Monad Transformers step by step

[lambda.git] / code / intensionality-monad.ml

diff --git a/code/intensionality-monad.ml b/code/intensionality-monad.ml
index eebe5ee..b5dc9f5 100644 (file)
--- a/code/intensionality-monad.ml
+++ b/code/intensionality-monad.ml
@@ -1,4 +1,4 @@
-(* 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 *)
@@ -8,38 +8,40 @@ 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 *)
+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 *)