diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,5 +1,11 @@
 # Revision history for squares
 
+## 0.0.1 -- 2020-05-23
+
+* Included README.
+* Added `Control.Arrow.Square`.
+* Removed use of BlockArguments to support older GHC versions.
+
 ## 0 -- 2020-05-22
 
 * First version. Released on an unsuspecting world.
diff --git a/README.md b/README.md
new file mode 100644
--- /dev/null
+++ b/README.md
@@ -0,0 +1,6 @@
+# squares
+
+`squares` is a library for working with natural transformations of type `forall a b. p a b -> q (f a) (g b)`.
+These are squares in the double category of Haskell functors and profunctors.
+
+See the `Data.Square` module for an introduction.
diff --git a/squares.cabal b/squares.cabal
--- a/squares.cabal
+++ b/squares.cabal
@@ -1,8 +1,9 @@
 cabal-version:       >=1.10
 
 name:                squares
-version:             0
+version:             0.0.1
 synopsis:            The double category of Hask functors and profunctors
+description:         A library for working with natural transformations of type @forall a b. p a b -> q (f a) (g b)@.
 homepage:            https://github.com/sjoerdvisscher/squares
 bug-reports:         https://github.com/sjoerdvisscher/squares/issues
 license:             BSD3
@@ -11,16 +12,19 @@
 maintainer:          sjoerd@w3future.com
 category:            Math
 build-type:          Simple
-extra-source-files:  CHANGELOG.md
+extra-source-files:
+  CHANGELOG.md
+  README.md
 
 library
   exposed-modules:     Data.Square
                        Data.Type.List
                        Data.Functor.Compose.List
                        Data.Profunctor.Composition.List
+                       Control.Arrow.Square
+                       Control.Monad.Square
                        Data.Profunctor.Square
                        Data.Traversable.Square
-                       Control.Monad.Square
   build-depends:       base == 4.*, profunctors == 5.*
   hs-source-dirs:      src
   default-language:    Haskell2010
diff --git a/src/Control/Arrow/Square.hs b/src/Control/Arrow/Square.hs
new file mode 100644
--- /dev/null
+++ b/src/Control/Arrow/Square.hs
@@ -0,0 +1,70 @@
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE DataKinds #-}
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Control.Arrow.Square
+-- License     :  BSD-style (see the file LICENSE)
+-- Maintainer  :  sjoerd@w3future.com
+--
+-----------------------------------------------------------------------------
+module Control.Arrow.Square where
+
+import Data.Square
+import Data.Functor.Compose.List
+import Data.Profunctor
+import Data.Profunctor.Composition.List
+import qualified Control.Arrow as A
+
+-- |
+-- > +-----+
+-- > |     |
+-- > |  @--a
+-- > |     |
+-- > +-----+
+arr :: A.Arrow a => Square '[] '[a] '[] '[]
+arr = Square (P . A.arr . dimap unId Id . unHom)
+
+-- |
+-- > +-----+
+-- > a--\  |
+-- > |  @--a
+-- > a--/  |
+-- > +-----+
+(>>>) :: A.Arrow a => Square '[a, a] '[a] '[] '[]
+(>>>) = Square (\(PComp p (P q)) -> P (A.arr Id A.<<< q A.<<< p A.<<< A.arr unId))
+
+-- |
+-- > +-_⊗d-+
+-- > |  v  |
+-- > a--@--a
+-- > |  v  |
+-- > +-_⊗d-+
+second :: A.Arrow a => Square '[a] '[a] '[(,) d] '[(,) d]
+second = Square (P . (A.>>> A.arr F) . (A.<<< A.arr unF) . A.second . unP)
+
+-- |
+-- > H²-⊗--H
+-- > |  v  |
+-- > a²-@--a
+-- > |  v  |
+-- > H²-⊗--H
+(***) :: A.Arrow a => Square21 '[a] '[a] '[a] (,) (,)
+(***) = Square $ \(P p1 :**: P p2) -> P (A.arr UncurryF A.<<< p1 A.*** p2 A.<<< A.arr curryF)
+
+-- |
+-- > +-_⊕d-+
+-- > |  v  |
+-- > a--@--a
+-- > |  v  |
+-- > +-_⊕d-+
+right :: A.ArrowChoice a => Square '[a] '[a] '[Either d] '[Either d]
+right = Square (P . (A.>>> A.arr F) . (A.<<< A.arr unF) . A.right . unP)
+
+-- |
+-- > H²-⊕--H
+-- > |  v  |
+-- > a²-@--a
+-- > |  v  |
+-- > H²-⊕--H
+(+++) :: A.ArrowChoice a => Square21 '[a] '[a] '[a] Either Either
+(+++) = Square $ \(P p1 :**: P p2) -> P (A.arr UncurryF A.<<< p1 A.+++ p2 A.<<< A.arr curryF)
diff --git a/src/Data/Square.hs b/src/Data/Square.hs
--- a/src/Data/Square.hs
+++ b/src/Data/Square.hs
@@ -4,7 +4,6 @@
 {-# LANGUAGE PolyKinds #-}
 {-# LANGUAGE RankNTypes #-}
 {-# LANGUAGE TypeOperators #-}
-{-# LANGUAGE BlockArguments #-}
 {-# LANGUAGE FlexibleContexts #-}
 #if __GLASGOW_HASKELL__ >= 810
 {-# LANGUAGE StandaloneKindSignatures #-}
@@ -46,7 +45,7 @@
 --
 -- The empty square is the identity transformation.
 emptySquare :: Square '[] '[] '[] '[]
-emptySquare = Square $ dimap unId Id
+emptySquare = Square (dimap unId Id)
 
