fun testEven([]) = []
  | testEven(x::rest) = (x mod 2 = 0) :: testEven(rest);

fun scale(f, []) = []
  | scale(f, x::rest) = x * f :: scale(f, rest);

fun makeReals([]) = []
  | makeReals(x::rest) = real(x)::makeReals(rest);

fun listify([]) = []
  | listify(x::rest) = [x]::listify(rest);

fun applyFunToList(f, []) = []
  | applyFunToList(f, a::rest) =
    f(a)::applyFunToList(f, rest);

fun map(f, []) = []
  | map(f, a::rest) = f(a)::map(f, rest);

fun testEven(xx) = map(fn (x) => x mod 2 = 0, xx);

fun scale(f, xx) = map (fn (x) => f * x, xx);

fun makeReals(xx) = map(real, xx);

fun listify(xx) = map(fn(x) => [x], xx);


fun keepEvens([]) = []
  | keepEvens(a::rest) = 
    if a mod 2 = 0 
    then a::keepEvens(rest) 
    else keepEvens(rest);

fun contains(x, []) = false
  | contains(x, y::rest) =
     x = y orelse contains(x, rest);

fun intersection([], bb) = []
  | intersection(a::rest, bb) = 
    if contains(a, bb) 
    then a::intersection(rest, bb) 
    else intersection(rest, bb);

fun filter(f, []) = []
  | filter(f, a::rest) = 
    if f(a) 
    then a::filter(f, rest) 
    else filter(f, rest);

fun keepEvens(xx) = 
    filter(fn(x) => x mod 2 = 0, xx);

fun intersection(aa, bb) = 
    filter(fn(x) => contains(x, bb), aa);