(* 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);


(* Wrong! *)
fun sumProduct([]) = (0, 1)
  | sumProduct(x::rest) = 
(*
        (x + #1(sumProduct(rest)),
               x * #2(sumProduct(rest)));
*)

        let val (a, b) = sumProduct(rest)
        in
        (x +a, x * b)
        end;

(* 2.2.4 -- in class*)
fun count([]) = 0
    | count(a::rest) = 1 + count(rest);


(* 2.2.5 -- in class *)
fun findIth([], i) = ~1
  | findIth(a::rest, 0) = a
  | findIth(a::rest, i) = findIth(rest, i - 1);


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


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



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


(* 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) = (a + b)::sumPairs(rest);


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



(* For the homework assigned next time (for Jan 27) *)

(* Ex 2.4.14 -- homework *)
(* The second parameter is a list of lists *)
fun addToEach(x, []) = ??
  | addToEach(x, aa::rest) = ??     (* aa is itself a list ! *)

(* Ex 2.4.15  -- homework *)
fun powerset([]) = ??    (* Think carefully: What is the powerset of the empty set? *)
  | powerset(a::rest) = ??