Added assignmemnt 6

[lambda.git] / intensionality_monad.mdwn

diff --git a/intensionality_monad.mdwn b/intensionality_monad.mdwn
index 6887487..83824a4 100644 (file)
--- a/intensionality_monad.mdwn
+++ b/intensionality_monad.mdwn
@@ -1,13 +1,25 @@
-The intensionality monad
-------------------------
+Now we'll look at using monads to do intensional function application.
+This really is just another application of the reader monad, not a new monad.
+In Shan (2001) [Monads for natural
+language semantics](http://arxiv.org/abs/cs/0205026v1), Ken shows that
+making expressions sensitive to the world of evaluation is conceptually
+the same thing as making use of the reader monad.
+This technique was beautifully re-invented
+by Ben-Avi and Winter (2007) in their paper [A modular
+approach to
+intensionality](http://parles.upf.es/glif/pub/sub11/individual/bena_wint.pdf),
+though without explicitly using monads.

 
 

-In the meantime, we'll look at several linguistic applications for
-monads, based on what's called the *reader monad*, starting with
-intensional function application.  
+All of the code in the discussion below can be found here: [[intensionality-monad.ml]].
+To run it, download the file, start OCaml, and say 
+
+       # #use "intensionality-monad.ml";;
+
+Note the extra `#` attached to the directive `use`.

 
 First, the familiar linguistic problem:
 
 
 First, the familiar linguistic problem:
 

-                  Bill left.  
+       Bill left.  

           Cam left.
           Ann believes [Bill left].
           Ann believes [Cam left].
           Cam left.
           Ann believes [Bill left].
           Ann believes [Cam left].


@@ -18,22 +30,6 @@ we have a problem: if the sentences *Bill left* and *Cam left* are
 both true, they denote the same object, and Ann's beliefs can't
 distinguish between them.
 
 both true, they denote the same object, and Ann's beliefs can't
 distinguish between them.
 

-In Shan (2001) [Monads for natural language
-semantics](http://arxiv.org/abs/cs/0205026v1), Ken shows that making
-expressions sensitive to the world of evaluation is conceptually the
-same thing as making use of a *reader monad*.  This technique was
-beautifully re-invented by Ben-Avi and Winter (2007) in their paper [A
-modular approach to
-intensionality](http://parles.upf.es/glif/pub/sub11/individual/bena_wint.pdf),
-though without explicitly using monads.
-
-All of the code in the discussion below can be found here: [[intensionality-monad.ml]].
-To run it, download the file, start OCaml, and say 
-
-       # #use "intensionality-monad.ml";;
-
-Note the extra `#` attached to the directive `use`.
-

 The traditional solution to the problem sketched above is to allow
 sentences to denote a function from worlds to truth values, what
 Montague called an intension.  So if `s` is the type of possible
 The traditional solution to the problem sketched above is to allow
 sentences to denote a function from worlds to truth values, what
 Montague called an intension.  So if `s` is the type of possible


@@ -59,16 +55,16 @@ generalized quantifiers.
 The main difference between the intensional types and the extensional
 types is that in the intensional types, the arguments are functions
 from worlds to extensions: intransitive verb phrases like "left" now
 The main difference between the intensional types and the extensional
 types is that in the intensional types, the arguments are functions
 from worlds to extensions: intransitive verb phrases like "left" now

-take intensional concepts as arguments (type s->e) rather than plain
+take individual concepts as arguments (type s->e) rather than plain

 individuals (type e), and attitude verbs like "think" now take
 propositions (type s->t) rather than truth values (type t).
 In addition, the result of each predicate is an intension.
 This expresses the fact that the set of people who left in one world
 may be different than the set of people who left in a different world.
 individuals (type e), and attitude verbs like "think" now take
 propositions (type s->t) rather than truth values (type t).
 In addition, the result of each predicate is an intension.
 This expresses the fact that the set of people who left in one world
 may be different than the set of people who left in a different world.

-Normally, the dependence of the extension of a predicate to the world
+(Normally, the dependence of the extension of a predicate to the world

 of evaluation is hidden inside of an evaluation coordinate, or built
 into the the lexical meaning function, but we've made it explicit here
 of evaluation is hidden inside of an evaluation coordinate, or built
 into the the lexical meaning function, but we've made it explicit here

-in the way that the intensionality monad makes most natural.
+in the way that the intensionality monad makes most natural.)

 
 The intenstional types are more complicated than the intensional
 types.  Wouldn't it be nice to make the complicated types available
 
 The intenstional types are more complicated than the intensional
 types.  Wouldn't it be nice to make the complicated types available