diff --git a/linear.cabal b/linear.cabal
--- a/linear.cabal
+++ b/linear.cabal
@@ -1,6 +1,6 @@
 name:          linear
 category:      Math, Algebra
-version:       1.10.1.2
+version:       1.11
 license:       BSD3
 cabal-version: >= 1.8
 license-file:  LICENSE
diff --git a/src/Linear/Metric.hs b/src/Linear/Metric.hs
--- a/src/Linear/Metric.hs
+++ b/src/Linear/Metric.hs
@@ -15,7 +15,7 @@
 -- Free metric spaces
 ----------------------------------------------------------------------------
 module Linear.Metric
-  ( Metric(..), normalize
+  ( Metric(..), normalize, project
   ) where
 
 import Data.Foldable as Foldable
@@ -82,3 +82,8 @@
 normalize :: (Floating a, Metric f, Epsilon a) => f a -> f a
 normalize v = if nearZero l || nearZero (1-l) then v else fmap (/sqrt l) v
   where l = quadrance v
+
+-- | @project u v@ computes the projection of @v@ onto @u@.
+project :: (Metric v, Fractional a) => v a -> v a -> v a
+project u v = ((v `dot` u) / quadrance u) *^ u
+
diff --git a/src/Linear/Plucker.hs b/src/Linear/Plucker.hs
--- a/src/Linear/Plucker.hs
+++ b/src/Linear/Plucker.hs
@@ -279,12 +279,12 @@
 -- | These elements form a basis for the Plücker space, or the Grassmanian manifold @Gr(2,V4)@.
 --
 -- @
--- 'p01' :: Lens' ('Plucker' a) a
--- 'p02' :: Lens' ('Plucker' a) a
--- 'p03' :: Lens' ('Plucker' a) a
--- 'p23' :: Lens' ('Plucker' a) a
--- 'p31' :: Lens' ('Plucker' a) a
--- 'p12' :: Lens' ('Plucker' a) a
+-- 'p01' :: 'Lens'' ('Plucker' a) a
+-- 'p02' :: 'Lens'' ('Plucker' a) a
+-- 'p03' :: 'Lens'' ('Plucker' a) a
+-- 'p23' :: 'Lens'' ('Plucker' a) a
+-- 'p31' :: 'Lens'' ('Plucker' a) a
+-- 'p12' :: 'Lens'' ('Plucker' a) a
 -- @
 p01, p02, p03, p23, p31, p12 :: Lens' (Plucker a) a
 p01 g (Plucker a b c d e f) = (\a' -> Plucker a' b c d e f) <$> g a
@@ -303,12 +303,12 @@
 -- | These elements form an alternate basis for the Plücker space, or the Grassmanian manifold @Gr(2,V4)@.
 --
 -- @
--- 'p10' :: 'Num' a => Lens' ('Plucker' a) a
--- 'p20' :: 'Num' a => Lens' ('Plucker' a) a
--- 'p30' :: 'Num' a => Lens' ('Plucker' a) a
--- 'p32' :: 'Num' a => Lens' ('Plucker' a) a
--- 'p13' :: 'Num' a => Lens' ('Plucker' a) a
--- 'p21' :: 'Num' a => Lens' ('Plucker' a) a
+-- 'p10' :: 'Num' a => 'Lens'' ('Plucker' a) a
+-- 'p20' :: 'Num' a => 'Lens'' ('Plucker' a) a
+-- 'p30' :: 'Num' a => 'Lens'' ('Plucker' a) a
+-- 'p32' :: 'Num' a => 'Lens'' ('Plucker' a) a
+-- 'p13' :: 'Num' a => 'Lens'' ('Plucker' a) a
+-- 'p21' :: 'Num' a => 'Lens'' ('Plucker' a) a
 -- @
 p10, p20, p30, p32, p13, p21 :: (Functor f, Num a) => (a -> f a) -> Plucker a -> f (Plucker a)
 p10 = anti p01
diff --git a/src/Linear/V.hs b/src/Linear/V.hs
--- a/src/Linear/V.hs
+++ b/src/Linear/V.hs
@@ -34,7 +34,7 @@
 ----------------------------------------------------------------------------
 
 module Linear.V
-  ( V(toVector)
+  ( V(V,toVector)
   , int
   , dim
   , Dim(..)
@@ -269,11 +269,10 @@
 #endif
 
 instance Dim n => Representable (V n) where
-  type Rep (V n) = E (V n)
-  tabulate f = V $ generate (reflectDim (Proxy :: Proxy n)) $ \i -> f $ E $ \g (V v) ->
-    (\a -> V $ v V.// [(i,a)]) <$> g (unsafeIndex v i)
+  type Rep (V n) = Int
+  tabulate = V . generate (reflectDim (Proxy :: Proxy n))
   {-# INLINE tabulate #-}
-  index xs (E l) = view l xs
+  index (V xs) i = xs V.! i
   {-# INLINE index #-}
 
