{-# LANGUAGE DataKinds #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE InstanceSigs #-}
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE StandaloneKindSignatures #-}
{-# LANGUAGE TypeApplications #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
module Fancy where

import Control.Monad (forM_)
import Control.Monad.ST
import Data.Coerce (coerce)
import Data.Kind
import Data.Proxy
import Data.Type.Equality
import Data.Type.Ord
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM

import Array (XArray, IxX(..), KnownShapeX(..), StaticShapeX(..), type (++))
import qualified Array as X
import Nats


type family Replicate n a where
  Replicate Z a = '[]
  Replicate (S n) a = a : Replicate n a

type family MapJust l where
  MapJust '[] = '[]
  MapJust (x : xs) = Just x : MapJust xs

lemCompareFalse1 :: (0 < n, 1 > n) => Proxy n -> a
lemCompareFalse1 = error "Incoherence"

lemKnownReplicate :: forall n. KnownNat n => Proxy n -> Dict KnownShapeX (Replicate n Nothing)
lemKnownReplicate _ = X.lemKnownShapeX (go (knownNat @n))
  where
    go :: SNat m -> StaticShapeX (Replicate m Nothing)
    go SZ = SZX
    go (SS n) = () :$? go n


type Mixed :: [Maybe Nat] -> Type -> Type
data family Mixed sh a

newtype instance Mixed sh Int = M_Int (XArray sh Int)
newtype instance Mixed sh Double = M_Double (XArray sh Double)
-- etc.

newtype instance Mixed sh () = M_Nil (IxX sh)  -- store the shape
data instance Mixed sh (a, b) = M_Tup2 (Mixed sh a) (Mixed sh b)
data instance Mixed sh (a, b, c) = M_Tup3 (Mixed sh a) (Mixed sh b) (Mixed sh c)
data instance Mixed sh (a, b, c, d) = M_Tup4 (Mixed sh a) (Mixed sh b) (Mixed sh c) (Mixed sh d)

newtype instance Mixed sh1 (Mixed sh2 a) = M_Nest (Mixed (sh1 ++ sh2) a)


type MixedVecs :: Type -> [Maybe Nat] -> Type -> Type
data family MixedVecs s sh a

newtype instance MixedVecs s sh Int = MV_Int (VU.MVector s Int)
newtype instance MixedVecs s sh Double = MV_Double (VU.MVector s Double)
-- etc.

data instance MixedVecs s sh () = MV_Nil
data instance MixedVecs s sh (a, b) = MV_Tup2 (MixedVecs s sh a) (MixedVecs s sh b)
data instance MixedVecs s sh (a, b, c) = MV_Tup3 (MixedVecs s sh a) (MixedVecs s sh b) (MixedVecs s sh c)
data instance MixedVecs s sh (a, b, c, d) = MV_Tup4 (MixedVecs s sh a) (MixedVecs s sh b) (MixedVecs s sh c) (MixedVecs s sh d)

data instance MixedVecs s sh1 (Mixed sh2 a) = MV_Nest (IxX sh2) (MixedVecs s (sh1 ++ sh2) a)


class GMixed a where
  mshape :: KnownShapeX sh => Mixed sh a -> IxX sh
  mindex :: Mixed sh a -> IxX sh -> a
  mindexPartial :: forall sh sh'. Mixed (sh ++ sh') a -> IxX sh -> Mixed sh' a

  -- | Create an empty array. The given shape must have size zero; this may or may not be checked.
  memptyArray :: IxX sh -> Mixed sh a

  -- | Return the size of the individual (SoA) arrays in this value. If @a@
  -- does not contain tuples, this coincides with the total number of scalars
  -- in the given value; if @a@ contains tuples, then it is some multiple of
  -- this number of scalars.
  mvecsNumElts :: a -> Int

  -- | Create uninitialised vectors for this array type, given the shape of
  -- this vector and an example for the contents. The shape must not have size
  -- zero; an error may be thrown otherwise.
  mvecsUnsafeNew :: IxX sh -> a -> ST s (MixedVecs s sh a)

  -- | Given the shape of this array, an index and a value, write the value at
  -- that index in the vectors.
  mvecsWrite :: IxX sh -> IxX sh -> a -> MixedVecs s sh a -> ST s ()

