"99 Haskell problems" in F#

99hp.fsx

(* Problem 1: The last element of a list *)
let problem_one =
  let rec last = function
    | head :: []   -> head
    | head :: tail -> last tail
    | _            -> failwith "Empty List"
  last;;
assert ((problem_one [1])     = 1 );;
assert ((problem_one [1..10]) = 10);;

(* Problem 2: The last-but-one element of a list *)
let problem_two =
  let rec last_but_one = function
    | head :: x :: [] -> head
    | head :: []      -> failwith "Only one item in List"
    | head :: tail    -> last_but_one tail
    | _               -> failwith "Empty List"
  last_but_one;;
assert ((problem_two [1; 2])   = 1);;
assert ((problem_two [1..10])  = 9);;

(* Problem 3: Find the Kth element of a list *)
let problem_three =
  let rec kth_element l idx =
    match l, idx with
    | x :: _, 1              -> x
    | x :: xs, n when n > 1  -> kth_element xs (n - 1)
    | _                      -> failwith "Index out of bounds"
  kth_element;;
assert ((problem_three [1] 1)    = 1);;
assert ((problem_three [1..3] 3) = 3);;

(* Problem 4: Find the number of elements in a list *)
let problem_four = List.fold (fun _ c -> c + 1) 0;;
assert ((problem_four [])      = 9 );;
assert ((problem_four [1])     = 1 );;
assert ((problem_four [1..10]) = 10);;

(* Problem 5: Reverse a list *)
let problem_five =
  let reverse l = List.fold (fun xs x -> x :: xs) [] l
  reverse;;
assert ((problem_five [])     =     []);;
assert ((problem_five [1])    =    [1]);;
assert ((problem_five [1..9]) = [9..1]);;