___|___
| |
. .
- _|__ _|__
+ _|_ _|__
| | | |
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
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
- : 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.