Past exam of the year 1 of the computer science course of the University of Oxford / 2017 / Functional programming, design and analysis of algorithms / 2 / b

Tie the three scaled streams back to the same shared lazy list:

hamming :: [Integer]
hamming = 1 : merge (map (2*) hamming)
                    (merge (map (3*) hamming) (map (5*) hamming))

The resulting values are precisely the Hamming numbers $2^i{3}^j{5}^k$ for nonnegative integers $i,j,k$. Every noninitial value has a smaller predecessor obtained by removing a factor, so the recursive demand can be supplied from earlier cells. This is the productivity argument for a sorted multiplicative closure stream. The merge algorithm removes duplicate representations such as $2\cdot 3=3\cdot 2$, retaining strict order and every generated value.