-(* This is the intensionality monad discussed in the lecture notes for week 7. *)
+(* This is the intensionality monad discussed in the lecture notes for week 8. *)
type s = int;; (* integers model possible worlds *)
type e = char;; (* chars model individuals *)
let bill = 'b';;
let cam = 'c';;
-let left1 (x:e) = true;; (* Everyone left *)
-let saw1 (x:e) (y:e) = y < x;; (* Ann saw Bill and Cam, and Bill saw Cam *)
+let left1 (x : e) = true;; (* Everyone left *)
+let saw1 (y : e) (x : e) = x < y;; (* Ann saw Bill and Cam, and Bill saw Cam *)
-left1 ann;;
-saw1 bill ann;;
-saw1 ann bill;;
+left1 ann;; (* true *)
+saw1 bill ann;; (* true *)
+saw1 ann bill;; (* false *)
(* Now we make the extension of "leave" sensitive to the world of evaluation *)
-let left (x:e) (w:s) = match (x, w) with ('c', 2) -> false | _ -> true;;
+let left (x : e) (w : s) = match (x, w) with ('c', 2) -> false | _ -> true;;
left ann 1;; (* Ann left in world 1 *)
left cam 2;; (* Cam didn't leave in world 2 *)
-let saw x y w = (w < 2) && (y < x);;
+let saw (y : e) (x : e) (w : s) = (w < 2) && (x < y);;
saw bill ann 1;; (* Ann saw Bill in world 1 *)
saw bill ann 2;; (* Ann didn't see Bill in world 2 *)
-(* The intensionality reader-monad: *)
+(* The intensionality reader-monad *)
type 'a intension = s -> 'a;;
-let unit x (w:s) = x;;
-let bind m f (w:s) = f (m w) w;;
-let lift2' f u v = bind u (fun x -> bind v (fun y -> f x y));;
+let mid x (w : s) = x;;
+let (>>=) xx k (w : s) = k (xx w) w;;
+let map2' f xx yy = xx >>= (fun x -> yy >>= (fun y -> f x y));;
-bind (unit ann) left 1;;
-bind (unit cam) left 2;;
+(mid ann >>= left) 1;; (* true *)
+(mid cam >>= left) 2;; (* false *)
-lift2' saw (unit bill) (unit ann) 1;;
-lift2' saw (unit bill) (unit ann) 2;;
+map2' saw (mid bill) (mid ann) 1;; (* true *)
+map2' saw (mid bill) (mid ann) 2;; (* false *)
-let thinks (p:s->t) (x:e) (w:s) =
+let thinks (p : s->t) (x : e) (w : s) =
match (x, p 2) with ('a', false) -> false | _ -> p w;;
-bind (unit ann) (thinks (bind (unit bill) left)) 1;;
-bind (unit ann) (thinks (bind (unit cam) left)) 1;;
+(mid bill >>= left) 1;; (* true *)
+(mid cam >>= left) 1;; (* true *)
+(mid ann >>= thinks (mid bill >>= left)) 1;; (* true *)
+(mid ann >>= thinks (mid cam >>= left)) 1;; (* false *)