    {-# OPTIONS_GHC -Wunused-imports #-}

    -- | Lists of length at least 2.
    --
    --   Import as:
    --   @
    --      import Agda.Utils.List2 (List2(List2))
    --      import qualified Agda.Utils.List2 as List2
    --   @

    module Agda.Utils.List2
      ( module Agda.Utils.List2
      , module Reexport
      ) where

    import Control.DeepSeq
    import Control.Monad                   ( (<=<) )

    import qualified Data.List as List
    import Data.Semigroup (sconcat)

    import GHC.Exts                        ( IsList(..) )
    import qualified GHC.Exts  as Reexport ( toList )

    import Agda.Utils.List1                ( List1, pattern (:|) )
    import qualified Agda.Utils.List1 as List1

    import Agda.Utils.Impossible

    -- | Lists of length ≥2.
    data List2 a = List2 a a [a]
      deriving (List2 a -> List2 a -> Bool
    (List2 a -> List2 a -> Bool)
    -> (List2 a -> List2 a -> Bool) -> Eq (List2 a)
    forall a. Eq a => List2 a -> List2 a -> Bool
    forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
    $c== :: forall a. Eq a => List2 a -> List2 a -> Bool
    == :: List2 a -> List2 a -> Bool
    $c/= :: forall a. Eq a => List2 a -> List2 a -> Bool
    /= :: List2 a -> List2 a -> Bool
    Eq, Eq (List2 a)
    Eq (List2 a) =>
    (List2 a -> List2 a -> Ordering)
    -> (List2 a -> List2 a -> Bool)
    -> (List2 a -> List2 a -> Bool)
    -> (List2 a -> List2 a -> Bool)
    -> (List2 a -> List2 a -> Bool)
    -> (List2 a -> List2 a -> List2 a)
    -> (List2 a -> List2 a -> List2 a)
    -> Ord (List2 a)
    List2 a -> List2 a -> Bool
    List2 a -> List2 a -> Ordering
    List2 a -> List2 a -> List2 a
    forall a.
    Eq a =>
    (a -> a -> Ordering)
    -> (a -> a -> Bool)
    -> (a -> a -> Bool)
    -> (a -> a -> Bool)
    -> (a -> a -> Bool)
    -> (a -> a -> a)
    -> (a -> a -> a)
    -> Ord a
    forall a. Ord a => Eq (List2 a)
    forall a. Ord a => List2 a -> List2 a -> Bool
    forall a. Ord a => List2 a -> List2 a -> Ordering
    forall a. Ord a => List2 a -> List2 a -> List2 a
    $ccompare :: forall a. Ord a => List2 a -> List2 a -> Ordering
    compare :: List2 a -> List2 a -> Ordering
    $c< :: forall a. Ord a => List2 a -> List2 a -> Bool
    < :: List2 a -> List2 a -> Bool
    $c<= :: forall a. Ord a => List2 a -> List2 a -> Bool
    <= :: List2 a -> List2 a -> Bool
    $c> :: forall a. Ord a => List2 a -> List2 a -> Bool
    > :: List2 a -> List2 a -> Bool
    $c>= :: forall a. Ord a => List2 a -> List2 a -> Bool
    >= :: List2 a -> List2 a -> Bool
    $cmax :: forall a. Ord a => List2 a -> List2 a -> List2 a
    max :: List2 a -> List2 a -> List2 a
    $cmin :: forall a. Ord a => List2 a -> List2 a -> List2 a
    min :: List2 a -> List2 a -> List2 a
    Ord, Int -> List2 a -> ShowS
    [List2 a] -> ShowS
    List2 a -> String
    (Int -> List2 a -> ShowS)
    -> (List2 a -> String) -> ([List2 a] -> ShowS) -> Show (List2 a)
    forall a. Show a => Int -> List2 a -> ShowS
    forall a. Show a => [List2 a] -> ShowS
    forall a. Show a => List2 a -> String
    forall a.
    (Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
    $cshowsPrec :: forall a. Show a => Int -> List2 a -> ShowS
    showsPrec :: Int -> List2 a -> ShowS
    $cshow :: forall a. Show a => List2 a -> String
    show :: List2 a -> String
    $cshowList :: forall a. Show a => [List2 a] -> ShowS
    showList :: [List2 a] -> ShowS
    Show, (forall a b. (a -> b) -> List2 a -> List2 b)
    -> (forall a b. a -> List2 b -> List2 a) -> Functor List2
    forall a b. a -> List2 b -> List2 a
    forall a b. (a -> b) -> List2 a -> List2 b
    forall (f :: * -> *).
    (forall a b. (a -> b) -> f a -> f b)
    -> (forall a b. a -> f b -> f a) -> Functor f
    $cfmap :: forall a b. (a -> b) -> List2 a -> List2 b
    fmap :: forall a b. (a -> b) -> List2 a -> List2 b
    $c<$ :: forall a b. a -> List2 b -> List2 a
    <$ :: forall a b. a -> List2 b -> List2 a
    Functor, (forall m. Monoid m => List2 m -> m)
    -> (forall m a. Monoid m => (a -> m) -> List2 a -> m)
    -> (forall m a. Monoid m => (a -> m) -> List2 a -> m)
    -> (forall a b. (a -> b -> b) -> b -> List2 a -> b)
    -> (forall a b. (a -> b -> b) -> b -> List2 a -> b)
    -> (forall b a. (b -> a -> b) -> b -> List2 a -> b)
    -> (forall b a. (b -> a -> b) -> b -> List2 a -> b)
