(* This is the intensionality monad discussed in the lecture notes for week 7. *) type s = int;; (* integers model possible worlds *) type e = char;; (* chars model individuals *) type t = bool;; (* booleans model truth values *) let ann = 'a';; 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 *) left1 ann;; saw1 bill ann;; saw1 ann bill;; (* 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;; 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);; 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: *) 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));; bind (unit ann) left 1;; bind (unit cam) left 2;; lift2' saw (unit bill) (unit ann) 1;; lift2' saw (unit bill) (unit ann) 2;; 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;;