    -- | Utility functions for lists.

    module Agda.Utils.List where

    import Control.Monad (filterM)

    import Data.Array (Array, array, listArray)
    import qualified Data.Array as Array
    import Data.Bifunctor
    import Data.Function
    import qualified Data.List as List
    import qualified Data.List.NonEmpty as List1
    import Data.List.NonEmpty (pattern (:|), (<|))
    import Data.Maybe
    import qualified Data.Map as Map
    import qualified Data.Set as Set

    import qualified Agda.Utils.Bag as Bag
    import Agda.Utils.Function (applyWhen)
    import Agda.Utils.Functor  ((<.>))
    import Agda.Utils.Tuple

    import {-# SOURCE #-} Agda.Utils.List1 (List1)

    import Agda.Utils.Impossible

    ---------------------------------------------------------------------------
    -- * Variants of list case, cons, head, tail, init, last
    ---------------------------------------------------------------------------

    -- | Append a single element at the end.
    --   Time: O(length); use only on small lists.
    snoc :: [a] -> a -> [a]
    snoc :: forall a. [a] -> a -> [a]
    snoc [a]
    xs a
    x = [a]
    xs [a] -> [a] -> [a]
    forall a. [a] -> [a] -> [a]
    ++ [a
    x]

    -- | Case distinction for lists, with list first.
    --   O(1).
    --
    --   Cf. 'Agda.Utils.Null.ifNull'.
    caseList :: [a] -> b -> (a -> [a] -> b) -> b
    caseList :: forall a b. [a] -> b -> (a -> [a] -> b) -> b
    caseList [a]
    xs b
    n a -> [a] -> b
    c = b -> (a -> [a] -> b) -> [a] -> b
    forall b a. b -> (a -> [a] -> b) -> [a] -> b
    listCase b
    n a -> [a] -> b
    c [a]
    xs

    -- | Case distinction for lists, with list first.
    --   O(1).
    --
    --   Cf. 'Agda.Utils.Null.ifNull'.
    caseListM :: Monad m => m [a] -> m b -> (a -> [a] -> m b) -> m b
    caseListM :: forall (m :: * -> *) a b.
    Monad m =>
    m [a] -> m b -> (a -> [a] -> m b) -> m b
    caseListM m [a]
    mxs m b
    n a -> [a] -> m b
    c = m b -> (a -> [a] -> m b) -> [a] -> m b
    forall b a. b -> (a -> [a] -> b) -> [a] -> b
    listCase m b
    n a -> [a] -> m b
    c ([a] -> m b) -> m [a] -> m b
    forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
    =<< m [a]
    mxs

    -- | Case distinction for lists, with list last.
    --   O(1).
    --
    listCase :: b -> (a -> [a] -> b) -> [a] -> b
    listCase :: forall b a. b -> (a -> [a] -> b) -> [a] -> b
    listCase b
    n a -> [a] -> b
    c []     = b
    n
    listCase b
    n a -> [a] -> b
    c (a
    x:[a]
    xs) = a -> [a] -> b
    c a
    x [a]
    xs

    -- | Head function (safe). Returns a default value on empty lists.
    --   O(1).
    --
    -- > headWithDefault 42 []      = 42
    -- > headWithDefault 42 [1,2,3] = 1
    headWithDefault :: a -> [a] -> a
    headWithDefault :: forall a. a -> [a] -> a
    headWithDefault a
    def = a -> Maybe a -> a
    forall a. a -> Maybe a -> a
    fromMaybe a
    def (Maybe a -> a) -> ([a] -> Maybe a) -> [a] -> a
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . [a] -> Maybe a
    forall a. [a] -> Maybe a
    listToMaybe

    -- | Tail function (safe).
    --   O(1).
    tailMaybe :: [a] -> Maybe [a]
    tailMaybe :: forall a. [a] -> Maybe [a]
    tailMaybe = ((a, [a]) -> [a]) -> Maybe (a, [a]) -> Maybe [a]
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap (a, [a]) -> [a]
    forall a b. (a, b) -> b
    snd (Maybe (a, [a]) -> Maybe [a])
    -> ([a] -> Maybe (a, [a])) -> [a] -> Maybe [a]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . [a] -> Maybe (a, [a])
    forall a. [a] -> Maybe (a, [a])
    uncons

    -- | Tail function (safe).  Returns a default list on empty lists.
    --   O(1).
    tailWithDefault :: [a] -> [a] -> [a]
    tailWithDefault :: forall a. [a] -> [a] -> [a]
    tailWithDefault [a]
    def = [a] -> Maybe [a] -> [a]
    forall a. a -> Maybe a -> a
    fromMaybe [a]
    def (Maybe [a] -> [a]) -> ([a] -> Maybe [a]) -> [a] -> [a]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . [a] -> Maybe [a]
    forall a. [a] -> Maybe [a]
    tailMaybe

    -- | Last element (safe).
    --   O(n).
    lastMaybe :: [a] -> Maybe a
    lastMaybe :: forall a. [a] -> Maybe a
    lastMaybe [] = Maybe a
    forall a. Maybe a
    Nothing
    lastMaybe [a]
    xs = a -> Maybe a
    forall a. a -> Maybe a
    Just (a -> Maybe a) -> a -> Maybe a
    forall a b. (a -> b) -> a -> b
    $ [a] -> a
    forall a. [a] -> a
    last [a]
    xs

    -- | Last element (safe).  Returns a default list on empty lists.
    --   O(n).
    lastWithDefault :: a -> [a] -> a
    lastWithDefault :: forall a. a -> [a] -> a
    lastWithDefault = a -> [a] -> a
    forall a. a -> [a] -> a
    last1

    -- | Last element of non-empty list (safe).
    --   O(n).
    --   @last1 a as = last (a : as)@
    last1 :: a -> [a] -> a
    last1 :: forall a. a -> [a] -> a
    last1 a
    a = \case
      [] -> a
    a
      a
    b:[a]
    bs -> a -> [a] -> a
    forall a. a -> [a] -> a
    last1 a
    b [a]
    bs

    -- | Last two elements (safe).
    --   O(n).
    last2 :: [a] -> Maybe (a, a)
    last2 :: forall a. [a] -> Maybe (a, a)
    last2 (a
    x : a
    y : [a]
    xs) = (a, a) -> Maybe (a, a)
    forall a. a -> Maybe a
    Just ((a, a) -> Maybe (a, a)) -> (a, a) -> Maybe (a, a)
    forall a b. (a -> b) -> a -> b
    $ a -> a -> [a] -> (a, a)
    forall {t}. t -> t -> [t] -> (t, t)
    loop a
    x a
    y [a]
    xs
      where
      loop :: t -> t -> [t] -> (t, t)
    loop t
    x t
    y []     = (t
    x, t
    y)
      loop t
    x t
    y (t
    z:[t]
    xs) = t -> t -> [t] -> (t, t)
    loop t
    y t
    z [t]
    xs
    last2 [a]
    _ = Maybe (a, a)
    forall a. Maybe a
    Nothing

    -- | Opposite of cons @(:)@, safe.
    --   O(1).
    uncons :: [a] -> Maybe (a, [a])
    uncons :: forall a. [a] -> Maybe (a, [a])
    uncons []     = Maybe (a, [a])
    forall a. Maybe a
    Nothing
    uncons (a
    x:[a]
    xs) = (a, [a]) -> Maybe (a, [a])
    forall a. a -> Maybe a
    Just (a
    x,[a]
    xs)

    -- | Maybe cons.
    --   O(1).
    --   @mcons ma as = maybeToList ma ++ as@
    mcons :: Maybe a -> [a] -> [a]
    mcons :: forall a. Maybe a -> [a] -> [a]
    mcons Maybe a
    ma [a]
    as = [a] -> (a -> [a]) -> Maybe a -> [a]
    forall b a. b -> (a -> b) -> Maybe a -> b
    maybe [a]
    as (a -> [a] -> [a]
    forall a. a -> [a] -> [a]
    :[a]
    as) Maybe a
    ma

    -- | 'init' and 'last' in one go, safe.
    --   O(n).
    initLast :: [a] -> Maybe ([a],a)
    initLast :: forall a. [a] -> Maybe ([a], a)
    initLast []     = Maybe ([a], a)
    forall a. Maybe a
    Nothing
    initLast (a
    a:[a]
    as) = ([a], a) -> Maybe ([a], a)
    forall a. a -> Maybe a
    Just (([a], a) -> Maybe ([a], a)) -> ([a], a) -> Maybe ([a], a)
    forall a b. (a -> b) -> a -> b
    $ a -> [a] -> ([a], a)
    forall a. a -> [a] -> ([a], a)
    initLast1 a
    a [a]
    as

    -- | 'init' and 'last' of non-empty list, safe.
    --   O(n).
    --   @initLast1 a as = (init (a:as), last (a:as)@
    initLast1 :: a -> [a] -> ([a], a)
    initLast1 :: forall a. a -> [a] -> ([a], a)
    initLast1 a
    a = \case
      []   -> ([], a
    a)
      a
    b:[a]
    bs -> ([a] -> [a]) -> ([a], a) -> ([a], a)
    forall (p :: * -> * -> *) a b c.
    Bifunctor p =>
    (a -> b) -> p a c -> p b c
    first (a
    aa -> [a] -> [a]
    forall a. a -> [a] -> [a]
    :) (([a], a) -> ([a], a)) -> ([a], a) -> ([a], a)
    forall a b. (a -> b) -> a -> b
    $ a -> [a] -> ([a], a)
    forall a. a -> [a] -> ([a], a)
    initLast1 a
    b [a]
    bs

