1{-# LANGUAGE CPP #-} 2{-# LANGUAGE GADTs #-} 3{-# LANGUAGE Rank2Types #-} 4{-# LANGUAGE FlexibleContexts #-} 5{-# LANGUAGE FlexibleInstances #-} 6{-# LANGUAGE ScopedTypeVariables #-} 7{-# LANGUAGE MultiParamTypeClasses #-} 8{-# LANGUAGE PolyKinds #-} 9#if __GLASGOW_HASKELL__ >= 800 10{-# LANGUAGE TypeInType #-} 11#endif 12{-# LANGUAGE Trustworthy #-} 13------------------------------------------------------------------------------- 14-- | 15-- Module : Control.Lens.Type 16-- Copyright : (C) 2012-16 Edward Kmett 17-- License : BSD-style (see the file LICENSE) 18-- Maintainer : Edward Kmett <ekmett@gmail.com> 19-- Stability : provisional 20-- Portability : Rank2Types 21-- 22-- This module exports the majority of the types that need to appear in user 23-- signatures or in documentation when talking about lenses. The remaining types 24-- for consuming lenses are distributed across various modules in the hierarchy. 25------------------------------------------------------------------------------- 26module Control.Lens.Type 27 ( 28 -- * Other 29 Equality, Equality', As 30 , Iso, Iso' 31 , Prism , Prism' 32 , Review , AReview 33 -- * Lenses, Folds and Traversals 34 , Lens, Lens' 35 , Traversal, Traversal' 36 , Traversal1, Traversal1' 37 , Setter, Setter' 38 , Getter, Fold 39 , Fold1 40 -- * Indexed 41 , IndexedLens, IndexedLens' 42 , IndexedTraversal, IndexedTraversal' 43 , IndexedTraversal1, IndexedTraversal1' 44 , IndexedSetter, IndexedSetter' 45 , IndexedGetter, IndexedFold 46 , IndexedFold1 47 -- * Index-Preserving 48 , IndexPreservingLens, IndexPreservingLens' 49 , IndexPreservingTraversal, IndexPreservingTraversal' 50 , IndexPreservingTraversal1, IndexPreservingTraversal1' 51 , IndexPreservingSetter, IndexPreservingSetter' 52 , IndexPreservingGetter, IndexPreservingFold 53 , IndexPreservingFold1 54 -- * Common 55 , Simple 56 , LensLike, LensLike' 57 , Over, Over' 58 , IndexedLensLike, IndexedLensLike' 59 , Optical, Optical' 60 , Optic, Optic' 61 ) where 62 63import Prelude () 64 65import Control.Lens.Internal.Prelude 66import Control.Lens.Internal.Setter 67import Control.Lens.Internal.Indexed 68import Data.Bifunctor 69import Data.Functor.Apply 70#if __GLASGOW_HASKELL__ >= 800 71import Data.Kind 72#endif 73 74-- $setup 75-- >>> :set -XNoOverloadedStrings 76-- >>> import Control.Lens 77-- >>> import Debug.SimpleReflect.Expr 78-- >>> import Debug.SimpleReflect.Vars as Vars hiding (f,g,h) 79-- >>> let f :: Expr -> Expr; f = Debug.SimpleReflect.Vars.f 80-- >>> let g :: Expr -> Expr; g = Debug.SimpleReflect.Vars.g 81-- >>> let h :: Expr -> Expr -> Expr; h = Debug.SimpleReflect.Vars.h 82-- >>> let getter :: Expr -> Expr; getter = fun "getter" 83-- >>> let setter :: Expr -> Expr -> Expr; setter = fun "setter" 84-- >>> import Numeric.Natural 85-- >>> let nat :: Prism' Integer Natural; nat = prism toInteger $ \i -> if i < 0 then Left i else Right (fromInteger i) 86 87------------------------------------------------------------------------------- 88-- Lenses 89------------------------------------------------------------------------------- 90 91-- | A 'Lens' is actually a lens family as described in 92-- <http://comonad.com/reader/2012/mirrored-lenses/>. 