    {-# LANGUAGE
        DataKinds,
        PolyKinds,
        TypeFamilies,
        TypeOperators,
        UndecidableInstances #-}

    -- | Lists.

    --

    -- See also "Fcf.Class.Foldable" for additional functions.

    module Fcf.Data.List
      ( -- * Basic functions

        type (++)
      , Head
      , Last
      , Tail
      , Cons
      , Snoc
      , Cons2
      , Init
      , Uncons
      , Unsnoc
      , Singleton
      , Null
      , Length

      -- * List transformations

      , Reverse
      , Intersperse
      , Intercalate

      -- * Reducing lists

      -- | See also "Fcf.Class.Foldable".

      , Foldr
      , UnList
      , Concat
      , ConcatMap

      -- * Unfolding and building

      , Unfoldr
      , Replicate

      -- * Sublists

      , Take
      , Drop
      , SplitAt
      , TakeWhile
      , DropWhile
      , Span
      , Break
      , Tails

      -- ** Predicates

      , IsPrefixOf
      , IsSuffixOf
      , IsInfixOf

      -- * Searching

      , Elem
      , Lookup
      , Find
      , Filter
      , Partition

      -- * Indexing lists

      , FindIndex
      , SetIndex

      -- * Zipping and unzipping

      , ZipWith
      , Zip
      , Unzip
      ) where

    import qualified GHC.TypeLits as TL

    import Fcf.Core
    import Fcf.Combinators
    import Fcf.Class.Functor (Map)
    import Fcf.Class.Monoid (type (<>))
    import Fcf.Class.Foldable
    import Fcf.Data.Bool
    import Fcf.Data.Common
    import Fcf.Data.Nat
    import Fcf.Utils (If, TyEq)

    -- $setup

    -- >>> :set -XGADTs -XUndecidableInstances -XDataKinds

    -- >>> import Fcf.Core (Exp, Eval)

    -- >>> import Fcf.Combinators

    -- >>> import Fcf.Class.Foldable (Concat)

    -- >>> import Fcf.Class.Functor ()

    -- >>> import Fcf.Class.Monoid ()

    -- >>> import Fcf.Data.Nat

    -- >>> import Fcf.Utils (If, TyEq)

    -- >>> import Data.Type.Ord ()

    -- >>> import qualified GHC.TypeLits as TL

    -- >>> import GHC.TypeLits (Nat)

    -- >>> import Numeric.Natural (Natural)

    -- | List catenation.

    --

    -- === __Example__

    --

    -- >>> data Example where Ex :: a -> Example  -- Hide the type of examples to avoid brittleness in different GHC versions

    -- >>> :kind! Ex (Eval ([1, 2] ++ [3, 4]) :: [Natural])

    -- Ex (Eval ([1, 2] ++ [3, 4]) :: [Natural]) :: Example

    -- = Ex [1, 2, 3, 4]

    --

    data (++) :: [a] -> [a] -> Exp [a]
    type instance Eval ((++) xs ys) = xs <> ys

    data Head :: [a] -> Exp (Maybe a)
    type instance Eval (Head '[]) = 'Nothing
    type instance Eval (Head (a ': _as)) = 'Just a

    data Last :: [a] -> Exp (Maybe a)
    type instance Eval (Last '[]) = 'Nothing
    type instance Eval (Last (a ': '[])) = 'Just a
    type instance Eval (Last (a ': b ': as)) = Eval (Last (b ': as))

    data Init :: [a] -> Exp (Maybe [a])
    type instance Eval (Init '[]) = 'Nothing
    type instance Eval (Init (a ': '[])) = 'Just '[]
    type instance Eval (Init (a ': b ': as)) =
      Eval (Map (Cons a) =<< (Init (b ': as)))

    data Uncons :: [a] -> Exp (Maybe (a, [a]))
    type instance Eval (Uncons '[]) = 'Nothing
    type instance Eval (Uncons (a ': xs)) = 'Just '(a, xs)