    -> (forall a. (a -> a -> a) -> List2 a -> a)
    -> (forall a. (a -> a -> a) -> List2 a -> a)
    -> (forall a. List2 a -> [a])
    -> (forall a. List2 a -> Bool)
    -> (forall a. List2 a -> Int)
    -> (forall a. Eq a => a -> List2 a -> Bool)
    -> (forall a. Ord a => List2 a -> a)
    -> (forall a. Ord a => List2 a -> a)
    -> (forall a. Num a => List2 a -> a)
    -> (forall a. Num a => List2 a -> a)
    -> Foldable List2
    forall a. Eq a => a -> List2 a -> Bool
    forall a. Num a => List2 a -> a
    forall a. Ord a => List2 a -> a
    forall m. Monoid m => List2 m -> m
    forall a. List2 a -> Bool
    forall a. List2 a -> Int
    forall a. List2 a -> [a]
    forall a. (a -> a -> a) -> List2 a -> a
    forall m a. Monoid m => (a -> m) -> List2 a -> m
    forall b a. (b -> a -> b) -> b -> List2 a -> b
    forall a b. (a -> b -> b) -> b -> List2 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
    $cfold :: forall m. Monoid m => List2 m -> m
    fold :: forall m. Monoid m => List2 m -> m
    $cfoldMap :: forall m a. Monoid m => (a -> m) -> List2 a -> m
    foldMap :: forall m a. Monoid m => (a -> m) -> List2 a -> m
    $cfoldMap' :: forall m a. Monoid m => (a -> m) -> List2 a -> m
    foldMap' :: forall m a. Monoid m => (a -> m) -> List2 a -> m
    $cfoldr :: forall a b. (a -> b -> b) -> b -> List2 a -> b
    foldr :: forall a b. (a -> b -> b) -> b -> List2 a -> b
    $cfoldr' :: forall a b. (a -> b -> b) -> b -> List2 a -> b
    foldr' :: forall a b. (a -> b -> b) -> b -> List2 a -> b
    $cfoldl :: forall b a. (b -> a -> b) -> b -> List2 a -> b
    foldl :: forall b a. (b -> a -> b) -> b -> List2 a -> b
    $cfoldl' :: forall b a. (b -> a -> b) -> b -> List2 a -> b
    foldl' :: forall b a. (b -> a -> b) -> b -> List2 a -> b
    $cfoldr1 :: forall a. (a -> a -> a) -> List2 a -> a
    foldr1 :: forall a. (a -> a -> a) -> List2 a -> a
    $cfoldl1 :: forall a. (a -> a -> a) -> List2 a -> a
    foldl1 :: forall a. (a -> a -> a) -> List2 a -> a
    $ctoList :: forall a. List2 a -> [a]
    toList :: forall a. List2 a -> [a]
    $cnull :: forall a. List2 a -> Bool
    null :: forall a. List2 a -> Bool
    $clength :: forall a. List2 a -> Int
    length :: forall a. List2 a -> Int
    $celem :: forall a. Eq a => a -> List2 a -> Bool
    elem :: forall a. Eq a => a -> List2 a -> Bool
    $cmaximum :: forall a. Ord a => List2 a -> a
    maximum :: forall a. Ord a => List2 a -> a
    $cminimum :: forall a. Ord a => List2 a -> a
    minimum :: forall a. Ord a => List2 a -> a
    $csum :: forall a. Num a => List2 a -> a
    sum :: forall a. Num a => List2 a -> a
    $cproduct :: forall a. Num a => List2 a -> a
    product :: forall a. Num a => List2 a -> a
    Foldable, Functor List2
    Foldable List2
    (Functor List2, Foldable List2) =>
    (forall (f :: * -> *) a b.
     Applicative f =>
     (a -> f b) -> List2 a -> f (List2 b))
    -> (forall (f :: * -> *) a.
        Applicative f =>
        List2 (f a) -> f (List2 a))
    -> (forall (m :: * -> *) a b.
        Monad m =>
        (a -> m b) -> List2 a -> m (List2 b))
    -> (forall (m :: * -> *) a. Monad m => List2 (m a) -> m (List2 a))
    -> Traversable List2
    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 (m :: * -> *) a. Monad m => List2 (m a) -> m (List2 a)
    forall (f :: * -> *) a. Applicative f => List2 (f a) -> f (List2 a)
    forall (m :: * -> *) a b.
    Monad m =>
    (a -> m b) -> List2 a -> m (List2 b)
    forall (f :: * -> *) a b.
    Applicative f =>
    (a -> f b) -> List2 a -> f (List2 b)
    $ctraverse :: forall (f :: * -> *) a b.
    Applicative f =>
    (a -> f b) -> List2 a -> f (List2 b)
    traverse :: forall (f :: * -> *) a b.
    Applicative f =>
    (a -> f b) -> List2 a -> f (List2 b)
    $csequenceA :: forall (f :: * -> *) a. Applicative f => List2 (f a) -> f (List2 a)
    sequenceA :: forall (f :: * -> *) a. Applicative f => List2 (f a) -> f (List2 a)
    $cmapM :: forall (m :: * -> *) a b.
    Monad m =>
    (a -> m b) -> List2 a -> m (List2 b)
    mapM :: forall (m :: * -> *) a b.
    Monad m =>
    (a -> m b) -> List2 a -> m (List2 b)
    $csequence :: forall (m :: * -> *) a. Monad m => List2 (m a) -> m (List2 a)
    sequence :: forall (m :: * -> *) a. Monad m => List2 (m a) -> m (List2 a)
    Traversable)

