lucas.hs

import Data.List
import Control.Lens
import Data.Bits.Lens
import Test.QuickCheck

pascal         = iterate stepper firstrow
  where
  firstrow     = [1]
  stepper    r = zipWith (+) ([0] ++ r) (r ++ [0])

binomial   n k = pascal !! n !! k

prop_lucas n k = n >= 0
             ==> k >= 0
             ==> k <= n
             ==> odd (binomial n k) == and (zipWith onBitMatches (toListOf bits k) (toListOf bits n))

onBitMatches True False = False
onBitMatches _    _     = True