Question

I want to use recursion in Haskell. I define:

pf:: Int -> Int
pf 1 = 1
pf n = pf 1 + sum[pf 1..pf n-1]

But the sum is not correct! What is the proper way to sum a list of functions?

Answer 1

[pf 1..pf (n-1)] is not the same as [pf 1, pf 2, pf 3, ..., pf (n-1)].

> let f x = 2^x
> [f 1 .. f 4]
[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]
> [f 1, f 2, f 3, f 4]
[2,4,8,16]

You probably want map:

pf n = pf 1 + sum (map pf [1..n-1])

And, just as a remark, pf x = 2^(x-1).