```{-# LANGUAGE TypeOperators, TemplateHaskell, ScopedTypeVariables #-}
{-# OPTIONS_HADDOCK hide #-}
-----------------------------------------------------------------------------
-- |
-- Module      :  Numeric.AD.Internal.Tensors
-- Copyright   :  (c) Edward Kmett 2010
-- License     :  BSD3
-- Maintainer  :  ekmett@gmail.com
-- Stability   :  experimental
-- Portability :  GHC only
--
-----------------------------------------------------------------------------

( Tensors(..)
, tailT
, tensors
) where

import Control.Applicative
import Data.Foldable
import Data.Traversable
import Data.Monoid
import Data.Typeable (Typeable1(..), Typeable(..), TyCon, mkTyCon, mkTyConApp, typeOfDefault)

infixl 3 :-

data Tensors f a = a :- Tensors f (f a)
-- Polymorphic recursion precludes Data in its current form, as no Data1 class exists

instance Functor f => Functor (Tensors f) where
fmap f (a :- as) = f a :- fmap (fmap f) as

instance Foldable f => Foldable (Tensors f) where
foldMap f (a :- as) = f a `mappend` foldMap (foldMap f) as

instance Traversable f => Traversable (Tensors f) where
traverse f (a :- as) = (:-) <\$> f a <*> traverse (traverse f) as

-- | While we can not be a 'Comonad' without a 'fzip'-like operation, you can use the
-- comonad for @'Stream' f a@ to manipulate a structure comonadically that you can turn
-- into 'Tensors'.
instance Functor f => Copointed (Tensors f) where
extract (a :- _) = a

tailT :: Tensors f a -> Tensors f (f a)
tailT (_ :- as) = as
{-# INLINE tailT #-}

headT :: Tensors f a -> a
headT (a :- _) = a
{-# INLINE headT #-}

tensors :: Functor f => Stream f a -> Tensors f a
tensors (a :< as) = a :- distribute (tensors <\$> as)
where
distribute :: Functor f => f (Tensors f a) -> Tensors f (f a)
distribute x = (headT <\$> x) :- distribute (tailT <\$> x)

instance Typeable1 f => Typeable1 (Tensors f) where
typeOf1 tfa = mkTyConApp tensorsTyCon [typeOf1 (undefined `asArgsType` tfa)]
where asArgsType :: f a -> t f a -> f a
asArgsType = const

instance (Typeable1 f, Typeable a) => Typeable (Tensors f a) where
typeOf = typeOfDefault

tensorsTyCon :: TyCon
tensorsTyCon = mkTyCon "Numeric.AD.Internal.Tensors.Tensors"
{-# NOINLINE tensorsTyCon #-}
```