haskell - Non exhaustive pattern in function noThirds

Question

So, my Problem is, that I have to write a program that filters all 3 * x (3,6,9...) elements from a list. My program looks like:

length'  :: [a] -> Int
length' = foldr (\_ -> (+1)) 0

help_ :: [a] -> [a] -> [a]
help_ (x:xs) [] = help_ (xs) [x]
help_ [] (x) = (x)
help_ (x:xs) (y)
    |((length' [xs]) ==0) = (y)
    |((length' [y]) `mod` 2 ==0) = help_ (xs) (y)
    |otherwise = help_ (xs) (y++[x])

noThirds :: [a] -> [a]
noThirds [x] = help_ [x] []

The compiler accepts this but gives the error "Non exhaustive pattern in function noThirds" when I enter "noThirds [1,2,3,4,5,6,7,8]" . I guess it's cause im missing a variety of "help_ .." but I don't get it. Im grateful for every help! Btw predefined list and arithmetic functions are not allowed.

Answer 1

It's because noThirds only has one pattern, [x] which only matches against a single element list. [x] is exactly equivalent to (x : []). What I think you meant was

noThirds :: [a] -> [a]
noThirda xs = help_ xs []