___|___
| |
. .
- _|__ _|__
+ _|_ _|__
| | | |
2 3 5 .
_|__
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
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)
-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.
-\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
-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
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;;
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
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:
- : 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.