manip trees: tweaks

[lambda.git] / manipulating_trees_with_monads.mdwn

diff --git a/manipulating_trees_with_monads.mdwn b/manipulating_trees_with_monads.mdwn
index d3ccc98..3a30561 100644 (file)
--- a/manipulating_trees_with_monads.mdwn
+++ b/manipulating_trees_with_monads.mdwn
@@ -35,7 +35,7 @@ We'll be using trees where the nodes are integers, e.g.,
         ___|___
         |     |
         .     .
         ___|___
         |     |
         .     .

-       _|__  _|__
+       _|_   _|__

        |  |  |  |
        2  3  5  .
                _|__
        |  |  |  |
        2  3  5  .
                _|__


@@ -48,7 +48,7 @@ Our first task will be to replace each leaf with its double:
          match t with
            | Leaf x -> Leaf (newleaf x)
            | Node (l, r) -> Node ((treemap newleaf l),
          match t with
            | Leaf x -> Leaf (newleaf x)
            | Node (l, r) -> Node ((treemap newleaf l),

-                                 (treemap newleaf r));;
+                                  (treemap newleaf r));;

 
 `treemap` takes a function that transforms old leaves into new leaves,
 and maps that function over all the leaves in the tree, leaving the
 
 `treemap` takes a function that transforms old leaves into new leaves,
 and maps that function over all the leaves in the tree, leaving the


@@ -87,27 +87,26 @@ to each subpart of the computation.  In other words, `treemap` has the
 behavior of a reader monad.  Let's make that explicit.
 
 In general, we're on a journey of making our treemap function more and
 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 transducer with
+more flexible.  So the next step---combining the tree transformer with

 a reader monad---is to have the treemap function return a (monadized)
 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.
 

-\tree (. (. (f2) (f3))(. (f5) (.(f7)(f11))))

 
 

-       \f    .
-         ____|____
-         |       |
-         .       .
-       __|__   __|__
-       |   |   |   |
-       f2  f3  f5  .
-                 __|___
-                 |    |
-                 f7  f11
+       \f      .
+          _____|____
+          |        |
+          .        .
+        __|___   __|___
+        |    |   |    |
+       f 2  f 3  f 5  .
+                    __|___
+                    |    |
+                   f 7  f 11

 
 That is, we want to transform the ordinary tree `t1` (of type `int
 
 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


@@ -115,9 +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;;
 


@@ -129,7 +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


@@ -151,7 +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:
 


@@ -159,7 +158,7 @@ result:
        - : int tree =
        Node (Node (Leaf 4, Leaf 9), Node (Leaf 25, Node (Leaf 49, Leaf 121)))
 
        - : int tree =
        Node (Node (Leaf 4, Leaf 9), Node (Leaf 25, Node (Leaf 49, Leaf 121)))
 

-Now that we have a tree transducer that accepts a monad as a
+Now that we have a tree transformer that accepts a monad as a

 parameter, we can see what it would take to swap in a different monad.
 For instance, we can use a state monad to count the number of nodes in
 the tree.
 parameter, we can see what it would take to swap in a different monad.
 For instance, we can use a state monad to count the number of nodes in
 the tree.