    -- | Decompose a list into 'init' and 'last'

    --

    -- === __Example__

    --

    -- >>> :kind! Eval (Unsnoc '[])

    -- Eval (Unsnoc '[]) :: Maybe ([a], a)

    -- = Nothing

    --

    -- >>> :kind! Eval (Unsnoc '[1])

    -- Eval (Unsnoc '[1]) :: Maybe ([Natural], Natural)

    -- = Just '( '[], 1)

    --

    -- >>> :kind! Eval (Unsnoc '[1,2,3])

    -- Eval (Unsnoc '[1,2,3]) :: Maybe ([Natural], Natural)

    -- = Just '([1, 2], 3)

    data Unsnoc :: [a] -> Exp (Maybe ([a], a))
    type instance Eval (Unsnoc '[]) = 'Nothing
    type instance Eval (Unsnoc (x ': '[])) = 'Just '( '[], x)
    type instance Eval (Unsnoc (x ': y ': ys)) = Eval (Map (PrependF x) =<< Unsnoc (y ': ys))

    data PrependF :: a -> ([a], a) -> Exp ([a], a)
    type instance Eval (PrependF x '(xs, y)) = '(x ': xs, y)

    data Singleton :: a -> Exp [a]
    type instance Eval (Singleton x) = '[x]

    data Tail :: [a] -> Exp (Maybe [a])
    type instance Eval (Tail '[]) = 'Nothing
    type instance Eval (Tail (_a ': as)) = 'Just as

    data Null :: [a] -> Exp Bool
    type instance Eval (Null '[]) = 'True
    type instance Eval (Null (a ': as)) = 'False

    data Length :: [a] -> Exp Nat
    type instance Eval (Length '[]) = 0
    type instance Eval (Length (a ': as)) = 1 TL.+ Eval (Length as)

    -- | Append an element to a list.

    --

    -- === __Example__

    --

    -- >>> :kind! Eval (Cons 1 [2, 3])

    -- Eval (Cons 1 [2, 3]) :: [Natural]

    -- = [1, 2, 3]

    -- >>> :kind! Eval (Cons Int [Char, Maybe Double])

    -- Eval (Cons Int [Char, Maybe Double]) :: [*]

    -- = [Int, Char, Maybe Double]

    --

    data Cons :: a -> [a] -> Exp [a]
    type instance Eval (Cons a as) = a ': as

    -- | Append elements to two lists. Used in the definition of 'Unzip'.

    data Cons2 :: (a, b) -> ([a], [b]) -> Exp ([a], [b])
    type instance Eval (Cons2 '(a, b) '(as, bs)) = '(a ': as, b ': bs)

    -- | Append an element to the end of a list.

    --

    -- === __Example__

    --

    -- >>> :kind! Eval (Snoc [1,2,3] 4)

    -- Eval (Snoc [1,2,3] 4) :: [Natural]

    -- = [1, 2, 3, 4]

    data Snoc :: [a] -> a -> Exp [a]
    type instance Eval (Snoc lst a) = Eval (lst ++ '[a])

    -- Helper for Reverse. This corresponds to rev in the data list lib.

    data Rev :: [a] -> [a] -> Exp [a]
    type instance Eval (Rev '[]       ys) = ys
    type instance Eval (Rev (x ': xs) ys) = Eval (Rev xs (x ': ys))

    -- | Reverse a list.

    --

    -- === __Example__

    --

    -- >>> :kind! Eval (Reverse [1,2,3,4,5])

    -- Eval (Reverse [1,2,3,4,5]) :: [Natural]

    -- = [5, 4, 3, 2, 1]

    data Reverse :: [a] -> Exp [a]
    type instance Eval (Reverse l) = Eval (Rev l '[])

    -- | Intersperse a separator between elements of a list.

