diff --git a/profunctor-optics/profunctor-optics.cabal b/profunctor-optics/profunctor-optics.cabal
index e084b19..ec8211f 100644
--- a/profunctor-optics/profunctor-optics.cabal
+++ b/profunctor-optics/profunctor-optics.cabal
@@ -40,6 +40,7 @@ library
 
       Data.Profunctor.Optic
       Data.Profunctor.Optic.Types
+      Data.Profunctor.Optic.Module
       Data.Profunctor.Optic.Property
       Data.Profunctor.Optic.Carrier
       Data.Profunctor.Optic.Combinator
diff --git a/profunctor-optics/src/Data/Profunctor/Optic.hs b/profunctor-optics/src/Data/Profunctor/Optic.hs
index 22f74a9..fda6f7a 100644
--- a/profunctor-optics/src/Data/Profunctor/Optic.hs
+++ b/profunctor-optics/src/Data/Profunctor/Optic.hs
@@ -7,6 +7,7 @@
 {-# LANGUAGE TypeFamilies          #-}
 module Data.Profunctor.Optic (
     module Types
+  , module Module
   , module Carrier
   , module Operator
   , module Iso
@@ -21,6 +22,7 @@ module Data.Profunctor.Optic (
 ) where
 
 import Data.Profunctor.Optic.Types            as Types
+import Data.Profunctor.Optic.Module           as Module
 import Data.Profunctor.Optic.Carrier          as Carrier
 import Data.Profunctor.Optic.Combinator       as Operator
 import Data.Profunctor.Optic.Iso              as Iso
diff --git a/profunctor-optics/src/Data/Profunctor/Optic/Fold.hs b/profunctor-optics/src/Data/Profunctor/Optic/Fold.hs
index 742e62c..93b3084 100644
--- a/profunctor-optics/src/Data/Profunctor/Optic/Fold.hs
+++ b/profunctor-optics/src/Data/Profunctor/Optic/Fold.hs
@@ -36,8 +36,7 @@ module Data.Profunctor.Optic.Fold (
   , (^?)
   , preview 
   , preuse
-  , is
-  , isnt
+  , fits
   , lists
   , (^..)
   , nelists
@@ -60,8 +59,7 @@ module Data.Profunctor.Optic.Fold (
   , endo
   , endoM
   , finds
-  , has
-  , hasnt 
+  , exists
   , contains
     -- * Auxilliary Types
   , Nedl(..)
@@ -128,7 +126,7 @@ fold0 f = to (\s -> maybe (Left s) Right (f s)) . right'
 
 infixl 3 `failing`
 
--- | If the first 'Fold0' has no focus then try the second one.
+-- | If the first 'Fold0' exists no focus then try the second one.
 --
 failing :: AFold0 a s a -> AFold0 a s a -> Fold0 s a
 failing a b = fold0 $ \s -> maybe (preview b s) Just (preview a s)
@@ -335,23 +333,14 @@ preuse :: MonadState s m => AFold0 a s a -> m (Maybe a)
 preuse o = State.gets $ preview o
 {-# INLINE preuse #-}
 
--- | Check whether the optic is matched.
+-- | Check whether the optic fits.
 --
--- >>> is just Nothing
+-- >>> fits just Nothing
 -- False
 --
-is :: AFold0 a s a -> s -> Bool
-is o s = isJust (preview o s)
-{-# INLINE is #-}
-
--- | Check whether the optic isn't matched.
---
--- >>> isnt just Nothing
--- True
---
-isnt :: AFold0 a s a -> s -> Bool
-isnt o s = not (isJust (preview o s))
-{-# INLINE isnt #-}
+fits :: AFold0 a s a -> s -> Bool
+fits o s = isJust (preview o s)
+{-# INLINE fits #-}
 
