type zbarre = Relatif of int | MoinsInf | PlusInf ;;type intervalle = {g : zbarre ; d : zbarre} ;;(* Q5 *)let intervalle_of_bornes p q =  if p > q then raise (Invalid_argument "intervalle_of_bornes")          else {g = Relatif p ; d = Relatif q} ;;(* Q6 *)let dd_g q = {g = MoinsInf ; d = Relatif q} ;;let dd_d p = {g = Relatif p ; d = PlusInf} ;;(* Q7 *)let z_pr�c�de_strict x y = match (x,y) with  | (MoinsInf,PlusInf) -> true  | (MoinsInf,Relatif _ ) -> true  | (Relatif _,PlusInf) -> true  | (Relatif p,Relatif q) -> p < q  | (_,_) -> false ;; let prefix << = z_pr�c�de_strict ;;let z_pr�c�de_large x y = (x = y) or (x << y) ;;(* Q8 *)let z_cons�cutifs x y = match (x,y) with  | (Relatif p,Relatif q) when q = p + 1 -> true  | (_,_) -> false ;;(* Q9 *)let cons�cutifs u v = z_cons�cutifs u.d v.g ;;let est_avant u v =  u.g << v.g or (u.g = v.g & u.d << v.d);; (* Q10 *)let est_�_gauche_de u v = u.d << v.g ;;(* let contient u v = (z_pr�c�de_large u.g v.g) & (z_pr�c�de_large v.d u.d) ;; *)let rec compacter l = match l with  | [] -> []  | [i] -> [i]  | u::v::q when cons�cutifs u v -> let t = {g = u.g ; d = v.d} in compacter (t::q)  | u::v::q when est_�_gauche_de u v -> let q' = compacter (v::q) in u::q'  | u::v::q when z_pr�c�de_large u.d v.d    -> let t = {g = u.g ; d = v.d} in compacter (t::q)  | u::v::q -> let t = {g = u.g ; d = u.d} in compacter (t::q) ;;(* Q11 *)let r�duire l = let l1 = sort__sort est_avant l in  compacter l1 ;;(* Q12, m�thode bestiale *)let union l1 l2 = r�duire (l1 @ l2) ;;let i1 = intervalle_of_bornes 13 17  and i2 = intervalle_of_bornes 15 22  and i3 = intervalle_of_bornes 0 5  and i4 = dd_g 2  and i5 = dd_d 19 ;;(* Q13 *)let successeur = function  | Relatif p -> Relatif (p+1)  | _ -> raise (Invalid_argument "successeur") ;; let pr�d�cesseur = function  | Relatif p -> Relatif (p-1)  | _ -> raise (Invalid_argument "pr�d�cesseur") ;; let fin_compl�mentaire = function  | {g = _ ; d = PlusInf} -> []  | {g = _ ; d = Relatif p} -> [dd_d (p+1)]  | {g = _ ; d = MoinsInf} -> raise (Invalid_argument "fin_compl�mentaire") ;; let rec suite_compl�mentaire = function  | [u] -> fin_compl�mentaire u  | u::v::q -> let t' = {g = successeur u.d ; d = pr�d�cesseur v.g}    in t'::(suite_compl�mentaire (v::q))  | [] -> raise (Invalid_argument "suite_compl�mentaire") ;; let compl�mentaire_bis = function  | [] -> [{g = MoinsInf ; d = PlusInf}] | {g = MoinsInf ; d = _} as t::q -> suite_compl�mentaire (t::q)  | {g = Relatif p ; d = _} as t::q ->    let t' = {g = MoinsInf ; d = Relatif (p-1)}     in t'::(suite_compl�mentaire (t::q))  | {g = PlusInf ; d = _}::_ -> raise (Invalid_argument "compl�mentaire") ;; let compl�mentaire l = compl�mentaire_bis(r�duire l) ;;(* Q14 *)let intersection l1 l2 =  let l1' = compl�mentaire(r�duire l1) and l2' = compl�mentaire(r�duire l2)  in compl�mentaire (union l1' l2') ;;let j1 = intervalle_of_bornes 1 4 and j2 = dd_g 20 ;;let l1 = [i1;i5;i3;i4;i2] and l2 = [j1;j2];;