exo1.ml

let rec e1q1 n s = if n = 0 then "" else s ^ e1q1 (n-1) s

(* The current digit is n mod 10. The next digits are n/10. *)
let rec e1q2 n s = if n = 0 then "" else string_of_int (n mod 10) ^ s ^ (e1q2 (n/10) s)

let rec e1q3 n s = if n = 0 then "" else (e1q3 (n/10) s) ^ string_of_int (n mod 10) ^ s

let rec e1q4 n = if n = 0 then 0 else 1 + e1q4 (n/10)

let rec e1q5 n even =
  if n = 0 then true
  else
    let digit = n mod 10 in
    (if even then digit mod 2 = 0 else digit mod 2 = 1) && e1q5 (n/10) even

(* Another version. *)
let e1q5 n even =
  let accept = if even then fun x -> x mod 2 = 0 else fun x -> x mod 2 = 1 in
  let rec loop n = n = 0 || (accept n && loop (n/10)) in
  loop n
    
let rec e1q6 n m =
  if n = 0 && m = 0 then true
  else n mod 10 <= m mod 10 && e1q6 (n / 10) (m / 10)

(* Curried functions *)

let curry3 f a b c = f (a,b,c)
    
let uncurry3 f (a,b,c) = f a b c

let apply3 (f,g,h) (a,b,c) = (f a, g b, h c)

let sort2 f g x = if f x < g x then (f,g) else (g,f)

let comp3 f g h x = f (g (h x))

(* Pattern matching *)

(* We list all the cases, using the 'whatever' pattern _, and factorizing a few patterns. *)
let ext_and a b c = match (a,b,c) with
  | false, _, true
  | _, false, true -> false
    
  | false, _, false
  | _, false, false -> true
    
  | true, true, true -> true
  | true, true, false -> false 

let code_char = function
  | 'a' -> 'e'
  | 'e' -> 'i'
  | 'o' -> 'a'
  | 'i' -> 'y'
  | 'u' -> 'o'
  | 'y' -> 'u'
  | 'A' -> 'E'
  | 'E' -> 'I'
  | 'O' -> 'A'
  | 'I' -> 'Y'
  | 'U' -> 'O'
  | 'Y' -> 'U'
  | c -> c

let encode s = String.map code_char s