  -- | Given the shape of this array, an index and a value, write the value at
  -- that index in the vectors.
  mvecsWritePartial :: KnownShapeX sh' => IxX (sh ++ sh') -> IxX sh -> Mixed sh' a -> MixedVecs s (sh ++ sh') a -> ST s ()

  -- | Given the shape of this array, finalise the vectors into 'XArray's.
  mvecsFreeze :: IxX sh -> MixedVecs s sh a -> ST s (Mixed sh a)

-- TODO: this use of toVector is suboptimal
mvecsWritePartialPrimitive
  :: forall sh' sh a s. (KnownShapeX sh', VU.Unbox a)
  => IxX (sh ++ sh') -> IxX sh -> XArray sh' a -> VU.MVector s a -> ST s ()
mvecsWritePartialPrimitive sh i arr v = do
  let offset = X.toLinearIdx sh (X.ixAppend i (X.zeroIdx' (X.shape arr)))
  VU.copy (VUM.slice offset (X.shapeSize (X.shape arr)) v) (X.toVector arr)

instance GMixed Int where
  mshape (M_Int a) = X.shape a
  mindex (M_Int a) i = X.index a i
  mindexPartial (M_Int a) i = M_Int (X.indexPartial a i)
  memptyArray sh = M_Int (X.generate sh (error "memptyArray Int: shape was not empty"))

  mvecsNumElts _ = 1
  mvecsUnsafeNew sh _ = MV_Int <$> VUM.unsafeNew (X.shapeSize sh)
  mvecsWrite sh i x (MV_Int v) = VUM.write v (X.toLinearIdx sh i) x
  mvecsWritePartial sh i (M_Int @sh' arr) (MV_Int v) = mvecsWritePartialPrimitive @sh' sh i arr v
  mvecsFreeze sh (MV_Int v) = M_Int . X.fromVector sh <$> VU.freeze v

instance GMixed Double where
  mshape (M_Double a) = X.shape a
  mindex (M_Double a) i = X.index a i
  mindexPartial (M_Double a) i = M_Double (X.indexPartial a i)
  memptyArray sh = M_Double (X.generate sh (error "memptyArray Double: shape was not empty"))

  mvecsNumElts _ = 1
  mvecsUnsafeNew sh _ = MV_Double <$> VUM.unsafeNew (X.shapeSize sh)
  mvecsWrite sh i x (MV_Double v) = VUM.write v (X.toLinearIdx sh i) x
  mvecsWritePartial sh i (M_Double @sh' arr) (MV_Double v) = mvecsWritePartialPrimitive @sh' sh i arr v
  mvecsFreeze sh (MV_Double v) = M_Double . X.fromVector sh <$> VU.freeze v

instance GMixed () where
  mshape (M_Nil sh) = sh
  mindex _ _ = ()
  mindexPartial = \(M_Nil sh) i -> M_Nil (X.ixDrop sh i)
  memptyArray sh = M_Nil sh

  mvecsNumElts _ = 1
  mvecsUnsafeNew _ _ = return MV_Nil
  mvecsWrite _ _ _ _ = return ()
  mvecsWritePartial _ _ _ _ = return ()
  mvecsFreeze sh _ = return (M_Nil sh)

instance (GMixed a, GMixed b) => GMixed (a, b) where
  mshape (M_Tup2 a _) = mshape a
  mindex (M_Tup2 a b) i = (mindex a i, mindex b i)
  mindexPartial (M_Tup2 a b) i = M_Tup2 (mindexPartial a i) (mindexPartial b i)
  memptyArray sh = M_Tup2 (memptyArray sh) (memptyArray sh)

  mvecsNumElts (x, y) = mvecsNumElts x * mvecsNumElts y
  mvecsUnsafeNew sh (x, y) = MV_Tup2 <$> mvecsUnsafeNew sh x <*> mvecsUnsafeNew sh y
  mvecsWrite sh i (x, y) (MV_Tup2 a b) = do
    mvecsWrite sh i x a
    mvecsWrite sh i y b
  mvecsWritePartial sh i (M_Tup2 x y) (MV_Tup2 a b) = do
    mvecsWritePartial sh i x a
    mvecsWritePartial sh i y b
  mvecsFreeze sh (MV_Tup2 a b) = M_Tup2 <$> mvecsFreeze sh a <*> mvecsFreeze sh b