 -- | Collect the foci of an optic into a list.
 --
@@ -566,17 +555,11 @@ finds :: AFold ((Maybe-Endo) a) s a -> (a -> Bool) -> s -> Maybe a
 finds o f = foldsr o (\a y -> if f a then Just a else y) Nothing
 {-# INLINE finds #-}
 
--- | Determine whether an optic has at least one focus.
---
-has :: AFold (Additive Bool) s a -> s -> Bool
-has o s = unAdditive $ withFold o (const $ Additive True) s
-{-# INLINE has #-}
-
--- | Determine whether an optic does not have a focus.
+-- | Determine whether an optic exists at least one focus.
 --
-hasnt :: AFold (Multiplicative Bool) s a -> s -> Bool
-hasnt o s = unMultiplicative $ withFold o (const $ Multiplicative False) s
-{-# INLINE hasnt #-}
+exists :: AFold (Additive Bool) s a -> s -> Bool
+exists o s = unAdditive $ withFold o (const $ Additive True) s
+{-# INLINE exists #-}
 
 -- | Determine whether the targets of a `Fold` contain a given element.
 --
diff --git a/profunctor-optics/src/Data/Profunctor/Optic/Lens.hs b/profunctor-optics/src/Data/Profunctor/Optic/Lens.hs
index 50a8303..7695a5d 100644
--- a/profunctor-optics/src/Data/Profunctor/Optic/Lens.hs
+++ b/profunctor-optics/src/Data/Profunctor/Optic/Lens.hs
@@ -31,6 +31,7 @@ module Data.Profunctor.Optic.Lens (
   , voided
   , represented
   , distributed
+  , distributed1
   , endomorphed
   , precomposed
   , dotted
@@ -104,7 +105,7 @@ lens sa sbt = dimap (id &&& sa) (uncurry sbt) . second'
 
 -- | Transform a Van Laarhoven lens into a profunctor lens.
 --
--- Compare 'Data.Profunctor.Optic.Grate.grateVl' and 'Data.Profunctor.Optic.Traversal.traversalVl'.
+-- Compare 'grateVl' and 'Data.Profunctor.Optic.Traversal.traversalVl'.
 --
 -- /Caution/: In order for the generated optic to be well-defined,
 -- you must ensure that the input satisfies the following properties:
@@ -297,6 +298,12 @@ distributed :: Distributive f => Grate (f a) (f b) a b
 distributed = grate (`cotraverse` id)
 {-# INLINE distributed #-}
 
