{-# LANGUAGE
    DataKinds
  , TypeOperators
  , KindSignatures
  , PolyKinds
  , TypeFamilies
  , GeneralizedNewtypeDeriving
  , DeriveGeneric
  , DeriveDataTypeable
  , DeriveFunctor
  , DeriveTraversable
  #-}

module Data.NTuple
  ( NTuple
  , empty
  , proj
  , incl
  , toVector
  , -- * Proxies
    _1
  , _2
  , _3
  , _4
  , _5
  , _6
  , _7
  , _8
  , _9
  , _10
  ) where

import Data.Vector (Vector)
import qualified Data.Vector as V

import GHC.TypeLits
import Data.Proxy (Proxy (..))
import Data.List (intercalate)
import Prelude.Singletons (If)
import Data.Eq.Singletons (PEq ((==)))
import Data.Ord.Singletons (POrd ((>)))

import Data.Data (Data, Typeable)
import GHC.Generics (Generic)


newtype NTuple (size :: Nat) a = NTuple
  { forall (size :: Nat) a. NTuple size a -> Vector a
toVector :: Vector a
  } deriving (NTuple size a -> NTuple size a -> Bool
forall (size :: Nat) a.
Eq a =>
NTuple size a -> NTuple size a -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: NTuple size a -> NTuple size a -> Bool
$c/= :: forall (size :: Nat) a.
Eq a =>
NTuple size a -> NTuple size a -> Bool
== :: NTuple size a -> NTuple size a -> Bool
$c== :: forall (size :: Nat) a.
Eq a =>
NTuple size a -> NTuple size a -> Bool
Eq, NTuple size a -> DataType
NTuple size a -> Constr
forall {size :: Nat} {a}.
(KnownNat size, Data a) =>
Typeable (NTuple size a)
forall (size :: Nat) a.
(KnownNat size, Data a) =>
NTuple size a -> DataType
forall (size :: Nat) a.
(KnownNat size, Data a) =>
NTuple size a -> Constr
forall (size :: Nat) a.
(KnownNat size, Data a) =>
(forall b. Data b => b -> b) -> NTuple size a -> NTuple size a
forall (size :: Nat) a u.
(KnownNat size, Data a) =>
Int -> (forall d. Data d => d -> u) -> NTuple size a -> u
forall (size :: Nat) a u.
(KnownNat size, Data a) =>
(forall d. Data d => d -> u) -> NTuple size a -> [u]
forall (size :: Nat) a r r'.
(KnownNat size, Data a) =>
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> NTuple size a -> r
forall (size :: Nat) a r r'.
(KnownNat size, Data a) =>
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> NTuple size a -> r
forall (size :: Nat) a (m :: * -> *).
(KnownNat size, Data a, Monad m) =>
(forall d. Data d => d -> m d)
-> NTuple size a -> m (NTuple size a)
forall (size :: Nat) a (m :: * -> *).
(KnownNat size, Data a, MonadPlus m) =>
(forall d. Data d => d -> m d)
-> NTuple size a -> m (NTuple size a)
forall (size :: Nat) a (c :: * -> *).
(KnownNat size, Data a) =>
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (NTuple size a)
forall (size :: Nat) a (c :: * -> *).
(KnownNat size, Data a) =>
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> NTuple size a -> c (NTuple size a)
forall (size :: Nat) a (t :: * -> *) (c :: * -> *).
(KnownNat size, Data a, Typeable t) =>
(forall d. Data d => c (t d)) -> Maybe (c (NTuple size a))
forall (size :: Nat) a (t :: * -> * -> *) (c :: * -> *).
(KnownNat size, Data a, Typeable t) =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c (NTuple size a))
forall a.
Typeable a
-> (forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> a -> c a)
-> (forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c a)
-> (a -> Constr)
-> (a -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c a))
-> (forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a))
-> ((forall b. Data b => b -> b) -> a -> a)
-> (forall r r'.
