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{-# LANGUAGE RankNTypes #-}
module SmallRing where
import Data.Ratio
odds :: (Integral i, Num a) => i -> [a]
odds x = [ 1 + 2 * fromIntegral n | n <- [0..x] ]
pts :: (Fractional a, Integral b) => b -> [a]
pts i = let d = 2^i in [ k / d | k <- odds (2^(i-1) - 1) ]
fractions :: Fractional b => [b]
fractions = concatMap pts [1..]
vis :: Int -> Ratio Int -> [Char]
vis w α = let i = numerator α
n = denominator α
x = (w * i) `div` n
in replicate (x-1) '.' ++ "x" ++ replicate (w-max x 1) '.' ++ show α
data Giver a
= Give0
| Give1 (forall b. (a -> b) -> b)
| Give2 (forall b. (a -> a -> b) -> b)
| Give3 (forall b. (a -> a -> a -> b) -> b)
pushFront :: a -> Giver a -> Giver a
pushFront a Give0 = Give1 ($ a)
pushFront a (Give1 f) = Give2 (\g -> f (g a))
pushFront a (Give2 f) = Give3 (\g -> f (g a))
pushFront a (Give3 f) = f $ \b c _ -> Give3 $ \g -> g a b c
front :: Giver a -> Maybe a
front Give0 = Nothing
front (Give1 f) = f Just
front (Give2 g) = g (\x _ -> Just x)
front (Give3 h) = h (\x _ _ -> Just x)
take3 :: (a -> a -> a -> b) -> Giver a -> Maybe b
take3 f (Give3 g) = Just (g f)
take3 _ _ = Nothing
with3 :: Applicative f => Giver a -> (a -> a -> a -> f ()) -> f ()
with3 (Give3 g) f = g f
with3 _ _ = pure ()
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