+-- | Obtain a 'Grate' from a partially distributive functor.
+--
+distributed1 :: Monoid (f a) => Distributive1 f => Grate (f a) (f b) a b
+distributed1 = grate (`cotraverse1` id)
+{-# INLINE distributed1 #-}
+
 -- | Obtain a 'Grate' from an endomorphism. 
 --
 -- >>> flip appEndo 2 $ zipsWith2 endomorphed (+) (Endo (*3)) (Endo (*4))
diff --git a/profunctor-optics/src/Data/Profunctor/Optic/Module.hs b/profunctor-optics/src/Data/Profunctor/Optic/Module.hs
new file mode 100644
index 0000000..0005d53
--- /dev/null
+++ b/profunctor-optics/src/Data/Profunctor/Optic/Module.hs
@@ -0,0 +1,313 @@
+{-# LANGUAGE FlexibleContexts      #-}
+{-# LANGUAGE FlexibleInstances     #-}
+{-# LANGUAGE QuantifiedConstraints #-}
+{-# LANGUAGE RankNTypes            #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE TupleSections         #-}
+{-# LANGUAGE TypeOperators         #-}
+{-# LANGUAGE TypeFamilies          #-}
+{-# LANGUAGE UndecidableInstances  #-}
+{-# LANGUAGE ConstraintKinds       #-}
+{-# LANGUAGE QuantifiedConstraints #-}
+{-# LANGUAGE ScopedTypeVariables   #-}
+{-# LANGUAGE TypeOperators         #-}
+{-# LANGUAGE TypeApplications      #-}
+{-# LANGUAGE ExistentialQuantification #-}
+
+module Data.Profunctor.Optic.Module where
+
+import Data.Profunctor.Optic.Carrier
+import Data.Profunctor.Optic.Combinator
+import Data.Profunctor.Optic.Import
+import Data.Profunctor.Optic.Iso
+import Data.Profunctor.Optic.Lens
+import Data.Profunctor.Optic.Prism
+import Data.Profunctor.Optic.Types
+import Data.Tuple.Optic
+
+import Data.Kind (Type)
+
+-- $setup
+-- >>> :set -XNoOverloadedStrings
+-- >>> :set -XTypeApplications
+-- >>> :set -XFlexibleContexts
+-- >>> :set -XTypeOperators
+-- >>> :set -XRankNTypes
+-- >>> :load Data.Profunctor.Optic
+
+---------------------------------------------------------------------
+-- Module
+---------------------------------------------------------------------
+
+type Is = Module Tagged
+
+type As = Module (+)
+
+type Has = Module (,)
+
+type With = Module (->)
+
+-- | A (right) Tambara module on the tensor /o/.
+--
+class Module (o :: Type -> Type -> Type) a s where
+  optic :: FreeTambara o a a s s
+
+-- | Obtain an iso from an 'Is' instance.
+--
+-- >>> view (is @Int @Int) 4
+-- 4
+--
+is :: Is a s => Iso' s a
+is = lowerIso optic
+
+-- | Obtain a prism from an 'As' instance.
+--
+-- >>> review (as @Int @Int) 4
+-- 4
+-- >>> Left "oops" ^? as @String @(String + Int)
+-- Just "oops"
+--
+as :: As a s => Prism' s a
+as = handling' optic
+
+-- | Obtain a coprism from an 'As' instance.
+--
+-- >>> 4 ^. coas @Int @(String + Int)
+-- Right 4
+--
+coas :: As t b => Coprism' t b
+coas = re $ handling' optic
+
+-- | Obtain a lens from a 'Has' instance.
+--
+-- >>> (1,2,"foo") ^. has @String @(Int,Int,String)
+-- "foo"
+--
+has :: Has a s => Lens' s a
+has = matching' optic
+
+-- | Obtain a colens from a 'Has' instance.
+--
+-- >>> review (cohas @Int @(Int,String)) (2, "two")
+-- 2
+-- >>> zipsWith2 (cohas @Int @Int) (+) 2 2
+-- 4
+--
+cohas :: Has t b => Colens' t b
+cohas = re $ matching' optic
+
+-- | Obtain a grate from a 'With' instance.
+--
+-- >>> review (with @Int @Int) 4
+-- 4
+-- >>> zipsWith2 (with @String @String) (++) "foo" "bar" 
+-- "foobar"
+--
+with :: With a s => Grate' s a
+with = inverting' optic
+
+-- | Obtain a traversal from a 'Has' instance.
+--
+-- >>> foldsr (have @Int @Int @[]) (\i -> (show i ++)) [] [1..5]
+-- "12345"
+--
+have :: Has a s => Traversable f => Traversal' (f s) a
+have = repn traverse . has
+
+-- | Obtain a non-empty traversal from a 'Has' instance.
+-- 
+have1 :: Has a s => Traversable1 f => Traversal1' (f s) a
+have1 = repn traverse1 . has
+
+-- | Obtain a cotraversal from a 'Has' instance.
+--
+cohave :: Has t b => Distributive g => Cotraversal' (g t) b
+cohave = corepn cotraverse . cohas
+
+-- | Obtain a partial cotraversal from a 'Has' instance.
+--
+cohave1 :: Has t b => Distributive1 g => Cotraversal1' (g t) b
+cohave1 = corepn cotraverse1 . cohas
+
+---------------------------------------------------------------------
+-- FreeTambara
+---------------------------------------------------------------------
+
+type FreeIso s t a b = FreeTambara Tagged a b s t
+
+type FreeIso' s a = FreeIso s s a a
+
+type FreeLens s t a b = FreeTambara (,) a b s t
+
+type FreeLens' s a = FreeLens s s a a
+
+type FreeGrate s t a b = FreeTambara (->) a b s t
+
+type FreeGrate' s a = FreeGrate s s a a
+
+type FreeColens s t a b = FreeTambara (,) t s b a
+
+type FreeColens' t b = FreeColens b b t t
+
+type FreePrism s t a b = FreeTambara (+) a b s t
+
+type FreePrism' s a = FreePrism s s a a
+
+type FreeCoprism s t a b = FreeTambara (+) t s b a
+
+type FreeCoprism' t b = FreeCoprism t t b b
+
+type FreeTambara' o a s = FreeTambara o a a s s
+
+data FreeTambara o a b s t = forall x. FreeTambara (s -> x `o` a) (x `o` b -> t)
+
+lowerIso :: FreeIso s t a b -> Iso s t a b
+lowerIso (FreeTambara f g) = iso (unTagged . f) (g . Tagged)
+
+handling' :: FreePrism s t a b -> Prism s t a b
+handling' (FreeTambara f g) = handling f g
+
