Our first task will be to replace each leaf with its double:
- let rec treemap (newleaf:'a -> 'b) (t:'a tree):('b tree) =
+ let rec treemap (newleaf : 'a -> 'b) (t : 'a tree) : 'b tree =
match t with
| Leaf x -> Leaf (newleaf x)
| Node (l, r) -> Node ((treemap newleaf l),
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;;
+ 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;;
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
tree? A binary tree is not the kind of thing that we can apply a
function of type `int->int` to.
- let rec treemonadizer (f:'a -> 'b reader) (t:'a tree):('b tree) reader =
+ let rec treemonadizer (f : 'a -> 'b reader) (t : 'a tree) : 'b tree reader =
match t with
| Leaf x -> reader_bind (f x) (fun x' -> reader_unit (Leaf x'))
| Node (l, r) -> reader_bind (treemonadizer f l) (fun x ->
modification whatsoever, except for replacing the (parametric) type
`reader` with `state`:
- let rec treemonadizer (f:'a -> 'b state) (t:'a tree):('b tree) state =
+ let rec treemonadizer (f : 'a -> 'b state) (t : 'a tree) : 'b tree state =
match t with
| Leaf x -> state_bind (f x) (fun x' -> state_unit (Leaf x'))
| Node (l, r) -> state_bind (treemonadizer f l) (fun x ->
let continuation_unit x c = c x;;
let continuation_bind u f c = u (fun a -> f a c);;
- let rec treemonadizer (f:'a -> ('b, 'r) continuation) (t:'a tree):(('b tree), 'r) continuation =
+ let rec treemonadizer (f : 'a -> ('b, 'r) continuation) (t : 'a tree) : ('b tree, 'r) continuation =
match t with
| Leaf x -> continuation_bind (f x) (fun x' -> continuation_unit (Leaf x'))
| Node (l, r) -> continuation_bind (treemonadizer f l) (fun x ->
monad, the binary tree monad:
type 'a tree = Leaf of 'a | Node of ('a tree) * ('a tree);;
- let tree_unit (x:'a) = Leaf x;;
- let rec tree_bind (u:'a tree) (f:'a -> 'b tree):'b tree =
+ let tree_unit (x: 'a) = Leaf x;;
+ let rec tree_bind (u : 'a tree) (f : 'a -> 'b tree) : 'b tree =
match u with
| Leaf x -> f x
| Node (l, r) -> Node ((tree_bind l f), (tree_bind r f));;