What is the difference between the `fun` and `function` keywords?

The semantics for this is the same as in F# (probably because F# is based on OCaml):

• function allows the use of pattern matching (i.e. |), but consequently it can be passed only one argument.

  function p_1 -> exp_1 | … | p_n -> exp_n
  

  is equivalent to

  fun exp -> match exp with p_1 -> exp_1 | … | p_n -> exp_n
  

• fun does not allow pattern matching, but can be passed multiple arguments, e.g.

  fun x y -> x + y
  

When either of the two forms can be used, fun is generally preferred due to its compactness.

See also OCaml documentation on Functions.

The way I think about it

function patterns

is shorthand for

(fun x -> match x with patterns)

where 'patterns' is e.g.

| Some(x) -> yadda | None -> blah

(And

fun args -> expr

is how you define a lambda.)

Russ Cam is correct in his answer.

Here is a posting on the OCaml list talking about it

http://caml.inria.fr/pub/ml-archives/ocaml-beginners/2003/11/b8036b7a0c1d082111d7a83c8f6dbfbb.en.html

function only allows for one argument but allows for pattern matching, while fun is the more general and flexible way to define a function.

I generally use fun unless there is a good reason to use function.

You can see this in the code you posted where the fun declaration takes 3 arguments and the function declaration does pattern matching on it's input