    -- | 'init' of non-empty list, safe.
    --   O(n).
    --   @init1 a as = init (a:as)@
    init1 :: a -> [a] -> [a]
    init1 :: forall a. a -> [a] -> [a]
    init1 a
    a = \case
      []   -> []
      a
    b:[a]
    bs -> a
    a a -> [a] -> [a]
    forall a. a -> [a] -> [a]
    : a -> [a] -> [a]
    forall a. a -> [a] -> [a]
    init1 a
    b [a]
    bs

    -- | @init@, safe.
    --   O(n).
    initMaybe :: [a] -> Maybe [a]
    initMaybe :: forall a. [a] -> Maybe [a]
    initMaybe = \case
      []   -> Maybe [a]
    forall a. Maybe a
    Nothing
      a
    a:[a]
    as -> [a] -> Maybe [a]
    forall a. a -> Maybe a
    Just ([a] -> Maybe [a]) -> [a] -> Maybe [a]
    forall a b. (a -> b) -> a -> b
    $ a -> [a] -> [a]
    forall a. a -> [a] -> [a]
    init1 a
    a [a]
    as

    -- | @init@, safe.
    --   O(n).
    initWithDefault :: [a] -> [a] -> [a]
    initWithDefault :: forall a. [a] -> [a] -> [a]
    initWithDefault [a]
    as []     = [a]
    as
    initWithDefault [a]
    _  (a
    a:[a]
    as) = a -> [a] -> [a]
    forall a. a -> [a] -> [a]
    init1 a
    a [a]
    as

    ---------------------------------------------------------------------------
    -- * Lookup and indexing
    ---------------------------------------------------------------------------

    -- | Lookup function (partially safe).
    --   O(min n index).
    (!!!) :: [a] -> Int -> Maybe a
    []       !!! :: forall a. [a] -> Int -> Maybe a
    !!! Int
    _         = Maybe a
    forall a. Maybe a
    Nothing
    (a
    x : [a]
    _)  !!! Int
    0         = a -> Maybe a
    forall a. a -> Maybe a
    Just a
    x
    (a
    _ : [a]
    xs) !!! Int
    n         = [a]
    xs [a] -> Int -> Maybe a
    forall a. [a] -> Int -> Maybe a
    !!! (Int
    n Int -> Int -> Int
    forall a. Num a => a -> a -> a
    - Int
    1)

    -- | Lookup function with default value for index out of range.
    --   O(min n index).
    --
    --   The name is chosen akin to 'Data.List.genericIndex'.
    indexWithDefault :: a -> [a] -> Int -> a
    indexWithDefault :: forall a. a -> [a] -> Int -> a
    indexWithDefault a
    a []       Int
    _ = a
    a
    indexWithDefault a
    a (a
    x : [a]
    _)  Int
    0 = a
    x
    indexWithDefault a
    a (a
    _ : [a]
    xs) Int
    n = a -> [a] -> Int -> a
    forall a. a -> [a] -> Int -> a
    indexWithDefault a
    a [a]
    xs (Int
    n Int -> Int -> Int
    forall a. Num a => a -> a -> a
    - Int
    1)

    -- | Find an element satisfying a predicate and return it with its index.
    --   O(n) in the worst case, e.g. @findWithIndex f xs = Nothing@.
    --
    --   TODO: more efficient implementation!?
    findWithIndex :: (a -> Bool) -> [a] -> Maybe (a, Int)
    findWithIndex :: forall a. (a -> Bool) -> [a] -> Maybe (a, Int)
    findWithIndex a -> Bool
    p [a]
    as = ((a, Int) -> Bool) -> [(a, Int)] -> Maybe (a, Int)
    forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Maybe a
    List.find (a -> Bool
    p (a -> Bool) -> ((a, Int) -> a) -> (a, Int) -> Bool
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . (a, Int) -> a
    forall a b. (a, b) -> a
    fst) ([a] -> [Int] -> [(a, Int)]
    forall a b. [a] -> [b] -> [(a, b)]
    zip [a]
    as [Int
    0..])

    -- | A generalised variant of 'elemIndex'.
    -- O(n).
    genericElemIndex :: (Eq a, Integral i) => a -> [a] -> Maybe i
    genericElemIndex :: forall a i. (Eq a, Integral i) => a -> [a] -> Maybe i
    genericElemIndex a
    x [a]
    xs =
      [i] -> Maybe i
    forall a. [a] -> Maybe a
    listToMaybe ([i] -> Maybe i) -> [i] -> Maybe i
    forall a b. (a -> b) -> a -> b
    $
      ((i, Bool) -> i) -> [(i, Bool)] -> [i]
    forall a b. (a -> b) -> [a] -> [b]
    map (i, Bool) -> i
    forall a b. (a, b) -> a
    fst ([(i, Bool)] -> [i]) -> [(i, Bool)] -> [i]
    forall a b. (a -> b) -> a -> b
    $
      ((i, Bool) -> Bool) -> [(i, Bool)] -> [(i, Bool)]
    forall a. (a -> Bool) -> [a] -> [a]
    filter (i, Bool) -> Bool
    forall a b. (a, b) -> b
    snd ([(i, Bool)] -> [(i, Bool)]) -> [(i, Bool)] -> [(i, Bool)]
    forall a b. (a -> b) -> a -> b
    $
      [i] -> [Bool] -> [(i, Bool)]
    forall a b. [a] -> [b] -> [(a, b)]
    zip [i
    0..] ([Bool] -> [(i, Bool)]) -> [Bool] -> [(i, Bool)]
    forall a b. (a -> b) -> a -> b
    $
      (a -> Bool) -> [a] -> [Bool]
    forall a b. (a -> b) -> [a] -> [b]
    map (a -> a -> Bool
    forall a. Eq a => a -> a -> Bool
    == a
    x) [a]
    xs

    -- | @downFrom n = [n-1,..1,0]@.
    --   O(n).
    downFrom :: Integral a => a -> [a]
    downFrom :: forall a. Integral a => a -> [a]
    downFrom a
    n | a
    n a -> a -> Bool
    forall a. Ord a => a -> a -> Bool
    <= a
    0     = []
               | Bool
    otherwise = let n' :: a
    n' = a
    na -> a -> a
    forall a. Num a => a -> a -> a
    -a
    1 in a
    n' a -> [a] -> [a]
    forall a. a -> [a] -> [a]
    : a -> [a]
    forall a. Integral a => a -> [a]
    downFrom a
    n'

    ---------------------------------------------------------------------------
    -- * Update
    ---------------------------------------------------------------------------

    -- | Update the first element of a list, if it exists.
    --   O(1).
    updateHead :: (a -> a) -> [a] -> [a]
    updateHead :: forall a. (a -> a) -> [a] -> [a]
    updateHead a -> a
    _ []       = []
    updateHead a -> a
    f (a
    a : [a]
    as) = a -> a
    f a
    a a -> [a] -> [a]
    forall a. a -> [a] -> [a]
    : [a]
    as

    -- | Update the last element of a list, if it exists.
    --   O(n).
    updateLast :: (a -> a) -> [a] -> [a]
    updateLast :: forall a. (a -> a) -> [a] -> [a]
    updateLast a -> a
    _ [] = []
    updateLast a -> a
    f (a
    a : [a]
    as) = a -> [a] -> [a]
    loop a
    a [a]
    as
      -- Using a helper function to minimize the pattern matching.
      where
      loop :: a -> [a] -> [a]
    loop a
    a []       = [a -> a
    f a
    a]
      loop a
    a (a
    b : [a]
    bs) = a
    a a -> [a] -> [a]
    forall a. a -> [a] -> [a]
    : a -> [a] -> [a]
    loop a
    b [a]
    bs

    -- | Update nth element of a list, if it exists.
    --   @O(min index n)@.
    --
    --   Precondition: the index is >= 0.
    updateAt :: Int -> (a -> a) -> [a] -> [a]
    updateAt :: forall a. Int -> (a -> a) -> [a] -> [a]
    updateAt Int
    _ a -> a
    _ [] = []
    updateAt Int
    0 a -> a
    f (a
    a : [a]
    as) = a -> a
    f a
    a a -> [a] -> [a]
    forall a. a -> [a] -> [a]
    : [a]
    as
    updateAt Int
    n a -> a
    f (a
    a : [a]
    as) = a
    a a -> [a] -> [a]
    forall a. a -> [a] -> [a]
    : Int -> (a -> a) -> [a] -> [a]
    forall a. Int -> (a -> a) -> [a] -> [a]
    updateAt (Int
    nInt -> Int -> Int
    forall a. Num a => a -> a -> a
    -Int
    1) a -> a
    f [a]
    as

    ---------------------------------------------------------------------------
    -- * Sublist extraction and partitioning
    ---------------------------------------------------------------------------

    type Prefix a = [a]  -- ^ The list before the split point.
    type Suffix a = [a]  -- ^ The list after the split point.

