Elegant way to combine multiple filtering functions in Haskell

What about this?

import Control.Applicative (liftA2)
-- given f1 etc.
filtered = filter (f1 <&&> f2 <&&> f3) [1..90]
  where
    (<&&>) = liftA2 (&&)

Here, lifting && to Applicative gives what you marked as <?>, i.e. an operator to "and" together the results of two unary predicates.

---

I initially used the name .&&. for the lifted operator, but amalloy suggested that <&&> would be a better name by analogy with the other Functor/Applicative lifted operators like <$>.

> filter (and . sequence [f1, f2, f3]) [1..100]
[33,36,39,42,45,48,51,54,57]

Essentially the above works because sequence (on the (->) a monad as used above) takes a list-of-functions and returns a function-returning-a-list. E.g.

sequence [f, g, h] = \x -> [f x, g x, h x]

Post-composing with and :: [Bool] -> Bool gives you a single boolean result, so you can use that in filter.

Also, there is no shame in being point-ful:

> filter (\x -> f1 x && f2 x && f3 x) [1..100]

is only marginally longer, and arguably simpler to read.