Lazy functional languages like Haskell and Miranda support features that are not found in other programming languages, including infinite lists. Consider the following simple (and useful) recursive declaration:
letrec
count n = cons n (count (n+1))
in
count 0
The function cons constructs lists, so the above declaration creates the following structure:
cons 0 (count 1)
= cons 0 (cons 1 (count 2))
= cons 0 (cons 1 (cons 2 ...))
= [0,1,2,...]
Lazy languages can do this because they only evaluate expressions that are actually used. If a program creates an infinite list and only looks at items 2 and 3 in it, the values in positions 0 and 1 are never evaluated and the list structure is only evaluated so far as the fourth node.
It is also possible to use more than one function to build an infinite list. Here is a declaration that creates the list ["even","odd","even",...]:
letrec
even = cons "even" odd
odd = cons "odd" even
in
even
There are also functions that manipulate infinite lists. The functions take and drop can be used to remove elements from the start of the list, returning the (removed) front elements or the remainder of the list, respectively. Another useful function is zip, which combines two lists like the slider on a zipper combines the teeth. For example,
zip (count 0) (count 10) = [0,10,1,11,2,12,...]
Your task is to implement a subset of this functionality.