    -- | @splitExactlyAt n xs = Just (ys, zs)@ iff @xs = ys ++ zs@
    --   and @genericLength ys = n@.
    splitExactlyAt :: Integral n => n -> [a] -> Maybe (Prefix a, Suffix a)
    splitExactlyAt :: forall n a. Integral n => n -> [a] -> Maybe ([a], [a])
    splitExactlyAt n
    0 [a]
    xs       = ([a], [a]) -> Maybe ([a], [a])
    forall (m :: * -> *) a. Monad m => a -> m a
    return ([], [a]
    xs)
    splitExactlyAt n
    n []       = Maybe ([a], [a])
    forall a. Maybe a
    Nothing
    splitExactlyAt n
    n (a
    x : [a]
    xs) = ([a] -> [a]) -> ([a], [a]) -> ([a], [a])
    forall a c b. (a -> c) -> (a, b) -> (c, b)
    mapFst (a
    x a -> [a] -> [a]
    forall a. a -> [a] -> [a]
    :) (([a], [a]) -> ([a], [a])) -> Maybe ([a], [a]) -> Maybe ([a], [a])
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> n -> [a] -> Maybe ([a], [a])
    forall n a. Integral n => n -> [a] -> Maybe ([a], [a])
    splitExactlyAt (n
    nn -> n -> n
    forall a. Num a => a -> a -> a
    -n
    1) [a]
    xs

    -- | Drop from the end of a list.
    --   O(length).
    --
    --   @dropEnd n = reverse . drop n . reverse@
    --
    --   Forces the whole list even for @n==0@.
    dropEnd :: forall a. Int -> [a] -> Prefix a
    dropEnd :: forall a. Int -> [a] -> [a]
    dropEnd Int
    n = (Int, [a]) -> [a]
    forall a b. (a, b) -> b
    snd ((Int, [a]) -> [a]) -> ([a] -> (Int, [a])) -> [a] -> [a]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . (a -> (Int, [a]) -> (Int, [a])) -> (Int, [a]) -> [a] -> (Int, [a])
    forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr a -> (Int, [a]) -> (Int, [a])
    f (Int
    n, [])
      where
      f :: a -> (Int, [a]) -> (Int, [a])
      f :: a -> (Int, [a]) -> (Int, [a])
    f a
    x (Int
    n, [a]
    xs) = (Int
    nInt -> Int -> Int
    forall a. Num a => a -> a -> a
    -Int
    1, Bool -> ([a] -> [a]) -> [a] -> [a]
    forall a. Bool -> (a -> a) -> a -> a
    applyWhen (Int
    n Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    <= Int
    0) (a
    xa -> [a] -> [a]
    forall a. a -> [a] -> [a]
    :) [a]
    xs)

    -- | Split off the largest suffix whose elements satisfy a predicate.
    --   O(n).
    --
    --   @spanEnd p xs = (ys, zs)@
    --   where @xs = ys ++ zs@
    --   and @all p zs@
    --   and @maybe True (not . p) (lastMaybe yz)@.
    spanEnd :: forall a. (a -> Bool) -> [a] -> (Prefix a, Suffix a)
    spanEnd :: forall a. (a -> Bool) -> [a] -> ([a], [a])
    spanEnd a -> Bool
    p = (Bool, ([a], [a])) -> ([a], [a])
    forall a b. (a, b) -> b
    snd ((Bool, ([a], [a])) -> ([a], [a]))
    -> ([a] -> (Bool, ([a], [a]))) -> [a] -> ([a], [a])
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . (a -> (Bool, ([a], [a])) -> (Bool, ([a], [a])))
    -> (Bool, ([a], [a])) -> [a] -> (Bool, ([a], [a]))
    forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr a -> (Bool, ([a], [a])) -> (Bool, ([a], [a]))
    f (Bool
    True, ([], []))
      where
      f :: a -> (Bool, ([a], [a])) -> (Bool, ([a], [a]))
      f :: a -> (Bool, ([a], [a])) -> (Bool, ([a], [a]))
    f a
    x (Bool
    b', ([a]
    xs, [a]
    ys)) = (Bool
    b, if Bool
    b then ([a]
    xs, a
    xa -> [a] -> [a]
    forall a. a -> [a] -> [a]
    :[a]
    ys) else (a
    xa -> [a] -> [a]
    forall a. a -> [a] -> [a]
    :[a]
    xs, [a]
    ys))
        where b :: Bool
    b = Bool
    b' Bool -> Bool -> Bool
    && a -> Bool
    p a
    x

    -- | Breaks a list just /after/ an element satisfying the predicate is
    --   found.
    --
    --   >>> breakAfter1 even 1 [3,5,2,4,7,8]
    --   ([1,3,5,2],[4,7,8])

    breakAfter1 :: (a -> Bool) -> a -> [a] -> (List1 a, [a])
    breakAfter1 :: forall a. (a -> Bool) -> a -> [a] -> (List1 a, [a])
    breakAfter1 a -> Bool
    p = a -> [a] -> (NonEmpty a, [a])
    loop
      where
      loop :: a -> [a] -> (NonEmpty a, [a])
    loop a
    x = \case
        xs :: [a]
    xs@[]         -> (a
    x a -> [a] -> NonEmpty a
    forall a. a -> [a] -> NonEmpty a
    :| [], [a]
    xs)
        xs :: [a]
    xs@(a
    y : [a]
    ys)
          | a -> Bool
    p a
    x       -> (a
    x a -> [a] -> NonEmpty a
    forall a. a -> [a] -> NonEmpty a
    :| [], [a]
    xs)
          | Bool
    otherwise -> let (NonEmpty a
    vs, [a]
    ws) = a -> [a] -> (NonEmpty a, [a])
    loop a
    y [a]
    ys in (a
    x a -> NonEmpty a -> NonEmpty a
    forall a. a -> NonEmpty a -> NonEmpty a
    <| NonEmpty a
    vs, [a]
    ws)

    -- | Breaks a list just /after/ an element satisfying the predicate is
    --   found.
    --
    --   >>> breakAfter even [1,3,5,2,4,7,8]
    --   ([1,3,5,2],[4,7,8])

    breakAfter :: (a -> Bool) -> [a] -> ([a], [a])
    breakAfter :: forall a. (a -> Bool) -> [a] -> ([a], [a])
    breakAfter a -> Bool
    p = \case
      []   -> ([], [])
      a
    x:[a]
    xs -> (NonEmpty a -> [a]) -> (NonEmpty a, [a]) -> ([a], [a])
    forall (p :: * -> * -> *) a b c.
    Bifunctor p =>
    (a -> b) -> p a c -> p b c
    first NonEmpty a -> [a]
    forall a. NonEmpty a -> [a]
    List1.toList ((NonEmpty a, [a]) -> ([a], [a]))
    -> (NonEmpty a, [a]) -> ([a], [a])
    forall a b. (a -> b) -> a -> b
    $ (a -> Bool) -> a -> [a] -> (NonEmpty a, [a])
    forall a. (a -> Bool) -> a -> [a] -> (List1 a, [a])
    breakAfter1 a -> Bool
    p a
    x [a]
    xs

    -- | A generalized version of @takeWhile@.
    --   (Cf. @mapMaybe@ vs. @filter@).
    --   @O(length . takeWhileJust f).
    --
    --   @takeWhileJust f = fst . spanJust f@.
    takeWhileJust :: (a -> Maybe b) -> [a] -> Prefix b
    takeWhileJust :: forall a b. (a -> Maybe b) -> [a] -> Prefix b
    takeWhileJust a -> Maybe b
    p = [a] -> [b]
    loop
      where
        loop :: [a] -> [b]
    loop (a
    a : [a]
    as) | Just b
    b <- a -> Maybe b
    p a
    a = b
    b b -> [b] -> [b]
    forall a. a -> [a] -> [a]
    : [a] -> [b]
    loop [a]
    as
        loop [a]
    _ = []

    -- | A generalized version of @span@.
    --   @O(length . fst . spanJust f)@.
    spanJust :: (a -> Maybe b) -> [a] -> (Prefix b, Suffix a)
    spanJust :: forall a b. (a -> Maybe b) -> [a] -> (Prefix b, [a])
    spanJust a -> Maybe b
    p = [a] -> ([b], [a])
    loop
      where
        loop :: [a] -> ([b], [a])
    loop (a
    a : [a]
    as) | Just b
    b <- a -> Maybe b
    p a
    a = ([b] -> [b]) -> ([b], [a]) -> ([b], [a])
    forall a c b. (a -> c) -> (a, b) -> (c, b)
    mapFst (b
    b b -> [b] -> [b]
    forall a. a -> [a] -> [a]
    :) (([b], [a]) -> ([b], [a])) -> ([b], [a]) -> ([b], [a])
    forall a b. (a -> b) -> a -> b
    $ [a] -> ([b], [a])
    loop [a]
    as
        loop [a]
    as                       = ([], [a]
    as)

