{-# LANGUAGE DeriveDataTypeable #-} {-# LANGUAGE DeriveGeneric #-} {-# LANGUAGE EmptyCase #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE GADTs #-} {-# LANGUAGE InstanceSigs #-} {-# LANGUAGE PolyKinds #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE TemplateHaskell #-} {-# LANGUAGE TypeApplications #-} {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE TypeInType #-} {-# LANGUAGE TypeOperators #-} {-# LANGUAGE TypeSynonymInstances #-} {-# LANGUAGE UndecidableInstances #-} -- | -- Module : Data.Type.Lens -- Copyright : (c) Justin Le 2018 -- License : BSD3 -- -- Maintainer : justin@jle.im -- Stability : experimental -- Portability : non-portable -- -- Lenses and optics for manipulating DataKind-based types, powered by -- /singletons/ defunctionalization. -- -- See "Data.Type.Lens.Examples" for example usage and syntax. -- -- For the most part, you should be able to use them just like you'd use -- the functions from the /lens/ or /microlens/ libraries; just remember -- to capitalize names like 'Over' and 'Set', since they are type families. -- -- Note that the ways of "creating" a lens or optic ('Sets_', 'Traverse_', -- 'To_', 'MkLens_', etc. are all suffixed with @_@ for convenience, to -- reserve the underscoreless identifiers for the fully applied type family -- as per /singletons/ library convention. -- -- "Value level" versions of these lenses and functions are not exported, -- because they would be more or less completely compatible with the same -- functions from /microlens/ and /lens/ packages. However, when the names -- of these functions differ from the names of their /lens/ counterpart -- ('mkLens' and 'ixList'), value-level versions are provided. -- -- There are two main ways to define optics. -- -- First, you can write them by hand using 'singletonsOnly': -- -- @ -- $(singletonsOnly [d| -- l1 :: Functor f => LensLike (a, c) (b, c) a b -- l1 f (x, y) = (\x' -> (x', y)) <$> f x -- -- l1Alt :: Functor f => LensLike (a, c) (b, c) a b -- l1Alt = mkLens fst (\(_, y) x -> (x', y)) -- -- getFirst :: Getting a (a, b) a -- getFirst = to fst -- |]) -- @ -- -- This creates the /type families/ @L1@, @L1Alt@, and @GetFirst@; however, -- these aren't lenses, because they aren't partially applied. The lactual -- lenses are @L1Sym0@, @L1AltSym0@, and @GetFirstSym0@. As a convention, -- it is recommend to alias the /actual/ lenses with an underscore suffix: -- -- @ -- -- L1_ :: Functor f => LensLike f (a, c) (b, c) a b -- type L1_ = L1Sym0 -- -- -- L1Alt_ :: Functor f => LensLike f (a, c) (b, c) a b -- type L1Alt_ = L1AltSym0 -- -- -- GetFirst_ :: Getting a (a, b) a -- type GetFirst_ = GetFirstSym0 -- @ -- -- The number after the @Sym@ is determined by how many arguments you need -- to apply to your function before you get to the actual lens. For -- example, `IxList` requires one argument (the index) to get to the actual -- traversal, so the definition in the library is: -- -- @ -- type IxList_ i = IxListSym1 i -- @ -- -- Second, you can write them directly at the type level using combinators -- like 'MkLens_' and 'To_': -- -- @ -- type GetFirst_ = 'To_' 'FstSym0' -- @ -- -- ('FstSym0' is the promotion of 'fst' from -- "Data.Singletons.Prelude.Tuple") module Data.Type.Lens ( LensLike, LensLike' -- * Setting , ASetter -- ** Using -- | Ways of consuming a setter. , Over, type (%~), sOver, (%%~) , Set, type (.~), sSet, (%.