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The higher-order function with type (a -> [b]) -> [a] -> [b] and value concat (map f xs). It replaces each input element by a list and concatenates those lists in input order. A direct definition is concatMap f = foldr (\x rest -> f x ++ rest) []. This formulation processes an input element's produced list once; it need not repeatedly append an already accumulated output prefix.

The higher-order function iterate :: (a -> a) -> a -> [a], satisfying iterate f x = x : iterate f (f x). Its result begins with the initial value and continues with successive applications. Lazy evaluation permits finite prefixes of this infinite list to be observed whenever the necessary applications terminate.

The higher-order function takeWhile :: (a -> Bool) -> [a] -> [a] retains the longest initial segment whose elements all satisfy its predicate. It stops at the first failure and does not resume later. Thus it differs from a list filter, which tests later elements as well.