Question

I need to make a function “powers” that takes a number n and returns the infinite list of that number to the power of every number e.g.

powers 2 = 2,4,8,16,32......

I need to do this using very specific subset of the language where my only available built in functions are: div, mod, even, odd, head, tail, not, null, length, reverse, elem, map, filter, foldr, sum, product, take, drop, takewhile, dropWhile, zipWith and from.

the subset also has no ^ operator.

there are some further important constraints:

• the code must not exceed 1 line of more than 80 characters
• no “helper functions” allowed, i.e i cannot write another function to use within this definition.

So far my thinking is along these lines:

powers = \n -> map (\x -> "some function to get n to the power of x") (from 1)

but i cant figure out how to get the function to do this without a helper function.

for example if i was to use a function inflist that returned an infinite list of the number x then i could just do the following.

powers = \n -> map (\x -> product(take x (inflist n))) (from 1)

but i cant do this or anything like it because i couldn’t use that function.

Sorry if the notation is a different to normal haskell, its a very strict core haskell subset that uses this notation.

Answer 1

This is a recursion question.

powers n = n : map (* n) (powers n)

(Are you allowed to use :?)