Define a pure, recursive function stream$-$zip that takes two arguments, each of which is a stream, and produces a stream of pairs, where the

n

th

pair$$s car is the

n

th

element of xs and the

n

th

pair$$s cdr is the

n

th

element of ys$.$ If xs and ys do not have the same length, then stream$-$zip should return a stream that has as many elements as the $$shortest$$ of xs and ys$.$ That is$,$ if stream$-$zip runs out of items in either xs or ys$,$ it can stop producing pairs. The behavior of stream$-$zip is undefined if either xs or ys is not a stream.

Note that stream$-$zip is like zip from Homework $1,$ but it operates on streams. Unlike zip, we cannot assume that the two streams have the same length. The stream$-$zip function must also potentially handle infinite streams$$there is no guarantee that xs and ys are finite streams.