Stack overflow during evaluation (looping recursion?)

i’m new to ocaml and i’m trying to create a function that takes an int list and turn it into a list of int list that are have the first element + the second element, followed by the rest of the list, until there is one element left, for example:

[1; 2; 0; 4; 2; 1] 
[3; 0; 4; 2; 1]
[3; 4; 2; 1]
[7; 2; 1]
[9; 1]
[10]

And here is my code:

let rec nth l k =
  match l with
  | [] -> 0
  | s::t -> if k = 0 then s else nth t (k - 1);;

let no_first l =
  match l with
  | [] -> []
  | s::t -> t

let rec left_comp_once l =
  match l with
  | [] -> []
  | s::t -> (s + nth t 0) :: no_first t

let rec left_comps l =
  match l with 
  | [] -> []
  | s::t -> let x = (s + nth t 0) :: no_first t in
      [x] @ left_comps x

The left_comp_once function works, however, i get looping recursion error when i try the left_comps function

I cannot figure out where the issue is coming from

Also, i would like to have a return element in this format:

int list -> (int list) list

However, what i wrote gives me:

int list -> int list list

What do these parenthesis imply ?

>Solution :

If you look at this expression:

let x = (s + nth t 0) :: no_first t in
      [x] @ left_comps x

you can see that x can’t possibly be an empty list. It always has at least one element. Therefore left_comps will never terminate when given a non-empty list.