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{-# LANGUAGE NoMonomorphismRestriction #-}
{-# LANGUAGE PatternSynonyms #-}
{-# LANGUAGE PatternGuards #-}
{-# LANGUAGE ViewPatterns #-}
{-# LANGUAGE LambdaCase #-}
{-# LANGUAGE ScopedTypeVariables #-}
module IndexList where
import Prelude hiding (length, (!!))
import Control.Arrow
data List a
= Nil
| Z !(List (a, a))
| S a !(List (a, a))
deriving Show
z Nil = Nil
z v = Z v
length :: List a -> Int
length Nil = 0
length (Z v) = 2 * length v
length (S _ v) = 1 + 2 * length v
(!!) :: List a -> Int -> a
S x v !! 0 = x
S x v !! i = Z v !! (i-1)
Z v !! i
| even i = fst $ v !! (i `div` 2)
| otherwise = snd $ v !! (i `div` 2)
Nil !! i = error $ "index out of bounds: " ++ show i
update :: List a -> Int -> (a -> a) -> List a
update (S x v) 0 f = S (f x) v
update (S x v) i f
| even (i-1) = S x $ update v ((i-1) `div` 2) (first f)
| otherwise = S x $ update v ((i-1) `div` 2) (second f)
update (Z v) i f
| even i = Z $ update v (i `div` 2) (first f)
| otherwise = Z $ update v (i `div` 2) (second f)
update Nil i _ = error $ "update index out of bounds: " ++ show i
pattern Cons :: a -> List a -> List a
pattern Cons a v <- (getCons -> Just (a, v))
where Cons x Nil = S x Nil
Cons x (Z v) = S x v
Cons x (S y v) = Z (Cons (x, y) v)
getCons :: List a -> Maybe (a, List a)
getCons Nil = Nothing
getCons (S x v) = Just (x, z v)
getCons (Z v) = (\((x, y), v) -> (x, S y v)) <$> getCons v
pattern List :: [a] -> List a
pattern List a <- (fromList -> a)
where List = foldr Cons Nil
fromList :: List a -> [a]
fromList (Cons x xs) = x: fromList xs
fromList Nil = []
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