Question

In OCaml, for list, we always do first::rest. it is convenient to get the first element out of a list, or insert an element in front of a list.

But why does OCaml not have rest::last? Without List‘s functions, we can’t easily do getting last element of a list or insert an element to the end of a list.

Answer 1

The list datatype is not a magic builtin, only a regular recursive datatype with some syntactic sugar. You could implement it yourself, using Nil instead of [] and Cons(first,rest) instead of first::rest, in the following way:

type 'a mylist =
  | Nil
  | Cons of 'a * 'a mylist

I’m not sure if you will see the definition above as an answer to your question, but it really is: when you write first::rest, you’re not calling a function, you’re just using a datatype constructor that builds a new value (in constant time and space).

This definition is simple and has clear algorithmic properties: lists are immutable, accessing the first element of the list is O(1), accessing the k-th element is O(k), concatenation of two lists li1 and li2 is O(length(li1)), etc. In particular, accessing the last element or adding something at the end of a list li would be O(length(li)); we’re not eager to expose this as a convenient operation because it is costly.

If you want to add elements at the end of a sequence, lists are not the right data structure. You may want to use a queue (if you follow a first-in, first-out access discipline), a deque, etc. There is a (mutable) Queue structure in the standard library, and the two third-party overlays Core and Batteries have a deque module (persistent in Batteries, mutable in Core).