+cohandling' :: FreeCoprism s t a b -> Coprism s t a b
+cohandling' (FreeTambara f g) = cohandling g f
+
+matching' :: FreeLens s t a b -> Lens s t a b
+matching' (FreeTambara f g) = matching f g
+
+comatching' :: FreeColens s t a b -> Colens s t a b
+comatching' (FreeTambara f g) = comatching g f
+
+inverting' :: FreeGrate s t a b -> Grate s t a b
+inverting' (FreeTambara l r) = dimap l r . closed
+
+liftIso :: Is a1 a2 => Iso' s a2 -> FreeIso' s a1
+liftIso o = withIso (o . is) $ \ba ab -> FreeTambara (Tagged . ba) (ab . unTagged)
+
+liftPrism :: As a1 a2 => Prism' s a2 -> FreePrism' s a1 
+liftPrism o = withPrism o liftChoice
+
+liftCoprism :: As b1 b2 => Coprism' b2 t -> FreeCoprism' b1 t
+liftCoprism o = withPrism (re o) liftChoice
+
+liftLens :: Has a1 a2 => Lens' s a2 -> FreeLens' s a1
+liftLens o = withLens o liftStrong
+
+liftColens :: Has b1 b2 => Colens' b2 t -> FreeColens' t b1
+liftColens o = withLens (re o) liftStrong
+
+liftGrate :: With a1 a2 => Grate' s a2 -> FreeGrate' s a1
+liftGrate o = withGrate (o . with) $ \sabt -> FreeTambara (curry eval) sabt
+
+liftChoice :: As a1 a2 => (s -> s + a2) -> (a2 -> s) -> FreeTambara' (+) a1 s
+liftChoice ssb bs = withPrism as $ \bba ab ->
+  FreeTambara (first (either id bs) . eassocl . fmap bba . ssb) (either id (bs.ab) )
+
+liftStrong :: Has a1 a2 => (s -> a2) -> (s -> a2 -> s) -> FreeTambara' (,) a1 s
+liftStrong sb sbs = withLens has $ \ba bab ->
+  FreeTambara (\s -> (s, ba.sb $ s)) (\(s,a) -> sbs s (bab (sb s) a))
+
+---------------------------------------------------------------------
+-- FreeTambara instances
+---------------------------------------------------------------------
+
+instance Profunctor (FreeTambara o a b) where
+  dimap f g (FreeTambara l r) = FreeTambara (l . f) (g . r) 
+
+instance Strong (FreeTambara (,) a b) where
+  second' (FreeTambara l r) = FreeTambara l' r' where
+    l' (d,s) = ((d , fst (l s)), snd (l s))
+    r' ((d,c),b) = (d,r (c,b))
+
+instance Choice (FreeTambara (+) a b) where
+  right' (FreeTambara l r) = FreeTambara l' r' where
+    l' = (either (Left . Left) (either (Left . Right) Right . l))
+    r' = (either (either Left (Right . r . Left)) (Right . r . Right))
+
+instance Closed (FreeTambara (->) a b) where
+  closed (FreeTambara l r) = FreeTambara l' r' where
+    l' f (d , c) = l (f d) c
+    r' = (r .) . curry
+
+---------------------------------------------------------------------
+-- Is instances
+---------------------------------------------------------------------
+
+instance Module Tagged a a where
+  optic = FreeTambara Tagged unTagged 
+
+---------------------------------------------------------------------
+-- As instances
+---------------------------------------------------------------------
+
+instance Module (+) a a where
+  optic = FreeTambara Right rgt'
+
+instance Module (+) a (a + b) where
+  optic = liftPrism left'
+
+instance Module (+) b (a + b) where
+  optic = liftPrism right'
+
+instance Module (+) a (Maybe a) where
+  optic = liftPrism just
+
+instance Module (+) () (Maybe a) where
+  optic = liftPrism nothing
+
+---------------------------------------------------------------------
+-- Has instances
+---------------------------------------------------------------------
+
+instance Module (,) a a where
+  optic = FreeTambara ((,) ()) snd
+
+instance Module (,) a (a , b) where
+  optic = liftLens t21 
+
+instance Module (,) b (a , b) where
+  optic = liftLens t22
+
+instance Module (,) a (a,b,c) where
+  optic = liftLens t31
+
+instance Module (,) b (a,b,c) where
+  optic = liftLens t32
+
+instance Module (,) c (a,b,c) where
+  optic = liftLens t33
+
+instance Module (,) a (a,b,c,d) where
+  optic = liftLens t41
+
+instance Module (,) b (a,b,c,d) where
+  optic = liftLens t42
+
+instance Module (,) c (a,b,c,d) where
+  optic = liftLens t43
+
+instance Module (,) d (a,b,c,d) where
+  optic = liftLens t44
+
+instance Module (,) a (a,b,c,d,e) where
+  optic = liftLens t51
+
+instance Module (,) b (a,b,c,d,e) where
+  optic = liftLens t52
+
+instance Module (,) c (a,b,c,d,e) where
+  optic = liftLens t53
+
+instance Module (,) d (a,b,c,d,e) where
+  optic = liftLens t54
+
+instance Module (,) e (a,b,c,d,e) where
+  optic = liftLens t55
+
+---------------------------------------------------------------------
+-- With instances
+---------------------------------------------------------------------
+
+instance Module (->) a a where
+  optic = FreeTambara const ($ ())
+
+instance Distributive f => Module (->) a (f a) where
+  optic = liftGrate distributed
diff --git a/profunctor-optics/src/Data/Profunctor/Optic/Prism.hs b/profunctor-optics/src/Data/Profunctor/Optic/Prism.hs
index d98e267..f40cacd 100644
--- a/profunctor-optics/src/Data/Profunctor/Optic/Prism.hs
+++ b/profunctor-optics/src/Data/Profunctor/Optic/Prism.hs
@@ -17,7 +17,7 @@ module Data.Profunctor.Optic.Prism (
   , clonePrism
   , coprism
   , coprism'
-  , rehandling
+  , cohandling
   , cloneCoprism
     -- * Optics
   , just
@@ -132,8 +132,8 @@ coprism' tb bt = coprism tb $ \b -> maybe (Left b) Right (bt b)
 
