Lots of optics

src/Control/Optics/Linear/Internal.hs

@@ -22,28 +22,39 @@ module Control.Optics.Linear.Internal
   , _Left, _Right
   , _Just, _Nothing
   , traversed
+  , both
     -- * Using optics
   , get, set, gets
+  , set', set''
   , match, build
+  , preview
   , over, over'
   , traverseOf, traverseOf'
   , lengthOf
-  , withIso, withPrism
+  , toListOf
+  , withIso, withLens, withPrism, withTraversal
     -- * Constructing optics
-  , iso, prism
+  , iso, prism, lens, traversal
   )
   where
 
 import qualified Control.Arrow as NonLinear
 import qualified Data.Bifunctor.Linear as Bifunctor
+import qualified Control.Monad.Linear as Control
+import Data.Functor.Linear.Internal.Traversable
 import Data.Bifunctor.Linear (SymmetricMonoidal)
-import Data.Profunctor.Linear
+import Data.Monoid.Linear
+import Data.Functor.Const
 import Data.Functor.Linear
+import Data.Profunctor.Linear
 import qualified Data.Profunctor.Kleisli.Linear as Linear
 import Data.Void
 import Prelude.Linear
 import qualified Prelude as P
 
+-- TODO: documentation in this module
+-- Put the functions in some sensible order: possibly split into separate
+-- Lens/Prism/Traversal/Iso modules
 newtype Optic_ arr a b s t = Optical (a `arr` b -> s `arr` t)
 
 type Optic c a b s t =
@@ -55,7 +66,7 @@ type Lens a b s t = Optic (Strong (,) ()) a b s t
 type Lens' a s = Lens a a s s
 type Prism a b s t = Optic (Strong Either Void) a b s t
 type Prism' a s = Prism a a s s
-type Traversal a b s t = Optic Wandering a b s t
+type Traversal a b s t = Optic Traversing a b s t
 type Traversal' a s = Traversal a a s s
 
 swap :: SymmetricMonoidal m u => Iso (a `m` b) (c `m` d) (b `m` a) (d `m` c)
@@ -67,6 +78,12 @@ assoc = iso Bifunctor.lassoc Bifunctor.rassoc
 (.>) :: Optic_ arr a b s t -> Optic_ arr x y a b -> Optic_ arr x y s t
 Optical f .> Optical g = Optical (f P.. g)
 
+lens :: (s ->. (a, b ->. t)) -> Lens a b s t
+lens k = Optical $ \f -> dimap k (\(x,g) -> g $ x) (first f)
+
+withLens :: Optic_ (Linear.Kleisli (OtherFunctor a b)) a b s t -> s ->. (a, b ->. t)
+withLens (Optical l) s = runOtherFunctor (Linear.runKleisli (l (Linear.Kleisli (\a -> OtherFunctor (a, id)))) s)
+
 prism :: (b ->. t) -> (s ->. Either t a) -> Prism a b s t
 prism b s = Optical $ \f -> dimap s (either id id) (second (rmap b f))
 
@@ -76,6 +93,28 @@ _1 = Optical first
 _2 :: Lens a b (c,a) (c,b)
 _2 = Optical second
 
+both :: Traversal a b (a,a) (b,b)
+both = _Pairing .> traversed
+
+-- XXX: these are a special case of Bitraversable, but just the simple case
+-- is included here for now
+_Pairing :: Iso (Pair a) (Pair b) (a,a) (b,b)
+_Pairing = iso Paired unpair
+
+newtype Pair a = Paired (a,a)
+unpair :: Pair a ->. (a,a)
+unpair (Paired x) = x
+
+instance P.Functor Pair where
+  fmap f (Paired (x,y)) = Paired (f x, f y)
+instance Functor Pair where
+  fmap f (Paired (x,y)) = Paired (f x, f y)
+instance Traversable Pair where
+  traverse f (Paired (x,y)) = Paired <$> ((,) <$> f x <*> f y)
+
+toListOf :: Optic_ (NonLinear.Kleisli (Const [a])) a b s t -> s -> [a]
+toListOf l = gets l (\a -> [a])
+
 _Left :: Prism a b (Either a c) (Either b c)
 _Left = Optical first
 
@@ -88,9 +127,6 @@ _Just = prism Just (maybe (Left Nothing) Right)
 _Nothing :: Prism' () (Maybe a)
 _Nothing = prism (\() -> Nothing) Left
 
