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] ...])].  
 
     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)))))
 
 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
       d  _|__
          |  |
          S  e

+</pre>

 
 First we QR the lower shift operator
 
 \tree (. (S) ((\\x) ((a)((S)((d)((x)(e)))))))
 
 
 First we QR the lower shift operator
 
 \tree (. (S) ((\\x) ((a)((S)((d)((x)(e)))))))
 

+<pre>

    .
 ___|___
 |     |
    .
 ___|___
 |     |


@@ -138,11 +143,13 @@ S  ___|___
              d  _|__
                 |  |
                 x  e
              d  _|__
                 |  |
                 x  e

+</pre>

 
 Next, we QR the upper shift operator
 
 \tree (. (S) ((\\y) ((S) ((\\x) ((a)((y)((d)((x)(e)))))))))
 
 
 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
                     d  _|__
                        |  |
                        x  e

+</pre>

 
 We then evaluate, using the same value for the shift operator proposed before:
 
 
 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)))))))
 
 
 \tree (. (S) ((\\y) ((a)((y)((d)(((a)((y)((d)(("")(e)))))(e)))))))
 

+<pre>

    .
 ___|___
 |     |
    .
 ___|___
 |     |


@@ -196,6 +205,7 @@ S  ___|____
                     d  __|__
                        |   |
                        ""  e
                     d  __|__
                        |   |
                        ""  e

+</pre>

 
 
 Repeating the process for the upper shift operator replaces each
 
 
 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))))))
 
 
 \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
                                  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.
 
 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:
 
 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        |
     |______________|             |______________|          |______________|
     _______________               _______________           _______________ 
     | [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
 
 For people who are familiar with Discourse Representation Theory (Kamp
 1981, Kamp and Reyle 1993), this separation of boxes into payload and