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Date: Mon, 17 Apr 2006 15:09:36 +0200
From: Xavier Leroy <Xavier.Leroy@inria.fr>
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To: Tato Thetza <thetza@sent.com>
Cc: caml-list@yquem.inria.fr
Subject: Re: [Caml-list] recursion/iterator question
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> Given a list, I would like to iterate over all triplets in the list. For
> example, in mathematcs, its not uncommon to have expressions such as
> "for all i,j,k in set X, do f(i,j,k)"
>
> The only way I can think of is to create a list with all triplets of the
> list, so:
>   triplets([1,2,3,4]) = [(1,2,3),(1,2,4),(1,3,4),(2,3,4)]
> and take this list and map a function f to it.

Folds are more general than maps and tend to compose better.
Consider:

let list_fold_right_3 f l1 l2 l3 =
  List.fold_right
    (fun x1 -> List.fold_right (fun x2 -> List.fold_right (f x1 x2) l3) l2)
    l1

Examples:

# list_fold_right_3 (fun x y z a -> (x,y,z)::a) [1;2] [3;4] [5;6] [];;
- : (int * int * int) list =
[(1, 3, 5); (1, 3, 6); (1, 4, 5); (1, 4, 6); (2, 3, 5); (2, 3, 6); (2,
4, 5);
 (2, 4, 6)]
# list_fold_right_3 (fun x y z a -> (x+y+z)::a) [1;2] [3;4] [5;6] [];;
- : int list = [9; 10; 10; 11; 10; 11; 11; 12]
# list_fold_right_3 (fun x y z a -> x*y*z + a) [1;2] [3;4] [5;6] 0;;
- : int = 231

But, yes, if you find yourself doing this often, it's a good idea to
use the syntax extension for list comprehensions.

- Xavier Leroy