X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=week7.mdwn;h=52bc8eb5d2e9855e872cfca13bc469d1582e8b36;hp=812f0496194160a66ec5fef774a848be07e2cc4d;hb=80761171a28334806b396982c66e7f8ff4267eec;hpb=5eb5b091a62e66068007e326cc97ea1faaad2960;ds=sidebyside diff --git a/week7.mdwn b/week7.mdwn index 812f0496..52bc8eb5 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 @@ -190,7 +192,7 @@ though without explicitly using monads. All of the code in the discussion below can be found here: [[intensionality-monad.ml]]. To run it, download the file, start Ocaml, and say `# #use -"intensionality-monad.ml"`. +"intensionality-monad.ml";;`. Here's the idea: since people can have different attitudes towards different propositions that happen to have the same truth value, we