X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=manipulating_trees_with_monads.mdwn;h=20039c28d7d03aefc0b44c1b295e0a6d80fea657;hp=dcba312629435861a915ee767767cd9dad97b58d;hb=625eaf0570f1b96129bd22861202fa5503caf9b5;hpb=3ed8e56bf33b1c0cfa09b672abf26e9c397ea0f1

diff --git a/manipulating_trees_with_monads.mdwn b/manipulating_trees_with_monads.mdwn
index dcba3126..20039c28 100644
--- a/manipulating_trees_with_monads.mdwn
+++ b/manipulating_trees_with_monads.mdwn
@@ -89,7 +89,7 @@ behavior of a reader monad.  Let's make that explicit.
 In general, we're on a journey of making our treemap function more and
 more flexible.  So the next step---combining the tree transformer with
 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
+tree that is ready to accept any `int -> int` function and produce the
 updated tree.
 
 
@@ -105,30 +105,30 @@ updated tree.
 	            f 7  f 11
 
 That is, we want to transform the ordinary tree `t1` (of type `int
-tree`) into a reader object of type `(int->int)-> int tree`: something
-that, when you apply it to an `int->int` function returns an `int
-tree` in which each leaf `x` has been replaced with `(f x)`.
+tree`) into a reader object of type `(int -> int) -> int tree`: something
+that, when you apply it to an `int -> int` function `f` returns an `int
+tree` in which each leaf `x` has been replaced with `f x`.
 
 With previous readers, we always knew which kind of environment to
 expect: either an assignment function (the original calculator
 simulation), a world (the intensionality monad), an integer (the
 Jacobson-inspired link monad), etc.  In this situation, it will be
 enough for now to expect that our reader will expect a function of
-type `int->int`.
+type `int -> int`.
 
-	type 'a reader = (int->int) -> 'a;;  (* mnemonic: e for environment *)
-	let reader_unit (x : 'a) : 'a reader = fun _ -> x;;
-	let reader_bind (u: 'a reader) (f : 'a -> 'c reader) : 'c reader = fun e -> f (u e) e;;
+	type 'a reader = (int -> int) -> 'a;;  (* mnemonic: e for environment *)
+	let reader_unit (a : 'a) : 'a reader = fun _ -> a;;
+	let reader_bind (u: 'a reader) (f : 'a -> 'b reader) : 'b reader = fun e -> f (u e) e;;
 
 It's easy to figure out how to turn an `int` into an `int reader`:
 
-	let int2int_reader (x : 'a): 'b reader = fun (op : 'a -> 'b) -> op x;;
+	let int2int_reader (x : 'a) : 'b reader = fun (op : 'a -> 'b) -> op x;;
 	int2int_reader 2 (fun i -> i + i);;
 	- : int = 4
 
 But what do we do when the integers are scattered over the leaves of a
 tree?  A binary tree is not the kind of thing that we can apply a
-function of type `int->int` to.
+function of type `int -> int` to.
 
 	let rec treemonadizer (f : 'a -> 'b reader) (t : 'a tree) : 'b tree reader =
 	    match t with
@@ -150,7 +150,7 @@ monad through the leaves.
 
 Here, our environment is the doubling function (`fun i -> i + i`).  If
 we apply the very same `int tree reader` (namely, `treemonadizer
-int2int_reader t1`) to a different `int->int` function---say, the
+int2int_reader t1`) to a different `int -> int` function---say, the
 squaring function, `fun i -> i * i`---we get an entirely different
 result: