>");
    }
    echo("</ul>");
}

Having this xml:

<?xml version="1.0" ?>
<menu>
<food type="Pizza">
    <item>
            <name>Tomato &amp; Cheese</name>
            <small price="5.50"/>
            <large price="9.75"/>
    </item>
    <item>
            <name>Onions</name>
            <small price="6.85"/>
            <large price="10.85"/>
    </item>
</food>
<food type="Pasta">
    <item>
            <name>Bolognese</name>
            <small price="5.50"/>
            <large price="9.75"/>
    </item>
    <item>
            <name>Carbonara</name>
            <small price="6.85"/>
            <large price="10.85"/>
    </item>
</food>
</menu>

... the above code will produce:

<h1>Pizza</h1>
<ul>
  <li>Tomato & Cheese</li>
  <li>Onions</li>
</ul>

<h1>Pasta</h1>
<ul>
  <li>Bolognese</li>
  <li>Carbonara</li>
</ul>

Try changing

  $menu = $xml->xpath("/menu/food[@type=$type]");     
  echo("<ul>");
  foreach($menu as $submenu){
     echo ("<li>$submenu</li>");
  }

to

  $menu = $xml->xpath("/menu/food[@type='$type']/item/name");     
  echo("<ul>");
  foreach($menu as $submenu){
     echo ("<li>$submenu</li>");
  }