X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=code%2Ftree_monadize.ml;h=d9c5a5900e520c3fb78c918dd0abbd08f41ea8ae;hp=7c419a342402ce77a965eb1c2810e4b332cdfcde;hb=0c48836d5dbaa454898800a73183d6775cc3664c;hpb=ff95f5a38d61a6fa0b9c5e4da4253a6a3266a7dc

diff --git a/code/tree_monadize.ml b/code/tree_monadize.ml
index 7c419a34..d9c5a590 100644
--- a/code/tree_monadize.ml
+++ b/code/tree_monadize.ml
@@ -10,9 +10,9 @@ module Reader_monad = struct
     (* change this to suit your needs *)
     type env = int -> int;;
 
-    type 'a monad = env -> 'a;;
-    let unit a : 'a monad = fun e -> a;;
-    let bind (u : 'a monad) (f : 'a -> 'b monad) : 'b monad =
+    type 'a m = env -> 'a;;
+    let unit a : 'a m = fun e -> a;;
+    let bind (u : 'a m) (f : 'a -> 'b m) : 'b m =
       fun e -> f (u e) e;;
 end
 
@@ -20,16 +20,16 @@ module State_monad = struct
     (* change this to suit your needs *)
     type store = int;;
 
-    type 'a monad = store -> 'a * store;;
-    let unit a : 'a monad  = fun s -> (a, s);;
-    let bind (u : 'a monad) (f : 'a -> 'b monad) : 'b monad =
+    type 'a m = store -> 'a * store;;
+    let unit a : 'a m  = fun s -> (a, s);;
+    let bind (u : 'a m) (f : 'a -> 'b m) : 'b m =
       fun s -> (let (a, s') = u s in (f a) s');;
 end
 
 module List_monad = struct
-    type 'a monad = 'a list;;
-    let unit a : 'a monad = [a];;
-    let bind (u: 'a monad) (f : 'a -> 'b monad) : 'b monad =
+    type 'a m = 'a list;;
+    let unit a : 'a m = [a];;
+    let bind (u: 'a m) (f : 'a -> 'b m) : 'b m =
       List.concat(List.map f u);;
 end
 
@@ -54,9 +54,9 @@ end
  * argument, or the State_monad, or another?
  *
  * There is a way to do this, but it requires putting the `... bind ...` code in
- * its own module, and making that module parameterized on some X_monad
+ * its own module, and making that module parameterized on some M_monad
  * module. Also we have to explicitly declare what commonality we're expecting
- * from X_monad modules we're going to use as parameters. We'll explain how to
+ * from M_monad modules we're going to use as parameters. We'll explain how to
  * do this in a moment.
  *
  * As preparation, a general observation:
@@ -80,15 +80,15 @@ end
  *       * module parameter that will choose
  *       * whether b = list or b = option or b = reader...
  *       * This module parameter may supply values as well as types *)
- *      X : sig
+ *      M : sig
  *          type ('a) b
  *      end
  *      ) = 
  *      (* A struct...end block gives a module value
  *       * What we're doing here is building a new module that makes
- *       * use of the module that was supplied as X *)
+ *       * use of the module that was supplied as M *)
  *      struct
- *          type ('a) t = 'a -> ('a) X.b
+ *          type ('a) t = 'a -> ('a) M.b
  *      end
  * And here's how you'd use it:
  *      module T_list = T_maker(struct type 'a b = 'a list end);;
@@ -99,7 +99,7 @@ end
  *
  * I know, it seems unnecessarily complicated. Nonetheless, that's how it
  * works. And that is also the technique we'll use to make our
- * `... bind ...` code parametric on some X_monad module.
+ * `... bind ...` code parametric on some M_monad module.
  *)
 
 type 'a tree = Leaf of 'a | Node of ('a tree) * ('a tree);;
@@ -113,24 +113,24 @@ let t1 = Node
                 (Leaf 7, Leaf 11)));;
 
 
-module Tree_monadizer(X : sig
+module Tree_monadizer(M : sig
   (* the module we're using as a parameter has to supply function values
-   * for unit and bind, as well as a monadic type constructor m *)
-  type 'a monad
-  val unit : 'a -> 'a monad
-  val bind : 'a monad -> ('a -> 'b monad) -> 'b monad
+   * for unit and bind, as well as a monadic type constructor *)
+  type 'a m
+  val unit : 'a -> 'a m
+  val bind : 'a m -> ('a -> 'b m) -> 'b m
 end) = struct
-  let rec monadize (f: 'a -> 'b X.monad) (t: 'a tree) : 'b tree X.monad =
+  let rec monadize (f: 'a -> 'b M.m) (t: 'a tree) : 'b tree M.m =
     match t with
-    | Leaf a -> X.bind (f a) (fun b -> X.unit (Leaf b))
+    | Leaf a -> M.bind (f a) (fun b -> M.unit (Leaf b))
     | Node(l, r) ->
-        X.bind (monadize f l) (fun l' ->
-          X.bind (monadize f r) (fun r' ->
-            X.unit (Node (l', r'))))
+        M.bind (monadize f l) (fun l' ->
+          M.bind (monadize f r) (fun r' ->
+            M.unit (Node (l', r'))))
 end;;
 
 
-(* Now we supply the Reader monad as a parameter to Tree_monadizer.
+(* Now we supply Reader_monad as a parameter to Tree_monadizer.
  * We'll get back a module TreeReader that contains a single value,
  * the monadize function specialized to the Reader monad *)
 module TreeReader = Tree_monadizer(Reader_monad);;
@@ -146,31 +146,31 @@ module TreeList =  Tree_monadizer(List_monad);;
 