-traversed :: Traversable t => Traversal a b (t a) (t b)
-traversed = Optical wander
-
 over :: Optic_ LinearArrow a b s t -> (a ->. b) -> s ->. t
 over (Optical l) f = getLA (l (LA f))
 
@@ -103,8 +139,17 @@ get l = gets l P.id
 gets :: Optic_ (NonLinear.Kleisli (Const r)) a b s t -> (a -> r) -> s -> r
 gets (Optical l) f s = getConst' (NonLinear.runKleisli (l (NonLinear.Kleisli (Const P.. f))) s)
 
+preview :: Optic_ (NonLinear.Kleisli (Const (Maybe (First a)))) a b s t -> s -> Maybe a
+preview l s = P.fmap getFirst (gets l (\a -> Just (First a)) s)
+
+set' :: Optic_ (Linear.Kleisli (MyFunctor a b)) a b s t -> s ->. b ->. (a, t)
+set' (Optical l) s = runMyFunctor (Linear.runKleisli (l (Linear.Kleisli (\a -> MyFunctor (\b -> (a,b))))) s)
+
+set'' :: Optic_ (NonLinear.Kleisli (Control.Reader b)) a b s t -> b ->. s -> t
+set'' (Optical l) b s = Control.runReader (NonLinear.runKleisli (l (NonLinear.Kleisli (const (Control.reader id)))) s) b
+
 set :: Optic_ (->) a b s t -> b -> s -> t
-set (Optical l) x = l (const x)
+set l b = over' l (const b)
 
 match :: Optic_ (Market a b) a b s t -> s ->. Either t a
 match (Optical l) = snd (runMarket (l (Market id Right)))
@@ -139,3 +184,23 @@ withIso (Optical l) f = f fro to
 withPrism :: Optic_ (Market a b) a b s t -> ((b ->. t) -> (s ->. Either t a) -> r) -> r
 withPrism (Optical l) f = f b m
   where Market b m = l (Market id Right)
+
+traversal :: (s ->. Batch a b t) -> Traversal a b s t
+traversal h = Optical (\k -> dimap h fuse (traverse' k))
+
+traverse' :: (Strong Either Void arr, Monoidal (,) () arr) => a `arr` b -> Batch a c t `arr` Batch b c t
+traverse' k = dimap fromBatch toBatch (second (k *** traverse' k))
+
+fromBatch :: Batch a b t ->. Either t (a, Batch a b (b ->. t))
+fromBatch (Done t) = Left t
+fromBatch (More l x) = Right (l, x)
+
+toBatch :: Either t (a, Batch a b (b ->. t)) ->. Batch a b t
+toBatch (Left t) = Done t
+toBatch (Right (l, x)) = More l x
+
+traversed :: Traversable t => Traversal a b (t a) (t b)
+traversed = traversal (traverse batch)
+
+withTraversal :: Optic_ (Linear.Kleisli (Batch a b)) a b s t -> s ->. Batch a b t
+withTraversal (Optical l) = Linear.runKleisli (l (Linear.Kleisli batch))

src/Data/Functor/Linear/Internal/Traversable.hs

@@ -14,6 +14,7 @@ module Data.Functor.Linear.Internal.Traversable
     Traversable(..)
   , mapM, sequenceA, for, forM
   , mapAccumL, mapAccumR
+  , batch, runWith, Batch(..), fuse
   ) where
 
 import qualified Control.Monad.Linear.Internal as Control
@@ -79,6 +80,29 @@ instance Control.Applicative (StateR s) where
     where go :: (a, (a ->. b, s)) ->. (b, s)
           go (a, (h, s'')) = (h a, s'')
 
+data Batch a b c = Done c | More a (Batch a b (b ->. c))
+  deriving (Data.Functor, Data.Applicative) via Control.Data (Batch a b)
+
+instance Control.Functor (Batch a b) where
+  fmap f (Done c)   = Done (f c)
+  fmap f (More x l) = More x ((f.) Control.<$> l)
+
+instance Control.Applicative (Batch a b) where
+  pure = Done
+  Done f <*> l' = Control.fmap f l'
+  More x l <*> l' = More x (flip Control.<$> l Control.<*> l')
+
+batch :: a ->. Batch a b b
+batch x = More x (Done id)
+
+runWith :: Control.Applicative f => (a ->. f b) -> Batch a b c ->. f c
+runWith _ (Done c) = Control.pure c
+runWith f (More x l) = runWith f l Control.<*> f x
+
+fuse :: Batch b b t ->. t
+fuse (Done i) = i
+fuse (More x l) = fuse l x
+
 ------------------------
 -- Standard instances --
 ------------------------

src/Data/Profunctor/Kleisli/Linear.hs

@@ -41,22 +41,17 @@ instance Control.Applicative f => Strong Either Void (Kleisli f) where
   first  (Kleisli f) = Kleisli (either (Data.fmap Left . f) (Control.pure . Right))
   second (Kleisli g) = Kleisli (either (Control.pure . Left) (Data.fmap Right . g))
 