 type instance Index (V n a) = E (V n)
diff --git a/src/Linear/V0.hs b/src/Linear/V0.hs
--- a/src/Linear/V0.hs
+++ b/src/Linear/V0.hs
@@ -90,7 +90,7 @@
 
 instance Apply V0 where
   V0 <.> V0 = V0
-  {-@ INLINE (<.>) #-}
+  {-# INLINE (<.>) #-}
 
 instance Applicative V0 where
   pure _ = V0
diff --git a/src/Linear/V1.hs b/src/Linear/V1.hs
--- a/src/Linear/V1.hs
+++ b/src/Linear/V1.hs
@@ -108,13 +108,13 @@
 
 instance Apply V1 where
   V1 f <.> V1 x = V1 (f x)
-  {-@ INLINE (<.>) #-}
+  {-# INLINE (<.>) #-}
 
 instance Applicative V1 where
   pure = V1
   {-# INLINE pure #-}
   V1 f <*> V1 x = V1 (f x)
-  {-@ INLINE (<*>) #-}
+  {-# INLINE (<*>) #-}
 
 instance Additive V1 where
   zero = pure 0
diff --git a/src/Linear/V2.hs b/src/Linear/V2.hs
--- a/src/Linear/V2.hs
+++ b/src/Linear/V2.hs
@@ -183,7 +183,7 @@
   -- V2 1 3
   --
   -- @
-  -- '_y' :: Lens' (t a) a
+  -- '_y' :: 'Lens'' (t a) a
   -- @
   _y :: Functor f => (a -> f a) -> t a -> f (t a)
   _y = _xy._y
@@ -191,7 +191,7 @@
 
   -- |
   -- @
-  -- '_xy' :: Lens' (t a) ('V2' a)
+  -- '_xy' :: 'Lens'' (t a) ('V2' a)
   -- @
   _xy :: Functor f => (V2 a -> f (V2 a)) -> t a -> f (t a)
 
diff --git a/src/Linear/V3.hs b/src/Linear/V3.hs
--- a/src/Linear/V3.hs
+++ b/src/Linear/V3.hs
@@ -167,12 +167,12 @@
 class R2 t => R3 t where
   -- |
   -- @
-  -- '_z' :: Lens' (t a) a
+  -- '_z' :: 'Lens'' (t a) a
   -- @
   _z :: Functor f => (a -> f a) -> t a -> f (t a)
   -- |
   -- @
-  -- '_xyz' :: Lens' (t a) ('V3' a)
+  -- '_xyz' :: 'Lens'' (t a) ('V3' a)
   -- @
   _xyz :: Functor f => (V3 a -> f (V3 a)) -> t a -> f (t a)
 
diff --git a/src/Linear/V4.hs b/src/Linear/V4.hs
--- a/src/Linear/V4.hs
+++ b/src/Linear/V4.hs
@@ -173,12 +173,12 @@
 class R3 t => R4 t where
   -- |
   -- @
-  -- '_w' :: Lens' (t a) a
+  -- '_w' :: 'Lens'' (t a) a
   -- @
   _w :: Functor f => (a -> f a) -> t a -> f (t a)
   -- |
   -- @
-  -- '_xyzw' :: Lens' (t a) ('V4' a)
+  -- '_xyzw' :: 'Lens'' (t a) ('V4' a)
   -- @
   _xyzw :: Functor f => (V4 a -> f (V4 a)) -> t a -> f (t a)
 
diff --git a/src/Linear/Vector.hs b/src/Linear/Vector.hs
--- a/src/Linear/Vector.hs
+++ b/src/Linear/Vector.hs
@@ -376,8 +376,8 @@
 
 -- | Produce a default basis for a vector space. If the dimensionality
 -- of the vector space is not statically known, see 'basisFor'.
-basis :: (Applicative t, Traversable t, Num a) => [t a]
-basis = choices $ traverse (\a -> SetOne 0 [a]) (pure 1)
+basis :: (Additive t, Traversable t, Num a) => [t a]
+basis = basisFor (zero :: Additive v => v Int)
 
 -- | Produce a default basis for a vector space from which the
 -- argument is drawn.
@@ -392,8 +392,8 @@
 --
 -- >>> unit _x :: V2 Int
 -- V2 1 0
-unit :: (Applicative t, Num a) => ASetter' (t a) a -> t a
-unit l = set' l 1 (pure 0)
+unit :: (Additive t, Num a) => ASetter' (t a) a -> t a
+unit l = set' l 1 zero
 
 fillFromList :: Traversable t => [a] -> t b -> t a
 fillFromList l = snd . mapAccumL aux l