manip trees: tweaks

[lambda.git] / list_monad_as_continuation_monad.mdwn

diff --git a/list_monad_as_continuation_monad.mdwn b/list_monad_as_continuation_monad.mdwn
index 7a57ea7..e4772f8 100644 (file)
--- a/list_monad_as_continuation_monad.mdwn
+++ b/list_monad_as_continuation_monad.mdwn
@@ -112,7 +112,7 @@ will provide a connection with continuations.
 Recall that `List.map` takes a function and a list and returns the
 result to applying the function to the elements of the list:
 
-       List.map (fun i -> [i;i+1]) [1;2] ~~> [[1; 2]; [2; 3]]
+       List.map (fun i -> [i; i+1]) [1; 2] ~~> [[1; 2]; [2; 3]]
 
 and `List.concat` takes a list of lists and erases the embedded list
 boundaries:
@@ -121,12 +121,12 @@ boundaries:
 
 And sure enough,
 
-       l_bind [1;2] (fun i -> [i, i+1]) ~~> [1; 2; 2; 3]
+       l_bind [1; 2] (fun i -> [i; i+1]) ~~> [1; 2; 2; 3]
 
 Now, why this unit, and why this bind?  Well, ideally a unit should
 not throw away information, so we can rule out `fun x -> []` as an
 ideal unit.  And units should not add more information than required,
-so there's no obvious reason to prefer `fun x -> [x;x]`.  In other
+so there's no obvious reason to prefer `fun x -> [x; x]`.  In other
 words, `fun x -> [x]` is a reasonable choice for a unit.
 
 As for bind, an `'a list` monadic object contains a lot of objects of
@@ -136,7 +136,7 @@ thing we know for sure we can do with an object of type `'a` is apply
 the function of type `'a -> 'a list` to them.  Once we've done so, we
 have a collection of lists, one for each of the `'a`'s.  One
 possibility is that we could gather them all up in a list, so that
-`bind' [1;2] (fun i -> [i;i]) ~~> [[1;1];[2;2]]`.  But that restricts
+`bind' [1; 2] (fun i -> [i; i]) ~~> [[1; 1]; [2; 2]]`.  But that restricts
 the object returned by the second argument of `bind` to always be of
 type `'b list list`.  We can eliminate that restriction by flattening
 the list of lists into a single list: this is
@@ -198,7 +198,7 @@ Take an `'a` and return its v3-style singleton. No problem.  Arriving at bind
 is a little more complicated, but exactly the same principles apply, you just
 have to be careful and systematic about it.
 
-       l'_bind (u : ('a,'b) list') (f : 'a -> ('c, 'd) list') : ('c, 'd) list'  = ...
+       l'_bind (u : ('a, 'b) list') (f : 'a -> ('c, 'd) list') : ('c, 'd) list'  = ...
 
 Unpacking the types gives:
 
@@ -292,7 +292,7 @@ For future reference, we might make two eta-reductions to our formula, so that w
 
 Let's make some more tests:
 
-       l_bind [1;2] (fun i -> [i, i+1]) ~~> [1; 2; 2; 3]
+       l_bind [1; 2] (fun i -> [i; i+1]) ~~> [1; 2; 2; 3]
        
        l'_bind (fun f z -> f 1 (f 2 z))
            (fun i -> fun f z -> f i (f (i+1) z)) ~~> <fun>
@@ -357,6 +357,8 @@ This can be eta-reduced to:
 
        let l'_unit a = fun k -> k a
 
+and:
+
        let l'_bind u f =
            (* we mentioned three versions of this, the fully eta-expanded: *)
            fun k z -> u (fun a b -> f a k b) z