X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=manipulating_trees_with_monads.mdwn;h=47fa6f0da08ad5fafebd6f3fec494152a705a175;hp=94a88e706b29582ef2f79c5b3a2806ce8a63f002;hb=f719b082e2cfe4249565a8fb189e983731ada27f;hpb=1438c72f97b89eebb8524bc51f36918ba4b132b4

diff --git a/manipulating_trees_with_monads.mdwn b/manipulating_trees_with_monads.mdwn
index 94a88e70..47fa6f0d 100644
--- a/manipulating_trees_with_monads.mdwn
+++ b/manipulating_trees_with_monads.mdwn
@@ -288,7 +288,7 @@ One more revealing example before getting down to business: replacing
 
 Unlike the previous cases, instead of turning a tree into a function
 from some input to a result, this transformer replaces each `int` with
-a list of `int`'s. We might also have done this with a Reader monad, though then our environments would need to be of type `int -> int list`. Experiment with what happens if you supply the `tree_monadize` based on the List monad an operation like `fun -> [ i; [2*i; 3*i] ]`. Use small trees for your experiment.
+a list of `int`'s. We might also have done this with a Reader monad, though then our environments would need to be of type `int -> int list`. Experiment with what happens if you supply the `tree_monadize` based on the List monad an operation like `fun i -> [2*i; 3*i]`. Use small trees for your experiment.
 
 [Why is the argument to `tree_monadize` `int -> int list list` instead
 of `int -> int list`?  Well, as usual, the List monad bind operation
@@ -329,7 +329,7 @@ In a moment, we'll return to the same-fringe problem.  Since the
 simple but inefficient way to solve it is to map each tree to a list
 of its leaves, this transformation is on the path to a more efficient
 solution.  We'll just have to figure out how to postpone computing the
-tail of the list until its needed...
+tail of the list until it's needed...
 
 The Continuation monad is amazingly flexible; we can use it to
 simulate some of the computations performed above.  To see how, first
@@ -360,8 +360,14 @@ interesting functions for the first argument of `tree_monadize`:
 	# tree_monadize (fun a -> fun k -> 1 + k a) t1 (fun t -> 0);;
 	- : int = 5
 
-We could simulate the tree state example too, but it would require
-generalizing the type of the Continuation monad to
+[To be fixed: exactly which kind of monad each of these computations simulates.]
+
+We could simulate the tree state example too by setting the relevant 
+type to `('a, 'state -> 'result) continuation`.
+In fact, Andre Filinsky has suggested that the continuation monad is
+able to simulate any other monad (Google for "mother of all monads").
+
+We would eventually want to generalize the continuation type to
 
 	type ('a, 'b, 'c) continuation = ('a -> 'b) -> 'c;;
 
@@ -525,7 +531,7 @@ quantification.
 
 This sentence means (roughly)
 
-    &Forall; x . yesterday(saw x) john
+    forall x . yesterday(saw x) john
 
 That is, the quantifier *everyone* contributes a variable in the
 direct object position, and a universal quantifier that takes scope
@@ -669,7 +675,7 @@ called a
 that is intended to represent non-deterministic computations as a tree.
 
 
-What's this have to do with tree\_mondadize?
+What's this have to do with tree\_monadize?
 --------------------------------------------
 
 So we've defined a Tree monad: