(* ML ASSESSED EXERCISES. TICK 6 SUBMISSION *)

(* PROBLEM 1. Definition of integer streams                   *)

datatype stream = Item of int * (unit->stream);
fun cons (x,xs) = Item(x, xs);
fun head (Item(i,xf)) = i;
fun tail (Item(i,xf)) = xf();
fun makeints n = cons(n, fn()=> makeints(n+1));

(* PROBLEM 2. A function maps that applies a function to all  *)
(*            elements in the stream                          *)

fun maps f xs = cons(f (head xs), fn()=> maps f (tail xs));

(* PROBLEM 3. A function nth that returns the nth element of  *)
(*            a stream s                                      *)

fun nth(s,1)=head(s)
  | nth(s,n)=nth(tail(s),n-1);

(* PROBLEM 4. A function filters that returns a stream of all *)
(*            elements of a stream xs that satisfy f          *)

fun filters f xs=if f(head(xs)) then
                   cons(head xs,fn()=>filters f (tail xs))
                 else
                   filters f (tail xs);