Haskell function non-exaustive patters in function error

Question

I'm trying to make a function that finds the local Maximum number in a list.

localMaxima :: [Integer] -> [Integer]
localMaxima [] = []
localMaxima [x] = []
localMaxima (e1:e2:e3:xs)
    |    (e2 > e3) && (e2 > e1) = e2 : (localMaxima (e2:(e3:xs)))
    |    otherwise = (localMaxima (e2:(e3:xs)))

After inputting a list of [2,3,4,1,5], the console outputs:

Non-exhaustive patterns in function localMaxima

What do you want `localMaxima [1,2]` to do? – Joseph Sible-Reinstate Monica Apr 08 '19 at 23:22 — Joseph Sible-Reinstate Monica, Apr 08 '19 at 23:22

score 0 · Accepted Answer · edited Jun 20 '20 at 09:12

Problem

As you can tell from the error, your pattern matching does not cover all the cases: what happens if you give it a list with 2 elements? e1:e2:[] does not match any of your cases, resulting in a non-exhaustive patterns error.

Solution

The solution is fairly easy: add a base-case for a list with two elements only. Assuming a point on the boundary cannot be a local min/max, your function should look something like this.

localMaxima :: [Integer] -> [Integer]
localMaxima [] = []
localMaxima [x] = []
localMaxima [a,b] = []
localMaxima (e1:e2:e3:xs)
    |    (e2 > e3) && (e2 > e1) = e2 : (localMaxima (e2:(e3:xs)))
    |    otherwise = (localMaxima (e2:(e3:xs)))

Furthermore, you can simplify this even more by

noting : is right-associative
use pattern wildcard _
make your type signature more generic

You can now have

localMaxima :: Ord a => [a] -> [a]
localMaxima (e1:e2:e3:xs)
    |    (e2 > e3) && (e2 > e1) = e2 : localMaxima (e2:e3:xs)
    |    otherwise = localMaxima (e2:e3:xs)
localMaxima _ = []

Haskell function non-exaustive patters in function error

1 Answers1

Problem

Solution