(******** 7.2 *******)
(* Define a function member of type ''a * ''a list -> bool
so that member(e, L) is true if and only if e is an element of the list L. *)

(* Correct, but non-pattern matching version: 
fun member (e, L) =
  if null L 
     then false
     else if e = hd(L) 
             then true
             else member (e, tl(L));
*)

fun member (e, nil) = false
 |  member (e, x::xs) = if (e=x) 
                          then true
                          else member(e, xs);

member (1, []);
member (1, [1, 2]);
member (1, [2, 1, 3]);
member (1, [2, 3]);


(*********** 7.3 *************)
(* Define a function less of type int * int list -> int list
   so that less (e, L) is a list of all the integers in L that 
   are less than e  
*)

(* Correct, but non-pattern matching version:
fun less (e, L) =
  if null L
    then nil
    else if hd(L) < e
           then hd(L) :: less(e, tl(L))
           else less (e, tl(L));
*)

fun less (e, nil) = nil
 |  less (e, x::xs) = if x < e
                        then x :: less(e, xs)
                        else less (e, xs);


(************ 7.4 *****************)
(* Define a function repeats of type ''a list -> bool so that
   repeats (L) is true if and only if the list L has two equal
   elements next to each other
*)

(* Correct, but non-pattern matching version:
fun repeats (L) =
  if null L orelse null(tl(L)) 
    then false
    else if hd(L) = hd(tl(L)) then true
                              else repeats (tl(L));
*)

fun repeats (nil) = false
 |  repeats (x::nil) = false
 |  repeats (x::xs) = if x = hd(xs) then true
                                    else repeats(xs);