Checking for empty list in Haskell: Is (length list == 0) or (list == []) more efficient?

Question

Say I want to check if a list is empty in a guard in Haskell there are two options:

1. length list == 0
2. list == []

Which of these two logical tests are more efficient? I'm inclined to say the empty list test because relies on more basic constructs rather than the prelude function length but I'm not sure.

Answer 1

length list == 0 needs to traverse the whole list to get its length, which means it is O(n). list == [] yields an Eq constraint on the element type. null list runs in constant time and has no typeclass constraints.

However, there is a neat trick to do something like length list == 0 which has the advantage that it generalizes nicely to length list1 == length list2 without going through the longer list: you can use genericLength with a sufficiently lazy representation of natural numbers so that comparison will only force traversing the shorter of the lists.

One example is to use the Natural type:

import Data.Number.Natural
import Data.List (genericLength)

nats :: [Int]
nats = iterate succ 0

areThereTenNats :: Bool
areThereTenNats = genericLength nats >= (10 :: Natural)

Answer 2

You can check if your list is empty in constant time with null list, which returns a boolean.

Prelude> null []
True
Prelude> null [1]
False
Prelude> null ""
True
Prelude> null "Test"
False