 (* The Continuation monad is a bit more complicated *)
 module Continuation_monad = struct
-    type ('a,'r) monad = ('a -> 'r) -> 'r;;
-    let unit a : ('a,'r) monad = fun k -> k a;;
-    let bind (u: ('a,'r) monad) (f: 'a -> ('b,'r) monad) : ('b,'r) monad =
+    type ('r,'a) m = ('a -> 'r) -> 'r;;
+    let unit a : ('r,'a) m = fun k -> k a;;
+    let bind (u: ('r,'a) m) (f: 'a -> ('r,'b) m) : ('r,'b) m =
       fun k -> u (fun a -> f a k);;
 end
 
 (* Since the Continuation monad is parameterized on two types---it's
- * ('a,'r) cont not ('a) cont---we can't match the type ('a) monad that
+ * ('r,'a) cont not ('a) cont---we can't match the type ('a) monad that
  * Tree_monadizer expects in its parameter. So we have to make a different
- * Tree_monadizer2 that takes a ('a,'z) monad type constructor in its
+ * Tree_monadizer2 that takes a ('r,'a) monad type constructor in its
  * parameter instead *)
-module Tree_monadizer2(X : sig
-  type ('a,'z) monad
-  val unit : 'a -> ('a,'z) monad
-  val bind : ('a,'z) monad -> ('a -> ('b,'z) monad) -> ('b,'z) monad
+module Tree_monadizer2(M : sig
+  type ('r,'a) m
+  val unit : 'a -> ('r,'a) m
+  val bind : ('r,'a) m -> ('a -> ('r,'b) m) -> ('r,'b) m
 end) = struct
   (* the body of the monadize function is the same; the only difference is in
    * the types *)
-  let rec monadize (f: 'a -> ('b,'x) X.monad) (t: 'a tree) : ('b tree,'x) X.monad =
+  let rec monadize (f: 'a -> ('r,'b) M.m) (t: 'a tree) : ('r,'b tree) M.m =
     match t with
-    | Leaf a -> X.bind (f a) (fun b -> X.unit (Leaf b))
+    | Leaf a -> M.bind (f a) (fun b -> M.unit (Leaf b))
     | Node(l, r) ->
-        X.bind (monadize f l) (fun l' ->
-          X.bind (monadize f r) (fun r' ->
-            X.unit (Node (l', r'))))
+        M.bind (monadize f l) (fun l' ->
+          M.bind (monadize f r) (fun r' ->
+            M.unit (Node (l', r'))))
 end;;
 
 (* Make a TreeCont module containing monadize specialized to the Cont monad *)
@@ -184,55 +184,55 @@ module TreeCont =  Tree_monadizer2(Continuation_monad);;
  *)
 
 
-let int_readerize : int -> int Reader_monad.monad =
+let asker : int -> int Reader_monad.m =
   fun (a : int) -> fun (env : int -> int) -> env a;;
 
-(* int_readerize takes an int and returns a Reader monad that
+(* asker takes an int and returns a Reader monad that
  * "looks up" that int in the environment (i.e. modifies it)
  * this is structurally parallel to the function `lookup` we used
  * before to "look up" variables in the environment *)
 
 (* double each leaf *)
 let env = fun i -> i + i in
-TreeReader.monadize int_readerize t1 env;;
+TreeReader.monadize asker t1 env;;
 
 (* You can also avoid declaring a separate toplevel TreeReader module
- * (or even a separate Reader_monad module) by ysing one of these forms:
+ * (or even a separate Reader_monad module) by using one of these forms:
  *     ...
  *     let module T = Tree_monadizer(Reader_monad) in
- *     T.monadize int_readerize t1 env;;
+ *     T.monadize asker t1 env;;
  * or:
  *     ...
  *     let env = fun i -> i + i in
  *     let module Monad = struct
  *       type env = int -> int;;
- *       type 'a monad = env -> 'a;;
- *       let unit a : 'a monad = fun e -> a;;
- *       let bind (u : 'a monad) (f : 'a -> 'b monad) : 'b monad =
+ *       type 'a m = env -> 'a;;
+ *       let unit a : 'a m = fun e -> a;;
+ *       let bind (u : 'a m) (f : 'a -> 'b m) : 'b m =
  *         fun e -> f (u e) e;;
  *     end in
  *     let module T = Tree_monadizer(Monad) in
- *     T.monadize int_readerize t1 env;;
+ *     T.monadize asker t1 env;;
  * or:
  *     ...
  *     let module T = Tree_monadizer(struct
  *       type env = int -> int;;
- *       type 'a monad = env -> 'a;;
- *       let unit a : 'a monad = fun e -> a;;
- *       let bind (u : 'a monad) (f : 'a -> 'b monad) : 'b monad =
+ *       type 'a m = env -> 'a;;
+ *       let unit a : 'a m = fun e -> a;;
+ *       let bind (u : 'a m) (f : 'a -> 'b m) : 'b m =
  *         fun e -> f (u e) e;;
  *     end) in
- *     T.monadize int_readerize t1 env;;
+ *     T.monadize asker t1 env;;
  *)
 
 
 (* square each leaf *)
 let env = fun i -> i * i in
-TreeReader.monadize int_readerize t1 env;;
+TreeReader.monadize asker t1 env;;
 
 
 
-let incrementer : int -> int State_monad.monad =
+let incrementer : int -> int State_monad.m =
   fun (a : int) -> fun s -> (a, s+1);;
 
 (* incrementer takes an 'a and returns it wrapped in a