instance (GMixed a, KnownShapeX sh') => GMixed (Mixed sh' a) where
  -- TODO: this is quadratic in the nesting level
  mshape :: forall sh. KnownShapeX sh => Mixed sh (Mixed sh' a) -> IxX sh
  mshape (M_Nest arr)
    | Dict <- X.lemAppKnownShapeX (knownShapeX @sh) (knownShapeX @sh')
    = ixAppPrefix (knownShapeX @sh) (mshape arr)
    where
      ixAppPrefix :: StaticShapeX sh1 -> IxX (sh1 ++ sh') -> IxX sh1
      ixAppPrefix SZX _ = IZX
      ixAppPrefix (_ :$@ ssh) (i ::@ idx) = i ::@ ixAppPrefix ssh idx
      ixAppPrefix (_ :$? ssh) (i ::? idx) = i ::? ixAppPrefix ssh idx

  mindex (M_Nest arr) i = mindexPartial arr i

  mindexPartial :: forall sh1 sh2.
                   Mixed (sh1 ++ sh2) (Mixed sh' a) -> IxX sh1 -> Mixed sh2 (Mixed sh' a)
  mindexPartial (M_Nest arr) i
    | Refl <- X.lemAppAssoc (Proxy @sh1) (Proxy @sh2) (Proxy @sh')
    = M_Nest (mindexPartial @a @sh1 @(sh2 ++ sh') arr i)

  memptyArray sh = M_Nest (memptyArray (X.ixAppend sh (X.zeroIdx (knownShapeX @sh'))))

  mvecsNumElts arr =
    let n = X.shapeSize (mshape arr)
    in if n == 0 then 0 else n * mvecsNumElts (mindex arr (X.zeroIdx (knownShapeX @sh')))

  mvecsUnsafeNew sh example
    | X.shapeSize sh' == 0 = error "mvecsUnsafeNew: empty example"
    | otherwise = MV_Nest sh' <$> mvecsUnsafeNew (X.ixAppend sh (mshape example))
                                                 (mindex example (X.zeroIdx (knownShapeX @sh')))
    where
      sh' = mshape example

  mvecsWrite sh idx val (MV_Nest sh' vecs) = mvecsWritePartial (X.ixAppend sh sh') idx val vecs

  mvecsWritePartial :: forall sh1 sh2 s. KnownShapeX sh2
                    => IxX (sh1 ++ sh2) -> IxX sh1 -> Mixed sh2 (Mixed sh' a)
                    -> MixedVecs s (sh1 ++ sh2) (Mixed sh' a)
                    -> ST s ()
  mvecsWritePartial sh12 idx (M_Nest arr) (MV_Nest sh' vecs)
    | Dict <- X.lemKnownShapeX (X.ssxAppend (knownShapeX @sh2) (knownShapeX @sh'))
    , Refl <- X.lemAppAssoc (Proxy @sh1) (Proxy @sh2) (Proxy @sh')
    = mvecsWritePartial @a @(sh2 ++ sh') @sh1 (X.ixAppend sh12 sh') idx arr vecs

  mvecsFreeze sh (MV_Nest sh' vecs) = M_Nest <$> mvecsFreeze (X.ixAppend sh sh') vecs

mgenerate :: forall sh a. (KnownShapeX sh, GMixed a) => IxX sh -> (IxX sh -> a) -> Mixed sh a
mgenerate sh f
  | not (checkBounds sh (knownShapeX @sh)) =
      error $ "mgenerate: Shape " ++ show sh ++ " not valid for shape type " ++ show (knownShapeX @sh)
  -- We need to be very careful here to ensure that neither 'sh' nor
  -- 'firstelem' that we pass to 'mvecsUnsafeNew' are empty.
  | X.shapeSize sh == 0 = memptyArray sh
  | otherwise =
      let firstidx = X.zeroIdx' sh
          firstelem = f (X.zeroIdx' sh)
      in if mvecsNumElts firstelem == 0
           then memptyArray sh
           else runST $ do
                  vecs <- mvecsUnsafeNew sh firstelem
                  mvecsWrite sh firstidx firstelem vecs
                  forM_ (tail (X.enumShape sh)) $ \idx ->
                    mvecsWrite sh idx (f idx) vecs
                  mvecsFreeze sh vecs
  where
    checkBounds :: IxX sh' -> StaticShapeX sh' -> Bool
    checkBounds IZX SZX = True
    checkBounds (n ::@ sh') (n' :$@ ssh') = n == fromIntegral (unSNat n') && checkBounds sh' ssh'
    checkBounds (_ ::? sh') (() :$? ssh') = checkBounds sh' ssh'


