(* --- recursive functions --- *)

(* From Section 1.12 *)


fun factorial(0) = 1
  | factorial(n) = n * factorial(n-1);


(* Ex 1.12.4. Homemade multiply  *)
fun multiply(x, 0) = 0
  | multiply(x, y) = x + multiply(x, y-1);


(* Ex 1.12.6.  Summation. *)
fun sum(1) = 1
  | sum(n) = n + sum(n-1);


(* --- list functions  (didn't get to, we'll do these next time) --- *)

(* examples from the text *)

fun repeatEach([]) = []
  | repeatEach(a::rest) = a::a::repeatEach(rest);

fun sum([]) = 0
  | sum(a::rest) = a + sum(rest);

fun switchPair([]) = []
  | switchPair((a,b)::rest) = (b, a)::switchPair(rest);



(* 2.2.4 -- in class*)
fun count([]) = 
    | count(a::rest) = 


(* 2.2.5 -- in class *)
fun findIth([], i) = (print("item not found"); ~1)
  | findIth(a::rest, 0) =
  | findIth(a::rest, i) =


(* 2.2.6 -- in class *)
fun reverse([]) =
  | reverse(a::rest) = 


(* Ex 2.2.10 -- in class *)
fun listify([]) =
  | listify(a::rest) = 



(* Ex 2.2.12 -- in class *)
fun splitList([]) =
 | splitList((a,b)::rest) = 
    let val (aRest, bRest) =
    in
        
   end;

(* sample use of splitlist: *)

splitList([(1,2), (3,4), (5,6)]);

(* results in ([1,3,5],[2,4,6])  *)


(* problems below marked "homework" assigned 1/28, due 1/30 *)

(* Ex 2.2.13 -- homework  *)
fun tuplify([], []) = []
  | tuplify(a::rest, []) =  ?? 
  | tuplify([], b::rest) =  ??
  | tuplify(a::aRest, b::bRest) =  ??


(* Ex 2.2.14 -- in class *)
fun sumPairs([]) = 
  | sumPairs((a,b)::rest) = 


(* Ex 2.2.15  -- homework *)
fun sumPairList([]) = (0, 0)
  | sumPairList((a,b)::rest) =
    let val (c, d) = sumPairList(rest)
    in
        ??
    end;

(* Extra hint on sumPairList: use splitList (above) as a pattern to follow. 
    Sample us of sumPairList: *)
sumPairList([(1,2), (3,4), (5,6)]);

(* Result should be (9, 12), that is, (1+3+5, 2+4+6) *)