    -- * Conversion from and to other list types.

    -- | 'fromList' is unsafe.
    instance IsList (List2 a) where
      type Item (List2 a) = a

      -- Unsafe! O(1).
      fromList :: [a] -> List2 a
      fromList :: [a] -> List2 a
    fromList (a
    a : a
    b : [a]
    cs) = a -> a -> [a] -> List2 a
    forall a. a -> a -> [a] -> List2 a
    List2 a
    a a
    b [a]
    cs
      fromList [a]
    _            = List2 a
    forall a. HasCallStack => a
    __IMPOSSIBLE__

      toList :: List2 a -> [a]
      toList :: List2 a -> [a]
    toList (List2 a
    a a
    b [a]
    cs) = a
    a a -> [a] -> [a]
    forall a. a -> [a] -> [a]
    : a
    b a -> [a] -> [a]
    forall a. a -> [a] -> [a]
    : [a]
    cs

    -- | Unsafe! O(1).
    fromList1 :: List1 a -> List2 a
    fromList1 :: forall a. List1 a -> List2 a
    fromList1 (a
    a :| a
    b : [a]
    cs) = a -> a -> [a] -> List2 a
    forall a. a -> a -> [a] -> List2 a
    List2 a
    a a
    b [a]
    cs
    fromList1 NonEmpty a
    _             = List2 a
    forall a. HasCallStack => a
    __IMPOSSIBLE__