type Ranked :: Nat -> Type -> Type
newtype Ranked n a = Ranked (Mixed (Replicate n Nothing) a)

type Shaped :: [Nat] -> Type -> Type
newtype Shaped sh a = Shaped (Mixed (MapJust sh) a)

newtype instance Mixed sh (Ranked n a) = M_Ranked (Mixed sh (Mixed (Replicate n Nothing) a))
newtype instance Mixed sh (Shaped sh' a) = M_Shaped (Mixed sh (Mixed (MapJust sh') a))

newtype instance MixedVecs s sh (Ranked n a) = MV_Ranked (MixedVecs s sh (Mixed (Replicate n Nothing) a))
newtype instance MixedVecs s sh (Shaped sh' a) = MV_Shaped (MixedVecs s sh (Mixed (MapJust sh') a))


instance (KnownNat n, GMixed a) => GMixed (Ranked n a) where
  mshape (M_Ranked arr) | Dict <- lemKnownReplicate (Proxy @n) = mshape arr
  mindex (M_Ranked arr) i | Dict <- lemKnownReplicate (Proxy @n) = Ranked (mindex arr i)

  mindexPartial :: forall sh sh'. Mixed (sh ++ sh') (Ranked n a) -> IxX sh -> Mixed sh' (Ranked n a)
  mindexPartial (M_Ranked arr) i
    | Dict <- lemKnownReplicate (Proxy @n)
    = coerce @(Mixed sh' (Mixed (Replicate n 'Nothing) a)) @(Mixed sh' (Ranked n a)) $
        mindexPartial arr i

  memptyArray :: forall sh. IxX sh -> Mixed sh (Ranked n a)
  memptyArray i
    | Dict <- lemKnownReplicate (Proxy @n)
    = coerce @(Mixed sh (Mixed (Replicate n 'Nothing) a)) @(Mixed sh (Ranked n a)) $
        memptyArray i

  mvecsNumElts (Ranked arr)
    | Dict <- lemKnownReplicate (Proxy @n)
    = mvecsNumElts arr

  mvecsUnsafeNew idx (Ranked arr)
    | Dict <- lemKnownReplicate (Proxy @n)
    = MV_Ranked <$> mvecsUnsafeNew idx arr

  mvecsWrite :: forall sh s. IxX sh -> IxX sh -> Ranked n a -> MixedVecs s sh (Ranked n a) -> ST s ()
  mvecsWrite sh idx (Ranked arr) vecs
    | Dict <- lemKnownReplicate (Proxy @n)
    = mvecsWrite sh idx arr
        (coerce @(MixedVecs s sh (Ranked n a)) @(MixedVecs s sh (Mixed (Replicate n Nothing) a))
           vecs)

  mvecsWritePartial :: forall sh sh' s. KnownShapeX sh'
                    => IxX (sh ++ sh') -> IxX sh -> Mixed sh' (Ranked n a)
                    -> MixedVecs s (sh ++ sh') (Ranked n a)
                    -> ST s ()
  mvecsWritePartial sh idx arr vecs
    | Dict <- lemKnownReplicate (Proxy @n)
    = mvecsWritePartial sh idx
        (coerce @(Mixed sh' (Ranked n a))
                @(Mixed sh' (Mixed (Replicate n Nothing) a))
           arr)
        (coerce @(MixedVecs s (sh ++ sh') (Ranked n a))
                @(MixedVecs s (sh ++ sh') (Mixed (Replicate n Nothing) a))
           vecs)

