From 0a621c3ef165f707ce3af6ca684fe5f8f8378316 Mon Sep 17 00:00:00 2001 From: Chris Barker Date: Mon, 1 Nov 2010 10:25:19 -0400 Subject: [PATCH] edits --- week7.mdwn | 34 +++++++++++++++++----------------- 1 file changed, 17 insertions(+), 17 deletions(-) diff --git a/week7.mdwn b/week7.mdwn index e4e884bc..8daff8a0 100644 --- a/week7.mdwn +++ b/week7.mdwn @@ -310,8 +310,8 @@ homework may recognize this last expression. You can think of the notation like this: take the singing box `u` and evaluate it (which includes listening to the song). Take the int contained in the singing box (the end result of evaluting `u`) and bind the variable -`x` to that int. So `x <- u` means "Sing me up an int, and I'll call -it `x`". +`x` to that int. So `x <- u` means "Sing me up an int, which I'll call +`x`". (Note that the above "do" notation comes from Haskell. We're mentioning it here because you're likely to see it when reading about monads. It won't work in @@ -372,8 +372,8 @@ them from hurting the people that use them or themselves. # let unit x = Some x;; val unit : 'a -> 'a option = - # let ( * ) u f = match u with None -> None | Some x -> f x;; - val ( * ) : 'a option -> ('a -> 'b option) -> 'b option = + # let ( >>= ) u f = match u with None -> None | Some x -> f x;; + val ( >>= ) : 'a option -> ('a -> 'b option) -> 'b option = The parentheses is the magic for telling OCaml that the function to be defined (in this case, the name of the function @@ -382,44 +382,44 @@ them from hurting the people that use them or themselves. # unit 2;; - : int option = Some 2 - # unit 2 * unit;; + # unit 2 >>= unit;; - : int option = Some 2 # let divide x y = if 0 = y then None else Some (x/y);; val divide : int -> int -> int option = # divide 6 2;; - : int option = Some 3 - # unit 2 * divide 6;; + # unit 2 >>= divide 6;; - : int option = Some 3 # divide 6 0;; - : int option = None - # unit 0 * divide 6;; + # unit 0 >>= divide 6;; - : int option = None * **Associativity: bind obeys a kind of associativity**. Like this: - (u * f) * g == u * (fun x -> f x * g) + (u >>= f) >>= g == u >>= (fun x -> f x >>= g) 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`. Some examples of associativity in the option monad: - # Some 3 * unit * unit;; + # Some 3 >>= unit >>= unit;; - : int option = Some 3 - # Some 3 * (fun x -> unit x * unit);; + # Some 3 >>= (fun x -> unit x >>= unit);; - : int option = Some 3 - # Some 3 * divide 6 * divide 2;; + # Some 3 >>= divide 6 >>= divide 2;; - : int option = Some 1 - # Some 3 * (fun x -> divide 6 x * divide 2);; + # Some 3 >>= (fun x -> divide 6 x >>= divide 2);; - : int option = Some 1 - # Some 3 * divide 2 * divide 6;; + # Some 3 >>= divide 2 >>= divide 6;; - : int option = None - # Some 3 * (fun x -> divide 2 x * divide 6);; + # Some 3 >>= (fun x -> divide 2 x >>= divide 6);; - : int option = None Of course, associativity must hold for *arbitrary* functions of @@ -433,11 +433,11 @@ computations will again result in `None`; and if the value of to `g y`. * **Right identity: unit is a right identity for bind.** That is, - `u * unit == u` for all monad objects `u`. For instance, + `u >>= unit == u` for all monad objects `u`. For instance, - # Some 3 * unit;; + # Some 3 >>= unit;; - : int option = Some 3 - # None * unit;; + # None >>= unit;; - : 'a option = None -- 2.11.0