    (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
-> (forall r r'.
    (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
-> (forall u. (forall d. Data d => d -> u) -> a -> [u])
-> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u)
-> (forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> Data a
forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (NTuple size a)
forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> NTuple size a -> c (NTuple size a)
gmapMo :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d)
-> NTuple size a -> m (NTuple size a)
$cgmapMo :: forall (size :: Nat) a (m :: * -> *).
(KnownNat size, Data a, MonadPlus m) =>
(forall d. Data d => d -> m d)
-> NTuple size a -> m (NTuple size a)
gmapMp :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d)
-> NTuple size a -> m (NTuple size a)
$cgmapMp :: forall (size :: Nat) a (m :: * -> *).
(KnownNat size, Data a, MonadPlus m) =>
(forall d. Data d => d -> m d)
-> NTuple size a -> m (NTuple size a)
gmapM :: forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d)
-> NTuple size a -> m (NTuple size a)
$cgmapM :: forall (size :: Nat) a (m :: * -> *).
(KnownNat size, Data a, Monad m) =>
(forall d. Data d => d -> m d)
-> NTuple size a -> m (NTuple size a)
gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> NTuple size a -> u
$cgmapQi :: forall (size :: Nat) a u.
(KnownNat size, Data a) =>
Int -> (forall d. Data d => d -> u) -> NTuple size a -> u
gmapQ :: forall u. (forall d. Data d => d -> u) -> NTuple size a -> [u]
$cgmapQ :: forall (size :: Nat) a u.
(KnownNat size, Data a) =>
(forall d. Data d => d -> u) -> NTuple size a -> [u]
gmapQr :: forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> NTuple size a -> r
$cgmapQr :: forall (size :: Nat) a r r'.
(KnownNat size, Data a) =>
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> NTuple size a -> r
gmapQl :: forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> NTuple size a -> r
$cgmapQl :: forall (size :: Nat) a r r'.
(KnownNat size, Data a) =>
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> NTuple size a -> r
gmapT :: (forall b. Data b => b -> b) -> NTuple size a -> NTuple size a
$cgmapT :: forall (size :: Nat) a.
(KnownNat size, Data a) =>
(forall b. Data b => b -> b) -> NTuple size a -> NTuple size a
dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c (NTuple size a))
$cdataCast2 :: forall (size :: Nat) a (t :: * -> * -> *) (c :: * -> *).
(KnownNat size, Data a, Typeable t) =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c (NTuple size a))
dataCast1 :: forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c (NTuple size a))
$cdataCast1 :: forall (size :: Nat) a (t :: * -> *) (c :: * -> *).
(KnownNat size, Data a, Typeable t) =>
(forall d. Data d => c (t d)) -> Maybe (c (NTuple size a))
dataTypeOf :: NTuple size a -> DataType
$cdataTypeOf :: forall (size :: Nat) a.
(KnownNat size, Data a) =>
NTuple size a -> DataType
toConstr :: NTuple size a -> Constr
$ctoConstr :: forall (size :: Nat) a.
(KnownNat size, Data a) =>
NTuple size a -> Constr
gunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (NTuple size a)
$cgunfold :: forall (size :: Nat) a (c :: * -> *).
(KnownNat size, Data a) =>
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (NTuple size a)
gfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> NTuple size a -> c (NTuple size a)
