Question

UPDATE – Solution

Thanks to jacobm for his help, I came up with a solution.

// Folding Recursion
let reverse_list_3 theList = 
    List.fold_left (fun element recursive_call -> recursive_call::element) [] theList;;

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I’m learning about the different ways of recursion in OCaml (for class) and for some exercise, I’m writing a function to reverse a list using different recursion styles.

// Forward Recursion
let rec reverse_list_forward theList =
    match theList with [] -> [] | (head::tail) -> (reverse_list_1 tail) @ [head];;

// Tail Recursion
let rec reverse_list_tail theList result =
    match theList with [] -> result | (head::tail) -> reverse_list_2 tail (head::result);;

Now, I’m trying to write a reverse function using List.fold_left but I’m stuck and can’t figure it out. How would I write this reverse function using folding?

Also, if anyone has good references on functional programming, the different types of recursion, higher-order-functions, etc…, links would be greatly appreciated 🙂

Answer 1

I find it helpful to think of the fold operations as a generalization of what to do with a sequence of operations

a + b + c + d + e

fold_right (+) 0 applies the + operation right-associatively, using 0 as a base case:

(a + (b + (c + (d + (e + 0)))))

fold_left 0 (+) applies it left-associatively:

(((((0 + a) + b) + c) + d) + e)

Now consider what happens if you replace + with :: and 0 with [] in both right- and left-folds.

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It may also be useful to think about the way fold_left and fold_right work as “replacing” the :: and [] operators in a list. For instance, the list [1,2,3,4,5] is really just shorthand for 1::(2::(3::(4::(5::[])))). It may be useful to think of fold_right op base as letting you “replace” :: with op and [] with base: for instance

fold_right (+) 0 1::(2::(3::(4::(5::[]))))

becomes

1 + (2 + (3 + (4 + (5 + 0))))

:: became +, [] became 0. From this perspective, it’s easy to see that fold_right (::) [] just gives you back your original list. fold_left base op does something a bit weirder: it rewrites all the parentheses around the list to go the other direction, moves [] from the back of the list to the front, and then replaces :: with op and [] with base. So for instance:

fold_left 0 (+) 1::(2::(3::(4::(5::[]))))

becomes

(((((0 + 1) + 2) + 3) + 4) + 5)

With + and 0, fold_left and fold_right produce the same result. But in other cases, that’s not so: for instance if instead of + you used - the results would be different: 1 – (2 – (3 – (4 – (5 – 0)))) = 3, but (((((0 – 1) – 2) – 3) – 4) – 5) = -15.