    -- | Partition a list into 'Nothing's and 'Just's.
    --   O(n).
    --
    --   @partitionMaybe f = partitionEithers . map (\ a -> maybe (Left a) Right (f a))@
    --
    --   Note: @'mapMaybe' f = snd . partitionMaybe f@.
    partitionMaybe :: (a -> Maybe b) -> [a] -> ([a], [b])
    partitionMaybe :: forall a b. (a -> Maybe b) -> [a] -> ([a], [b])
    partitionMaybe a -> Maybe b
    f = [a] -> ([a], [b])
    loop
      where
        loop :: [a] -> ([a], [b])
    loop []       = ([], [])
        loop (a
    a : [a]
    as) = case a -> Maybe b
    f a
    a of
          Maybe b
    Nothing -> ([a] -> [a]) -> ([a], [b]) -> ([a], [b])
    forall a c b. (a -> c) -> (a, b) -> (c, b)
    mapFst (a
    a a -> [a] -> [a]
    forall a. a -> [a] -> [a]
    :) (([a], [b]) -> ([a], [b])) -> ([a], [b]) -> ([a], [b])
    forall a b. (a -> b) -> a -> b
    $ [a] -> ([a], [b])
    loop [a]
    as
          Just b
    b  -> ([b] -> [b]) -> ([a], [b]) -> ([a], [b])
    forall b d a. (b -> d) -> (a, b) -> (a, d)
    mapSnd (b
    b b -> [b] -> [b]
    forall a. a -> [a] -> [a]
    :) (([a], [b]) -> ([a], [b])) -> ([a], [b]) -> ([a], [b])
    forall a b. (a -> b) -> a -> b
    $ [a] -> ([a], [b])
    loop [a]
    as

    -- | Like 'filter', but additionally return the last partition
    --   of the list where the predicate is @False@ everywhere.
    --   O(n).
    filterAndRest :: (a -> Bool) -> [a] -> ([a], Suffix a)
    filterAndRest :: forall a. (a -> Bool) -> [a] -> ([a], [a])
    filterAndRest a -> Bool
    p = (a -> Maybe a) -> [a] -> ([a], [a])
    forall a b. (a -> Maybe b) -> [a] -> (Prefix b, [a])
    mapMaybeAndRest ((a -> Maybe a) -> [a] -> ([a], [a]))
    -> (a -> Maybe a) -> [a] -> ([a], [a])
    forall a b. (a -> b) -> a -> b
    $ \ a
    a -> if a -> Bool
    p a
    a then a -> Maybe a
    forall a. a -> Maybe a
    Just a
    a else Maybe a
    forall a. Maybe a
    Nothing

    -- | Like 'mapMaybe', but additionally return the last partition
    --   of the list where the function always returns @Nothing@.
    --   O(n).
    mapMaybeAndRest :: (a -> Maybe b) -> [a] -> ([b], Suffix a)
    mapMaybeAndRest :: forall a b. (a -> Maybe b) -> [a] -> (Prefix b, [a])
    mapMaybeAndRest a -> Maybe b
    f = [a] -> [a] -> ([b], [a])
    loop [] where
      loop :: [a] -> [a] -> ([b], [a])
    loop [a]
    acc = \case
        []                   -> ([], [a] -> [a]
    forall a. [a] -> [a]
    reverse [a]
    acc)
        a
    x:[a]
    xs | Just b
    y <- a -> Maybe b
    f a
    x -> ([b] -> [b]) -> ([b], [a]) -> ([b], [a])
    forall (p :: * -> * -> *) a b c.
    Bifunctor p =>
    (a -> b) -> p a c -> p b c
    first (b
    yb -> [b] -> [b]
    forall a. a -> [a] -> [a]
    :) (([b], [a]) -> ([b], [a])) -> ([b], [a]) -> ([b], [a])
    forall a b. (a -> b) -> a -> b
    $ [a] -> [a] -> ([b], [a])
    loop [] [a]
    xs
             | Bool
    otherwise     -> [a] -> [a] -> ([b], [a])
    loop (a
    xa -> [a] -> [a]
    forall a. a -> [a] -> [a]
    :[a]
    acc) [a]
    xs

    -- | Sublist relation.
    isSublistOf :: Eq a => [a] -> [a] -> Bool
    isSublistOf :: forall a. Eq a => [a] -> [a] -> Bool
    isSublistOf = [a] -> [a] -> Bool
    forall a. Eq a => [a] -> [a] -> Bool
    List.isSubsequenceOf

    -- | All ways of removing one element from a list.
    --   O(n²).
    holes :: [a] -> [(a, [a])]
    holes :: forall a. [a] -> [(a, [a])]
    holes []     = []
    holes (a
    x:[a]
    xs) = (a
    x, [a]
    xs) (a, [a]) -> [(a, [a])] -> [(a, [a])]
    forall a. a -> [a] -> [a]
    : ((a, [a]) -> (a, [a])) -> [(a, [a])] -> [(a, [a])]
    forall a b. (a -> b) -> [a] -> [b]
    map (([a] -> [a]) -> (a, [a]) -> (a, [a])
    forall (p :: * -> * -> *) b c a.
    Bifunctor p =>
    (b -> c) -> p a b -> p a c
    second (a
    xa -> [a] -> [a]
    forall a. a -> [a] -> [a]
    :)) ([a] -> [(a, [a])]
    forall a. [a] -> [(a, [a])]
    holes [a]
    xs)

    ---------------------------------------------------------------------------
    -- * Prefix and suffix
    ---------------------------------------------------------------------------

    -- ** Prefix

    -- | Compute the common prefix of two lists.
    --   O(min n m).
    commonPrefix :: Eq a => [a] -> [a] -> Prefix a
    commonPrefix :: forall a. Eq a => [a] -> [a] -> [a]
    commonPrefix [] [a]
    _ = []
    commonPrefix [a]
    _ [] = []
    commonPrefix (a
    x:[a]
    xs) (a
    y:[a]
    ys)
      | a
    x a -> a -> Bool
    forall a. Eq a => a -> a -> Bool
    == a
    y    = a
    x a -> [a] -> [a]
    forall a. a -> [a] -> [a]
    : [a] -> [a] -> [a]
    forall a. Eq a => [a] -> [a] -> [a]
    commonPrefix [a]
    xs [a]
    ys
      | Bool
    otherwise = []

    -- | Drops from both lists simultaneously until one list is empty.
    --   O(min n m).
    dropCommon :: [a] -> [b] -> (Suffix a, Suffix b)
    dropCommon :: forall a b. [a] -> [b] -> ([a], [b])
    dropCommon (a
    x : [a]
    xs) (b
    y : [b]
    ys) = [a] -> [b] -> ([a], [b])
    forall a b. [a] -> [b] -> ([a], [b])
    dropCommon [a]
    xs [b]
    ys
    dropCommon [a]
    xs [b]
    ys = ([a]
    xs, [b]
    ys)

    -- | Check if a list has a given prefix. If so, return the list
    --   minus the prefix.
    --   O(length prefix).
    stripPrefixBy :: (a -> a -> Bool) -> Prefix a -> [a] -> Maybe (Suffix a)
    stripPrefixBy :: forall a.
    (a -> a -> Bool) -> Prefix a -> Prefix a -> Maybe (Prefix a)
    stripPrefixBy a -> a -> Bool
    eq = [a] -> [a] -> Maybe [a]
    loop
      where
      loop :: [a] -> [a] -> Maybe [a]
    loop []    [a]
    rest = [a] -> Maybe [a]
    forall a. a -> Maybe a
    Just [a]
    rest
      loop (a
    _:[a]
    _) []   = Maybe [a]
    forall a. Maybe a
    Nothing
      loop (a
    p:[a]
    pat) (a
    r:[a]
    rest)
        | a -> a -> Bool
    eq a
    p a
    r    = [a] -> [a] -> Maybe [a]
    loop [a]
    pat [a]
    rest
        | Bool
    otherwise = Maybe [a]
    forall a. Maybe a
    Nothing

    -- ** Suffix

    -- | Compute the common suffix of two lists.
    --   O(n + m).
    commonSuffix :: Eq a => [a] -> [a] -> Suffix a
    commonSuffix :: forall a. Eq a => [a] -> [a] -> [a]
    commonSuffix [a]
    xs [a]
    ys = [a] -> [a]
    forall a. [a] -> [a]
    reverse ([a] -> [a]) -> [a] -> [a]
    forall a b. (a -> b) -> a -> b
    $ ([a] -> [a] -> [a]
    forall a. Eq a => [a] -> [a] -> [a]
    commonPrefix ([a] -> [a] -> [a]) -> ([a] -> [a]) -> [a] -> [a] -> [a]
    forall b c a. (b -> b -> c) -> (a -> b) -> a -> a -> c
    `on` [a] -> [a]
    forall a. [a] -> [a]
    reverse) [a]
    xs [a]
    ys

    -- | @stripSuffix suf xs = Just pre@ iff @xs = pre ++ suf@.
    -- O(n).
    stripSuffix :: Eq a => Suffix a -> [a] -> Maybe (Prefix a)
    stripSuffix :: forall a. Eq a => Suffix a -> Suffix a -> Maybe (Suffix a)
    stripSuffix [] = [a] -> Maybe [a]
    forall a. a -> Maybe a
    Just
    stripSuffix [a]
    s  = [a] -> [a] -> Maybe [a]
    forall a. Eq a => Suffix a -> Suffix a -> Maybe (Suffix a)
    stripReversedSuffix ([a] -> [a]
    forall a. [a] -> [a]
    reverse [a]
    s)

    type ReversedSuffix a = [a]

