X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=manipulating_trees_with_monads.mdwn;h=d0897efd40ef34360d051c96a349accffb6fdca5;hp=a05fa2599ed2a9c07878ac4f7df07f790d42573f;hb=eb8ac48a126c26a8195d19dfc0e1f60009198746;hpb=c4a2655a636328b4e3fe183717402a02f1d97a90

diff --git a/manipulating_trees_with_monads.mdwn b/manipulating_trees_with_monads.mdwn
index a05fa259..d0897efd 100644
--- a/manipulating_trees_with_monads.mdwn
+++ b/manipulating_trees_with_monads.mdwn
@@ -92,6 +92,7 @@ a reader monad---is to have the treemap function return a (monadized)
 tree that is ready to accept any `int -> int` function and produce the
 updated tree.
 
+\tree (. (. (f 2) (f 3)) (. (f 5) (. (f 7) (f 11))))
 
 	\f      .
 	   _____|____
@@ -280,7 +281,7 @@ interesting functions for the first argument of `treemonadizer`:
 We could simulate the tree state example too, but it would require
 generalizing the type of the continuation monad to
 
-	type ('a -> 'b -> 'k) continuation = ('a -> 'b) -> 'k;;
+	type ('a, 'b, 'c) continuation = ('a -> 'b) -> 'c;;
 
 The binary tree monad
 ---------------------
@@ -297,29 +298,29 @@ monad, the binary tree monad:
 
 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
+    Left identity: bind (unit a) f = bind (Leaf a) f = f a
 
 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
 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`:
+except that each leaf `a` has been replaced with `f a`:
 
-\tree (. (fa1) (. (. (. (fa2)(fa3)) (fa4)) (fa5)))
+\tree (. (f a1) (. (. (. (f a2) (f a3)) (f a4)) (f a5)))
 
 	                .                         .
 	              __|__                     __|__
 	              |   |                     |   |
-	              a1  .                    fa1  .
+	              a1  .                   f a1  .
 	                 _|__                     __|__
 	                 |  |                     |   |
-	                 .  a5                    .  fa5
+	                 .  a5                    .  f a5
 	   bind         _|__       f   =        __|__
 	                |  |                    |   |
-	                .  a4                   .  fa4
+	                .  a4                   .  f a4
 	              __|__                   __|___
 	              |   |                   |    |
-	              a2  a3                 fa2  fa3
+	              a2  a3                f a2  f a3
 
 Given this equivalence, the right identity law
 
@@ -336,26 +337,26 @@ As for the associative law,
 we'll give an example that will show how an inductive proof would
 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)))))
 
 	                                           .
 	                                       ____|____
 	          .               .            |       |
 	bind    __|__   f  =    __|_    =      .       .
 	        |   |           |   |        __|__   __|__
-	        a1  a2         fa1 fa2       |   |   |   |
+	        a1  a2        f a1 f a2      |   |   |   |
 	                                     a1  a1  a1  a1
 
 Now when we bind this tree to `g`, we get
 
-	           .
-	       ____|____
-	       |       |
-	       .       .
-	     __|__   __|__
-	     |   |   |   |
-	    ga1 ga1 ga1 ga1
+	            .
+	       _____|______
+	       |          |
+	       .          .
+	     __|__      __|__
+	     |   |      |   |
+	   g a1 g a1  g a1 g a1
 
 At this point, it should be easy to convince yourself that
 using the recipe on the right hand side of the associative law will