While or Tail Recursion in F#, what to use when?

Question

Ok, only just in F# and this is how I understand it now :

• Some problems are recursive in nature (building or reading out a treestructure to name just one) and then you use recursion. In these cases you preferably use tail-recursion to give the stack a break

• Some languagues are pure functional, so you have to use recursion in stead of while-loops, even if the problem is not recursive in nature

So my question : since F# also support the imperative paradigm, would you use tail recursion in F# for problems that aren't naturally recursive ones? Especially since I have read the compiler recongnizes tail recursion and just transforms it in a while loop anyway?

If so : why ?

Answer 1

The best answer is 'neither'. :)

There's some ugliness associated with both while loops and tail recursion.

While loops require mutability and effects, and though I have nothing against using these in moderation, especially when encapsulated in the context of a local function, you do sometimes feel like you're cluttering/uglifying your program when you start introducing effects merely to loop.

Tail recursion often has the disadvantage of requiring an extra accumulator parameter or continuation-passing style. This clutters the program with extra boilerplate to massage the startup conditions of the function.

The best answer is to use neither while loops nor recursion. Higher-order functions and lambdas are your saviors here, especially maps and folds. Why fool around with messy control structures for looping when you can encapsulate those in reusable libraries and then just state the essence of your computation simply and declaratively?

If you get in the habit of often calling map/fold rather than using loops/recursion, as well as providing a fold function along with any new tree-structured data type you introduce, you'll go far. :)

For those interested in learning more about folds in F#, why not check out my first three blog posts in a series on the topic?

Answer 2

In order of preference and general programming style, I will write code as follows:

Map/fold if its available

let x = [1 .. 10] |> List.map ((*) 2)

Its just convenient and easy to use.

Non-tail recursive function

> let rec map f = function
    | x::xs -> f x::map f xs
    | [] -> [];;

val map : ('a -> 'b) -> 'a list -> 'b list

> [1 .. 10] |> map ((*) 2);;
val it : int list = [2; 4; 6; 8; 10; 12; 14; 16; 18; 20]

Most algorithms are easiest to read and express without tail-recursion. This works particularly well when you don't need to recurse too deeply, making it suitable for many sorting algorithms and most operations on balanced data structures.

Remember, log₂(1,000,000,000,000,000) ~= 50, so log(n) operation without tail-recursion isn't scary at all.

Tail-recursive with accumulator

> let rev l =
    let rec loop acc = function
        | [] -> acc
        | x::xs -> loop (x::acc) xs
    loop [] l

let map f l =
    let rec loop acc = function
        | [] -> rev acc
        | x::xs -> loop (f x::acc) xs
    loop [] l;;

val rev : 'a list -> 'a list
val map : ('a -> 'b) -> 'a list -> 'b list

> [1 .. 10] |> map ((*) 2);;
val it : int list = [2; 4; 6; 8; 10; 12; 14; 16; 18; 20]

It works, but the code is clumsy and elegance of the algorithm is slightly obscured. The example above isn't too bad to read, but once you get into tree-like data structures, it really starts to become a nightmare.

Tail-recursive with continuation passing

> let rec map cont f = function
    | [] -> cont []
    | x::xs -> map (fun l -> cont <| f x::l) f xs;;

val map : ('a list -> 'b) -> ('c -> 'a) -> 'c list -> 'b

> [1 .. 10] |> map id ((*) 2);;
val it : int list = [2; 4; 6; 8; 10; 12; 14; 16; 18; 20]

Whenever I see code like this, I say to myself "now that's a neat trick!". At the cost of readability, it maintains the shape of the non-recursive function, and found it really interesting for tail-recursive inserts into binary trees.

Its probably my monad-phobia speaking here, or maybe my inherent lack of familiarity with Lisp's call/cc, but I think those occasions when CSP actually simplifies algorithms are few and far between. Counter-examples are welcome in the comments.

While loops / for loops

It occurs to me that, aside from sequence comprehensions, I've never used while or for loops in my F# code. In any case...

> let map f l =
    let l' = ref l
    let acc = ref []
    while not <| List.isEmpty !l' do
        acc := (!l' |> List.hd |> f)::!acc
        l' := !l' |> List.tl
    !acc |> List.rev;;

val map : ('a -> 'b) -> 'a list -> 'b list

> [1 .. 10] |> map ((*) 2);;
val it : int list = [2; 4; 6; 8; 10; 12; 14; 16; 18; 20]

Its practically a parody of imperative programming. You might be able to maintain a little sanity by declaring let mutable l' = l instead, but any non-trivial function will require the use of ref.