 -- | Obtain a 'Coprism' from its free tensor representation.
 --
-rehandling :: (c + s -> a) -> (b -> c + t) -> Coprism s t a b
-rehandling csa bct = unright . dimap csa bct
+cohandling :: (c + s -> a) -> (b -> c + t) -> Coprism s t a b
+cohandling csa bct = unright . dimap csa bct
 
 -- | TODO: Document
 --
diff --git a/profunctor-optics/src/Data/Profunctor/Optic/Traversal.hs b/profunctor-optics/src/Data/Profunctor/Optic/Traversal.hs
index b6850d1..d9dfff5 100644
--- a/profunctor-optics/src/Data/Profunctor/Optic/Traversal.hs
+++ b/profunctor-optics/src/Data/Profunctor/Optic/Traversal.hs
@@ -224,11 +224,12 @@ cotraversing sabt = corepn cotraverse . grate sabt
 -- | Obtain a 'Cotraversal' by embedding a reversed lens getter and setter into a 'Distributive' functor.
 --
 -- @
---  'withLens' ('re' o) 'cotraversing' ≡ 'cotraversed' . o
+--  'withColens' o 'retraversing' ≡ 'cotraversed' . o
+--  'withLens' ('re' o) $ 'flip' 'retraversing' ≡ 'cotraversed' . o
 -- @
 --
-retraversing :: Distributive g => (b -> t) -> (b -> s -> a) -> Cotraversal (g s) (g t) a b
-retraversing bsa bt = corepn cotraverse . (re $ lens bsa bt)
+retraversing :: Distributive g => (b -> s -> a) -> (b -> t) -> Cotraversal (g s) (g t) a b
+retraversing bsa bt = corepn cotraverse . colens bsa bt
 