    -- | @stripReversedSuffix rsuf xs = Just pre@ iff @xs = pre ++ reverse suf@.
    --   O(n).
    stripReversedSuffix :: forall a. Eq a => ReversedSuffix a -> [a] -> Maybe (Prefix a)
    stripReversedSuffix :: forall a. Eq a => Suffix a -> Suffix a -> Maybe (Suffix a)
    stripReversedSuffix ReversedSuffix a
    rs = StrSufSt a -> Maybe (ReversedSuffix a)
    final (StrSufSt a -> Maybe (ReversedSuffix a))
    -> (ReversedSuffix a -> StrSufSt a)
    -> ReversedSuffix a
    -> Maybe (ReversedSuffix a)
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . (a -> StrSufSt a -> StrSufSt a)
    -> StrSufSt a -> ReversedSuffix a -> StrSufSt a
    forall (t :: * -> *) a b.
    Foldable t =>
    (a -> b -> b) -> b -> t a -> b
    foldr a -> StrSufSt a -> StrSufSt a
    step (ReversedSuffix a -> StrSufSt a
    forall a. ReversedSuffix a -> StrSufSt a
    SSSStrip ReversedSuffix a
    rs)
      where
      -- Step of the automaton (reading input from right to left).
      step :: a -> StrSufSt a -> StrSufSt a
      step :: a -> StrSufSt a -> StrSufSt a
    step a
    x = \case
        StrSufSt a
    SSSMismatch   -> StrSufSt a
    forall a. StrSufSt a
    SSSMismatch
        SSSResult ReversedSuffix a
    xs  -> ReversedSuffix a -> StrSufSt a
    forall a. ReversedSuffix a -> StrSufSt a
    SSSResult (a
    xa -> ReversedSuffix a -> ReversedSuffix a
    forall a. a -> [a] -> [a]
    :ReversedSuffix a
    xs)
        SSSStrip []   -> ReversedSuffix a -> StrSufSt a
    forall a. ReversedSuffix a -> StrSufSt a
    SSSResult [a
    x]
        SSSStrip (a
    y:ReversedSuffix a
    ys)
          | a
    x a -> a -> Bool
    forall a. Eq a => a -> a -> Bool
    == a
    y    -> ReversedSuffix a -> StrSufSt a
    forall a. ReversedSuffix a -> StrSufSt a
    SSSStrip ReversedSuffix a
    ys
          | Bool
    otherwise -> StrSufSt a
    forall a. StrSufSt a
    SSSMismatch

      -- Output of the automaton.
      final :: StrSufSt a -> Maybe (Prefix a)
      final :: StrSufSt a -> Maybe (ReversedSuffix a)
    final = \case
        SSSResult ReversedSuffix a
    xs -> ReversedSuffix a -> Maybe (ReversedSuffix a)
    forall a. a -> Maybe a
    Just ReversedSuffix a
    xs
        SSSStrip []  -> ReversedSuffix a -> Maybe (ReversedSuffix a)
    forall a. a -> Maybe a
    Just []
        StrSufSt a
    _            -> Maybe (ReversedSuffix a)
    forall a. Maybe a
    Nothing  -- We have not stripped the whole suffix or encountered a mismatch.

    -- | Internal state for stripping suffix.
    data StrSufSt a
      = SSSMismatch                 -- ^ Error.
      | SSSStrip (ReversedSuffix a) -- ^ "Negative string" to remove from end. List may be empty.
      | SSSResult [a]               -- ^ "Positive string" (result). Non-empty list.

    -- ** Finding overlap

    -- | Find out whether the first string @xs@
    --   has a suffix that is a prefix of the second string @ys@.
    --   So, basically, find the overlap where the strings can be glued together.
    --   Returns the index where the overlap starts and the length of the overlap.
    --   The length of the overlap plus the index is the length of the first string.
    --   Note that in the worst case, the empty overlap @(length xs,0)@ is returned.
    findOverlap :: forall a. Eq a => [a] -> [a] -> (Int, Int)
    findOverlap :: forall a. Eq a => [a] -> [a] -> (Int, Int)
    findOverlap [a]
    xs [a]
    ys =
      (Int, Int) -> [(Int, Int)] -> (Int, Int)
    forall a. a -> [a] -> a
    headWithDefault (Int, Int)
    forall a. HasCallStack => a
    __IMPOSSIBLE__ ([(Int, Int)] -> (Int, Int)) -> [(Int, Int)] -> (Int, Int)
    forall a b. (a -> b) -> a -> b
    $ ((Int, [a]) -> Maybe (Int, Int)) -> [(Int, [a])] -> [(Int, Int)]
    forall a b. (a -> Maybe b) -> [a] -> Prefix b
    mapMaybe (Int, [a]) -> Maybe (Int, Int)
    maybePrefix ([(Int, [a])] -> [(Int, Int)]) -> [(Int, [a])] -> [(Int, Int)]
    forall a b. (a -> b) -> a -> b
    $ [Int] -> [[a]] -> [(Int, [a])]
    forall a b. [a] -> [b] -> [(a, b)]
    zip [Int
    0..] ([a] -> [[a]]
    forall a. [a] -> [[a]]
    List.tails [a]
    xs)
      where
      maybePrefix :: (Int, [a]) -> Maybe (Int, Int)
      maybePrefix :: (Int, [a]) -> Maybe (Int, Int)
    maybePrefix (Int
    k, [a]
    xs')
        | [a]
    xs' [a] -> [a] -> Bool
    forall a. Eq a => [a] -> [a] -> Bool
    `List.isPrefixOf` [a]
    ys = (Int, Int) -> Maybe (Int, Int)
    forall a. a -> Maybe a
    Just (Int
    k, [a] -> Int
    forall (t :: * -> *) a. Foldable t => t a -> Int
    length [a]
    xs')
        | Bool
    otherwise                = Maybe (Int, Int)
    forall a. Maybe a
    Nothing

    ---------------------------------------------------------------------------
    -- * Groups and chunks
    ---------------------------------------------------------------------------

    -- | @'groupOn' f = 'groupBy' (('==') \`on\` f) '.' 'List.sortBy' ('compare' \`on\` f)@.
    -- O(n log n).
    groupOn :: Ord b => (a -> b) -> [a] -> [[a]]
    groupOn :: forall b a. Ord b => (a -> b) -> [a] -> [[a]]
    groupOn a -> b
    f = (a -> a -> Bool) -> [a] -> [[a]]
    forall a. (a -> a -> Bool) -> [a] -> [[a]]
    List.groupBy (b -> b -> Bool
    forall a. Eq a => a -> a -> Bool
    (==) (b -> b -> Bool) -> (a -> b) -> a -> a -> Bool
    forall b c a. (b -> b -> c) -> (a -> b) -> a -> a -> c
    `on` a -> b
    f) ([a] -> [[a]]) -> ([a] -> [a]) -> [a] -> [[a]]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . (a -> a -> Ordering) -> [a] -> [a]
    forall a. (a -> a -> Ordering) -> [a] -> [a]
    List.sortBy (b -> b -> Ordering
    forall a. Ord a => a -> a -> Ordering
    compare (b -> b -> Ordering) -> (a -> b) -> a -> a -> Ordering
    forall b c a. (b -> b -> c) -> (a -> b) -> a -> a -> c
    `on` a -> b
    f)

    -- | A variant of 'List.groupBy' which applies the predicate to consecutive
    -- pairs.
    -- O(n).
    -- DEPRECATED in favor of 'Agda.Utils.List1.groupBy''.
    groupBy' :: (a -> a -> Bool) -> [a] -> [[a]]
    groupBy' :: forall a. (a -> a -> Bool) -> [a] -> [[a]]
    groupBy' a -> a -> Bool
    _ []           = []
    groupBy' a -> a -> Bool
    p xxs :: [a]
    xxs@(a
    x : [a]
    xs) = a -> [(Bool, a)] -> [[a]]
    forall {a}. a -> [(Bool, a)] -> [[a]]
    grp a
    x ([(Bool, a)] -> [[a]]) -> [(Bool, a)] -> [[a]]
    forall a b. (a -> b) -> a -> b
    $ (a -> a -> (Bool, a)) -> [a] -> [a] -> [(Bool, a)]
    forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
    zipWith (\a
    x a
    y -> (a -> a -> Bool
    p a
    x a
    y, a
    y)) [a]
    xxs [a]
    xs
      where
      grp :: a -> [(Bool, a)] -> [[a]]
    grp a
    x [(Bool, a)]
    ys = (a
    x a -> [a] -> [a]
    forall a. a -> [a] -> [a]
    : ((Bool, a) -> a) -> [(Bool, a)] -> [a]
    forall a b. (a -> b) -> [a] -> [b]
    map (Bool, a) -> a
    forall a b. (a, b) -> b
    snd [(Bool, a)]
    xs) [a] -> [[a]] -> [[a]]
    forall a. a -> [a] -> [a]
    : [[a]]
    tail
        where ([(Bool, a)]
    xs, [(Bool, a)]
    rest) = ((Bool, a) -> Bool) -> [(Bool, a)] -> ([(Bool, a)], [(Bool, a)])
    forall a. (a -> Bool) -> [a] -> ([a], [a])
    span (Bool, a) -> Bool
    forall a b. (a, b) -> a
    fst [(Bool, a)]
    ys
              tail :: [[a]]
    tail = case [(Bool, a)]
    rest of
                       []            -> []
                       ((Bool
    _, a
    z) : [(Bool, a)]
    zs) -> a -> [(Bool, a)] -> [[a]]
    grp a
    z [(Bool, a)]
    zs