~) -- ** Making -- | Ways of creating a setter-only. , Sets_, Sets, sSets -- * Getting , Getting -- ** Using -- | Ways of consuming a getter , View, type (^.), sView, (%^.) -- ** Making -- | Ways of creating a getter-only. , To_, To, sTo -- * Lenses , ALens -- ** Making -- | Ways of creating a lens , MkLens_, MkLens, sMkLens, mkLens -- ** Cloning , CloneLens_, CloneLens -- * Traversals and Folds , ATraversal -- ** Using -- | Ways of consuming traversals and folds , Preview, type (^?), sPreview, (%^?) , ToListOf, type (^..), sToListOf, (%^..) , UnsafePreview, type (^?!), sUnsafePreview, (%^?!) -- ** Making -- | Ways of creating traversals and folds , Folding_, Folding, sFolding , Folded_, Folded, sFolded , Traverse_, Traverse, sTraverse -- ** Cloning , CloneTraversal_, CloneTraversal, sCloneTraversal -- * Samples -- | Some sample lenses and traversals -- -- ** Tuple , L1_, L1, sL1 , L2_, L2, sL2 -- ** List , N(..), SN , IxList_, IxList, sIxList, ixList -- * Util , type (.@) , Sing (SZ, SS, SMkContext) -- * Defunctionalization Symbols , ASetterSym0, ASetterSym1, ASetterSym2, ASetterSym3, ASetterSym4 , OverSym0, OverSym1, OverSym2, OverSym3 , SetSym0, SetSym1, SetSym2, SetSym3 , SetsSym0, SetsSym1, SetsSym2, SetsSym3 , GettingSym0, GettingSym1, GettingSym2, GettingSym3 , ViewSym0, ViewSym1, ViewSym2 , ToSym0, ToSym1, ToSym2, ToSym3 , ToListOfSym0, ToListOfSym1, ToListOfSym2 , LensLikeSym0, LensLikeSym1, LensLikeSym2, LensLikeSym3, LensLikeSym4, LensLikeSym5 , LensLike'Sym0, LensLike'Sym1, LensLike'Sym2, LensLike'Sym3 , MkLensSym0, MkLensSym1, MkLensSym2, MkLensSym3, MkLensSym4 , CloneLensSym0, CloneLensSym1, CloneLensSym2, CloneLensSym3 , FoldingSym0, FoldingSym1, FoldingSym2, FoldingSym3 , FoldedSym0, FoldedSym1, FoldedSym2 , L1Sym0, L1Sym1, L1Sym2 , L2Sym0, L2Sym1, L2Sym2 , ZSym0, SSym0, SSym1 , IxListSym0, IxListSym1, IxListSym2, IxListSym3 ) where import Control.Applicative import Data.Foldable import Data.Functor.Identity import Data.Monoid import Data.Singletons.Prelude.Const import Data.Singletons.Prelude.Foldable hiding (Traverse_) import Data.Singletons.Prelude.Function hiding (Const, ConstSym0) import Data.Singletons.Prelude.Functor import Data.Singletons.Prelude.Identity import Data.Singletons.Prelude.Maybe import Data.Singletons.Prelude.Monoid import Data.Singletons.TH import Data.Type.Lens.Internal import Data.Typeable (Typeable) import GHC.Generics (Generic) -- | The general shape of optics in this library. ("van Laarhoven") -- -- For different levels of polymorphism on @f@, you get different types of -- optics: -- -- * If @f@ can be any 'Functor', you have a Lens (see 'ALens') -- * If @f@ is only 'Identity', you have a setter (see 'ASetter') -- * If @f@ is only @'Const' R@ for a specific @R@, you have a getter -- of @R@ (see 'Getting') -- * If @f@ can be @'Const' r@ for any 'Monoid' @r@, you have a Fold. -- * If @f@ can be any 'Applicative', you have a Traversal (see -- 'ATraversal') -- -- Normal lens libraries implement the constraints for lenses, folds, and -- traversals using RankN types, but we don't do that here to avoid working -- with RankN kinds. type LensLike f s t a b = (a -> f b) -> (s -> f t) -- | A 'LensLike' that does not change any types. type LensLike' f s a = LensLike f s s a a -- | A settable "lens". Usable with 'Over' ('%~'), constructable with 'To' -- or any of the general lens constructors. -- -- See 'LensLike' for more information. type ASetter s t a b = LensLike Identity s t a b -- | A retrieving "lens". If @r@ is fixed to a type, it's a Getter for -- that type. If @r@ is polymorphic over all 'Monoid', then it's a Fold -- over @a@s. -- -- As a Getter, usable with 'View' ('^.'); as a Fold, usable with -- 'ToListOf' ('^..'), 'Preview' ('^?'), etc. -- -- Normal lens libraries implement the constraints for folds using RankN -- types, but we don't do that here to avoid working with RankN kinds. -- -- See 'LensLike' for more information. type Getting r s a = LensLike (Const r) s s a a -- | Peano nats, used for implementation of list index traversals in -- a termination-sane way. data N = Z | S N deriving (Show, Eq, Ord, Read, Generic, Typeable) genSingletons [''LensLike, ''LensLike', ''ASetter, ''Getting, ''N] singEqInstance ''N singOrdInstance ''N singDecideInstance ''N singShowInstance ''N -- | If a function expects an 'ALens', it can be given any Lens (a -- @'LensLike' f@ that works for any 'Functor' f). -- -- You can use an 'ALens' as a normal lens by using 'CloneLens_'. type ALens s t a b = LensLike (Context a b) s t a b -- | If a function expects an 'ATraversal', it can be given any Traversal -- (a @'LensLike' f@ that works for any 'Applicative' f). -- -- You can use an 'ATraversal' as a normal traversal by using -- 'CloneTraversal_'. type ATraversal s t a b = LensLike (Bazaar a b) s t a b $(singletonsOnly [d| over :: ASetter s t a b -> (a -> b) -> (s -> t) over l f x = case l (Identity . f) x of Identity y -> y set :: ASetter s t a b -> b -> s -> t set l y = over l (\_ -> y) view :: Getting a s a -> s -> a view l x = case l Const x of Const y -> y sets :: ((a -> b) -> (s -> t)) -> ASetter s t a b sets f g = Identity . f (\x -> case g x of Identity y -> y) to :: (s -> a) -> Getting r s a to f g x = case g (f x) of Const y -> Const y toListOf :: Getting [a] s a -> s -> [a] toListOf l x = case l (Const . (:[])) x of Const ys -> ys preview :: Getting (First a) s a -> s -> Maybe a preview l x = case l (Const . First . Just) x of Const (First y) -> y unsafePreview :: Getting (First a) s a -> s -> a unsafePreview l x = case preview l x of Just y -> y Nothing -> error "Failed indexing into empty traversal" folding :: (Foldable f, Monoid r) => (s -> f a) -> Getting r s a folding f g x = case traverse_ g (f x) of Const y -> Const y folded :: (Foldable f, Monoid r) => Getting r (f a) a folded f x = case traverse_ f x of Const y -> Const y cloneLens :: Functor f => LensLike (Context a b) s t a b -> LensLike f s t a b cloneLens l f x = case l (\y -> MkContext id y) x of MkContext g y -> g <$> f y cloneTraversal :: Applicative f => LensLike (Bazaar a b) s t a b -> LensLike f s t a b cloneTraversal l f xs = unBazaar f $ l (`More` Done id) xs l1 :: Functor f => LensLike f (a, c) (b, c) a b l1 f (x, y) = (\x' -> (x', y)) <$> f x l2 :: Functor f => LensLike f (a, b) (a, c) b c l2 f (x, y) = (\y' -> (x, y')) <$> f y |]) $(singletons [d| mkLens :: Functor f => (s -> a) -> (s -> b -> t) -> LensLike f s t a b mkLens v s f x = s x <$> f (v x) ixList :: Applicative f => N -> LensLike' f [a] a ixList _ _ [] = pure [] ixList Z f (x:xs) = (:xs) <$> f x ixList (S i) f (x:xs) = (x:) <$> ixList i f xs |]) -- | Infix application of 'Over' type l %~ f = OverSym2 l f -- | Infix application of 'Set' type l .~ x = SetSym2 l x -- | Infix application of 'View' type x ^. l = View l x -- | Infix application of 'Preview' type x ^? l = Preview l x -- | Infix application of 'UnsafePreview' type x ^?! l = UnsafePreview l x -- | Infix application of 'ToListOf' type x ^.. l = ToListOf l x -- | Shorter name for type-level function composition type f .