$cgfoldl :: forall (size :: Nat) a (c :: * -> *).
(KnownNat size, Data a) =>
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> NTuple size a -> c (NTuple size a)
Data, Typeable, forall (size :: Nat) a x. Rep (NTuple size a) x -> NTuple size a
forall (size :: Nat) a x. NTuple size a -> Rep (NTuple size a) x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
$cto :: forall (size :: Nat) a x. Rep (NTuple size a) x -> NTuple size a
$cfrom :: forall (size :: Nat) a x. NTuple size a -> Rep (NTuple size a) x
Generic, forall (size :: Nat) a b. a -> NTuple size b -> NTuple size a
forall (size :: Nat) a b.
(a -> b) -> NTuple size a -> NTuple size b
forall a b. a -> NTuple size b -> NTuple size a
forall a b. (a -> b) -> NTuple size a -> NTuple size b
forall (f :: * -> *).
(forall a b. (a -> b) -> f a -> f b)
-> (forall a b. a -> f b -> f a) -> Functor f
<$ :: forall a b. a -> NTuple size b -> NTuple size a
$c<$ :: forall (size :: Nat) a b. a -> NTuple size b -> NTuple size a
fmap :: forall a b. (a -> b) -> NTuple size a -> NTuple size b
$cfmap :: forall (size :: Nat) a b.
(a -> b) -> NTuple size a -> NTuple size b
Functor, forall (size :: Nat) a. Eq a => a -> NTuple size a -> Bool
forall (size :: Nat) a. Num a => NTuple size a -> a
forall (size :: Nat) a. Ord a => NTuple size a -> a
forall (size :: Nat) m. Monoid m => NTuple size m -> m
forall (size :: Nat) a. NTuple size a -> Bool
forall (size :: Nat) a. NTuple size a -> Int
forall (size :: Nat) a. NTuple size a -> [a]
forall (size :: Nat) a. (a -> a -> a) -> NTuple size a -> a
forall (size :: Nat) m a.
Monoid m =>
(a -> m) -> NTuple size a -> m
forall (size :: Nat) b a. (b -> a -> b) -> b -> NTuple size a -> b
forall (size :: Nat) a b. (a -> b -> b) -> b -> NTuple size a -> b
forall a. Eq a => a -> NTuple size a -> Bool
forall a. Num a => NTuple size a -> a
forall a. Ord a => NTuple size a -> a
forall m. Monoid m => NTuple size m -> m
forall a. NTuple size a -> Bool
forall a. NTuple size a -> Int
forall a. NTuple size a -> [a]
forall a. (a -> a -> a) -> NTuple size a -> a
forall m a. Monoid m => (a -> m) -> NTuple size a -> m
forall b a. (b -> a -> b) -> b -> NTuple size a -> b
forall a b. (a -> b -> b) -> b -> NTuple size a -> b
forall (t :: * -> *).
(forall m. Monoid m => t m -> m)
-> (forall m a. Monoid m => (a -> m) -> t a -> m)
-> (forall m a. Monoid m => (a -> m) -> t a -> m)
-> (forall a b. (a -> b -> b) -> b -> t a -> b)
-> (forall a b. (a -> b -> b) -> b -> t a -> b)
-> (forall b a. (b -> a -> b) -> b -> t a -> b)
-> (forall b a. (b -> a -> b) -> b -> t a -> b)
-> (forall a. (a -> a -> a) -> t a -> a)
-> (forall a. (a -> a -> a) -> t a -> a)
-> (forall a. t a -> [a])
-> (forall a. t a -> Bool)
-> (forall a. t a -> Int)
-> (forall a. Eq a => a -> t a -> Bool)
-> (forall a. Ord a => t a -> a)
-> (forall a. Ord a => t a -> a)
-> (forall a. Num a => t a -> a)
-> (forall a. Num a => t a -> a)
-> Foldable t
product :: forall a. Num a => NTuple size a -> a
$cproduct :: forall (size :: Nat) a. Num a => NTuple size a -> a
sum :: forall a. Num a => NTuple size a -> a
$csum :: forall (size :: Nat) a. Num a => NTuple size a -> a
minimum :: forall a. Ord a => NTuple size a -> a
$cminimum :: forall (size :: Nat) a. Ord a => NTuple size a -> a
maximum :: forall a. Ord a => NTuple size a -> a
$cmaximum :: forall (size :: Nat) a. Ord a => NTuple size a -> a
elem :: forall a. Eq a => a -> NTuple size a -> Bool