    -- | Split a list into sublists. Generalisation of the prelude function
    --   @words@.
    --   O(n).
    --
    --   > words xs == wordsBy isSpace xs
    wordsBy :: (a -> Bool) -> [a] -> [[a]]
    wordsBy :: forall a. (a -> Bool) -> [a] -> [[a]]
    wordsBy a -> Bool
    p [a]
    xs = [a] -> [[a]]
    yesP [a]
    xs
        where
            yesP :: [a] -> [[a]]
    yesP [a]
    xs = [a] -> [[a]]
    noP ((a -> Bool) -> [a] -> [a]
    forall a. (a -> Bool) -> [a] -> [a]
    dropWhile a -> Bool
    p [a]
    xs)

            noP :: [a] -> [[a]]
    noP []  = []
            noP [a]
    xs  = [a]
    ys [a] -> [[a]] -> [[a]]
    forall a. a -> [a] -> [a]
    : [a] -> [[a]]
    yesP [a]
    zs
                where
                    ([a]
    ys,[a]
    zs) = (a -> Bool) -> [a] -> ([a], [a])
    forall a. (a -> Bool) -> [a] -> ([a], [a])
    break a -> Bool
    p [a]
    xs

    -- | Chop up a list in chunks of a given length.
    -- O(n).
    chop :: Int -> [a] -> [[a]]
    chop :: forall a. Int -> [a] -> [[a]]
    chop Int
    _ [] = []
    chop Int
    n [a]
    xs = [a]
    ys [a] -> [[a]] -> [[a]]
    forall a. a -> [a] -> [a]
    : Int -> [a] -> [[a]]
    forall a. Int -> [a] -> [[a]]
    chop Int
    n [a]
    zs
        where ([a]
    ys,[a]
    zs) = Int -> [a] -> ([a], [a])
    forall a. Int -> [a] -> ([a], [a])
    splitAt Int
    n [a]
    xs

    -- | Chop a list at the positions when the predicate holds. Contrary to
    --   'wordsBy', consecutive separator elements will result in an empty segment
    --   in the result.
    --   O(n).
    --
    --    > intercalate [x] (chopWhen (== x) xs) == xs
    chopWhen :: forall a. (a -> Bool) -> [a] -> [[a]]
    chopWhen :: forall a. (a -> Bool) -> [a] -> [[a]]
    chopWhen a -> Bool
    p []     = []
    chopWhen a -> Bool
    p (a
    x:[a]
    xs) = List1 a -> [[a]]
    loop (a
    x a -> [a] -> List1 a
    forall a. a -> [a] -> NonEmpty a
    :| [a]
    xs)
      where
      -- Local function to avoid unnecessary pattern matching.
      loop :: List1 a -> [[a]]
      loop :: List1 a -> [[a]]
    loop List1 a
    xs = case (a -> Bool) -> List1 a -> ([a], [a])
    forall a. (a -> Bool) -> NonEmpty a -> ([a], [a])
    List1.break a -> Bool
    p List1 a
    xs of
        ([a]
    w, []        ) -> [[a]
    w]
        ([a]
    w, a
    _ : []    ) -> [[a]
    w, []]
        ([a]
    w, a
    _ : a
    y : [a]
    ys) -> [a]
    w [a] -> [[a]] -> [[a]]
    forall a. a -> [a] -> [a]
    : List1 a -> [[a]]
    loop (a
    y a -> [a] -> List1 a
    forall a. a -> [a] -> NonEmpty a
    :| [a]
    ys)

    ---------------------------------------------------------------------------
    -- * List as sets
    ---------------------------------------------------------------------------

    -- | Check membership for the same list often.
    --   Use partially applied to create membership predicate
    --   @hasElem xs :: a -> Bool@.
    --
    --   * First time: @O(n log n)@ in the worst case.
    --   * Subsequently: @O(log n)@.
    --
    --   Specification: @hasElem xs == (`elem` xs)@.
    hasElem :: Ord a => [a] -> a -> Bool
    hasElem :: forall a. Ord a => [a] -> a -> Bool
    hasElem [a]
    xs = (a -> Set a -> Bool
    forall a. Ord a => a -> Set a -> Bool
    `Set.member` [a] -> Set a
    forall a. Ord a => [a] -> Set a
    Set.fromList [a]
    xs)

    -- | Check whether a list is sorted.
    -- O(n).
    --
    -- Assumes that the 'Ord' instance implements a partial order.

    sorted :: Ord a => [a] -> Bool
    sorted :: forall a. Ord a => [a] -> Bool
    sorted [] = Bool
    True
    sorted [a]
    xs = [Bool] -> Bool
    forall (t :: * -> *). Foldable t => t Bool -> Bool
    and ([Bool] -> Bool) -> [Bool] -> Bool
    forall a b. (a -> b) -> a -> b
    $ (a -> a -> Bool) -> [a] -> [a] -> [Bool]
    forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
    zipWith a -> a -> Bool
    forall a. Ord a => a -> a -> Bool
    (<=) [a]
    xs ([a] -> [a]
    forall a. [a] -> [a]
    tail [a]
    xs)

    -- | Check whether all elements in a list are distinct from each other.
    --   Assumes that the 'Eq' instance stands for an equivalence relation.
    --
    --   O(n²) in the worst case @distinct xs == True@.
    distinct :: Eq a => [a] -> Bool
    distinct :: forall a. Eq a => [a] -> Bool
    distinct []     = Bool
    True
    distinct (a
    x:[a]
    xs) = a
    x a -> [a] -> Bool
    forall (t :: * -> *) a. (Foldable t, Eq a) => a -> t a -> Bool
    `notElem` [a]
    xs Bool -> Bool -> Bool
    && [a] -> Bool
    forall a. Eq a => [a] -> Bool
    distinct [a]
    xs

    -- | An optimised version of 'distinct'.
    --   O(n log n).
    --
    --   Precondition: The list's length must fit in an 'Int'.

    fastDistinct :: Ord a => [a] -> Bool
    fastDistinct :: forall a. Ord a => [a] -> Bool
    fastDistinct [a]
    xs = Set a -> Int
    forall a. Set a -> Int
    Set.size ([a] -> Set a
    forall a. Ord a => [a] -> Set a
    Set.fromList [a]
    xs) Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == [a] -> Int
    forall (t :: * -> *) a. Foldable t => t a -> Int
    length [a]
    xs

    -- | Returns an (arbitrary) representative for each list element
    --   that occurs more than once.
    --   O(n log n).
    duplicates :: Ord a => [a] -> [a]
    duplicates :: forall a. Ord a => [a] -> [a]
    duplicates = ([a] -> Maybe a) -> [[a]] -> [a]
    forall a b. (a -> Maybe b) -> [a] -> Prefix b
    mapMaybe [a] -> Maybe a
    forall a. [a] -> Maybe a
    dup ([[a]] -> [a]) -> ([a] -> [[a]]) -> [a] -> [a]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . Bag a -> [[a]]
    forall a. Bag a -> [[a]]
    Bag.groups (Bag a -> [[a]]) -> ([a] -> Bag a) -> [a] -> [[a]]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . [a] -> Bag a
    forall a. Ord a => [a] -> Bag a
    Bag.fromList
      where
        dup :: [a] -> Maybe a
    dup (a
    a : a
    _ : [a]
    _) = a -> Maybe a
    forall a. a -> Maybe a
    Just a
    a
        dup [a]
    _           = Maybe a
    forall a. Maybe a
    Nothing

    -- | Remove the first representative for each list element.
    --   Thus, returns all duplicate copies.
    --   O(n log n).
    --
    --   @allDuplicates xs == sort $ xs \\ nub xs@.
    allDuplicates :: Ord a => [a] -> [a]
    allDuplicates :: forall a. Ord a => [a] -> [a]
    allDuplicates = ([a] -> [a]) -> [[a]] -> [a]
    forall (t :: * -> *) a b. Foldable t => (a -> [b]) -> t a -> [b]
    concatMap (Int -> [a] -> [a]
    forall a. Int -> [a] -> [a]
    drop Int
    1 ([a] -> [a]) -> ([a] -> [a]) -> [a] -> [a]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . [a] -> [a]
    forall a. [a] -> [a]
    reverse) ([[a]] -> [a]) -> ([a] -> [[a]]) -> [a] -> [a]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . Bag a -> [[a]]
    forall a. Bag a -> [[a]]
    Bag.groups (Bag a -> [[a]]) -> ([a] -> Bag a) -> [a] -> [[a]]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . [a] -> Bag a
    forall a. Ord a => [a] -> Bag a
    Bag.fromList
      -- The reverse is necessary to actually remove the *first* occurrence
      -- of each element.