    --

    -- === __Example__

    --

    -- >>> :kind! Eval (Intersperse 0 [1,2,3,4])

    -- Eval (Intersperse 0 [1,2,3,4]) :: [Natural]

    -- = [1, 0, 2, 0, 3, 0, 4]

    data Intersperse :: a -> [a] -> Exp [a]
    type instance Eval (Intersperse _   '[]      ) = '[]
    type instance Eval (Intersperse sep (x ': xs)) = x ': Eval (PrependToAll sep xs)

    -- | Helper for Intersperse

    data PrependToAll :: a -> [a] -> Exp [a]
    type instance Eval (PrependToAll _   '[]      ) = '[]
    type instance Eval (PrependToAll sep (x ': xs)) = sep ': x ': Eval (PrependToAll sep xs)

    -- | Join a list of words separated by some word.

    --

    -- === __Example__

    --

    -- >>> :kind! Eval (Intercalate '[", "] [ '["Lorem"], '["ipsum"], '["dolor"] ])

    -- Eval (Intercalate '[", "] [ '["Lorem"], '["ipsum"], '["dolor"] ]) :: [TL.Symbol]

    -- = ["Lorem", ", ", "ipsum", ", ", "dolor"]

    data Intercalate :: [a] -> [[a]] -> Exp [a]
    type instance Eval (Intercalate xs xss) = Eval (Concat =<< Intersperse xs xss)

    -- | This is 'Foldr' with its argument flipped.

    data UnList :: b -> (a -> b -> Exp b) -> [a] -> Exp b
    type instance Eval (UnList y f xs) = Eval (Foldr f y xs)

    -- Helper for the Unfoldr.

    data UnfoldrCase :: (b -> Exp (Maybe (a, b))) -> Maybe (a, b) -> Exp [a]
    type instance Eval (UnfoldrCase f ('Just ab)) =
      Eval (Fst ab) ': Eval (Unfoldr f (Eval (Snd ab)))
    type instance Eval (UnfoldrCase _ 'Nothing) = '[]

    -- | Unfold a generator into a list.

    --

    -- === __Example__

    --

    -- >>> data ToThree :: Nat -> Exp (Maybe (Nat, Nat))

    -- >>> :{

    -- type instance Eval (ToThree b) =

    --   If (4 TL.<=? b)

    --     Nothing

    --     (Just '(b, b TL.+ 1))

    -- :}

    --

    -- >>> :kind! Eval (Unfoldr ToThree 0)

    -- Eval (Unfoldr ToThree 0) :: [Natural]

    -- = [0, 1, 2, 3]

    --

    -- See also the definition of `Replicate`.

    data Unfoldr :: (b -> Exp (Maybe (a, b))) -> b -> Exp [a]
    type instance Eval (Unfoldr f c) = Eval (UnfoldrCase f (f @@ c))

    -- Helper for the Replicate.

    data NumIter :: a -> Nat -> Exp (Maybe (a, Nat))
    type instance Eval (NumIter a s) =
      If (Eval (s > 0))
        ('Just '(a, s TL.- 1))
        'Nothing

    -- | Repeat the same element in a list.

    --

    -- === __Example__

    --

    -- >>> :kind! Eval (Replicate 4 '("ok", 2))

    -- Eval (Replicate 4 '("ok", 2)) :: [(TL.Symbol, Natural)]

    -- = ['("ok", 2), '("ok", 2), '("ok", 2), '("ok", 2)]

    data Replicate :: Nat -> a -> Exp [a]
    type instance Eval (Replicate n a) = Eval (Unfoldr (NumIter a) n)

    -- | Take a prefix of fixed length.

    --

    -- === __Example__

    --

    -- >>> :kind! Eval (Take 2 [1,2,3,4,5])

    -- Eval (Take 2 [1,2,3,4,5]) :: [Natural]

    -- = [1, 2]

    data Take :: Nat -> [a] -> Exp [a]
    type instance Eval (Take n as) = Take_ n as

    type family Take_ (n :: Nat) (xs :: [a]) :: [a] where
      Take_ 0 _         = '[]
      Take_ _ '[]       = '[]
      Take_ n (x ': xs) = x ': Take_ (n TL.- 1) xs

    -- | Drop a prefix of fixed length, evaluate to the remaining suffix.