93-- 94-- With great power comes great responsibility and a 'Lens' is subject to the 95-- three common sense 'Lens' laws: 96-- 97-- 1) You get back what you put in: 98-- 99-- @ 100-- 'Control.Lens.Getter.view' l ('Control.Lens.Setter.set' l v s) ≡ v 101-- @ 102-- 103-- 2) Putting back what you got doesn't change anything: 104-- 105-- @ 106-- 'Control.Lens.Setter.set' l ('Control.Lens.Getter.view' l s) s ≡ s 107-- @ 108-- 109-- 3) Setting twice is the same as setting once: 110-- 111-- @ 112-- 'Control.Lens.Setter.set' l v' ('Control.Lens.Setter.set' l v s) ≡ 'Control.Lens.Setter.set' l v' s 113-- @ 114-- 115-- These laws are strong enough that the 4 type parameters of a 'Lens' cannot 116-- vary fully independently. For more on how they interact, read the \"Why is 117-- it a Lens Family?\" section of 118-- <http://comonad.com/reader/2012/mirrored-lenses/>. 119-- 120-- There are some emergent properties of these laws: 121-- 122-- 1) @'Control.Lens.Setter.set' l s@ must be injective for every @s@ This is a consequence of law #1 123-- 124-- 2) @'Control.Lens.Setter.set' l@ must be surjective, because of law #2, which indicates that it is possible to obtain any 'v' from some 's' such that @'Control.Lens.Setter.set' s v = s@ 125-- 126-- 3) Given just the first two laws you can prove a weaker form of law #3 where the values @v@ that you are setting match: 127-- 128-- @ 129-- 'Control.Lens.Setter.set' l v ('Control.Lens.Setter.set' l v s) ≡ 'Control.Lens.Setter.set' l v s 130-- @ 131-- 132-- Every 'Lens' can be used directly as a 'Control.Lens.Setter.Setter' or 'Traversal'. 133-- 134-- You can also use a 'Lens' for 'Control.Lens.Getter.Getting' as if it were a 135-- 'Fold' or 'Getter'. 136-- 137-- Since every 'Lens' is a valid 'Traversal', the 138-- 'Traversal' laws are required of any 'Lens' you create: 139-- 140-- @ 141-- l 'pure' ≡ 'pure' 142-- 'fmap' (l f) '.' l g ≡ 'Data.Functor.Compose.getCompose' '.' l ('Data.Functor.Compose.Compose' '.' 'fmap' f '.' g) 143-- @ 144-- 145-- @ 146-- type 'Lens' s t a b = forall f. 'Functor' f => 'LensLike' f s t a b 147-- @ 148type Lens s t a b = forall f. Functor f => (a -> f b) -> s -> f t 149 150-- | @ 151-- type 'Lens'' = 'Simple' 'Lens' 152-- @ 153type Lens' s a = Lens s s a a 154 155-- | Every 'IndexedLens' is a valid 'Lens' and a valid 'Control.Lens.Traversal.IndexedTraversal'. 156type IndexedLens i s t a b = forall f p. (Indexable i p, Functor f) => p a (f b) -> s -> f t 157 158-- | @ 159-- type 'IndexedLens'' i = 'Simple' ('IndexedLens' i) 160-- @ 161type IndexedLens' i s a = IndexedLens i s s a a 162 163-- | An 'IndexPreservingLens' leaves any index it is composed with alone. 164type IndexPreservingLens s t a b = forall p f. (Conjoined p, Functor f) => p a (f b) -> p s (f t) 165 166-- | @ 167-- type 'IndexPreservingLens'' = 'Simple' 'IndexPreservingLens' 168-- @ 169type IndexPreservingLens' s a = IndexPreservingLens s s a a 170 171------------------------------------------------------------------------------ 172-- Traversals 173------------------------------------------------------------------------------ 174 175-- | A 'Traversal' can be used directly as a 'Control.Lens.Setter.Setter' or a 'Fold' (but not as a 'Lens') and provides 176-- the ability to both read and update multiple fields, subject to some relatively weak 'Traversal' laws. 177-- 178-- These have also been known as multilenses, but they have the signature and spirit of 179-- 180-- @ 181-- 'Data.Traversable.traverse' :: 'Data.Traversable.Traversable' f => 'Traversal' (f a) (f b) a b 182-- @ 183-- 184-- and the more evocative name suggests their application. 