How to break down 2-3-4 tree in OCAML

Question

I want to break down a 2-3-4 tree to small nodes.

These are the types I am using:

        type ele = int 
        type color = Red|Black
        type ab = Vide | Node of ( ele * color * ab * ab *ab) 
        type ab234 = Vide
        |Node_1 of (ele * ab234* ab234)
        |Node_2 of(ele * ele * ab234 *ab234 *ab234) ``
        |Node_3 of(ele * ele * ele *ab234 * ab234* ab234 *ab234)

I based my mapping on this:

I need help doing my transformation. I tried with this function but it doesn't seem to work, it does break down the root but it doesn't continue to the branches:

    let rec eclat = function
    | Vide -> Vide 
    | Node_3(r,x,y,ag,mg,md,ad) -> eclat ( Node_1(x,(Node_1(r,ag,mg)),Node_1(y,md,ad)))
    | Node_2(r,x,ag,ml,ad) -> eclat(Node_1(r,(Node_1(x,ag,ml)),ad))
    | _ -> failwith("zebi") ;;

Answer 1

If I enter your eclat function as you have it now, I get this:

Hint: If this is a recursive definition, you should add the 'rec' keyword on line 1

So that's one problem.

I also note that you changed ab to ab234, but you didn't change the internal appearances inside the type. So the contents of the ab234 type are all defined to be of type ab. This doesn't seem correct.