Question

A simple append function like this (in F#):

let rec app s t =
   match s with
      | [] -> t
      | (x::ss) -> x :: (app ss t)

will crash when s becomes big, since the function is not tail recursive. I noticed that F#’s standard append function does not crash with big lists, so it must be implemented differently. So I wondered: How does a tail recursive definition of append look like? I came up with something like this:

let rec comb s t =
   match s with
      | [] -> t
      | (x::ss) -> comb ss (x::t)
let app2 s t = comb (List.rev s) t 

which works, but looks rather odd. Is there a more elegant definition?

Answer 1

Traditional (not tail-recursive)

let rec append a b =
    match a, b with
    | [], ys -> ys
    | x::xs, ys -> x::append xs ys

With an accumulator (tail-recursive)

let append2 a b =
    let rec loop acc = function
        | [] -> acc
        | x::xs -> loop (x::acc) xs
    loop b (List.rev a)

With continuations (tail-recursive)

let append3 a b =
    let rec append = function
        | cont, [], ys -> cont ys
        | cont, x::xs, ys -> append ((fun acc -> cont (x::acc)), xs, ys)
    append(id, a, b)

Its pretty straight-forward to convert any non-tail recursive function to recursive with continuations, but I personally prefer accumulators for straight-forward readability.