Summation notation in Haskell

Question

On the Wikipedia page about summation it says that the equivalent operation in Haskell is to use foldl. My question is: Is there any reason why it says to use this instead of sum? Is one more 'purist' than the other, or is there no real difference?

Answer 1

foldl is a general tail-recursive reduce function. Recursion is the usual way of thinking about manipulating lists of items in a functional programming languages, and provides an alternative to loop iteration that is often much more elegant. In the case of a reduce function like fold, the tail-recursive implementation is very efficient. As others have explained, sum is then just a convenient mnemonic for foldl (+) 0 l.

Presumably its use on the wikipedia page is to illustrate the general principle of summation through tail-recursion. But since the Haskell Prelude library contains sum, which is shorter and more obvious to understand, you should use that in your code.

Here's a nice discussion of Haskell's fold functions with simple examples that's well worth reading.

Answer 2

I don't see where it says anything about Haskell or foldl on that Wikipedia page, but sum in Haskell is just a more specific case of foldl. It can be implemented like this, for example:

sum l = foldl (+) 0 l

Which can be reduced to:

sum = foldl (+) 0