--- /dev/null
+------------------------------------------------------------------------------
+-- |
+-- Module : Data.Param.TFVec
+-- Copyright : (c) 2009 Christiaan Baaij
+-- Licence : BSD-style (see the file LICENCE)
+--
+-- Maintainer : christiaan.baaij@gmail.com
+-- Stability : experimental
+-- Portability : non-portable
+--
+-- 'TFVec': Fixed sized vectors. Vectors with numerically parameterized size,
+-- using type-level numerals from 'tfp' library
+--
+------------------------------------------------------------------------------
+
+module Data.Param.TFVec
+ ( TFVec
+ , empty
+ , (+>)
+ , singleton
+ , vectorCPS
+ , vectorTH
+ , unsafeVector
+ , readTFVec
+ , length
+ , lengthT
+ , fromVector
+ , null
+ , (!)
+ , replace
+ , head
+ , last
+ , init
+ , tail
+ , take
+ , drop
+ , select
+ , group
+ , (<+)
+ , (++)
+ , map
+ , zipWith
+ , foldl
+ , foldr
+ , zip
+ , unzip
+ , shiftl
+ , shiftr
+ , rotl
+ , rotr
+ , concat
+ , reverse
+ , iterate
+ , generate
+ , copy
+ ) where
+
+
+import Types
+import Types.Data.Num.Decimal.Literals.TH
+import Data.RangedWord
+
+import Data.Generics (Data, Typeable)
+import qualified Prelude as P
+import Prelude hiding (
+ null, length, head, tail, last, init, take, drop, (++), map, foldl, foldr,
+ zipWith, zip, unzip, concat, reverse, iterate )
+import qualified Data.Foldable as DF (Foldable, foldr)
+import qualified Data.Traversable as DT (Traversable(traverse))
+import Language.Haskell.TH
+import Language.Haskell.TH.Syntax (Lift(..))
+
+newtype (NaturalT s) => TFVec s a = TFVec {unTFVec :: [a]}
+ deriving (Eq, Typeable)
+
+deriving instance (NaturalT s, Typeable s, Data s, Typeable a, Data a) => Data (TFVec s a)
+
+-- ==========================
+-- = Constructing functions =
+-- ==========================
+
+empty :: TFVec D0 a
+empty = TFVec []
+
+{-# NOINLINE (+>) #-}
+(+>) :: a -> TFVec s a -> TFVec (Succ s) a
+x +> (TFVec xs) = TFVec (x:xs)
+
+infix 5 +>
+
+singleton :: a -> TFVec D1 a
+singleton x = x +> empty
+
+vectorCPS :: [a] -> (forall s . NaturalT s => TFVec s a -> w) -> w
+vectorCPS xs = unsafeVectorCPS (toInteger (P.length xs)) xs
+
+vectorTH :: Lift a => [a] -> ExpQ
+vectorTH xs = (vectorCPS xs) lift
+
+unsafeVector :: NaturalT s => s -> [a] -> TFVec s a
+unsafeVector l xs
+ | fromIntegerT l /= P.length xs =
+ error (show 'unsafeVector P.++ ": dynamic/static lenght mismatch")
+ | otherwise = TFVec xs
+
+readTFVec :: (Read a, NaturalT s) => String -> TFVec s a
+readTFVec = read
+
+readTFVecCPS :: Read a => String -> (forall s . NaturalT s => TFVec s a -> w) -> w
+readTFVecCPS str = unsafeVectorCPS (toInteger l) xs
+ where fName = show 'readTFVecCPS
+ (xs,l) = case [(xs,l) | (xs,l,rest) <- readTFVecList str,
+ ("","") <- lexTFVec rest] of
+ [(xs,l)] -> (xs,l)
+ [] -> error (fName P.++ ": no parse")
+ _ -> error (fName P.++ ": ambiguous parse")
+
+-- =======================
+-- = Observing functions =
+-- =======================
+length :: forall s a . NaturalT s => TFVec s a -> Int
+length _ = fromIntegerT (undefined :: s)
+
+lengthT :: NaturalT s => TFVec s a -> s
+lengthT = undefined
+
+fromVector :: NaturalT s => TFVec s a -> [a]
+fromVector (TFVec xs) = xs
+
+null :: TFVec D0 a -> Bool
+null _ = True
+
+(!) :: ( PositiveT s
+ , NaturalT u
+ , (s :>: u) ~ True) => TFVec s a -> RangedWord u -> a
+(TFVec xs) ! i = xs !! (fromInteger (toInteger i))
+
+-- ==========================
+-- = Transforming functions =
+-- ==========================
+replace :: (PositiveT s, NaturalT u, (s :>: u) ~ True) =>
