tree monads

diff --git a/zipper-lists-continuations.mdwn b/zipper-lists-continuations.mdwn
index 48ae04c..d16a24e 100644 (file)
--- a/zipper-lists-continuations.mdwn
+++ b/zipper-lists-continuations.mdwn
@@ -652,8 +652,8 @@ monad, the 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 = 
 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 = 

-  match u with Leaf x -> f x | Node (l, r) -> Node ((tree_bind l f),
-  (tree_bind r f));;
+  match u with Leaf x -> f x 
+             | Node (l, r) -> Node ((tree_bind l f), (tree_bind r f));;

 </pre>
 
 For once, let's check the Monad laws.  The left identity law is easy:
 </pre>
 
 For once, let's check the Monad laws.  The left identity law is easy:


@@ -668,19 +668,19 @@ except that each leaf `a` has been replaced with `fa`:
 
 \tree (. (fa1) (. (. (. (fa2)(fa3)) (fa4)) (fa5)))
 <pre>
 
 \tree (. (fa1) (. (. (. (fa2)(fa3)) (fa4)) (fa5)))
 <pre>

-                .                         .           
-              __|__                    __|__   
-              |   |                    |   |   
-              a1  .                   fa1  .   
-                 _|__                    __|__ 
-                 |  |                    |   | 
-                 .  a5                   .  fa5
+                .                         .       
+              __|__                     __|__   
+              |   |                     |   |   
+              a1  .                    fa1  .   
+                 _|__                     __|__ 
+                 |  |                     |   | 
+                 .  a5                    .  fa5

    bind         _|__       f   =        __|__   
    bind         _|__       f   =        __|__   

-                |  |                   |   |   
-                .  a4                  .  fa4  
-              __|__                  __|___       
-              |   |                  |    |       
-              a2  a3                fa2  fa3         
+                |  |                    |   |   
+                .  a4                   .  fa4  
+              __|__                   __|___   
+              |   |                   |    |   
+              a2  a3                 fa2  fa3         

 </pre>   
 
 Given this equivalence, the right identity law
 </pre>   
 
 Given this equivalence, the right identity law


@@ -701,24 +701,24 @@ have to proceed.  Let `f a = Node (Leaf a, Leaf a)`.  Then
 \tree (. (. (. (. (a1)(a2)))))
 \tree (. (. (. (. (a1) (a1)) (. (a1) (a1)))  ))
 <pre>
 \tree (. (. (. (. (a1)(a2)))))
 \tree (. (. (. (. (a1) (a1)) (. (a1) (a1)))  ))
 <pre>

-                                           .           
-                                      ____|____        
-          .               .                   |       |        
-bind    __|__   f  =    __|_    =      .       .        
-        |   |          |   |        __|__   __|__      
-        a1  a2                fa1 fa2       |   |   |   |      
-                                    a1  a1  a1  a1  
+                                           .
+                                       ____|____
+          .               .            |       |
+bind    __|__   f  =    __|_    =      .       .
+        |   |           |   |        __|__   __|__
+        a1  a2         fa1 fa2       |   |   |   |
+                                     a1  a1  a1  a1  

 </pre>
 
 Now when we bind this tree to `g`, we get
 
 <pre>
 </pre>
 
 Now when we bind this tree to `g`, we get
 
 <pre>

-           .           
-       ____|____       
-       |       |       
-       .       .       
-     __|__   __|__     
-     |   |   |   |     
+           .
+       ____|____
+       |       |
+       .       .
+     __|__   __|__
+     |   |   |   |

     ga1 ga1 ga1 ga1  
 </pre>
 
     ga1 ga1 ga1 ga1  
 </pre>