Question

I have [a] that can be converted to [b]. Each a is distinct, but each b may not be. I want to filter my [a] on the condition that the filtered [a] contains no duplicates when converted to [b].

Can someone help me to achieve this?

Edit

To serve as assistance, I’ll provide an example.

as = [1..10]
conv = even
bs = map even as
-- bs = [False,True,False,True,False,True,False,True,False,True]
-- filter <cond> as -- [1,2]

Answer 1

Assume that f is the function that converts from a to b. You can then proceed in three steps:

1. You pair each element of your list with its image under f: map (id &&& f);
2. You remove every pair of which the second element has already appeared in the now obtained list: nubBy (on (==) snd);
3. You drop the second component of each pair: map fst.

Hence:

import Control.Arrow ((&&&))
import Data.Function (on)
import Data.List (nubBy)

filterOn :: Eq b => (a -> b) -> [a] -> [a]
filterOn f = map fst . nubBy ((==) `on` snd) . map (id &&& f)

For example:

> filterOn even [1 .. 10]
[1,2]