//////////////////////////////////////////////////////////////////////////////
//
// list functions
//
//////////////////////////////////////////////////////////////////////////////

map func list = 
    if (empty list) then
        []
    else
        func (head list) :: map func (tail list);

map2 func list1 list2 = 
    if (empty list1) then
        []
    else
        func (head list1) (head list2) :: map2 func (tail list1) (tail list2);

nth index list =
    if (equal index 0) then
        head list
    else
        nth (index - 1) (tail list);

firstn index list =
    if (equal index 0) then
        []
    else
        head list :: firstn (index - 1) (tail list);

aftern index list =
    if (empty list) then
        []
    else if (equal index 0) then
        list
    else
        aftern (index - 1) (tail list);

middlen min max list =
    firstn (max - min) (aftern min list);

filter func list =
    if (empty list) then
        []
    else if (func (head list)) then
        head list :: filter func (tail list)
    else
        filter func (tail list);

//////////////////////////////////////////////////////////////////////////////
//
// Junk
//
//////////////////////////////////////////////////////////////////////////////

integers = 1 :: map (1 +) integers;
fib = 1 :: 2 :: map2 add fib (tail fib);

//////////////////////////////////////////////////////////////////////////////
//
// TypeDelay
//
//////////////////////////////////////////////////////////////////////////////

removens n list =
    filter (function x -> not (equal (mod x n) 0)) list;

makeprimes numbers = 
    head numbers :: makeprimes (removens (head numbers) numbers);

primes = makeprimes (tail integers);

diff = map2 sub (tail primes) primes;

result = middlen 0 10 primes;