  mvecsFreeze :: forall sh s. IxX sh -> MixedVecs s sh (Ranked n a) -> ST s (Mixed sh (Ranked n a))
  mvecsFreeze sh vecs
    | Dict <- lemKnownReplicate (Proxy @n)
    = coerce @(Mixed sh (Mixed (Replicate n Nothing) a))
             @(Mixed sh (Ranked n a))
        <$> mvecsFreeze sh
              (coerce @(MixedVecs s sh (Ranked n a))
                      @(MixedVecs s sh (Mixed (Replicate n Nothing) a))
                      vecs)


data SShape sh where
  ShNil :: SShape '[]
  ShCons :: SNat n -> SShape sh -> SShape (n : sh)
deriving instance Show (SShape sh)

class KnownShape sh where knownShape :: SShape sh
instance KnownShape '[] where knownShape = ShNil
instance (KnownNat n, KnownShape sh) => KnownShape (n : sh) where knownShape = ShCons knownNat knownShape

-- instance (KnownShape sh, GMixed a) => GMixed (Shaped sh a) where


type IxR :: Nat -> Type
data IxR n where
  IZR :: IxR Z
  (:::) :: Int -> IxR n -> IxR (S n)

type IxS :: [Nat] -> Type
data IxS sh where
  IZS :: IxS '[]
  (::$) :: Int -> IxS sh -> IxS (n : sh)

ixCvtXR :: IxX sh -> IxR (X.Rank sh)
ixCvtXR IZX = IZR
ixCvtXR (n ::@ sh) = n ::: ixCvtXR sh
ixCvtXR (n ::? sh) = n ::: ixCvtXR sh

ixCvtRX :: IxR n -> IxX (Replicate n Nothing)
ixCvtRX IZR = IZX
ixCvtRX (n ::: sh) = n ::? ixCvtRX sh

lemRankReplicate :: forall n. KnownNat n => Proxy n -> X.Rank (Replicate n (Nothing @Nat)) :~: n
lemRankReplicate _ = go (knownNat @n)
  where
    go :: SNat m -> X.Rank (Replicate m (Nothing @Nat)) :~: m
    go SZ = Refl
    go (SS n) | Refl <- go n = Refl

lemReplicatePlusApp :: forall n m a. KnownNat n => Proxy n -> Proxy m -> Proxy a
                    -> Replicate (n + m) a :~: Replicate n a ++ Replicate m a
lemReplicatePlusApp _ _ _ = go (knownNat @n)
  where
    go :: SNat n' -> Replicate (n' + m) a :~: Replicate n' a ++ Replicate m a
    go SZ = Refl
    go (SS n) | Refl <- go n = Refl


rshape :: forall n a. (KnownNat n, GMixed a) => Ranked n a -> IxR n
rshape (Ranked arr)
  | Dict <- lemKnownReplicate (Proxy @n)
  , Refl <- lemRankReplicate (Proxy @n)
  = ixCvtXR (mshape arr)

rindex :: GMixed a => Ranked n a -> IxR n -> a
rindex (Ranked arr) idx = mindex arr (ixCvtRX idx)

rewriteMixed :: sh1 :~: sh2 -> Mixed sh1 a -> Mixed sh2 a
rewriteMixed Refl x = x

rindexPartial :: forall n m a. (KnownNat n, GMixed a) => Ranked (n + m) a -> IxR n -> Ranked m a
rindexPartial (Ranked arr) idx
  | Refl <- lemReplicatePlusApp (Proxy @n) (Proxy @m) (Proxy @Nothing)
  = Ranked (mindexPartial @a @(Replicate n Nothing) @(Replicate m Nothing)
              (rewriteMixed (lemReplicatePlusApp (Proxy @n) (Proxy @m) (Proxy @Nothing)) arr)
              (ixCvtRX idx))

rgenerate :: forall n a. (KnownNat n, GMixed a) => IxR n -> (IxR n -> a) -> Ranked n a
rgenerate sh f
  | Dict <- lemKnownReplicate (Proxy @n)
  , Refl <- lemRankReplicate (Proxy @n)
  = Ranked (mgenerate (ixCvtRX sh) (f . ixCvtXR))