How to count in haskell

count.hs

count1 c (x:xs) = count1' (c == x) + count1 c xs
count1 c [] = 0
count1' True = 1
count1' False = 0

count2 c (x:xs) | c /= x = 0 + count2 c xs
                | otherwise = 1 + count2 c xs
count2 c [] = 0

count3 c (x:xs) = (if c == x then 1 else 0) + count3 c xs
count3 c [] = 0

count4 c xs = sum [1 | x <- xs, x == c] 

count5 c xs = length (filter (==c) xs)