From 8e42213815ea8a2e0013aa4039a5d9bc44697425 Mon Sep 17 00:00:00 2001
From: Chris
Date: Wed, 13 May 2015 09:28:57 -0400
Subject: [PATCH] edits
---
topics/_week15_continuation_applications.mdwn | 27 +++++++++++++++++++++++++--
1 file changed, 25 insertions(+), 2 deletions(-)
diff --git a/topics/_week15_continuation_applications.mdwn b/topics/_week15_continuation_applications.mdwn
index 3bdbd2a1..328b506e 100644
--- a/topics/_week15_continuation_applications.mdwn
+++ b/topics/_week15_continuation_applications.mdwn
@@ -377,7 +377,7 @@ hole in it. For instance, we might have g[x] = \forall x.P[x].
We'll use a simply-typed system with two atomic types, DP (the type of
individuals) and S (the type of truth values).
-## LIFT
+## LIFT (mid)
Then in the spirit of monadic thinking, we'll have a way of lifting an
arbitrary value into the tower system:
@@ -569,7 +569,7 @@ We'll change these arrows into left-leaning and right-leaning versions
too, according to the following scheme:
Î³|Î´
- --- == Î³//((Î±/Î²) \\\\ Î´)
+ --- == Î³//((Î±/Î²) \\ Î´)
Î±/Î²
As we'll see in a minute, each of these for implications (\\, /, \\\\,
@@ -580,3 +580,26 @@ As we'll see in a minute, each of these for implications (\\, /, \\\\,
\\ argument is surrounded by the functor
// argument surrounds the functor
+## LOWER (reset)
+
+One more ingredient: one thing that shifty continuation operators
+require is an upper bound, a reset to show the extent of the remainder
+of the computation that the shift operator captures. In the list
+version of the doubling task, we have
+
+ "a#bdeSfg" ~~> "abdebdefg" continuation captured: bde
+ "ab#deSfg" ~~> "abdedefg" continuation captured: de
+
+In programming languages, resets are encoded in the computation
+explicitly. In natural language, resets are always invisible.
+We'll deal with this in the natural language setting by allowing
+spontaneous resets, as long as the types match the following recipe:
+
+ g[] Î±|S
+ LOWER (---:---) == g[p]:Î±
+ p S
+
+This will be easiest to explain by presenting our first complete
+example from natural language:
+
+
--
2.11.0