Write a function which multiplies a given number by ten. What is its type?

(* int -> int *)
let times_ten x =
  x * 10
;;

Write a function which returns true if both of its arguments are non-zero, and false otherwise. What is the type of your function?

(* int -> int -> bool *)
let non_zeros x y =
  x <> 0 && y <> 0
;;

Write a recursive function which, given a number n, calculates the sum 1 + 2 + 3 + ... + n. What is its type?

(* int -> int *)
let rec sum_up_to n =
  if n = 0 then n else n + sum_up_to (n - 1)
;;

Write a function power x n which raises x to the power n. Give its type.

(* int -> int -> int *)
let rec power x n =
  if n = 0 then 1 else
    if n = 1 then x else
      x * power x (n - 1)
;;

Write a function isconsonant which, given a lower-case character in the range 'a'...'z', determines if it is a consonant.

(* char -> bool *)
let is_consonant c =
  c <> 'a' && c <> 'e' && c <> 'i' && c <> 'o' && c <> 'u'
;;

What is the result of the expression let x = 1 in let x = 2 in x + x?

4;; (* because shadowing *)

Can you suggest a way of preventing the non-termination of the factorial function in the case of a zero or negative argument?

(* we could return zero in those cases *)
let rec factorial x =
  if x <= 0 then 0 else
    if x = 1 then 1 else
      x * factorial (x - 1)
;;