    --

    -- === __Example__

    --

    -- >>> :kind! Eval (Drop 2 [1,2,3,4,5])

    -- Eval (Drop 2 [1,2,3,4,5]) :: [Natural]

    -- = [3, 4, 5]

    data Drop :: Nat -> [a] -> Exp [a]
    type instance Eval (Drop n as) = Drop_ n as

    type family Drop_ (n :: Nat) (xs :: [a]) :: [a] where
      Drop_ 0 xs        = xs
      Drop_ _ '[]       = '[]
      Drop_ n (x ': xs) = Drop_ (n TL.- 1) xs

    -- | Return a tuple where first element is @xs@ prefix of length @n@

    -- and second element is the remainder of the list.

    --

    -- === __Example__

    --

    -- >>> :kind! Eval (SplitAt 3 '[1,2,3,4,5])

    -- Eval (SplitAt 3 '[1,2,3,4,5]) :: ([Natural], [Natural])

    -- = '([1, 2, 3], [4, 5])

    data SplitAt :: Nat -> [a] -> Exp ([a], [a])
    type instance Eval (SplitAt n xs) = '(Eval (Take n xs), Eval (Drop n xs))

    -- | Take the longest prefix of elements satisfying a predicate.

    --

    -- === __Example__

    --

    -- >>> :kind! Eval (TakeWhile ((>=) 3) [1, 2, 3, 4, 5])

    -- Eval (TakeWhile ((>=) 3) [1, 2, 3, 4, 5]) :: [Natural]

    -- = [1, 2, 3]

    data TakeWhile :: (a -> Exp Bool) -> [a] -> Exp [a]
    type instance Eval (TakeWhile p '[]) = '[]
    type instance Eval (TakeWhile p (x ': xs)) =
      Eval (If (Eval (p x))
          ('(:) x <$> TakeWhile p xs)
          (Pure '[]))

    -- | Drop the longest prefix of elements satisfying a predicate,

    -- evaluate to the remaining suffix.

    --

    -- === __Example__

    --

    -- :kind! Eval (DropWhile ((>=) 3) [1, 2, 3, 4, 5])

    -- Eval (DropWhile ((>=) 3) [1, 2, 3, 4, 5]) :: [Natural]

    -- = [4, 5]

    data DropWhile :: (a -> Exp Bool) -> [a] -> Exp [a]
    type instance Eval (DropWhile p '[]) = '[]
    type instance Eval (DropWhile p (x ': xs)) =
      Eval (If (Eval (p x))
          (DropWhile p xs)
          (Pure (x ': xs)))

    -- | 'Span', applied to a predicate @p@ and a list @xs@, returns a tuple:

    -- the first component is the longest prefix (possibly empty) of @xs@ whose elements

    -- satisfy @p@;

    -- the second component is the remainder of the list.

    --

    -- See also 'TakeWhile', 'DropWhile', and 'Break'.

    --

    -- === __Example__

    --

    -- >>> :kind! Eval (Span (Flip (<) 3) [1,2,3,4,1,2])

    -- Eval (Span (Flip (<) 3) [1,2,3,4,1,2]) :: ([Natural], [Natural])

    -- = '([1, 2], [3, 4, 1, 2])

    --

    -- >>> :kind! Eval (Span (Flip (<) 9) [1,2,3])

    -- Eval (Span (Flip (<) 9) [1,2,3]) :: ([Natural], [Natural])

    -- = '([1, 2, 3], '[])

    --

    -- >>> :kind! Eval (Span (Flip (<) 0) [1,2,3])

    -- Eval (Span (Flip (<) 0) [1,2,3]) :: ([Natural], [Natural])

    -- = '( '[], [1, 2, 3])

    data Span :: (a -> Exp Bool) -> [a] -> Exp ([a],[a])
    type instance Eval (Span p lst) = '( Eval (TakeWhile p lst), Eval (DropWhile p lst))

    -- | 'Break', applied to a predicate @p@ and a list @xs@, returns a tuple:

    -- the first component is the longest prefix (possibly empty) of @xs@ whose elements

    -- /do not satisfy/ @p@; the second component is the remainder of the list.