    -- | Safe. O(1).
    toList1 :: List2 a -> List1 a
    toList1 :: forall a. List2 a -> List1 a
    toList1 (List2 a
    a a
    b [a]
    cs) = a
    a a -> [a] -> NonEmpty a
    forall a. a -> [a] -> NonEmpty a
    :| a
    b a -> [a] -> [a]
    forall a. a -> [a] -> [a]
    : [a]
    cs

    -- | Safe. O(1).
    fromListMaybe :: [a] -> Maybe (List2 a)
    fromListMaybe :: forall a. [a] -> Maybe (List2 a)
    fromListMaybe = List1 a -> Maybe (List2 a)
    forall a. List1 a -> Maybe (List2 a)
    fromList1Maybe (List1 a -> Maybe (List2 a))
    -> ([a] -> Maybe (List1 a)) -> [a] -> Maybe (List2 a)
    forall (m :: * -> *) b c a.
    Monad m =>
    (b -> m c) -> (a -> m b) -> a -> m c
    <=< [a] -> Maybe (List1 a)
    forall a. [a] -> Maybe (NonEmpty a)
    List1.nonEmpty

    -- | Safe. O(1).
    fromList1Maybe :: List1 a -> Maybe (List2 a)
    fromList1Maybe :: forall a. List1 a -> Maybe (List2 a)
    fromList1Maybe = \case
      (a
    a :| a
    b : [a]
    cs) -> List2 a -> Maybe (List2 a)
    forall a. a -> Maybe a
    Just (a -> a -> [a] -> List2 a
    forall a. a -> a -> [a] -> List2 a
    List2 a
    a a
    b [a]
    cs)
      List1 a
    _ -> Maybe (List2 a)
    forall a. Maybe a
    Nothing

    -- | Any 'List1' is either a singleton or a 'List2'. O(1).
    fromList1Either :: List1 a -> Either a (List2 a)
    fromList1Either :: forall a. List1 a -> Either a (List2 a)
    fromList1Either (a
    a :| [a]
    as) = case [a]
    as of
      []   -> a -> Either a (List2 a)
    forall a b. a -> Either a b
    Left a
    a
      a
    b:[a]
    bs -> List2 a -> Either a (List2 a)
    forall a b. b -> Either a b
    Right (a -> a -> [a] -> List2 a
    forall a. a -> a -> [a] -> List2 a
    List2 a
    a a
    b [a]
    bs)

    -- | Inverse of 'fromList1Either'. O(1).
    toList1Either :: Either a (List2 a) -> List1 a
    toList1Either :: forall a. Either a (List2 a) -> List1 a
    toList1Either = \case
      Left  a
    a              -> a
    a a -> [a] -> List1 a
    forall a. a -> [a] -> NonEmpty a
    :| []
      Right (List2 a
    a a
    b [a]
    bs) -> a
    a a -> [a] -> List1 a
    forall a. a -> [a] -> NonEmpty a
    :| a
    b a -> [a] -> [a]
    forall a. a -> [a] -> [a]
    : [a]
    bs

    -- * Construction

    -- | O(1).
    cons :: a -> List1 a -> List2 a
    cons :: forall a. a -> List1 a -> List2 a
    cons a
    x (a
    y :| [a]
    ys) = a -> a -> [a] -> List2 a
    forall a. a -> a -> [a] -> List2 a
    List2 a
    x a
    y [a]
    ys

    -- | O(n).
    snoc :: List1 a -> a -> List2 a
    snoc :: forall a. List1 a -> a -> List2 a
    snoc (a
    x :| [a]
    xs) a
    z = a -> a -> [a] -> List2 a
    forall a. a -> a -> [a] -> List2 a
    List2 a
    x a
    y [a]
    ys
      where
        a
    y :| [a]
    ys = [a] -> a -> NonEmpty a
    forall a. [a] -> a -> List1 a
    List1.snoc [a]
    xs a
    z