 -- |
 -- > +-----+
@@ -62,7 +61,7 @@
 -- Note that `emptySquare` is `proId` for the profunctor @(->)@.
 -- We don't draw a line for @(->)@ because it is the identity for profunctor composition.
 proId :: Profunctor p => Square '[p] '[p] '[] '[]
-proId = Square $ dimap unId Id
+proId = Square (dimap unId Id)
 
 -- |
 -- > +--f--+
@@ -78,7 +77,7 @@
 --
 -- We don't draw lines for the identity functor, because it is the identity for functor composition.
 funId :: Functor f => Square '[] '[] '[f] '[f]
-funId = Square \(Hom f) -> Hom (fmap f)
+funId = Square (Hom . fmap . unHom)
 
 -- |
 -- > +--f--+
@@ -94,7 +93,7 @@
 -- @forall a. f a -> g a@. The type above you get when `fmap`ping before or after.
 -- (It doesn't matter which, because of naturality!)
 funNat :: (Functor f, Functor g) => (f ~> g) -> Square '[] '[] '[f] '[g]
-funNat n = Square $ Hom . dimap unF F . (.) n . fmap . unHom
+funNat n = Square (Hom . dimap unF F . (.) n . fmap . unHom)
 
 -- |
 -- > +-----+
@@ -107,7 +106,7 @@
 --
 -- Natural transformations between profunctors.
 proNat :: (Profunctor p, Profunctor q) => (p :-> q) -> Square '[p] '[q] '[] '[]
-proNat n = Square $ P . dimap unId Id . n . unP
+proNat n = Square (P . dimap unId Id . n . unP)
 
 -- |
 -- > +--f--+
@@ -149,10 +148,11 @@
 -- > +--g--+     +--i--+       +--g--i--+
 --
 -- Horizontal composition of squares. `proId` is the identity of `(|||)`.
+-- This is regular function composition of the underlying functions.
 infixl 6 |||
 (|||) :: (Profunctor (PList rs), FAppend fs, FAppend gs, Functor (FList hs), Functor (FList is))
       => Square ps qs fs gs -> Square qs rs hs is -> Square ps rs (fs ++ hs) (gs ++ is) -- ^
-Square pq ||| Square qr = Square $ dimap funappend fappend . qr . pq
+Square pq ||| Square qr = Square (dimap funappend fappend . qr . pq)
 
 -- |
 -- > +--f--+
@@ -171,7 +171,7 @@
 infixl 5 ===
 (===) :: (PAppend ps, PAppend qs, Profunctor (PList ss))
       => Square ps qs fs gs -> Square rs ss gs hs -> Square (ps ++ rs) (qs ++ ss) fs hs -- ^
-Square pq === Square rs = Square \pr -> case punappend pr of P.Procompose r p -> pappend (P.Procompose (rs r) (pq p))
+Square pq === Square rs = Square (\pr -> case punappend pr of P.Procompose r p -> pappend (P.Procompose (rs r) (pq p)))
 
 
 -- * Proarrow equipment
@@ -189,7 +189,7 @@
 --
 -- A functor @f@ can be bent to the right to become the profunctor @`Star` f@.
 toRight :: Functor f => Square '[] '[Star f] '[f] '[]
-toRight = Square \(Hom f) -> P (Star (fmap (Id . f) . unF))
+toRight = Square (P . Star . (. unF) . fmap . (Id .) . unHom)
 
 -- |
 -- > +--f--+
@@ -200,7 +200,7 @@
 --
 -- A functor @f@ can be bent to the left to become the profunctor @`Costar` f@.
 toLeft :: Square '[Costar f] '[] '[f] '[]
-toLeft = Square \(P (Costar f)) -> Hom (Id . f . unF)
+toLeft = Square (Hom . dimap unF Id . runCostar . unP)
 
 -- |
 -- > +-----+
@@ -211,7 +211,7 @@
 --
 -- The profunctor @`Costar` f@ can be bent down to become the functor @f@ again.
 fromRight :: Functor f => Square '[] '[Costar f] '[] '[f]
-fromRight = Square \(Hom f) -> P (Costar (F . fmap (f . unId)))
+fromRight = Square (P . Costar . (F .) . fmap . (. unId) . unHom)
 
 -- |
 -- > +-----+
@@ -222,7 +222,7 @@
 --
 -- The profunctor @`Star` f@ can be bent down to become the functor @f@ again.
 fromLeft :: Square '[Star f] '[] '[] '[f]
-fromLeft = Square \(P (Star f)) -> Hom (F . f . unId)
+fromLeft = Square (Hom . dimap unId F . runStar . unP)
 
 -- |
 -- > +-----+