    --

    -- === __Example__

    --

    -- >>> :kind! Eval (Break (Flip (>) 3) [1,2,3,4,1,2])

    -- Eval (Break (Flip (>) 3) [1,2,3,4,1,2]) :: ([Natural], [Natural])

    -- = '([1, 2, 3], [4, 1, 2])

    --

    -- >>> :kind! Eval (Break (Flip (<) 9) [1,2,3])

    -- Eval (Break (Flip (<) 9) [1,2,3]) :: ([Natural], [Natural])

    -- = '( '[], [1, 2, 3])

    --

    -- >>> :kind! Eval (Break (Flip (>) 9) [1,2,3])

    -- Eval (Break (Flip (>) 9) [1,2,3]) :: ([Natural], [Natural])

    -- = '([1, 2, 3], '[])

    data Break :: (a -> Exp Bool) -> [a] -> Exp ([a],[a])
    type instance Eval (Break p lst) = Eval (Span (Not <=< p) lst)

    -- | List of suffixes of a list.

    --

    -- === __Example__

    --

    -- >>> :kind! Eval (Tails [0,1,2,3])

    -- Eval (Tails [0,1,2,3]) :: [[Natural]]

    -- = [[0, 1, 2, 3], [1, 2, 3], [2, 3], '[3]]

    data Tails :: [a] -> Exp [[a]]
    type instance Eval (Tails '[]) = '[]
    type instance Eval (Tails (a ': as)) = (a ': as) ': Eval (Tails as)

    -- | Return @True@ when the first list is a prefix of the second.

    --

    -- === __Example__

    --

    -- >>> :kind! Eval ([0,1,2] `IsPrefixOf` [0,1,2,3,4,5])

    -- Eval ([0,1,2] `IsPrefixOf` [0,1,2,3,4,5]) :: Bool

    -- = True

    --

    -- >>> :kind! Eval ([0,1,2] `IsPrefixOf` [0,1,3,2,4,5])

    -- Eval ([0,1,2] `IsPrefixOf` [0,1,3,2,4,5]) :: Bool

    -- = False

    --

    -- >>> :kind! Eval ('[] `IsPrefixOf` [0,1,3,2,4,5])

    -- Eval ('[] `IsPrefixOf` [0,1,3,2,4,5]) :: Bool

    -- = True

    --

    -- >>> :kind! Eval ([0,1,3,2,4,5] `IsPrefixOf` '[])

    -- Eval ([0,1,3,2,4,5] `IsPrefixOf` '[]) :: Bool

    -- = False

    data IsPrefixOf :: [a] -> [a] -> Exp Bool
    type instance Eval (IsPrefixOf xs ys) = IsPrefixOf_ xs ys

    -- helper for IsPrefixOf

    type family IsPrefixOf_ (xs :: [a]) (ys :: [a]) :: Bool where
      IsPrefixOf_ '[] _ = 'True
      IsPrefixOf_ _ '[] = 'False
      IsPrefixOf_ (x ': xs) (y ': ys) =
         Eval ((Eval (TyEq x y)) && IsPrefixOf_ xs ys)

    -- | Return @True@ when the first list is a suffix of the second.

