use a container metaphor: if `x` has type `int option`, then `x` is
a box that (may) contain an integer.
- type 'a option = None | Some of 'a;;
+ `type 'a option = None | Some of 'a;;`
* A way to turn an ordinary value into a monadic value. In Ocaml, we
did this for any integer n by mapping an arbitrary integer `n` to
the option `Some n`. To be official, we can define a function
called unit:
- let unit x = Some x;;
- val unit : 'a -> 'a option = <fun>
+ `let unit x = Some x;;`
+
+ `val unit : 'a -> 'a option = <fun>`
So `unit` is a way to put something inside of a box.
* A bind operation (note the type):
-<pre>
- let bind m f = match m with None -> None | Some n -> f n;;
- val bind : 'a option -> ('a -> 'b option) -> 'b option = <fun>
-</pre>
+ `let bind m f = match m with None -> None | Some n -> f n;;`
+
+ `val bind : 'a option -> ('a -> 'b option) -> 'b option = <fun>`
`bind` takes two arguments (a monadic object and a function from
ordinary objects to monadic objects), and returns a monadic
Then the second argument uses `x` to compute a new monadic
value. Conceptually, then, we have
- let bind m f = (let x = unwrap m in f x);;
+ `let bind m f = (let x = unwrap m in f x);;`
The guts of the definition of the `bind` operation amount to
specifying how to unwrap the monadic object `m`. In the bind
- : int option = Some 2
</pre>
- The parentheses is the magic for telling Ocaml that the
- function to be defined (in this case, the name of the function
- is `*`, pronounced "bind") is an infix operator, so we write
- `m * f` or `( * ) m f` instead of `* m f`.
+The parentheses is the magic for telling Ocaml that the
+function to be defined (in this case, the name of the function
+is `*`, pronounced "bind") is an infix operator, so we write
+`m * f` or `( * ) m f` instead of `* m f`.
* Associativity: bind obeys a kind of associativity, like this:
- (m * f) * g == m * (fun x -> f x * g)
+ `(m * f) * g == m * (fun x -> f x * g)`
- If you don't understand why the lambda form is necessary, you need
- to look again at the type of bind. This is important.
+ If you don't understand why the lambda form is necessary (the "fun
+ x" part), you need to look again at the type of bind.
For an illustration of associativity in the option monad: