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{-# LANGUAGE MonadComprehensions #-}

import Data.List.Ordered
import Data.Ord
import Control.Monad.Trans.Cont

fromList :: [a] -> Cont [Vec Double] a
fromList as = cont $ \k -> mergeAllBy (comparing norm) $ map k as

toList :: Cont [Vec Double] (Vec Double) -> [Vec Double]
toList = flip runCont return

genFromPair :: (Vec Double, Vec Double) -> [Vec Double]
genFromPair (e1, e2) = toList [x.*e1 + y.*e2 | x <- fromList [0..], y <- fromList [0..]]

data Vec a = Vec a a
    deriving (Eq, Show)

instance Num a => Num (Vec a) where
    (Vec x1 y1) + (Vec x2 y2) = Vec (x1+x2) (y1+y2)
    -- ...

s .* (Vec x y) = Vec (s*x) (s*y)
norm (Vec x y) = sqrt (x^2 + y^2)

test = take 5 $ genFromPair (Vec 0 1, Vec 1 0)