+ TFVec s a -> RangedWord u -> a -> TFVec s a
+replace (TFVec xs) i y = TFVec $ replace' xs (toInteger i) y
+ where replace' [] _ _ = []
+ replace' (_:xs) 0 y = (y:xs)
+ replace' (x:xs) n y = x : (replace' xs (n-1) y)
+
+head :: PositiveT s => TFVec s a -> a
+head = P.head . unTFVec
+
+tail :: PositiveT s => TFVec s a -> TFVec (Pred s) a
+tail = liftV P.tail
+
+last :: PositiveT s => TFVec s a -> a
+last = P.last . unTFVec
+
+init :: PositiveT s => TFVec s a -> TFVec (Pred s) a
+init = liftV P.init
+
+take :: NaturalT i => i -> TFVec s a -> TFVec (Min s i) a
+take i = liftV $ P.take (fromIntegerT i)
+
+drop :: NaturalT i => i -> TFVec s a -> TFVec (s :-: (Min s i)) a
+drop i = liftV $ P.drop (fromIntegerT i)
+
+select :: (NaturalT f, NaturalT s, NaturalT n, (f :<: i) ~ True,
+ (((s :*: n) :+: f) :<=: i) ~ True) =>
+ f -> s -> n -> TFVec i a -> TFVec n a
+select f s n = liftV (select' f' s' n')
+ where (f', s', n') = (fromIntegerT f, fromIntegerT s, fromIntegerT n)
+ select' f s n = ((selectFirst0 s n).(P.drop f))
+ selectFirst0 :: Int -> Int -> [a] -> [a]
+ selectFirst0 s n l@(x:_)
+ | n > 0 = x : selectFirst0 s (n-1) (P.drop s l)
+ | otherwise = []
+ selectFirst0 _ 0 [] = []
+
+group :: PositiveT n => n -> TFVec s a -> TFVec (Div s n) (TFVec n a)
+group n = liftV (group' (fromIntegerT n))
+ where group' :: Int -> [a] -> [TFVec s a]
+ group' n xs = case splitAtM n xs of
+ Nothing -> []
+ Just (ls, rs) -> TFVec ls : group' n rs
+
+(<+) :: TFVec s a -> a -> TFVec (Succ s) a
+(<+) (TFVec xs) x = TFVec (xs P.++ [x])
+
+(++) :: TFVec s a -> TFVec s2 a -> TFVec (s :+: s2) a
+(++) = liftV2 (P.++)
+
+infixl 5 <+
+infixr 5 ++
+
+map :: (a -> b) -> TFVec s a -> TFVec s b
+map f = liftV (P.map f)
+
+zipWith :: (a -> b -> c) -> TFVec s a -> TFVec s b -> TFVec s c
+zipWith f = liftV2 (P.zipWith f)
+
+foldl :: (a -> b -> a) -> a -> TFVec s b -> a
+foldl f e = (P.foldl f e) . unTFVec
+
+foldr :: (b -> a -> a) -> a -> TFVec s b -> a
+foldr f e = (P.foldr f e) . unTFVec
+
+zip :: TFVec s a -> TFVec s b -> TFVec s (a, b)
+zip = liftV2 P.zip
+
+unzip :: TFVec s (a, b) -> (TFVec s a, TFVec s b)
+unzip (TFVec xs) = let (a,b) = P.unzip xs in (TFVec a, TFVec b)
+
+shiftl :: (PositiveT s, NaturalT n, n ~ Pred s, s ~ Succ n) =>
+ TFVec s a -> a -> TFVec s a
+shiftl xs x = x +> init xs
+
+shiftr :: (PositiveT s, NaturalT n, n ~ Pred s, s ~ Succ n) =>
+ TFVec s a -> a -> TFVec s a
+shiftr xs x = tail xs <+ x
+
+rotl :: (PositiveT s, s ~ Succ (Pred s)) => TFVec s a -> TFVec s a
+rotl xs = last xs +> init xs
+
+class Rotr a where rotr :: a -> a
+instance Rotr (TFVec D0 a) where rotr xs = xs
+instance (PositiveT s, s ~ Succ (Pred s)) => Rotr (TFVec s a) where rotr xs = tail xs <+ head xs
+
+concat :: TFVec s1 (TFVec s2 a) -> TFVec (s1 :*: s2) a
+concat = liftV (P.foldr ((P.++).unTFVec) [])
+
+reverse :: TFVec s a -> TFVec s a
+reverse = liftV P.reverse
+
+iterate :: NaturalT s => s -> (a -> a) -> a -> TFVec s a
+iterate s f x = let s' = fromIntegerT s in TFVec (P.take s' $ P.iterate f x)
+
+generate :: NaturalT s => s -> (a -> a) -> a -> TFVec s a
+generate s f x = let s' = fromIntegerT s in TFVec (P.take s' $ P.tail $ P.iterate f x)
+
+copy :: NaturalT s => s -> a -> TFVec s a
+copy s x = iterate s id x
+
+-- =============
+-- = Instances =
+-- =============
+instance Show a => Show (TFVec s a) where
+ showsPrec _ = showV.unTFVec
+ where showV [] = showString "<>"
+ showV (x:xs) = showChar '<' . shows x . showl xs
+ where showl [] = showChar '>'
+ showl (x:xs) = showChar ',' . shows x .