-instance Control.Applicative f => Wandering (Kleisli f) where
-  wander (Kleisli f) = Kleisli (Data.traverse f)
+instance Control.Applicative f => Monoidal (,) () (Kleisli f) where
+  Kleisli f *** Kleisli g = Kleisli $ \(x,y) -> (,) Control.<$> f x Control.<*> g y
+  unit = Kleisli Control.pure
+
+instance Control.Applicative f => Traversing (Kleisli f)
 
 -- | Linear co-Kleisli arrows for the comonad `w`. These arrows are still
 -- useful in the case where `w` is not a comonad however, and some
 -- profunctorial properties still hold in this weaker setting.
 -- However stronger requirements on `f` are needed for profunctorial
 -- strength, so we have fewer instances.
---
--- Category theoretic remark: duality doesn't work in the obvious way, since
--- (,) isn't the categorical product. Instead, we have a product (&), called
--- "With", defined by
--- > type With a b = forall r. Either (a ->. r) (b ->. r) ->. r
--- which satisfies the universal property of the product of `a` and `b`.
--- CoKleisli arrows are strong with respect to this monoidal structure,
--- although this might not be useful...
 newtype CoKleisli w a b = CoKleisli { runCoKleisli :: w a ->. b }
 
 instance Data.Functor f => Profunctor (CoKleisli f) where

src/Data/Profunctor/Linear.hs

@@ -1,23 +1,28 @@
 {-# LANGUAGE FlexibleContexts #-}
-{-# LANGUAGE KindSignatures #-}
+{-# LANGUAGE FlexibleInstances #-}
 {-# LANGUAGE LambdaCase #-}
 {-# LANGUAGE LinearTypes #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
 {-# LANGUAGE NoImplicitPrelude #-}
 {-# LANGUAGE TupleSections #-}
 {-# LANGUAGE TypeOperators #-}
 
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+
 module Data.Profunctor.Linear
   ( Profunctor(..)
   , Monoidal(..)
   , Strong(..)
-  , Wandering(..)
+  , Traversing
   , LinearArrow(..), getLA
   , Exchange(..)
   , Market(..), runMarket
+  , MyFunctor(..), runMyFunctor
+  , OtherFunctor(..), runOtherFunctor
   ) where
 
 import qualified Data.Functor.Linear as Data
+import qualified Control.Monad.Linear as Control
 import Data.Bifunctor.Linear hiding (first, second)
 import Prelude.Linear
 import Data.Void
@@ -26,7 +31,7 @@ import Control.Arrow (Kleisli(..))
 
 -- TODO: write laws
 
-class Profunctor (arr :: * -> * -> *) where
+class Profunctor arr where
   {-# MINIMAL dimap | lmap, rmap #-}
 
   dimap :: (s ->. a) -> (b ->. t) -> a `arr` b -> s `arr` t
@@ -56,8 +61,7 @@ class (SymmetricMonoidal m u, Profunctor arr) => Strong m u arr where
   second arr = dimap swap swap (first arr)
   {-# INLINE second #-}
 
-class (Strong (,) () arr, Strong Either Void arr) => Wandering arr where
-  wander :: Data.Traversable f => a `arr` b -> f a `arr` f b
+class (Strong (,) () arr, Strong Either Void arr, Monoidal (,) () arr) => Traversing arr where
 
 ---------------
 -- Instances --
@@ -79,13 +83,23 @@ instance Strong Either Void LinearArrow where
   first  (LA f) = LA $ either (Left . f) Right
   second (LA g) = LA $ either Left (Right . g)
 
+instance Monoidal (,) () LinearArrow where
+  LA f *** LA g = LA $ \(a,x) -> (f a, g x)
+  unit = LA id
+
+instance Traversing LinearArrow
+
 instance Profunctor (->) where
   dimap f g h x = g (h (f x))
 instance Strong (,) () (->) where
   first f (x, y) = (f x, y)
 instance Strong Either Void (->) where
   first f (Left x) = Left (f x)
   first _ (Right y) = Right y
+instance Monoidal (,) () (->) where
+  (f *** g) (a,x) = (f a, g x)
+  unit () = ()
+instance Traversing (->)
 
 data Exchange a b s t = Exchange (s ->. a) (b ->. t)
 instance Profunctor (Exchange a b) where
@@ -103,6 +117,12 @@ instance Prelude.Applicative f => Strong Either Void (Kleisli f) where
                                    Left  x -> Prelude.fmap Left (f x)
                                    Right y -> Prelude.pure (Right y)
 