    -- | Partition a list into first and later occurrences of elements
    --   (modulo some quotient given by a representation function).
    --
    --  Time: O(n log n).
    --
    --  Specification:
    --
    --  > nubAndDuplicatesOn f xs = (ys, xs List.\\ ys)
    --  >   where ys = nubOn f xs

    nubAndDuplicatesOn :: Ord b => (a -> b) -> [a] -> ([a], [a])
    nubAndDuplicatesOn :: forall b a. Ord b => (a -> b) -> [a] -> ([a], [a])
    nubAndDuplicatesOn a -> b
    f = Set b -> [a] -> ([a], [a])
    loop Set b
    forall a. Set a
    Set.empty
      where
      loop :: Set b -> [a] -> ([a], [a])
    loop Set b
    s [] = ([], [])
      loop Set b
    s (a
    a:[a]
    as)
        | b
    b b -> Set b -> Bool
    forall a. Ord a => a -> Set a -> Bool
    `Set.member` Set b
    s = ([a] -> [a]) -> ([a], [a]) -> ([a], [a])
    forall (p :: * -> * -> *) b c a.
    Bifunctor p =>
    (b -> c) -> p a b -> p a c
    second (a
    aa -> [a] -> [a]
    forall a. a -> [a] -> [a]
    :) (([a], [a]) -> ([a], [a])) -> ([a], [a]) -> ([a], [a])
    forall a b. (a -> b) -> a -> b
    $ Set b -> [a] -> ([a], [a])
    loop Set b
    s [a]
    as
        | Bool
    otherwise        = ([a] -> [a]) -> ([a], [a]) -> ([a], [a])
    forall (p :: * -> * -> *) a b c.
    Bifunctor p =>
    (a -> b) -> p a c -> p b c
    first  (a
    aa -> [a] -> [a]
    forall a. a -> [a] -> [a]
    :) (([a], [a]) -> ([a], [a])) -> ([a], [a]) -> ([a], [a])
    forall a b. (a -> b) -> a -> b
    $ Set b -> [a] -> ([a], [a])
    loop (b -> Set b -> Set b
    forall a. Ord a => a -> Set a -> Set a
    Set.insert b
    b Set b
    s) [a]
    as
        where b :: b
    b = a -> b
    f a
    a

    -- | Efficient variant of 'nubBy' for lists, using a set to store already seen elements.
    -- O(n log n)
    --
    -- Specification:
    --
    -- > nubOn f xs == 'nubBy' ((==) `'on'` f) xs.

    nubOn :: Ord b => (a -> b) -> [a] -> [a]
    nubOn :: forall b a. Ord b => (a -> b) -> [a] -> [a]
    nubOn a -> b
    f = Set b -> [a] -> [a]
    loop Set b
    forall a. Set a
    Set.empty
      where
      loop :: Set b -> [a] -> [a]
    loop Set b
    s [] = []
      loop Set b
    s (a
    a:[a]
    as)
        | b
    b b -> Set b -> Bool
    forall a. Ord a => a -> Set a -> Bool
    `Set.member` Set b
    s = Set b -> [a] -> [a]
    loop Set b
    s [a]
    as
        | Bool
    otherwise        = a
    a a -> [a] -> [a]
    forall a. a -> [a] -> [a]
    : Set b -> [a] -> [a]
    loop (b -> Set b -> Set b
    forall a. Ord a => a -> Set a -> Set a
    Set.insert b
    b Set b
    s) [a]
    as
        where b :: b
    b = a -> b
    f a
    a

    -- -- | Efficient variant of 'nubBy' for finite lists (using sorting).
    -- -- O(n log n)
    -- --
    -- -- Specification:
    -- --
    -- -- > nubOn2 f xs == 'nubBy' ((==) `'on'` f) xs.
    --
    -- nubOn2 :: Ord b => (a -> b) -> [a] -> [a]
    -- nubOn2 tag =
    --     -- Throw away numbering
    --   map snd
    --     -- Restore original order
    --   . List.sortBy (compare `on` fst)
    --     -- Retain first entry of each @tag@ group
    --   . map (snd . head)
    --   . List.groupBy ((==) `on` fst)
    --     -- Sort by tag (stable)
    --   . List.sortBy (compare `on` fst)
    --     -- Tag with @tag@ and sequential numbering
    --   . map (\p@(_, x) -> (tag x, p))
    --   . zip [1..]

    -- | Efficient variant of 'nubBy' for finite lists.
    -- O(n log n).
    --
    -- > uniqOn f == 'List.sortBy' (compare `'on'` f) . 'nubBy' ((==) `'on'` f)
    --
    -- If there are several elements with the same @f@-representative,
    -- the first of these is kept.
    --
    uniqOn :: Ord b => (a -> b) -> [a] -> [a]
    uniqOn :: forall b a. Ord b => (a -> b) -> [a] -> [a]
    uniqOn a -> b
    key = Map b a -> [a]
    forall k a. Map k a -> [a]
    Map.elems (Map b a -> [a]) -> ([a] -> Map b a) -> [a] -> [a]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . (a -> a -> a) -> [(b, a)] -> Map b a
    forall k a. Ord k => (a -> a -> a) -> [(k, a)] -> Map k a
    Map.fromListWith (\ a
    _ -> a -> a
    forall a. a -> a
    id) ([(b, a)] -> Map b a) -> ([a] -> [(b, a)]) -> [a] -> Map b a
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . (a -> (b, a)) -> [a] -> [(b, a)]
    forall a b. (a -> b) -> [a] -> [b]
    map (\ a
    a -> (a -> b
    key a
    a, a
    a))

    -- | Checks if all the elements in the list are equal. Assumes that
    --   the 'Eq' instance stands for an equivalence relation.
    --   O(n).
    allEqual :: Eq a => [a] -> Bool
    allEqual :: forall a. Eq a => [a] -> Bool
    allEqual []       = Bool
    True
    allEqual (a
    x : [a]
    xs) = (a -> Bool) -> [a] -> Bool
    forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
    all (a -> a -> Bool
    forall a. Eq a => a -> a -> Bool
    == a
    x) [a]
    xs

    -- | Non-efficient, monadic 'nub'.
    -- O(n²).
    nubM :: Monad m => (a -> a -> m Bool) -> [a] -> m [a]
    nubM :: forall (m :: * -> *) a.
    Monad m =>
    (a -> a -> m Bool) -> [a] -> m [a]
    nubM a -> a -> m Bool
    eq = [a] -> m [a]
    loop where
      loop :: [a] -> m [a]
    loop []     = [a] -> m [a]
    forall (m :: * -> *) a. Monad m => a -> m a
    return []
      loop (a
    a:[a]
    as) = (a
    a a -> [a] -> [a]
    forall a. a -> [a] -> [a]
    :) ([a] -> [a]) -> m [a] -> m [a]
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> do [a] -> m [a]
    loop ([a] -> m [a]) -> m [a] -> m [a]
    forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
    =<< (a -> m Bool) -> [a] -> m [a]
    forall (m :: * -> *) a.
    Applicative m =>
    (a -> m Bool) -> [a] -> m [a]
    filterM (Bool -> Bool
    not (Bool -> Bool) -> (a -> m Bool) -> a -> m Bool
    forall (m :: * -> *) b c a.
    Functor m =>
    (b -> c) -> (a -> m b) -> a -> m c
    <.> a -> a -> m Bool
    eq a
    a) [a]
    as

    ---------------------------------------------------------------------------
    -- * Zipping
    ---------------------------------------------------------------------------

    -- | Requires both lists to have the same length.
    --   O(n).
    --
    --   Otherwise, @Nothing@ is returned.

    zipWith' :: (a -> b -> c) -> [a] -> [b] -> Maybe [c]
    zipWith' :: forall a b c. (a -> b -> c) -> [a] -> [b] -> Maybe [c]
    zipWith' a -> b -> c
    f = [a] -> [b] -> Maybe [c]
    loop
      where
      loop :: [a] -> [b] -> Maybe [c]
    loop []        []      = [c] -> Maybe [c]
    forall a. a -> Maybe a
    Just []
      loop (a
    x : [a]
    xs) (b
    y : [b]
    ys) = (a -> b -> c
    f a
    x b
    y c -> [c] -> [c]
    forall a. a -> [a] -> [a]
    :) ([c] -> [c]) -> Maybe [c] -> Maybe [c]
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> [a] -> [b] -> Maybe [c]
    loop [a]
    xs [b]
    ys
      loop []       (b
    _ : [b]
    _)  = Maybe [c]
    forall a. Maybe a
    Nothing
      loop (a
    _ : [a]
    _)  []       = Maybe [c]
    forall a. Maybe a
    Nothing

    -- | Like 'zipWith' but keep the rest of the second list as-is
    --   (in case the second list is longer).
    -- O(n).
    --
    -- @
    --   zipWithKeepRest f as bs == zipWith f as bs ++ drop (length as) bs
    -- @
    zipWithKeepRest :: (a -> b -> b) -> [a] -> [b] -> [b]
    zipWithKeepRest :: forall a b. (a -> b -> b) -> [a] -> [b] -> [b]
    zipWithKeepRest a -> b -> b
    f = [a] -> [b] -> [b]
    loop
      where
      loop :: [a] -> [b] -> [b]
    loop []       [b]
    bs       = [b]
    bs
      loop [a]
    as       []       = []
      loop (a
    a : [a]
    as) (b
    b : [b]
    bs) = a -> b -> b
    f a
    a b
    b b -> [b] -> [b]
    forall a. a -> [a] -> [a]
    : [a] -> [b] -> [b]
    loop [a]
    as [b]
    bs

