I'm Trying to figure out how I can Sum up the Arguments of a Function which has a given signature
sum :: Int -> ... -> Int with 1024 Int arguments...
Clever Currying / Recursion is surely the deal I just can't grasp how to even start.
The fact that it's 1024 is probably meant to be a clue that you should build up to it in powers of two. Here's a solution as far as 16 which you can extend.
It's using a continuation passing style as a way to let you have one function consume some arguments and then another consume some more. To see what's going on, try calculating out a small example by hand, say
add4 id 1 2 3 4.
add2 :: (Int -> a) -> Int -> Int -> a add2 k x y = k (x + y) add4 :: (Int -> a) -> Int -> Int -> Int -> Int -> a add4 k = add2 (add2 (add2 k)) -- type signatures omitted from now on... add8 k = add4 (add4 (add2 k)) add16 k = add8 (add8 (add2 k)) f = add16 id
And now you can do:
>f 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 136
I could also have written the functions more pointfree, for example:
add8 = add4 . add4 . add2