$celem :: forall (size :: Nat) a. Eq a => a -> NTuple size a -> Bool
length :: forall a. NTuple size a -> Int
$clength :: forall (size :: Nat) a. NTuple size a -> Int
null :: forall a. NTuple size a -> Bool
$cnull :: forall (size :: Nat) a. NTuple size a -> Bool
toList :: forall a. NTuple size a -> [a]
$ctoList :: forall (size :: Nat) a. NTuple size a -> [a]
foldl1 :: forall a. (a -> a -> a) -> NTuple size a -> a
$cfoldl1 :: forall (size :: Nat) a. (a -> a -> a) -> NTuple size a -> a
foldr1 :: forall a. (a -> a -> a) -> NTuple size a -> a
$cfoldr1 :: forall (size :: Nat) a. (a -> a -> a) -> NTuple size a -> a
foldl' :: forall b a. (b -> a -> b) -> b -> NTuple size a -> b
$cfoldl' :: forall (size :: Nat) b a. (b -> a -> b) -> b -> NTuple size a -> b
foldl :: forall b a. (b -> a -> b) -> b -> NTuple size a -> b
$cfoldl :: forall (size :: Nat) b a. (b -> a -> b) -> b -> NTuple size a -> b
foldr' :: forall a b. (a -> b -> b) -> b -> NTuple size a -> b
$cfoldr' :: forall (size :: Nat) a b. (a -> b -> b) -> b -> NTuple size a -> b
foldr :: forall a b. (a -> b -> b) -> b -> NTuple size a -> b
$cfoldr :: forall (size :: Nat) a b. (a -> b -> b) -> b -> NTuple size a -> b
foldMap' :: forall m a. Monoid m => (a -> m) -> NTuple size a -> m
$cfoldMap' :: forall (size :: Nat) m a.
Monoid m =>
(a -> m) -> NTuple size a -> m
foldMap :: forall m a. Monoid m => (a -> m) -> NTuple size a -> m
$cfoldMap :: forall (size :: Nat) m a.
Monoid m =>
(a -> m) -> NTuple size a -> m
fold :: forall m. Monoid m => NTuple size m -> m
$cfold :: forall (size :: Nat) m. Monoid m => NTuple size m -> m
Foldable, forall (size :: Nat). Functor (NTuple size)
forall (size :: Nat). Foldable (NTuple size)
forall (size :: Nat) (m :: * -> *) a.
Monad m =>
NTuple size (m a) -> m (NTuple size a)
forall (size :: Nat) (f :: * -> *) a.
Applicative f =>
NTuple size (f a) -> f (NTuple size a)
forall (size :: Nat) (m :: * -> *) a b.
Monad m =>
(a -> m b) -> NTuple size a -> m (NTuple size b)
forall (size :: Nat) (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> NTuple size a -> f (NTuple size b)
forall (t :: * -> *).
Functor t
-> Foldable t
-> (forall (f :: * -> *) a b.
    Applicative f =>
    (a -> f b) -> t a -> f (t b))
-> (forall (f :: * -> *) a. Applicative f => t (f a) -> f (t a))
-> (forall (m :: * -> *) a b.
    Monad m =>
    (a -> m b) -> t a -> m (t b))
-> (forall (m :: * -> *) a. Monad m => t (m a) -> m (t a))
-> Traversable t
forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> NTuple size a -> f (NTuple size b)
sequence :: forall (m :: * -> *) a.
Monad m =>
NTuple size (m a) -> m (NTuple size a)
$csequence :: forall (size :: Nat) (m :: * -> *) a.
Monad m =>
NTuple size (m a) -> m (NTuple size a)
mapM :: forall (m :: * -> *) a b.
Monad m =>
(a -> m b) -> NTuple size a -> m (NTuple size b)
$cmapM :: forall (size :: Nat) (m :: * -> *) a b.
Monad m =>
(a -> m b) -> NTuple size a -> m (NTuple size b)
sequenceA :: forall (f :: * -> *) a.
Applicative f =>
NTuple size (f a) -> f (NTuple size a)
$csequenceA :: forall (size :: Nat) (f :: * -> *) a.
Applicative f =>
NTuple size (f a) -> f (NTuple size a)
traverse :: forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> NTuple size a -> f (NTuple size b)
$ctraverse :: forall (size :: Nat) (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> NTuple size a -> f (NTuple size b)
Traversable)


