manip trees: tweaks

Signed-off-by: Jim Pryor <profjim@jimpryor.net>

diff --git a/manipulating_trees_with_monads.mdwn b/manipulating_trees_with_monads.mdwn
index dcba312..3a30561 100644 (file)
--- 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)
 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.
 
 
 updated tree.
 
 


@@ -105,8 +105,8 @@ updated tree.
                    f 7  f 11
 
 That is, we want to transform the ordinary tree `t1` (of type `int
                    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`) 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)`.
 
 With previous readers, we always knew which kind of environment to
 tree` in which each leaf `x` has been replaced with `(f x)`.
 
 With previous readers, we always knew which kind of environment to


@@ -114,9 +114,9 @@ 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
 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 *)
+       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;;
 
        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;;
 


@@ -128,7 +128,7 @@ It's easy to figure out how to turn an `int` into an `int reader`:
 
 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
 
 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
 
        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
 
 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:
 
 squaring function, `fun i -> i * i`---we get an entirely different
 result: