functional programming in haskell

5. (a) What is the type of the following unknown6 function? Give the most general type and include any required class constraints. The ($) is the low-precedence application operator. (I give several versions below, with and without the $).

> unknown6 m n = take m (map ($ n) . map (*) $ [1..]) > unknown6' m n = take m (map (\f -> f n) . map (*) $ [1..]) > unknown6'' m n = take m ((map (\f -> f n) . map (*)) [1..])

(The 3 definitions above are identical. Use whichever one you are comfortable with ). Note: *Main> ($5)(*)2 <-- prefix notation 10 *Main> (*)2$5 <-- infix notation 10 *Main> (\f -> f 5) (*2) <-- prefix notation 10 *Main>

(b) Give a description of what the unknown6 function in part (a) does. Describe what it does, not how it works.

(c) Give a non-trivial test case for the unknown6 function in part (a) and show the expected results.