    -- | O(length first list).
    append :: List1 a -> List1 a -> List2 a
    append :: forall a. List1 a -> List1 a -> List2 a
    append (a
    x :| [a]
    xs) NonEmpty a
    ys = a -> NonEmpty a -> List2 a
    forall a. a -> List1 a -> List2 a
    cons a
    x (NonEmpty a -> List2 a) -> NonEmpty a -> List2 a
    forall a b. (a -> b) -> a -> b
    $ [a] -> NonEmpty a -> NonEmpty a
    forall a. [a] -> NonEmpty a -> NonEmpty a
    List1.prependList [a]
    xs NonEmpty a
    ys

    -- | O(length first list).
    appendList :: List2 a -> [a] -> List2 a
    appendList :: forall a. List2 a -> [a] -> List2 a
    appendList (List2 a
    x a
    y [a]
    ys) [a]
    zs = a -> a -> [a] -> List2 a
    forall a. a -> a -> [a] -> List2 a
    List2 a
    x a
    y ([a] -> List2 a) -> [a] -> List2 a
    forall a b. (a -> b) -> a -> b
    $ [a] -> [a] -> [a]
    forall a. Monoid a => a -> a -> a
    mappend [a]
    ys [a]
    zs

    -- | Concatenate at least 2 lists of length at least 1.
    concat21 :: List2 (List1 a) -> List2 a
    concat21 :: forall a. List2 (List1 a) -> List2 a
    concat21 (List2 List1 a
    xs List1 a
    ys [List1 a]
    zss) = List1 a -> List1 a -> List2 a
    forall a. List1 a -> List1 a -> List2 a
    append List1 a
    xs (List1 a -> List2 a) -> List1 a -> List2 a
    forall a b. (a -> b) -> a -> b
    $ NonEmpty (List1 a) -> List1 a
    forall a. Semigroup a => NonEmpty a -> a
    sconcat (NonEmpty (List1 a) -> List1 a) -> NonEmpty (List1 a) -> List1 a
    forall a b. (a -> b) -> a -> b
    $ List1 a
    ys List1 a -> [List1 a] -> NonEmpty (List1 a)
    forall a. a -> [a] -> NonEmpty a
    :| [List1 a]
    zss

    -- * Destruction

    -- | Safe. O(1).
    head :: List2 a -> a
    head :: forall a. List2 a -> a
    head (List2 a
    a a
    _ [a]
    _) = a
    a

    -- | Safe. O(1).
    tail :: List2 a -> List1 a
    tail :: forall a. List2 a -> List1 a
    tail (List2 a
    a a
    b [a]
    cs) = a
    b a -> [a] -> NonEmpty a
    forall a. a -> [a] -> NonEmpty a
    :| [a]
    cs

    -- | Safe. O(n).
    init :: List2 a -> List1 a
    init :: forall a. List2 a -> List1 a
    init (List2 a
    a a
    b [a]
    cs) = a
    a a -> [a] -> NonEmpty a
    forall a. a -> [a] -> NonEmpty a
    :| NonEmpty a -> [a]
    forall a. NonEmpty a -> [a]
    List1.init (a
    b a -> [a] -> NonEmpty a
    forall a. a -> [a] -> NonEmpty a
    :| [a]
    cs)

    -- * Partition

    break :: (a -> Bool) -> List2 a -> ([a],[a])
    break :: forall a. (a -> Bool) -> List2 a -> ([a], [a])
    break a -> Bool
    p = (a -> Bool) -> [a] -> ([a], [a])
    forall a. (a -> Bool) -> [a] -> ([a], [a])
    List.break a -> Bool
    p ([a] -> ([a], [a])) -> (List2 a -> [a]) -> List2 a -> ([a], [a])
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . List2 a -> [a]
    List2 a -> [Item (List2 a)]
    forall l. IsList l => l -> [Item l]
    toList

    instance NFData a => NFData (List2 a) where
      rnf :: List2 a -> ()
    rnf (List2 a
    a a
    b [a]
    cs) = a -> ()
    forall a. NFData a => a -> ()
    rnf a
    a () -> () -> ()
    forall a b. a -> b -> b
    `seq` a -> ()
    forall a. NFData a => a -> ()
    rnf a
    b () -> () -> ()
    forall a b. a -> b -> b
    `seq` [a] -> ()
    forall a. NFData a => a -> ()
    rnf [a]
    cs