I have a pretty flat XML structure that I need to reorder into categorised sections and, for the life of me, I can't figure out how to do it in XSLT (not that I'm by any means an expert.)

Basically, the original XML looks kinda like:

<things>
  <thing>
    <value>one</value>
    <type>a</type>
  </thing>
  <thing>
    <value>two</value>
    <type>b</type>
  </thing>
  <thing>
    <value>thee</value>
    <type>b</type>
  </thing>
  <thing>
    <value>four</value>
    <type>a</type>
  </thing>
  <thing>
    <value>five</value>
    <type>d</type>
  </thing>
</things>

And I need to output something like:

<data>
  <a-things>
    <a>one</a>
    <a>four</a>
  </a-things>
  <b-things>
    <b>two</b>
    <b>three</b>
  </b-things>
  <d-things>
    <d>five</d>
  </d-things>
</data>

Note that I can't output <c-things> if there aren't any <c> elements, but I do know ahead of time what the complete list of types is, and it's fairly short so handcoding templates for each type is definitely possible. It feels like I could probably hack something together using <xsl:if> and <xsl:for-each> but it also feels like there must be a more ... 'templatey' way to do it. Can anyone help?

Cheers.