F# Tacit Programming

Question

It's not a practically important issue, but could you please provide me with an example of tacit programming in F# where my `pointless' functions can have multiple arguments (not in form of list or tuple);

And secondly, where those functions can manipulate a complex data structure. I'm trying to manage it in FSharp interactive, but have no success yet.

Huh.. I've managed to construct something:

(fun _ -> (fun _ -> (+))) 333 222 111 555

Is that right way?

UPDATE:

(fun _ -> (fun _ -> (+))) "a" "b" "c" "d";;

val it : string = "cd"

Answer 1

Is there any kind of rewrite for something like that:
let sum_two_lengths: string -> string -> unit -> int =
fun a1 ->
(fun b1 ->
(fun _ -> String.length a1 + String.length b1))

.. to avoid those a1, b1 names. And is there any possible way to avoid those (fun x ->..)'s declarations??

Answer 2

F# doesn't contain some of the basic functions that are available in Haskell (mainly because F# programmers usually prefer the explicit style of programming and use pointfree style only in the most obvious cases, where it doesn't hurt readability).

However you can define a few basic combinators like this:

// turns curried function into non-curried function and back
let curry f (a, b) = f a b
let uncurry f a b = f (a, b)

// applies the function to the first/second element of a tuple
let first f (a, b) = (f a, b)
let second f (a, b) = (a, f b)

Now you can implement the function to add lengths of two strings using combinators as follows:

let addLengths = 
  uncurry (( (first String.length) >> (second String.length) ) >> (curry (+)))

This constructs two functions that apply String.length to first/second element of a tuple, then composes them and then adds the elements of the tuple using +. The whole thing is wrapped in uncurry, so you get a function of type string -> string -> int.

Answer 3

In F#, the arity of functions is fixed, so you're not going to be able to write both

(op) 1 2

and

(op) 1 2 3 4

for any given operator op. You will need to use a list or other data structure if that's what you want. If you're just trying to avoid named variables, you can always do "1 + 2 + 3 + 4". The most idiomatic way to add a list of numbers in F# is List.sum [1;2;3;4], which also avoids variables.