X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=week7.mdwn;h=f5114046e16a064efb0cad3c2550eb78bddff93e;hp=62ef89f0ab8b7a2faa8fecf83aa141963d523a54;hb=d9044712f0cf116029c39c68095e703af3367cb1;hpb=7834e35d4a2de390ce6a1e9113186dcbb9c07a6f diff --git a/week7.mdwn b/week7.mdwn index 62ef89f0..f5114046 100644 --- a/week7.mdwn +++ b/week7.mdwn @@ -48,22 +48,24 @@ that provides at least the following three elements: 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 = + `let unit x = Some x;;` + + `val unit : 'a -> 'a option = ` So `unit` is a way to put something inside of a box. * A bind operation (note the type): - let bind m f = match m with None -> None | Some n -> f n;; - val bind : 'a option -> ('a -> 'b option) -> 'b option = + `let bind m f = match m with None -> None | Some n -> f n;;` + + `val bind : 'a option -> ('a -> 'b option) -> 'b option = ` `bind` takes two arguments (a monadic object and a function from ordinary objects to monadic objects), and returns a monadic @@ -75,7 +77,7 @@ that provides at least the following three elements: 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 @@ -113,9 +115,9 @@ val unit : 'a -> 'a option = 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`. +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: