Write a pure function cycle$-$streams that takes streams, xs and ys$,$ and returns a stream. The streams may or may not be the same length, and either one may be infinite, but you may assume they are both non$-$empty. The elements produced by the stream are pairs where the first part is from xs and the second part is from ys$.$ The stream returned by cycle$-$streams cycles forever through the streams xs and ys$.$ A constant$-$time $($

O

$($

$1$

$)$

$)$ solution is possible.

Examples:

$>($stream$->$list $($stream$-$take $($cycle$-$streams $($stream $123)($stream $"$a$""$b$"))8))$

$\text{'}((1."$a$")(2."$b$")(3."$a$")(1."$b$")(2."$a$")(3."$b$")(1."$a$")(2."$b$"))$

Hint:

Write a function that creates a stream that endlessly cycles through all the elements of a single, given stream. You can use a local environment to bind a variable to the original stream. Write a helper function that uses this local environment to refer to the original stream when it runs out of elements to cycle through.

Compose this function with your stream$-$zip to implement cycle$-$streams.