instance Show a => Show (NTuple size a) where
  show :: NTuple size a -> String
show (NTuple Vector a
xs) = String
"( " forall a. [a] -> [a] -> [a]
++ forall a. [a] -> [[a]] -> [a]
intercalate String
", " (forall a. Vector a -> [a]
V.toList (forall a. Show a => a -> String
show forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Vector a
xs)) forall a. [a] -> [a] -> [a]
++ String
")"


empty :: NTuple 0 a
empty :: forall a. NTuple 0 a
empty = forall (size :: Nat) a. Vector a -> NTuple size a
NTuple forall a. Vector a
V.empty


-- | Project an element out of the tuple
proj :: ( n <= size
        , (n > 0) ~ 'True
        , KnownNat n
        )
      => Proxy n -- ^ The index
      -> NTuple size a
      -> a
proj :: forall (n :: Nat) (size :: Nat) a.
(n <= size, (n > 0) ~ 'True, KnownNat n) =>
Proxy n -> NTuple size a -> a
proj Proxy n
p (NTuple Vector a
xs) = Vector a
xs forall a. Vector a -> Int -> a
V.! (forall a. Num a => Integer -> a
fromInteger (forall (n :: Nat) (proxy :: Nat -> *).
KnownNat n =>
proxy n -> Integer
natVal Proxy n
p) forall a. Num a => a -> a -> a
- Int
1)


-- | Include an element to the tuple, overwriting on an existing index
incl :: ( n <= (size + 1)
        , (n > 0) ~ 'True
        , KnownNat n
        , size' ~ If (n == (size + 1)) (size + 1) size
        )
     => Proxy n -- ^ The index
     -> a
     -> NTuple size a
     -> NTuple size' a
incl :: forall (n :: Nat) (size :: Nat) (size' :: Nat) a.
(n <= (size + 1), (n > 0) ~ 'True, KnownNat n,
 size' ~ If (n == (size + 1)) (size + 1) size) =>
Proxy n -> a -> NTuple size a -> NTuple size' a
incl Proxy n
p a
x (NTuple Vector a
xs) = forall (size :: Nat) a. Vector a -> NTuple size a
NTuple forall a b. (a -> b) -> a -> b
$
  let n :: Int
n = forall a. Num a => Integer -> a
fromInteger (forall (n :: Nat) (proxy :: Nat -> *).
KnownNat n =>
proxy n -> Integer
natVal Proxy n
p) forall a. Num a => a -> a -> a
- Int
1
      (Vector a
l,Vector a
r) = forall a. Int -> Vector a -> (Vector a, Vector a)
V.splitAt Int
n Vector a
xs

  in  Vector a
l forall a. Vector a -> Vector a -> Vector a
V.++ (a
x forall a. a -> Vector a -> Vector a
`V.cons` forall {a}. Vector a -> Vector a
tail' Vector a
r)
  where
    tail' :: Vector a -> Vector a
tail' Vector a
r
      | forall a. Vector a -> Bool
V.null Vector a
r  = forall a. Vector a
V.empty
      | Bool
otherwise = forall {a}. Vector a -> Vector a
V.tail Vector a
r




_1 :: Proxy 1
_1 :: Proxy 1
_1 = forall {k} (t :: k). Proxy t
Proxy

_2 :: Proxy 2
_2 :: Proxy 2
_2 = forall {k} (t :: k). Proxy t
Proxy

_3 :: Proxy 3
_3 :: Proxy 3
_3 = forall {k} (t :: k). Proxy t
Proxy

_4 :: Proxy 4
_4 :: Proxy 4
_4 = forall {k} (t :: k). Proxy t
Proxy

_5 :: Proxy 5
_5 :: Proxy 5
_5 = forall {k} (t :: k). Proxy t
Proxy

_6 :: Proxy 6
_6 :: Proxy 6
_6 = forall {k} (t :: k). Proxy t
Proxy

_7 :: Proxy 7
_7 :: Proxy 7
_7 = forall {k} (t :: k). Proxy t
Proxy

_8 :: Proxy 8
_8 :: Proxy 8
_8 = forall {k} (t :: k). Proxy t
Proxy

_9 :: Proxy 9
_9 :: Proxy 9
_9 = forall {k} (t :: k). Proxy t
Proxy

_10 :: Proxy 10
_10 :: Proxy 10
_10 = forall {k} (t :: k). Proxy t
Proxy