    --

    -- === __Example__

    --

    -- >>> :kind! Eval (IsSuffixOf [3,4,5] [0,1,2,3,4,5])

    -- Eval (IsSuffixOf [3,4,5] [0,1,2,3,4,5]) :: Bool

    -- = True

    --

    -- >>> :kind! Eval (IsSuffixOf [3,4,5] [0,1,3,2,4,5])

    -- Eval (IsSuffixOf [3,4,5] [0,1,3,2,4,5]) :: Bool

    -- = False

    --

    -- >>> :kind! Eval (IsSuffixOf '[] [0,1,3,2,4,5])

    -- Eval (IsSuffixOf '[] [0,1,3,2,4,5]) :: Bool

    -- = True

    --

    -- >>> :kind! Eval (IsSuffixOf [0,1,3,2,4,5] '[])

    -- Eval (IsSuffixOf [0,1,3,2,4,5] '[]) :: Bool

    -- = False

    data IsSuffixOf :: [a] -> [a] -> Exp Bool
    type instance Eval (IsSuffixOf xs ys) =
      Eval (IsPrefixOf (Reverse @@ xs) (Reverse @@ ys))

    -- | Return @True@ when the first list is contained within the second.

    --

    -- === __Example__

    --

    -- >>> :kind! Eval (IsInfixOf [2,3,4] [0,1,2,3,4,5,6])

    -- Eval (IsInfixOf [2,3,4] [0,1,2,3,4,5,6]) :: Bool

    -- = True

    --

    -- >>> :kind! Eval (IsInfixOf [2,4,4] [0,1,2,3,4,5,6])

    -- Eval (IsInfixOf [2,4,4] [0,1,2,3,4,5,6]) :: Bool

    -- = False

    data IsInfixOf :: [a] -> [a] -> Exp Bool
    type instance Eval (IsInfixOf xs ys) = Eval (Any (IsPrefixOf xs) =<< Tails ys)

    -- | Return @True@ if an element is in a list.

    --

    -- See also 'FindIndex'.

    --

    -- === __Example__

    --

    -- >>> :kind! Eval (Elem 1 [1,2,3])

    -- Eval (Elem 1 [1,2,3]) :: Bool

    -- = True

    -- >>> :kind! Eval (Elem 1 [2,3])

    -- Eval (Elem 1 [2,3]) :: Bool

    -- = False

    --

    data Elem :: a -> [a] -> Exp Bool
    type instance Eval (Elem a as) = Eval (IsJust =<< FindIndex (TyEq a) as)

    -- | Find an element associated with a key in an association list.

    data Lookup :: k -> [(k, b)] -> Exp (Maybe b)
    type instance Eval (Lookup (a :: k) (as :: [(k, b)])) =
      Eval (Map Snd (Eval (Find (TyEq a <=< Fst) as)) :: Exp (Maybe b))

    -- | Find @Just@ the first element satisfying a predicate, or evaluate to

    -- @Nothing@ if no element satisfies the predicate.

    --

    -- === __Example__

    --

    -- >>> :kind! Eval (Find (TyEq 0) [1,2,3])

    -- Eval (Find (TyEq 0) [1,2,3]) :: Maybe Natural

    -- = Nothing

    --

    -- >>> :kind! Eval (Find (TyEq 0) [1,2,3,0])

    -- Eval (Find (TyEq 0) [1,2,3,0]) :: Maybe Natural

    -- = Just 0

    data Find :: (a -> Exp Bool) -> [a] -> Exp (Maybe a)
    type instance Eval (Find _p '[]) = 'Nothing
    type instance Eval (Find p (a ': as)) =
      Eval (If (Eval (p a))
        (Pure ('Just a))
        (Find p as))

    -- | Keep all elements that satisfy a predicate, remove all that don't.

    --

    -- === __Example__

    --

    -- >>> :kind! Eval (Filter ((>) 3) [1,2,3,0])

    -- Eval (Filter ((>) 3) [1,2,3,0]) :: [Natural]

    -- = [1, 2, 0]

    data Filter :: (a -> Exp Bool) -> [a] -> Exp [a]
    type instance Eval (Filter _p '[]) = '[]
    type instance Eval (Filter p (a ': as)) =
      Eval (If (Eval (p a))
        ('(:) a <$> Filter p as)
        (Filter p as))

    -- | Split a list into one where all elements satisfy a predicate,

    -- and a second where no elements satisfy it.

