1 (* This is the intensionality monad discussed in the lecture notes for week 8. *)
3 type s = int;; (* integers model possible worlds *)
4 type e = char;; (* chars model individuals *)
5 type t = bool;; (* booleans model truth values *)
11 let left1 (x : e) = true;; (* Everyone left *)
12 let saw1 (y : e) (x : e) = x < y;; (* Ann saw Bill and Cam, and Bill saw Cam *)
14 left1 ann;; (* true *)
15 saw1 bill ann;; (* true *)
16 saw1 ann bill;; (* false *)
18 (* Now we make the extension of "leave" sensitive to the world of evaluation *)
19 let left (x : e) (w : s) = match (x, w) with ('c', 2) -> false | _ -> true;;
21 left ann 1;; (* Ann left in world 1 *)
22 left cam 2;; (* Cam didn't leave in world 2 *)
24 let saw (y : e) (x : e) (w : s) = (w < 2) && (x < y);;
25 saw bill ann 1;; (* Ann saw Bill in world 1 *)
26 saw bill ann 2;; (* Ann didn't see Bill in world 2 *)
28 (* The intensionality reader-monad *)
29 type 'a intension = s -> 'a;;
30 let mid x (w : s) = x;;
31 let (>>=) xx k (w : s) = k (xx w) w;;
32 let map2' f xx yy = xx >>= (fun x -> yy >>= (fun y -> f x y));;
34 (mid ann >>= left) 1;; (* true *)
35 (mid cam >>= left) 2;; (* false *)
37 map2' saw (mid bill) (mid ann) 1;; (* true *)
38 map2' saw (mid bill) (mid ann) 2;; (* false *)
40 let thinks (p : s->t) (x : e) (w : s) =
41 match (x, p 2) with ('a', false) -> false | _ -> p w;;
43 (mid bill >>= left) 1;; (* true *)
44 (mid cam >>= left) 1;; (* true *)
45 (mid ann >>= thinks (mid bill >>= left)) 1;; (* true *)
46 (mid ann >>= thinks (mid cam >>= left)) 1;; (* false *)