X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?a=blobdiff_plain;f=manipulating_trees_with_monads.mdwn;h=16bbd384885b3b088bab49dfdf3f0d758a8d9a63;hb=8431bdd30785d6fe5f551219823d41c640918df4;hp=94a88e706b29582ef2f79c5b3a2806ce8a63f002;hpb=1438c72f97b89eebb8524bc51f36918ba4b132b4;p=lambda.git

diff --git a/manipulating_trees_with_monads.mdwn b/manipulating_trees_with_monads.mdwn
index 94a88e70..16bbd384 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
@@ -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