+instance Prelude.Applicative f => Monoidal (,) () (Kleisli f) where
+  Kleisli f *** Kleisli g = Kleisli (\(x,y) -> (,) Prelude.<$> f x Prelude.<*> g y)
+  unit = Kleisli Prelude.pure
+
+instance Prelude.Applicative f => Traversing (Kleisli f) where
+
 data Market a b s t = Market (b ->. t) (s ->. Either t a)
 runMarket :: Market a b s t ->. (b ->. t, s ->. Either t a)
 runMarket (Market f g) = (f, g)
@@ -112,3 +132,21 @@ instance Profunctor (Market a b) where
 
 instance Strong Either Void (Market a b) where
   first (Market f g) = Market (Left . f) (either (either (Left . Left) Right . g) (Left . Right))
+
+-- TODO: pick a more sensible name for this
+newtype MyFunctor a b t = MyFunctor (b ->. (a, t))
+runMyFunctor :: MyFunctor a b t ->. b ->. (a, t)
+runMyFunctor (MyFunctor f) = f
+
+instance Data.Functor (MyFunctor a b) where
+  fmap f (MyFunctor g) = MyFunctor (getLA (second (LA f)) . g)
+instance Control.Functor (MyFunctor a b) where
+  fmap f (MyFunctor g) = MyFunctor (Control.fmap f . g)
+
+newtype OtherFunctor a b t = OtherFunctor (a, b ->. t)
+runOtherFunctor :: OtherFunctor a b t ->. (a, b ->. t)
+runOtherFunctor (OtherFunctor f) = f
+instance Data.Functor (OtherFunctor a b) where
+  fmap f (OtherFunctor (a,g)) = OtherFunctor (a,f . g)
+instance Control.Functor (OtherFunctor a b) where
+  fmap f (OtherFunctor (a,g)) = OtherFunctor (a,f . g)

src/Foreign/Marshal/Pure.hs

@@ -60,7 +60,7 @@ import Foreign.Marshal.Utils
 import Foreign.Ptr
 import Foreign.Storable
 import Foreign.Storable.Tuple ()
-import Prelude (($), return, (<*>))
+import Prelude (($), return, (<*>), (<$>))
 import Prelude.Linear hiding (($))
 import System.IO.Unsafe
 import qualified Unsafe.Linear as Unsafe

src/Prelude/Linear.hs

@@ -53,7 +53,7 @@ import Prelude hiding
   , foldr
   , maybe
   , (.)
-  , Functor(..)
+  , Functor(..), (<$>)
   , Applicative(..)
   , Monad(..)
   , Traversable(..)
@@ -83,10 +83,6 @@ maybe _ f (Just y) = f y
 forget :: (a ->. b) ->. a -> b
 forget f x = f x
 
--- | Replacement for the flip function with generalized multiplicities.
-flip :: (a -->.(p) b -->.(q) c) -->.(r) b -->.(q) a -->.(p) c
-flip f b a = f a b
-
 -- | Linearly typed replacement for the standard '(Prelude.<*)' function.
 (<*) :: (Data.Applicative f, Consumable b) => f a ->. f b ->. f a
 fa <* fb = Data.fmap (flip lseq) fa Data.<*> fb

src/Prelude/Linear/Internal/Simple.hs

@@ -56,3 +56,7 @@ foldr :: (a ->. b ->. b) -> b ->. [a] ->. b
 foldr f z = \case
   [] -> z
   x:xs -> f x (foldr f z xs)
+
+-- | Replacement for the flip function with generalized multiplicities.
+flip :: (a -->.(p) b -->.(q) c) -->.(r) b -->.(q) a -->.(p) c
+flip f b a = f a b

src/System/IO/Linear.hs

@@ -41,6 +41,7 @@ import qualified Control.Monad.Linear as Control
 import qualified Data.Functor.Linear as Data
 import GHC.Exts (State#, RealWorld)
 import Prelude.Linear hiding (IO)
+import Prelude ((<$>))
 import qualified Unsafe.Linear as Unsafe
 import qualified System.IO as System