@ g = f .@#@$$$ g infixr 4 %~ infixr 4 .~ infixl 8 ^. infixl 8 ^? infixl 8 ^?! infixl 8 ^.. infixr 9 .@ -- | Singleton mirror of 'Over' and '%~'. -- -- Note that this conflicts in naming from '%%~' in /lens/, which is 'id'. -- -- @since 0.1.1.0 (%%~) :: Sing l -> Sing f -> Sing x -> Sing (x & l %~ f) (%%~) = sOver -- | Singleton mirror of 'Set' and '.~'. -- -- @since 0.1.1.0 (%.~) :: Sing l -> Sing y -> Sing x -> Sing (x & l .~ y) (%.~) = sSet -- | Singleton mirror of 'View' and '%^.'. -- -- @since 0.1.1.0 (%^.) :: Sing x -> Sing l -> Sing (x ^. l) (%^.) = flip sView -- | Singleton mirror of 'Preview' and '%^?'. -- -- @since 0.1.1.0 (%^?) :: Sing x -> Sing l -> Sing (x ^? l) (%^?) = flip sPreview -- | Singleton mirror of 'UnsafePreview' and '%^?!'. -- -- @since 0.1.1.0 (%^?!) :: Sing x -> Sing l -> Sing (x ^?! l) (%^?!) = flip sUnsafePreview -- | Singleton mirror of 'ToListOf' and '%^..'. -- -- @since 0.1.1.0 (%^..) :: Sing x -> Sing l -> Sing (x ^.. l) (%^..) = flip sToListOf -- | Create a Getter from a getting function. -- -- @ -- 'To_' :: (a ~> b) -> 'Getting' b a b -- @ type To_ f = ToSym1 f -- | Create a Setter from a setting function. -- -- @ -- 'Sets_' :: ((a ~> b) ~> (s ~> t)) -> 'ASetter' s t a b -- @ type Sets_ f = SetsSym1 f -- | Create a Lens from a setter and a getter. -- -- @ -- 'MkLens_' -- :: 'Functor' f -- => (s ~> a) -- -> (s ~> b ~> t) -- -> 'LensLike' f s t a b -- @ type MkLens_ f g = MkLensSym2 f g -- | "Clone" a polymorphic lens so it can be used as more than one type of -- thing (getter or setter). -- -- @ -- 'CloneLens_' -- :: 'Functor' f -- => 'LensLike' (Context a b) s t a b -- -> 'LensLike' f s t a b -- @ -- -- Useful for writing a function that takes a lens and uses it in more than -- one way; if you have it take an 'ALens', you can then use 'CloneLens_' to -- use it as a getter or setter. type CloneLens_ l = CloneLensSym1 l -- | "Clone" a polymorphic traversal so it can be used as more than one type of -- thing (fold, traversal, getter, setter...). -- -- @ -- 'CloneTraversal_' -- :: 'Functor' f -- => 'LensLike' (Bazaar a b) s t a b -- -> 'LensLike' f s t a b -- @ -- -- Useful for writing a function that takes a traversal and uses it in more -- than one way; if you have it take an 'ATraversal', you can then use -- 'CloneTraversal_' to use it as a fold or traversal or anything else. type CloneTraversal_ l = CloneTraversalSym1 l -- | The canonical Traversal for any instance of 'Traversable'. -- -- @ -- 'Traverse_' -- :: 'Applicative' f -- => 'LensLike' f (t a) (t b) a b -- @ type Traverse_ = TraverseSym0 -- | Create a Fold from a "folding function": -- -- @ -- 'Folding_' -- :: ('Foldable' f, 'Monoid' r) -- => (s ~> f a) -- -> 'Getting' r s a -- @ type Folding_ f = FoldingSym1 f -- | The canonical Fold for any instance of 'Foldable'. -- -- @ -- 'Folded_' -- :: 'Monoid' r -- => 'Getting' r (t a) a -- @ type Folded_ = FoldedSym0 -- | Lens into the first field of a tuple type L1_ = L1Sym0 -- | Lens into the second field of a tuple type L2_ = L2Sym0 -- | @'IxList' i@ is a Traversal into the i-th item into a list. Defined -- in terms of 'N' to allow for sane termination guaruntees. -- -- @ -- 'IxList_' -- :: 'Applicative' f -- => 'N' -- -> 'LensLike'' f [a] a -- @ type IxList_ i = IxListSym1 i