various cleanup

[lambda.git] / intensionality_monad.mdwn

diff --git a/intensionality_monad.mdwn b/intensionality_monad.mdwn
index 5b0ec3a..acf154c 100644 (file)
--- a/intensionality_monad.mdwn
+++ b/intensionality_monad.mdwn
@@ -55,7 +55,7 @@ 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
-take individual concepts as arguments (type s->e) rather than plain
+take so-called "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.
@@ -66,7 +66,7 @@ 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.)
 
-The intenstional types are more complicated than the intensional
+The intensional types are more complicated than the extensional
 types.  Wouldn't it be nice to make the complicated types available
 for those expressions like attitude verbs that need to worry about
 intensions, and keep the rest of the grammar as extensional as
@@ -77,28 +77,22 @@ division-by-zero problems as much as possible.
 
 So here's what we do:
 
-In OCaml, we'll use integers to model possible worlds:
+In OCaml, we'll use integers to model possible worlds. Characters (characters in the computational sense, i.e., letters like `'a'` and `'b'`, not Kaplanian characters) will model individuals, and OCaml booleans will serve for truth values:
 
        type s = int;;
        type e = char;;
        type t = bool;;
 
-Characters (characters in the computational sense, i.e., letters like
-`'a'` and `'b'`, not Kaplanian characters) will model individuals, and
-OCaml booleans will serve for truth values.
+       let ann = 'a';;
+       let bill = 'b';;
+       let cam = 'c';;
 
-<pre>
-let ann = 'a';;
-let bill = 'b';;
-let cam = 'c';;
-
-let left1 (x:e) = true;; 
-let saw1 (x:e) (y:e) = y < x;; 
+       let left1 (x:e) = true;; 
+       let saw1 (x:e) (y:e) = y < x;; 
 
-left1 ann;;
-saw1 bill ann;; (* true *)
-saw1 ann bill;; (* false *)
-</pre>
+       left1 ann;;
+       saw1 bill ann;; (* true *)
+       saw1 ann bill;; (* false *)
 
 So here's our extensional system: everyone left, including Ann;
 and Ann saw Bill, but Bill didn't see Ann.  (Note that Ocaml word
@@ -133,8 +127,8 @@ Now we are ready for the intensionality monad:
 
 <pre>
 type 'a intension = s -> 'a;;
-let unit x (w:s) = x;;
-let bind m f (w:s) = f (m w) w;;
+let unit x = fun (w:s) -> x;;
+let bind m f = fun (w:s) -> f (m w) w;;
 </pre>
 
 Then the individual concept `unit ann` is a rigid designator: a
@@ -171,7 +165,7 @@ lift saw (unit bill) (unit ann) 2;;  (* false *)
 Ann did see bill in world 1, but Ann didn't see Bill in world 2.
 
 Finally, we can define our intensional verb *thinks*.  *Think* is
-intensional with respect to its sentential complement, but extensional
+intensional with respect to its sentential complement, though still extensional
 with respect to its subject.  (As Montague noticed, almost all verbs
 in English are extensional with respect to their subject; a possible
 exception is "appear".)
@@ -198,3 +192,5 @@ what is happening in world 2, where Cam doesn't leave.
  will be extensional with respect to the nominal they combine with
  (using bind), and the non-intersective adjectives will take
  intensional arguments.
+
+