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+-- you may not use this file except in compliance with the License. +-- You may obtain a copy of the License at +-- +-- http://www.apache.org/licenses/LICENSE-2.0 +-- +-- Unless required by applicable law or agreed to in writing, software +-- distributed under the License is distributed on an "AS IS" BASIS, +-- WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +-- See the License for the specific language governing permissions and +-- limitations under the License. + +-- | Lenses and related optics for 'Vec's. + +-- Work around +{-# OPTIONS_GHC -fno-float-in #-} +{-# OPTIONS_GHC -Wno-orphans #-} + +{-# LANGUAGE AllowAmbiguousTypes #-} +{-# LANGUAGE BangPatterns #-} +{-# LANGUAGE CPP #-} +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE DeriveDataTypeable #-} +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE KindSignatures #-} +{-# LANGUAGE MagicHash #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE RankNTypes #-} +{-# LANGUAGE RoleAnnotations #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE TypeApplications #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE UnboxedTuples #-} +{-# LANGUAGE ViewPatterns #-} +{-# LANGUAGE UndecidableInstances #-} + +module Data.Vec.Short.Lens + ( + -- ** List-based lenses + list + -- ** Arity-based lenses + , paired + + -- * List-like operators + -- ** Constructor views + -- *** The cons view + , consed + -- *** The snoc view + , snoced + -- ** Operator views + -- *** The append view + , chopped + -- *** The concat view + , subVecs + -- *** The reverse view + , reversed + -- *** The transposition view + , vtransposed + + -- * Misc lenses + , midElem, ixElem, ix + , sliced + , rotated + , vdiagonal + ) where + +import Prelude hiding ((++), concat, concatMap, iterate) + +import qualified Data.Foldable as F +import GHC.ST (runST) +import GHC.TypeLits (KnownNat, type (+), type (<=), type (-)) +import qualified GHC.TypeLits + +import Control.Lens (Iso, Lens', iso, lens, from, swapped) + +import Data.Fin.Int.Explicit (Fin, complementFin, finToInt, unsafeFin) +import Data.SInt (sintVal, unSInt) +import Data.Vec.Short.Internal + +#if !MIN_VERSION_lens(5,0,0) +import qualified Control.Lens as L +import Data.Foldable.WithIndex (FoldableWithIndex(..)) +import Data.Traversable.WithIndex (TraversableWithIndex(..)) +#endif + +-------------------------------------------------------------------------------- + +-- | A list (of the right length) is isomorphic to a vector. +-- The list-to-vector direction is partial. +list :: (KnownNat n) => Iso (Vec n a) (Vec n b) + [a] [b] +list = iso F.toList (fromList sintVal) + +-------------------------------------------------------------------------------- + +-- | Lens on a single element. +ix :: Fin n -> Lens' (Vec n a) a +ix i = i `seq` lens (! i) (upd i) +{-# INLINE ix #-} + +---------------- + +-- | An isomorphism with an element added at the beginning of a vector. +consed :: Iso (a, Vec n a) (b, Vec m b) + (Vec (n + 1) a) (Vec (m + 1) b) +consed = from (unsafeIxElem (const 0)) + +-- | An isomorphism with an element added at the end of a vector. +snoced :: Iso (Vec n a, a) (Vec m b, b) + (Vec (n + 1) a) (Vec (m + 1) b) +snoced = from (unsafeIxElem id . swapped) + +-- | Isomorphism between a vector with and without its middle element. +midElem :: forall m n a b. Iso (Vec (n+1) a) (Vec (m+1) b) + (a, Vec n a) (b, Vec m b) +midElem = unsafeIxElem (`quot` 2) + +---------------- + +-- | An isomorphism with a 'split' vector. +chopped :: (KnownNat m) => Iso (Vec (m + n) a) (Vec (o + p) b) + (Vec m a, Vec n a) (Vec o b, Vec p b) +chopped = iso (split sintVal) (uncurry (++)) + +-- | A vector can be split (isomorphically) into a vector of vectors. +subVecs :: (KnownNat m, (n GHC.TypeLits.