edits

diff --git a/topics/_week15_continuation_applications.mdwn b/topics/_week15_continuation_applications.mdwn
index ec0cb5d..cc5c9e2 100644 (file)
--- a/topics/_week15_continuation_applications.mdwn
+++ b/topics/_week15_continuation_applications.mdwn
@@ -104,11 +104,14 @@ Raising closely resembles the reduction rule for shift:
     Quantifier Raising: given a sentence [... [QDP] ...], build a new
     sentence [QDP (\x.[... [x] ...])].  
 
+Here, QDP is a scope-taking quantificational DP.
+
 Just to emphasize the similarity between QR and shift, we can use QR
 to provide insight into the tree task that mystified us earlier.
 
 \tree (. (a)((S)((d)((S)(e)))))
 
+<pre>
   .
 __|___
 |    |
@@ -119,11 +122,13 @@ a  __|___
       d  _|__
          |  |
          S  e
+</pre>
 
 First we QR the lower shift operator
 
 \tree (. (S) ((\\x) ((a)((S)((d)((x)(e)))))))
 
+<pre>
    .
 ___|___
 |     |
@@ -138,11 +143,13 @@ S  ___|___
              d  _|__
                 |  |
                 x  e
+</pre>
 
 Next, we QR the upper shift operator
 
 \tree (. (S) ((\\y) ((S) ((\\x) ((a)((y)((d)((x)(e)))))))))
 
+<pre>
    .
 ___|___
 |     |
@@ -161,6 +168,7 @@ S  ___|____
                     d  _|__
                        |  |
                        x  e
+</pre>
 
 We then evaluate, using the same value for the shift operator proposed before:
 
@@ -174,6 +182,7 @@ form:
 
 \tree (. (S) ((\\y) ((a)((y)((d)(((a)((y)((d)(("")(e)))))(e)))))))
 
+<pre>
    .
 ___|___
 |     |
@@ -196,6 +205,7 @@ S  ___|____
                     d  __|__
                        |   |
                        ""  e
+</pre>
 
 
 Repeating the process for the upper shift operator replaces each
@@ -203,6 +213,7 @@ occurrence of y with a copy of the whole tree.
 
 \tree (. ((a)((((a)(("")((d)(((a)(("")((d)(("")(e)))))(e))))))((d)(((a)((((a)(("")((d)(((a)(("")((d)(("")(e)))))(e))))))((d)(("")(e)))))(e))))))
 
+<pre>
       .
       |
 ______|______
@@ -235,8 +246,10 @@ a  ___|____           |      |
                                  d  __|__
                                     |   |
                                     ""  e
+</pre>
 
-The yield of this tree (the sequence of leaf nodes) is aadadeedaadadeedee.
+The yield of this tree (the sequence of leaf nodes) is
+aadadeedaadadeedee, which is the expected output of the double-shifted tree.
 
 Exercise: the result is different, by the way, if the QR occurs in a
 different order.
@@ -285,15 +298,14 @@ manipulates a list of information.  It is natural to imagine
 separating a box into two regions, the payload and the hidden scratch
 space:
 
+<pre>
     _______________               _______________           _______________ 
     | [x->2, y->3] |             | [x->2, y->3] |          | [x->2, y->3] |
   -------------------          ------------------         ------------------
     |              |     ¢        |              |    =     |              |
     |    +2        |             |     y        |          |     5        |
     |______________|             |______________|          |______________|
-
-
-(Imagine the + operation has been lifted into the Reader monad too.)
+</pre>
 
 For people who are familiar with Discourse Representation Theory (Kamp
 1981, Kamp and Reyle 1993), this separation of boxes into payload and