Question

we’ve been ask to write a function to see if the result of an applied filter function is an empty list. I tried following approach but it gives me mentioned error.

isListEmpty ::((a -> Bool) -> [a] -> [a]) -> Bool
isListEmpty f       | length f == 0 = True
                    | otherwise = False

Error:

...- Type error in application
*** Expression     : length f
*** Term           : f
*** Type           : (b -> Bool) -> [b] -> [b]
*** Does not match : [a]

the idea is practicing higher order functions.
any idea how can I solve this?

Answer 1

Seems like you have wrong type annotations. Consider the following solution:

isListEmpty :: (a -> Bool)        -- filtering function
            -> [a]                -- given list
            -> Bool               -- the result
isListEmpty f = null . filter f

Some examples:

> isListEmpty odd [2, 4]
True
> isListEmpty odd [1, 2, 4]
False
> 

Using length is not the best idea, since you have to loop through the entire list to do the check, and the list can even be infinite. null can handle this sutiation:

> isListEmpty even [1..]
False
> 

Edit 1:

our question asked us to use the built-in filter function as an argument

Don’t quite understand what it means, but you may want to do this:

isListEmpty :: ([a] -> [a]) -> [a] -> Bool
isListEmpty = (null .)

Example usage:

> isListEmpty (filter even) [1..]
False

Please provide me with the example of intended function call, if I am wrong.