1) Position of keyed element, 2) Determining unique a

In short, I am attempting to transfom something that looks like:
<?xml version="1.0" encoding="UTF-8"?>
<root>
<object id="a">
   <attribute name="color" value="red"/>
</object>
<object id="b">
    <attribute name="size" value="big"/>
</object>
<object id="c">
    <attribute name="size" value="small"/>
    <attribute name="color" value="purple"/>
</object>
<link fromobject="c" toobject="b"/>
</root>

into:
<?xml version="1.0" encoding="UTF-8"?>
<output>
  <thing id="1"/>
  <thing id="2"/>
  <thing id="3"/>
  <attributes name="color">
     <attribute idref="1" value="red"/>
     <attribute idref="3" value="purple"/>
  </attributes>
  <attributes name="size">
     <attribute idref="2" value="big"/>
     <attribute idref="3" value="small"/>
</attributes>
<relation fromthing="3" tothing="2"/>
</output>

1) Obtaining the positional information of elements in the input tree
from different context nodes.

2) Unable to determine all unique values of //attribute/@name to group
into the attributes element. (These would then be processed with the
solution to #1)

The the 'thing' IDs in the output MUST be non-negative integers, so
generate-id is out. I thought that it would be nice (and aesthetic,
IMHO) to use the position of the 'object's to assign IDs for the
'thing's. However, when I try to obtain positional information from
the input tree with position(), I get the location of the node in the
result node set of the xpath that selects the nodes, which is always
"1".

Any solutions with XSLT 2.0 constructs would be much appreciated. I
haven't followed the developments within the last three years and am
having some difficulty appreciating its full benefits.

Highest regards,
Tim Lebo

<xsl:template match="/">
<xsl:element name="output">
   <xsl:apply-templates select="//object"/>
   <xsl:apply-templates select="//object" mode="attributes"/>
   <xsl:apply-templates select="//link"/>
</xsl:element>
</xsl:template>

<xsl:template match="object">
<xsl:element name="thing">
   <xsl:attribute name="id" select="position()"/>
</xsl:element>
</xsl:template>

<xsl:template match="object" mode="attributes">
<xsl:element name="attributes">
   <xsl:attribute name="name" select="'WRONG: attribute elements
should be grouped by attribute/@name, not by object/@id'"/>
   <xsl:apply-templates select="attribute">
     <xsl:with-param name="id" select="position()"/>
   </xsl:apply-templates>
</xsl:element>
</xsl:template>

<xsl:template match="attribute">
<xsl:param name="id"/>
<xsl:element name="attribute">
   <xsl:attribute name="idref" select="$id"/>
   <xsl:attribute name="{@name}" select="@value"/>
</xsl:element>
</xsl:template>

<xsl:template match="link">
<xsl:variable name="toobjectID" select="@toobject"/>
<xsl:element name="relation">
   <xsl:attribute name="fromthing"
select="key('objects',@fromobj
ect)/position()"/>
   <xsl:attribute name="tothing"
select="//object[@id=$toobjectID]/position()"/>
   <xsl:attribute name="NB" select="'WRONG: ids should be position of
input object elmenents (3,2)'"/>
</xsl:element>
</xsl:template>

and the output is:
<?xml version="1.0" encoding="UTF-8"?>
<output>
  <thing id="1"/>
  <thing id="2"/>
  <thing id="3"/>
  <attributes name="WRONG: attribute elements should be grouped by
attribute/@name , not by object/@id">
     <attribute idref="1" color="red"/>
  </attributes>
  <attributes name="WRONG: attribute elements should be grouped by
attribute/@name , not by object/@id">
     <attribute idref="2" size="big"/>
  </attributes>
  <attributes name="WRONG: attribute elements should be grouped by
attribute/@name , not by object/@id">
     <attribute idref="3" size="small"/>
     <attribute idref="3" color="purple"/>
  </attributes>
  <relation fromthing="1" tothing="1"
            NB="WRONG: ids should be position of input object
elmenents (3,2)"/>
</output>