tree monads

diff --git a/zipper-lists-continuations.mdwn b/zipper-lists-continuations.mdwn
index d16a24e..052bdf6 100644 (file)
--- a/zipper-lists-continuations.mdwn
+++ b/zipper-lists-continuations.mdwn
@@ -642,11 +642,11 @@ generalizing the type of the continuation monad to
 
     type ('a -> 'b -> 'c) continuation = ('a -> 'b) -> 'c;;
 
 
     type ('a -> 'b -> 'c) continuation = ('a -> 'b) -> 'c;;
 

-The tree monad
---------------
+The binary tree monad
+---------------------

 
 Of course, by now you may have realized that we have discovered a new
 
 Of course, by now you may have realized that we have discovered a new

-monad, the tree monad:
+monad, the binary tree monad:

 
 <pre>
 type 'a tree = Leaf of 'a | Node of ('a tree) * ('a tree);;
 
 <pre>
 type 'a tree = Leaf of 'a | Node of ('a tree) * ('a tree);;


@@ -661,7 +661,7 @@ For once, let's check the Monad laws.  The left identity law is easy:
     Left identity: bind (unit a) f = bind (Leaf a) f = fa
 
 To check the other two laws, we need to make the following
     Left identity: bind (unit a) f = bind (Leaf a) f = fa
 
 To check the other two laws, we need to make the following

-observation: it is easy to prove based on tree_bind by a simple
+observation: it is easy to prove based on `tree_bind` by a simple

 induction on the structure of the first argument that the tree
 resulting from `bind u f` is a tree with the same strucure as `u`,
 except that each leaf `a` has been replaced with `fa`:
 induction on the structure of the first argument that the tree
 resulting from `bind u f` is a tree with the same strucure as `u`,
 except that each leaf `a` has been replaced with `fa`:


@@ -696,7 +696,7 @@ As for the associative law,
     Associativity: bind (bind u f) g = bind u (\a. bind (fa) g)
 
 we'll give an example that will show how an inductive proof would
     Associativity: bind (bind u f) g = bind u (\a. bind (fa) g)
 
 we'll give an example that will show how an inductive proof would

-have to proceed.  Let `f a = Node (Leaf a, Leaf a)`.  Then
+proceed.  Let `f a = Node (Leaf a, Leaf a)`.  Then

 
 \tree (. (. (. (. (a1)(a2)))))
 \tree (. (. (. (. (a1) (a1)) (. (a1) (a1)))  ))
 
 \tree (. (. (. (. (a1)(a2)))))
 \tree (. (. (. (. (a1) (a1)) (. (a1) (a1)))  ))