    --

    -- === __Example__

    --

    -- >>> :kind! Eval (Partition ((>=) 35) [20, 30, 40, 50])

    -- Eval (Partition ((>=) 35) [20, 30, 40, 50]) :: ([Natural],

    --                                                 [Natural])

    -- = '([20, 30], [40, 50])

    data Partition :: (a -> Exp Bool) -> [a] -> Exp ([a], [a])
    type instance Eval (Partition p lst) = Eval (Foldr (PartHelp p) '( '[], '[]) lst)

    -- | Helper for 'Partition'.

    data PartHelp :: (a -> Exp Bool) -> a -> ([a],[a]) -> Exp ([a],[a])
    type instance Eval (PartHelp p a '(xs,ys)) =
      If (Eval (p a))
        '(a ': xs, ys)
        '(xs, a ': ys)

    -- | Find the index of an element satisfying the predicate.

    --

    -- === __Example__

    --

    -- >>> :kind! Eval (FindIndex ((<=) 3) [1,2,3,1,2,3])

    -- Eval (FindIndex ((<=) 3) [1,2,3,1,2,3]) :: Maybe Natural

    -- = Just 2

    --

    -- >>> :kind! Eval (FindIndex ((>) 0) [1,2,3,1,2,3])

    -- Eval (FindIndex ((>) 0) [1,2,3,1,2,3]) :: Maybe Natural

    -- = Nothing

    data FindIndex :: (a -> Exp Bool) -> [a] -> Exp (Maybe Nat)
    type instance Eval (FindIndex _p '[]) = 'Nothing
    type instance Eval (FindIndex p (a ': as)) =
      Eval (If (Eval (p a))
        (Pure ('Just 0))
        (Map ((+) 1) =<< FindIndex p as))

    -- | Modify an element at a given index.

    --

    -- The list is unchanged if the index is out of bounds.

    --

    -- === __Example__

    --

    -- >>> :kind! Eval (SetIndex 2 7 [1,2,3])

    -- Eval (SetIndex 2 7 [1,2,3]) :: [Natural]

    -- = [1, 2, 7]

    data SetIndex :: Nat -> a -> [a] -> Exp [a]
    type instance Eval (SetIndex n a' as) = SetIndexImpl n a' as

    type family SetIndexImpl (n :: Nat) (a' :: k) (as :: [k]) where
      SetIndexImpl _n _a' '[] = '[]
      SetIndexImpl 0 a' (_a ': as) = a' ': as
      SetIndexImpl n a' (a ': as) = a ': SetIndexImpl (n TL.- 1) a' as

    -- | Combine elements of two lists pairwise.

    --

    -- === __Example__

    --

    -- >>> :kind! Eval (ZipWith (+) [1,2,3] [1,1,1])

    -- Eval (ZipWith (+) [1,2,3] [1,1,1]) :: [Natural]

    -- = [2, 3, 4]

    data ZipWith :: (a -> b -> Exp c) -> [a] -> [b] -> Exp [c]
    type instance Eval (ZipWith _f '[] _bs) = '[]
    type instance Eval (ZipWith _f _as '[]) = '[]
    type instance Eval (ZipWith f (a ': as) (b ': bs)) =
      Eval (f a b) ': Eval (ZipWith f as bs)

    data Zip :: [a] -> [b] -> Exp [(a, b)]
    type instance Eval (Zip as bs) = Eval (ZipWith (Pure2 '(,)) as bs)

    data Unzip :: Exp [(a, b)] -> Exp ([a], [b])
    type instance Eval (Unzip as) = Eval (Foldr Cons2 '( '[], '[]) (Eval as))