    -- -- UNUSED; a better type would be
    -- -- zipWithTails :: (a -> b -> c) -> [a] -> [b] -> ([c], Either [a] [b])

    -- -- | Like zipWith, but returns the leftover elements of the input lists.
    -- zipWithTails :: (a -> b -> c) -> [a] -> [b] -> ([c], [a] , [b])
    -- zipWithTails f xs       []       = ([], xs, [])
    -- zipWithTails f []       ys       = ([], [] , ys)
    -- zipWithTails f (x : xs) (y : ys) = (f x y : zs , as , bs)
    --   where (zs , as , bs) = zipWithTails f xs ys

    ---------------------------------------------------------------------------
    -- * Unzipping
    ---------------------------------------------------------------------------

    unzipWith :: (a -> (b, c)) -> [a] -> ([b], [c])
    unzipWith :: forall a b c. (a -> (b, c)) -> [a] -> ([b], [c])
    unzipWith a -> (b, c)
    f = [(b, c)] -> ([b], [c])
    forall a b. [(a, b)] -> ([a], [b])
    unzip ([(b, c)] -> ([b], [c])) -> ([a] -> [(b, c)]) -> [a] -> ([b], [c])
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . (a -> (b, c)) -> [a] -> [(b, c)]
    forall a b. (a -> b) -> [a] -> [b]
    map a -> (b, c)
    f

    ---------------------------------------------------------------------------
    -- * Edit distance
    ---------------------------------------------------------------------------

    -- | Implemented using tree recursion, don't run me at home!
    --   O(3^(min n m)).
    editDistanceSpec :: Eq a => [a] -> [a] -> Int
    editDistanceSpec :: forall a. Eq a => [a] -> [a] -> Int
    editDistanceSpec [] [a]
    ys = [a] -> Int
    forall (t :: * -> *) a. Foldable t => t a -> Int
    length [a]
    ys
    editDistanceSpec [a]
    xs [] = [a] -> Int
    forall (t :: * -> *) a. Foldable t => t a -> Int
    length [a]
    xs
    editDistanceSpec (a
    x : [a]
    xs) (a
    y : [a]
    ys)
      | a
    x a -> a -> Bool
    forall a. Eq a => a -> a -> Bool
    == a
    y    = [a] -> [a] -> Int
    forall a. Eq a => [a] -> [a] -> Int
    editDistanceSpec [a]
    xs [a]
    ys
      | Bool
    otherwise = Int
    1 Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + [Int] -> Int
    forall (t :: * -> *) a. (Foldable t, Ord a) => t a -> a
    minimum [ [a] -> [a] -> Int
    forall a. Eq a => [a] -> [a] -> Int
    editDistanceSpec (a
    x a -> [a] -> [a]
    forall a. a -> [a] -> [a]
    : [a]
    xs) [a]
    ys
                                , [a] -> [a] -> Int
    forall a. Eq a => [a] -> [a] -> Int
    editDistanceSpec [a]
    xs (a
    y a -> [a] -> [a]
    forall a. a -> [a] -> [a]
    : [a]
    ys)
                                , [a] -> [a] -> Int
    forall a. Eq a => [a] -> [a] -> Int
    editDistanceSpec [a]
    xs [a]
    ys ]

    -- | Implemented using dynamic programming and @Data.Array@.
    --   O(n*m).
    editDistance :: forall a. Eq a => [a] -> [a] -> Int
    editDistance :: forall a. Eq a => [a] -> [a] -> Int
    editDistance [a]
    xs [a]
    ys = Int -> Int -> Int
    editD Int
    0 Int
    0
      where
      editD :: Int -> Int -> Int
    editD Int
    i Int
    j = Array (Int, Int) Int
    tbl Array (Int, Int) Int -> (Int, Int) -> Int
    forall i e. Ix i => Array i e -> i -> e
    Array.! (Int
    i, Int
    j)
      -- Tabulate editD' in immutable boxed array (content computed lazily).
      tbl :: Array (Int,Int) Int
      tbl :: Array (Int, Int) Int
    tbl = ((Int, Int), (Int, Int))
    -> [((Int, Int), Int)] -> Array (Int, Int) Int
    forall i e. Ix i => (i, i) -> [(i, e)] -> Array i e
    array ((Int
    0,Int
    0), (Int
    n,Int
    m)) [ ((Int
    i, Int
    j), Int -> Int -> Int
    editD' Int
    i Int
    j) | Int
    i <- [Int
    0..Int
    n], Int
    j <- [Int
    0..Int
    m] ]
      editD' :: Int -> Int -> Int
    editD' Int
    i Int
    j =
        case (Int -> Int -> Ordering
    forall a. Ord a => a -> a -> Ordering
    compare Int
    i Int
    n, Int -> Int -> Ordering
    forall a. Ord a => a -> a -> Ordering
    compare Int
    j Int
    m) of
          -- Interior
          (Ordering
    LT, Ordering
    LT)
            | Array Int a
    xsA Array Int a -> Int -> a
    forall i e. Ix i => Array i e -> i -> e
    Array.! Int
    i a -> a -> Bool
    forall a. Eq a => a -> a -> Bool
    == Array Int a
    ysA Array Int a -> Int -> a
    forall i e. Ix i => Array i e -> i -> e
    Array.! Int
    j
                        -> Int -> Int -> Int
    editD Int
    i' Int
    j'
            | Bool
    otherwise -> Int
    1 Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + [Int] -> Int
    forall (t :: * -> *) a. (Foldable t, Ord a) => t a -> a
    minimum [ Int -> Int -> Int
    editD Int
    i' Int
    j, Int -> Int -> Int
    editD Int
    i Int
    j', Int -> Int -> Int
    editD Int
    i' Int
    j' ]
          -- Border: one list is empty
          (Ordering
    EQ, Ordering
    LT)      ->  Int
    m Int -> Int -> Int
    forall a. Num a => a -> a -> a
    - Int
    j
          (Ordering
    LT, Ordering
    EQ)      ->  Int
    n Int -> Int -> Int
    forall a. Num a => a -> a -> a
    - Int
    i
          -- Corner (EQ, EQ): both lists are empty
          (Ordering, Ordering)
    _             -> Int
    0
          -- GT cases are impossible.
        where (Int
    i',Int
    j') = (Int
    iInt -> Int -> Int
    forall a. Num a => a -> a -> a
    +Int
    1, Int
    jInt -> Int -> Int
    forall a. Num a => a -> a -> a
    +Int
    1)
      n :: Int
    n   = [a] -> Int
    forall (t :: * -> *) a. Foldable t => t a -> Int
    length [a]
    xs
      m :: Int
    m   = [a] -> Int
    forall (t :: * -> *) a. Foldable t => t a -> Int
    length [a]
    ys
      xsA, ysA :: Array Int a
      xsA :: Array Int a
    xsA = (Int, Int) -> [a] -> Array Int a
    forall i e. Ix i => (i, i) -> [e] -> Array i e
    listArray (Int
    0,Int
    nInt -> Int -> Int
    forall a. Num a => a -> a -> a
    -Int
    1) [a]
    xs
      ysA :: Array Int a
    ysA = (Int, Int) -> [a] -> Array Int a
    forall i e. Ix i => (i, i) -> [e] -> Array i e
    listArray (Int
    0,Int
    mInt -> Int -> Int
    forall a. Num a => a -> a -> a
    -Int
    1) [a]
    ys

    mergeStrictlyOrderedBy :: (a -> a -> Bool) -> [a] -> [a] -> Maybe [a]
    mergeStrictlyOrderedBy :: forall a.
    (a -> a -> Bool) -> Prefix a -> Prefix a -> Maybe (Prefix a)
    mergeStrictlyOrderedBy a -> a -> Bool
    (<) = [a] -> [a] -> Maybe [a]
    loop where
      loop :: [a] -> [a] -> Maybe [a]
    loop [] [a]
    ys = [a] -> Maybe [a]
    forall a. a -> Maybe a
    Just [a]
    ys
      loop [a]
    xs [] = [a] -> Maybe [a]
    forall a. a -> Maybe a
    Just [a]
    xs
      loop (a
    x:[a]
    xs) (a
    y:[a]
    ys)
        | a
    x a -> a -> Bool
    < a
    y = (a
    xa -> [a] -> [a]
    forall a. a -> [a] -> [a]
    :) ([a] -> [a]) -> Maybe [a] -> Maybe [a]
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> [a] -> [a] -> Maybe [a]
    loop [a]
    xs (a
    ya -> [a] -> [a]
    forall a. a -> [a] -> [a]
    :[a]
    ys)
        | a
    y a -> a -> Bool
    < a
    x = (a
    ya -> [a] -> [a]
    forall a. a -> [a] -> [a]
    :) ([a] -> [a]) -> Maybe [a] -> Maybe [a]
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> [a] -> [a] -> Maybe [a]
    loop (a
    xa -> [a] -> [a]
    forall a. a -> [a] -> [a]
    :[a]
    xs) [a]
    ys
        | Bool
    otherwise = Maybe [a]
    forall a. Maybe a
    Nothing