Renamed sets of presentations using suggested names.

The "set of controlling presentations" is now called the "set of controlled
presentations", and the "set of incoming presentations" is the "set of
presentation controllers".

Also fixed the wrong claim that the set of controlled presentations cannot
contain two presentations with the same URL and ID. It can contain only one
of such object per controlling browsing context, but there may indeed be
a similar object in other browsing contexts.

index.html

@@ -702,22 +702,25 @@ <h3>
           context</a>.
         </p>
         <p>
-          The <dfn>set of controlling presentations</dfn>, initially empty,
+          The <dfn>set of controlled presentations</dfn>, initially empty,
           contains the <a>presentation connections</a> created by the
           <a>controlling browsing contexts</a> for the <a>controlling user
           agent</a> (or a specific user profile within that user agent). The
-          <a>set of controlling presentations</a> is represented by a list of
+          <a>set of controlled presentations</a> is represented by a list of
           <a>PresentationConnection</a> objects that represent the underlying
-          <a>presentation connections</a>. The <a>presentation URL</a> and
-          <a>presentation identifier</a> uniquely identify a <a>presentation
-          connection</a> in this set.
+          <a>presentation connections</a>. Several
+          <a>PresentationConnection</a> objects may share the same
+          <a>presentation URL</a> and <a>presentation identifier</a> in that
+          set, but there can be only one <a>PresentationConnection</a> with a
+          specific <a>presentation URL</a> and <a>presentation identifier</a>
+          for a given <a>controlling browsing context</a>.
         </p>
         <p>
-          The <dfn>set of incoming presentations</dfn>, initially empty,
+          The <dfn>set of presentation controllers</dfn>, initially empty,
           contains the <a>presentation connections</a> created by a
           <a>receiving browsing context</a> for the <a>receiving user
-          agent</a>. The <a>set of incoming presentations</a> is represented by
-          a list of <a>PresentationConnection</a> objects that represent the
+          agent</a>. The <a>set of presentation controllers</a> is represented
+          by a list of <a>PresentationConnection</a> objects that represent the
           underlying <a>presentation connections</a>. All <a>presentation
           connections</a> in this set share the same <a>presentation URL</a>
           and <a>presentation identifier</a>.
@@ -741,9 +744,9 @@ <h3>
         <p>
           The <dfn for="Navigator"><code>presentation</code></dfn> attribute is
           used to retrieve an instance of the <a><code>Presentation</code></a>
-          If <a>presentation is disabled</a>, the attribute MUST return null.
-          Otherwise, it MUST return the <a><code>Presentation</code></a>
-          instance.
+          interface. If <a>presentation is disabled</a>, the attribute MUST
+          return null. Otherwise, it MUST return the
+          <a><code>Presentation</code></a> instance.
         </p>
         <section>
           <h4>
@@ -953,7 +956,7 @@ <h4>
             </li>
             <li>Let <var>I</var> be a new <a>valid presentation identifier</a>
             unique among all <a>presentation identifiers</a> for known
-            <a>presentation connections</a> in the <a>set of controlling
+            <a>presentation connections</a> in the <a>set of controlled
             presentations</a>.
             </li>
             <li>Create a new <a>PresentationConnection</a> <var>S</var>.
@@ -967,8 +970,7 @@ <h4>
             <li>Set the <a>presentation connection state</a> of <var>S</var> to
             <a for="PresentationConnectionState">connecting</a>.
             </li>
-            <li>Add <var>S</var> to the <a>set of controlling
-            presentations</a>.
+            <li>Add <var>S</var> to the <a>set of controlled presentations</a>.
             </li>
             <li>
               <a>Resolve</a> <var>P</var> with <var>S</var>.
@@ -1060,7 +1062,7 @@ <h4>
             <li>Return <var>P</var>, but continue running these steps in
             parallel.
             </li>
-            <li>Search the <a>set of controlling presentations</a> for a
+            <li>Search the <a>set of controlled presentations</a> for a
             <a>PresentationConnection</a> that meets the following criteria:
             its <a>controlling browsing context</a> is the current <a>browsing
             context</a>, its <a>presentation connection state</a> is not
@@ -1104,9 +1106,9 @@ <h4>
                 </li>
               </ol>
             </li>
-            <li>Search the <a>set of controlling presentations</a> for the
-            first <a>PresentationConnection</a> that meets the following
-            criteria: its <a>presentation connection state</a> is not <a for=
+            <li>Search the <a>set of controlled presentations</a> for the first
+            <a>PresentationConnection</a> that meets the following criteria:
+            its <a>presentation connection state</a> is not <a for=
             "PresentationConnectionState">terminated</a>, its <a>presentation
             URL</a> is equal to the <a>presentation request URL</a> of
             <var>presentationRequest</var>, and its <a>presentation
@@ -1128,7 +1130,7 @@ <h4>
                 <var>S</var> to <a for=
                 "PresentationConnectionState">connecting</a>.
                 </li>
-                <li>Add <var>S</var> to the <a>set of controlling
+                <li>Add <var>S</var> to the <a>set of controlled
                 presentations</a>.
                 </li>
                 <li>
@@ -2028,7 +2030,7 @@ <h4>
               connected</a>, then abort these steps.
             </li>
             <li>Otherwise, for each <var>known connection</var> in the <a>set
-            of controlling presentations</a> in the <a>controlling user
+            of controlled presentations</a> in the <a>controlling user
             agent</a>:
               <ol>
                 <li>If the <a>presentation identifier</a> of <var>known
@@ -2078,7 +2080,7 @@ <h4>
             SHOULD run the following steps:
           </p>
           <ol>
-            <li>For each <var>connection</var> in the <a>set of controlling
+            <li>For each <var>connection</var> in the <a>set of controlled
             presentations</a> that was connected to the <a>receiving browsing
             context</a>, <a>queue a task</a> to run the following steps:
               <ol>
@@ -2279,7 +2281,7 @@ <h3>
         <p>
           The <dfn for="PresentationConnectionList">connections</dfn> attribute
           MUST return the non-terminated set of <a>presentation connections</a>
-          in the <a>set of incoming presentations</a>.
+          in the <a>set of presentation controllers</a>.
         </p>
         <section>
           <h4>
@@ -2311,7 +2313,7 @@ <h4>
             <li>Set the <a>presentation connection state</a> of <var>S</var> to
             <a for="PresentationConnectionState">connected</a>.
             </li>
-            <li>Add <var>S</var> to the <a>set of incoming presentations</a>.
+            <li>Add <var>S</var> to the <a>set of presentation controllers</a>.
             </li>
             <li>
               <a>Queue a task</a> to <a>fire</a> a <a>trusted event</a> with
@@ -2445,7 +2447,7 @@ <h3>
       </p>
       <p>
         This specification allows a user agent to publish information about its
-        <a>set of controlling presentations</a>, and allows a browsing context
+        <a>set of controlled presentations</a>, and allows a browsing context
         on another user agent to connect to a running presentation via
         <code><a for="PresentationRequest">reconnect</a>()</code>. To connect,
         the additional browsing context must discover the presentation URL and