(*Maximum*)
    let max2 a b = if a >. b then a else b;;
    let max3 a b c = max a (max b c);;

(*Contr�le de type*)
    let equal x y = if x = y then true else false ;;
    (* equal : 'a -> 'a -> bool = <fun> *)
    let Entre3et5 x = (x > 3) & (x < 5) ;;
(* Entre3et5 : int -> bool = <fun> *)
    let Test0 x y = if (Test1 x) then 3 else 4;;
    (* The value identifier Test1 is unbound. *)
    (* ou bien si on d�clare Test1 avant Test0 *)
(* Test1 x: This expression has type int, but is used with type bool.*)
    let Test1 x = if Entre3et5 x = false then 1 else 2 ;;
(* Test1 : int -> int = <fun> *)
    let Test2 x = if equal (Entre3et5 x) false then true else false ;;
(* Test2 : int -> bool = <fun> *)
    let Test3 x y = let z = if(Test1 x) then 3 else 4 in z +. y;;
(* Test1 x : This expression has type int, but is used with type bool.*)
    let Test4 x y = if equal x y then Test1 x else Test2 y;;
(* Test2 y : This expression has type bool,but is used with type int.*)
    let Test5 x = if not (Entre3et5 x) then 1 else 2 ;;
(* Test5 : int -> int = <fun> *)
    let Test6 x y = if Entre3et5 x then not(Entre3et5 y);;
(* This expression has type unit,but is used with type bool.*)
    let Test7 x y = x + if(x>=y) then "bonjour" else "au revoir";;
(* This expression has type string, but is used with type int.*)

(*Fonctions bool�ennes*)
    (function x -> not(not x));;
    (*              booleen  --> booleen                                     *)
    (*                    x |--> x                                           *)
    (function x -> (x or (not x)));;
    (*              booleen  --> booleen                                     *)
    (*                    x |--> vrai                                        *)
    (function x -> function y -> (not x) or y);;
    (*    booleen X booleen  --> booleen                                     *)
    (*          (vrai,vrai) |--> vrai                                        *)
    (*          (vrai,faux) |--> faux                                        *)
    (*          (faux,vrai) |--> vrai                                        *)
    (*          (faux,faux) |--> vrai                                        *)
    (function x -> function y -> (not x) & (not y));;
    (*    booleen X booleen  --> booleen                                     *)
    (*          (vrai,vrai) |--> faux                                        *)
    (*          (vrai,faux) |--> faux                                        *)
    (*          (faux,vrai) |--> faux                                        *)
    (*          (faux,faux) |--> vrai                                        *)
    (function x -> function y -> (not(not y)) or (not x));;
    (*    booleen X booleen  --> booleen                                     *)
    (*          (vrai,vrai) |--> vrai                                        *)
    (*          (vrai,faux) |--> faux                                        *)
    (*          (faux,vrai) |--> vrai                                        *)
    (*          (faux,faux) |--> vrai                                        *)

    let ouex a b = if a then not b else b;;
    let ouex a b = not (Equivalent a b);;
    let equivalent a b = if a then b else not b;;

    let NOU a b = not a & not b ;;
    let NET a b = not a or not b ;;
    let IMP a b = not a or b ;;
    let IMP2 a b = not ( a & not b) ;;
    let EQUIV a b = not ( a & not b) & not ( b & not a) ;;
    let EQUIV2 a b = (not a or b) & (not b or a);;

(*Ann�e bissextile*)
    let bissextile a =
        if (a mod 4) = 0 then
            if (a mod 100) = 0 then
                if (a mod 400)= 0 then
                    true
                else
                    false
            else
                true
        else
            false ;;

    (*Aire d'une couronne*)
    let pi = acos (-1) ;;
    let aire_cercle r = pi *. r *. r ;;

    let aire_couronne r1 r2 =
        if r2 >. r1 then 
            aire_cercle r2 -. aire_cercle r1
        else 
            aire_cercle r1 -. aire_cercle r2 ;;

(*Facture*)
    let facturation1 q p =
        if p *. q > 100. then 
            p *. q
        else 
            1.1 *. p *. q ;;

    let facturation2 q p =
        if p *.q > 100. then 
            p *. q
        else 
            if 0.1 *. p *. q < 2. then 
                p *. q +. 2.
            else 
                1.1 *. p *. q ;;

    (*Nombre de solutions r�elles d'une �quation du second degr�*)
    let nb_sol a b c =
        let discriminant =  b *. b -. 4. *. a *. c in
            if discriminant > 0. then 
                2
            else 
                if discriminant < 0. then 
                    0
                else 
                    1 ;;

(*Imp�t sur le revenu*)
    let calc_revenu_net_imposable revenu frais =
        let apres_premier_abattement = 0.8 *. revenu in
        let forfait = 0.1 *. apres_premier_abattement in
        
        if forfait > frais then 0.9 *. 
            apres_premier_abattement
        else 
            apres_premier_abattement -. frais;;

    let calc_quotient_familial revenu_net_imposable nb_part = revenu_net_imposable /. nb_part;;

    let calc_impot_brut quotient_familial revenu_net_imposable nb_part =
        if quotient_familial <= 25890. then 0.0
        else if quotient_familial <= 50930. then revenu_net_imposable *. 0.105 -. nb_part *. 2718.45
        else if quotient_familial <= 89650. then revenu_net_imposable *. 0.24 -. nb_part *. 9594.
        else if quotient_familial <= 145160. then revenu_net_imposable *. 0.33 -. nb_part *. 17662.5
        else if quotient_familial <= 236190. then revenu_net_imposable *. 0.43 -. nb_part *. 32178.5
        else if quotient_familial <= 291270. then revenu_net_imposable *. 0.48 -. nb_part *. 43988.
        else revenu_net_imposable *. 0.54 -. nb_part *. 61464.2;;

    let impot revenu frais nb_part =
        let revenu_net_imposable = calc_revenu_net_imposable revenu frais in
        let quotient_familial = calc_quotient_familial revenu_net_imposable nb_part in
        let impot_brut = calc_impot_brut quotient_familial revenu_net_imposable nb_part in
        
        if impot_brut >=. 3300. then 
            impot_brut
        else
            let decote = 3300. -. impot_brut in
            let final = impot_brut -. decote in
            if final < 400. then 
                0.
            else 
                final;;