How do these two function definitions in OCaml differ?

Question

I have seen some implementation as follows:

let rec fact =
  fun n ->
    if n <= 0 then 1 else n * fact (n - 1)

Another implementation is:

let rec fact n =
  if n <= 0 then 1 else n * fact (n - 1)

Could anyone tell me if there is any difference between these 2 styles?

Answer 1

These definitions are equivalent. The notation

let rec f a b c = <expr>

is a handy way of writing (syntactic sugar for):

let rec f = fun a b c -> <expr>

You can find this described in section 6.7.1 of the OCaml manual, under the heading Local definitions.