* m) ~ nm, (p GHC.TypeLits.* o) ~ po) + => Iso (Vec nm a) (Vec po b) + (Vec n (Vec m a)) (Vec p (Vec o b)) +subVecs = iso (reshape sintVal) concat + +-- | A vector is isomorphic to its reversal. +reversed :: Iso (Vec n a) (Vec m b) + (Vec n a) (Vec m b) +reversed = iso rev rev + +-------------------------------- +-- Other misc lenses + +-- Unsafe version of ixElem, but with a function computing the +-- index from @valueOf @n@. +-- This allows unsafeIxElem to be used easily for midElem and snoced. +unsafeIxElem :: (Int -> Int) -> Iso (Vec (n+1) a) (Vec (m+1) b) + (a, Vec n a) (b, Vec m b) +unsafeIxElem fi = iso getf setf + where getf xs = + let !i = fi (vSize xs - 1) + in unsafeIndexK xs i $ \ xi -> + let !xs' = unsafeRemove i xs + in (xi, xs') + setf (xi, xs) = + let !i = fi (vSize xs) + in unsafeInsert i xi xs +{-# INLINE unsafeIxElem #-} + +-- | Isomorphism between a vector with and without a single element at +-- the given index. +ixElem :: forall n a b. Fin (n+1) -> Iso (Vec (n+1) a) (Vec (n+1) b) + (a, Vec n a) (b, Vec n b) +ixElem i = unsafeIxElem (const (finToInt i)) + + +-- | A lens to a slice of the vector. +sliced + :: forall m n a + . (KnownNat m, KnownNat n, m <= n) + => Fin (n - m + 1) + -> Lens' (Vec n a) (Vec m a) +sliced (finToInt -> !start) = lens getf setf + where + !m = unSInt @m sintVal + !n = unSInt @n sintVal + !end = start + m + !rest = n - end -- the length of the post-slice portion of the vector + + getf xs = sliceVec xs start sintVal + setf xs ys = + createVec sintVal $ \mv -> do + unsafeCopyVec xs 0 mv 0 start + unsafeCopyVec ys 0 mv start m + unsafeCopyVec xs end mv end rest + + +-- | A two-element vector is isomorphic to a pair. +paired :: Iso (Vec 2 a) (Vec 2 b) (a, a) (b, b) +paired = iso unvec2 (uncurry vec2) + where + unvec2 v = + indexK v (unsafeFin @Int 0) $ \x -> + indexK v (unsafeFin @Int 1) $ \y -> (x,y) + +-- | Isomorphism between a vector and a vector rotated @i@ steps. +-- The element at index 0 in the first vector is at index @i@ in the second. +-- E.g., @view (rotated 1) (fromList "ABCD") == fromList "DABC"@ +rotated :: forall n a b. Fin n -> Iso (Vec n a) (Vec n b) (Vec n a) (Vec n b) +rotated i = iso (rot i) (\v -> rot (complementFin (svSize v) i) v) +{-# INLINE rotated #-} + +-- | Isomorphism of transposed vectors. +vtransposed :: (KnownNat m, KnownNat p) + => Iso (Vec n (Vec m a)) (Vec p (Vec o b)) + (Vec m (Vec n a)) (Vec o (Vec p b)) +vtransposed = iso (vtranspose sintVal) (vtranspose sintVal) + +-- TODO: KnownNat not needed. +-- | Lens on the main diagonal. +vdiagonal :: forall n a. KnownNat n => Lens' (Vec n (Vec n a)) (Vec n a) +vdiagonal = lens getf setf + where + getf :: Vec n (Vec n a) -> Vec n a + getf = imap (flip (!)) + + setf :: Vec n (Vec n a) -> Vec n a -> Vec n (Vec n a) + setf m d = + mkVec sintVal $ \i -> + indexK m i $ \mi -> + indexK d i $ \di -> + runST $ do + mi' <- safeThawMV mi + writeMV mi' i di + unsafeFreezeMV mi' + +#if !MIN_VERSION_lens(5,0,0) +instance L.FunctorWithIndex (Fin n) (Vec n) where imap = imap +instance KnownNat n => L.FoldableWithIndex (Fin n) (Vec n) where + ifoldMap = ifoldMap +instance KnownNat n => L.TraversableWithIndex (Fin n) (Vec n) where + itraverse = itraverse +#endif