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.
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
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: