manip trees: tweaks

Signed-off-by: Jim Pryor <profjim@jimpryor.net>

diff --git a/manipulating_trees_with_monads.mdwn b/manipulating_trees_with_monads.mdwn
index 62c9465..d3ccc98 100644 (file)
--- a/manipulating_trees_with_monads.mdwn
+++ b/manipulating_trees_with_monads.mdwn
@@ -44,7 +44,7 @@ We'll be using trees where the nodes are integers, e.g.,
 
 Our first task will be to replace each leaf with its double:
 
-       let rec treemap (newleaf:'a -> 'b) (t:'a tree):('b tree) =
+       let rec treemap (newleaf : 'a -> 'b) (t : 'a tree) : 'b tree =
          match t with
            | Leaf x -> Leaf (newleaf x)
            | Node (l, r) -> Node ((treemap newleaf l),
@@ -118,12 +118,12 @@ enough for now to expect that our reader will expect a function of
 type `int->int`.
 
        type 'a reader = (int->int) -> 'a;;  (* mnemonic: e for environment *)
-       let reader_unit (x:'a): 'a reader = fun _ -> x;;
-       let reader_bind (u: 'a reader) (f:'a -> 'c reader):'c reader = fun e -> f (u e) e;;
+       let reader_unit (x : 'a) : 'a reader = fun _ -> x;;
+       let reader_bind (u: 'a reader) (f : 'a -> 'c reader) : 'c reader = fun e -> f (u e) e;;
 
 It's easy to figure out how to turn an `int` into an `int reader`:
 
-       let int2int_reader (x:'a): 'b reader = fun (op:'a -> 'b) -> op x;;
+       let int2int_reader (x : 'a): 'b reader = fun (op : 'a -> 'b) -> op x;;
        int2int_reader 2 (fun i -> i + i);;
        - : int = 4
 
@@ -131,7 +131,7 @@ But what do we do when the integers are scattered over the leaves of a
 tree?  A binary tree is not the kind of thing that we can apply a
 function of type `int->int` to.
 
-       let rec treemonadizer (f:'a -> 'b reader) (t:'a tree):('b tree) reader =
+       let rec treemonadizer (f : 'a -> 'b reader) (t : 'a tree) : 'b tree reader =
            match t with
            | Leaf x -> reader_bind (f x) (fun x' -> reader_unit (Leaf x'))
            | Node (l, r) -> reader_bind (treemonadizer f l) (fun x ->
@@ -172,7 +172,7 @@ Gratifyingly, we can use the `treemonadizer` function without any
 modification whatsoever, except for replacing the (parametric) type
 `reader` with `state`:
 
-       let rec treemonadizer (f:'a -> 'b state) (t:'a tree):('b tree) state =
+       let rec treemonadizer (f : 'a -> 'b state) (t : 'a tree) : 'b tree state =
            match t with
            | Leaf x -> state_bind (f x) (fun x' -> state_unit (Leaf x'))
            | Node (l, r) -> state_bind (treemonadizer f l) (fun x ->
@@ -219,7 +219,7 @@ of leaves?
        let continuation_unit x c = c x;;
        let continuation_bind u f c = u (fun a -> f a c);;
        
-       let rec treemonadizer (f:'a -> ('b, 'r) continuation) (t:'a tree):(('b tree), 'r) continuation =
+       let rec treemonadizer (f : 'a -> ('b, 'r) continuation) (t : 'a tree) : ('b tree, 'r) continuation =
            match t with
            | Leaf x -> continuation_bind (f x) (fun x' -> continuation_unit (Leaf x'))
            | Node (l, r) -> continuation_bind (treemonadizer f l) (fun x ->
@@ -276,8 +276,8 @@ Of course, by now you may have realized that we have discovered a new
 monad, the binary tree monad:
 
        type 'a tree = Leaf of 'a | Node of ('a tree) * ('a tree);;
-       let tree_unit (x:'a) = Leaf x;;
-       let rec tree_bind (u:'a tree) (f:'a -> 'b tree):'b tree =
+       let tree_unit (x: 'a) = Leaf x;;
+       let rec tree_bind (u : 'a tree) (f : 'a -> 'b tree) : 'b tree =
            match u with
            | Leaf x -> f x
            | Node (l, r) -> Node ((tree_bind l f), (tree_bind r f));;