 -- | Obtain a profunctor 'Cotraversal' from a Van Laarhoven 'Cotraversal'.
 --
@@ -316,11 +317,12 @@ cotraversing1 sabt = corepn cotraverse1 . grate sabt
 -- | Obtain a 'Cotraversal1' by embedding a reversed lens getter and setter into a 'Distributive1' functor.
 --
 -- @
---  'withLens' ('re' o) 'cotraversing' ≡ 'cotraversed' . o
+--  'withColens' o 'retraversing1' ≡ 'cotraversed1' . o
+--  'withLens' ('re' o) $ 'flip' 'retraversing1'  ≡ 'cotraversed1' . o
 -- @
 --
-retraversing1 :: Distributive1 g => (b -> t) -> (b -> s -> a) -> Cotraversal1 (g s) (g t) a b
-retraversing1 bsa bt = corepn cotraverse1 . (re $ lens bsa bt)
+retraversing1 :: Distributive1 g => (b -> s -> a) -> (b -> t) -> Cotraversal1 (g s) (g t) a b
+retraversing1 bsa bt = corepn cotraverse1 . colens bsa bt 
 
 -- | Obtain a profunctor 'Cotraversal1' from a Van Laarhoven 'Cotraversal1'.
 --
diff --git a/profunctor-optics/src/Data/Profunctor/Optic/Types.hs b/profunctor-optics/src/Data/Profunctor/Optic/Types.hs
index 804c422..e9a41c9 100644
--- a/profunctor-optics/src/Data/Profunctor/Optic/Types.hs
+++ b/profunctor-optics/src/Data/Profunctor/Optic/Types.hs
@@ -158,7 +158,7 @@ type Grate s t a b = forall p. Closed p => Optic p s t a b
 
 type Lens' s a = Lens s s a a
 
-type Colens' t b = Lens t t b b
+type Colens' t b = Colens t t b b
 
 type Grate' s a = Grate s s a a
 
diff --git a/profunctor-optics/test/doctest.hs b/profunctor-optics/test/doctest.hs
index 1c9f7eb..37b358a 100644
--- a/profunctor-optics/test/doctest.hs
+++ b/profunctor-optics/test/doctest.hs
@@ -6,6 +6,7 @@ import Prelude (IO)
 main :: IO ()
 main = doctest 
   [ "-isrc" 
+  , "src/Data/Profunctor/Optic/Module.hs"
   , "src/Data/Profunctor/Optic/Carrier.hs"
   , "src/Data/Profunctor/Optic/Combinator.hs"
   , "src/Data/Profunctor/Optic/Fold.hs"