+ showl xs
+
+instance (Read a, NaturalT nT) => Read (TFVec nT a) where
+ readsPrec _ str
+ | all fitsLength possibilities = P.map toReadS possibilities
+ | otherwise = error (fName P.++ ": string/dynamic length mismatch")
+ where
+ fName = "Data.Param.TFVec.read"
+ expectedL = fromIntegerT (undefined :: nT)
+ possibilities = readTFVecList str
+ fitsLength (_, l, _) = l == expectedL
+ toReadS (xs, _, rest) = (TFVec xs, rest)
+
+instance NaturalT s => DF.Foldable (TFVec s) where
+ foldr = foldr
+
+instance NaturalT s => Functor (TFVec s) where
+ fmap = map
+
+instance NaturalT s => DT.Traversable (TFVec s) where
+ traverse f = (fmap TFVec).(DT.traverse f).unTFVec
+
+instance (Lift a, NaturalT nT) => Lift (TFVec nT a) where
+ lift (TFVec xs) = [| unsafeTFVecCoerse
+ $(decLiteralV (fromIntegerT (undefined :: nT)))
+ (TFVec xs) |]
+
+-- ======================
+-- = Internal Functions =
+-- ======================
+liftV :: ([a] -> [b]) -> TFVec nT a -> TFVec nT' b
+liftV f = TFVec . f . unTFVec
+
+liftV2 :: ([a] -> [b] -> [c]) -> TFVec s a -> TFVec s2 b -> TFVec s3 c
+liftV2 f a b = TFVec (f (unTFVec a) (unTFVec b))
+
+splitAtM :: Int -> [a] -> Maybe ([a],[a])
+splitAtM n xs = splitAtM' n [] xs
+ where splitAtM' 0 xs ys = Just (xs, ys)
+ splitAtM' n xs (y:ys) | n > 0 = do
+ (ls, rs) <- splitAtM' (n-1) xs ys
+ return (y:ls,rs)
+ splitAtM' _ _ _ = Nothing
+
+unsafeTFVecCoerse :: nT' -> TFVec nT a -> TFVec nT' a
+unsafeTFVecCoerse _ (TFVec v) = (TFVec v)
+
+unsafeVectorCPS :: forall a w . Integer -> [a] ->
+ (forall s . NaturalT s => TFVec s a -> w) -> w
+unsafeVectorCPS l xs f = reifyNaturalD l
+ (\(_ :: lt) -> f ((TFVec xs) :: (TFVec lt a)))
+
+readTFVecList :: Read a => String -> [([a], Int, String)]
+readTFVecList = readParen' False (\r -> [pr | ("<",s) <- lexTFVec r,
+ pr <- readl s])
+ where
+ readl s = [([],0,t) | (">",t) <- lexTFVec s] P.++
+ [(x:xs,1+n,u) | (x,t) <- reads s,
+ (xs, n, u) <- readl' t]
+ readl' s = [([],0,t) | (">",t) <- lexTFVec s] P.++
+ [(x:xs,1+n,v) | (",",t) <- lex s,
+ (x,u) <- reads t,
+ (xs,n,v) <- readl' u]
+ readParen' b g = if b then mandatory else optional
+ where optional r = g r P.++ mandatory r
+ mandatory r = [(x,n,u) | ("(",s) <- lexTFVec r,
+ (x,n,t) <- optional s,
+ (")",u) <- lexTFVec t]
+
+-- Custom lexer for FSVecs, we cannot use lex directly because it considers
+-- sequences of < and > as unique lexemes, and that breaks nested FSVecs, e.g.
+-- <<1,2><3,4>>
+lexTFVec :: ReadS String
+lexTFVec ('>':rest) = [(">",rest)]
+lexTFVec ('<':rest) = [("<",rest)]
+lexTFVec str = lex str
+
\ No newline at end of file