The difference of the function keyword and match with in OCaml

Question

I'm currently learning OCaml today I came up to this piece of code.

let rec tree_to_list acc = function
  | Leaf x -> x::acc
  | Node (t1,t2) -> tree_to_list (tree_to_list acc t2) t1

As far as I understand this function does the same than this one

let rec tree_to_list2 acc t = match t with
  | Leaf x -> x::acc
  | Node (t1, t2) -> tree_to_list t1 (tree_to_list2 acc t2)

However, I do not understand the syntax behind the first function. I find the keyword function confusing. It is supposed to take one argument only such as :

function x -> x + 2

Could someone please help me understand the syntax of the first function and if any the difference in terms of how both functions are evaluated. Thanks in advance.

Answer 1

Functions in OCaml are defined by giving patterns for the arguments. The common case of a simple variable name (like acc in your first function) is just a particular kind of pattern that matches all values.

So, one way to look at it is that fun defines a function with any number of arguments that can each be given by one pattern. On the other hand, function defines a function with one argument that can be given by any number of patterns.

# let dot = fun (a, b) (c, d) -> a *. c +. b *. d
val dot : float * float -> float * float -> float = <fun>

# let geti = function None -> 0 | Some i -> i;;
val geti : int option -> int = <fun>

The fun form can, in essence, be absorbed into the left hand side of a let to give a more concise notation.

That is,

let f = fun p1 p2 -> ...

can be written as

let f p1 p2 = ...

So for example:

let dot (a, b) (c, d) = a *. c +. b *. d

Your first function is using a combination of the two (a concise fun and a function on the right).