185-- 186-- Most of the time the 'Traversal' you will want to use is just 'Data.Traversable.traverse', but you can also pass any 187-- 'Lens' or 'Iso' as a 'Traversal', and composition of a 'Traversal' (or 'Lens' or 'Iso') with a 'Traversal' (or 'Lens' or 'Iso') 188-- using ('.') forms a valid 'Traversal'. 189-- 190-- The laws for a 'Traversal' @t@ follow from the laws for 'Data.Traversable.Traversable' as stated in \"The Essence of the Iterator Pattern\". 191-- 192-- @ 193-- t 'pure' ≡ 'pure' 194-- 'fmap' (t f) '.' t g ≡ 'Data.Functor.Compose.getCompose' '.' t ('Data.Functor.Compose.Compose' '.' 'fmap' f '.' g) 195-- @ 196-- 197-- One consequence of this requirement is that a 'Traversal' needs to leave the same number of elements as a 198-- candidate for subsequent 'Traversal' that it started with. Another testament to the strength of these laws 199-- is that the caveat expressed in section 5.5 of the \"Essence of the Iterator Pattern\" about exotic 200-- 'Data.Traversable.Traversable' instances that 'Data.Traversable.traverse' the same entry multiple times was actually already ruled out by the 201-- second law in that same paper! 202type Traversal s t a b = forall f. Applicative f => (a -> f b) -> s -> f t 203 204-- | @ 205-- type 'Traversal'' = 'Simple' 'Traversal' 206-- @ 207type Traversal' s a = Traversal s s a a 208 209type Traversal1 s t a b = forall f. Apply f => (a -> f b) -> s -> f t 210type Traversal1' s a = Traversal1 s s a a 211 212-- | Every 'IndexedTraversal' is a valid 'Control.Lens.Traversal.Traversal' or 213-- 'Control.Lens.Fold.IndexedFold'. 214-- 215-- The 'Indexed' constraint is used to allow an 'IndexedTraversal' to be used 216-- directly as a 'Control.Lens.Traversal.Traversal'. 217-- 218-- The 'Control.Lens.Traversal.Traversal' laws are still required to hold. 219-- 220-- In addition, the index @i@ should satisfy the requirement that it stays 221-- unchanged even when modifying the value @a@, otherwise traversals like 222-- 'indices' break the 'Traversal' laws. 223type IndexedTraversal i s t a b = forall p f. (Indexable i p, Applicative f) => p a (f b) -> s -> f t 224 225-- | @ 226-- type 'IndexedTraversal'' i = 'Simple' ('IndexedTraversal' i) 227-- @ 228type IndexedTraversal' i s a = IndexedTraversal i s s a a 229 230type IndexedTraversal1 i s t a b = forall p f. (Indexable i p, Apply f) => p a (f b) -> s -> f t 231type IndexedTraversal1' i s a = IndexedTraversal1 i s s a a 232 233-- | An 'IndexPreservingLens' leaves any index it is composed with alone. 234type IndexPreservingTraversal s t a b = forall p f. (Conjoined p, Applicative f) => p a (f b) -> p s (f t) 235 236-- | @ 237-- type 'IndexPreservingTraversal'' = 'Simple' 'IndexPreservingTraversal' 238-- @ 239type IndexPreservingTraversal' s a = IndexPreservingTraversal s s a a 240 241type IndexPreservingTraversal1 s t a b = forall p f. (Conjoined p, Apply f) => p a (f b) -> p s (f t) 242type IndexPreservingTraversal1' s a = IndexPreservingTraversal1 s s a a 243 244------------------------------------------------------------------------------ 245-- Setters 246------------------------------------------------------------------------------ 247 248-- | The only 'LensLike' law that can apply to a 'Setter' @l@ is that 249-- 250-- @ 251-- 'Control.Lens.Setter.set' l y ('Control.Lens.Setter.set' l x a) ≡ 'Control.Lens.Setter.set' l y a 252-- @ 253-- 254-- You can't 'Control.Lens.Getter.view' a 'Setter' in general, so the other two laws are irrelevant. 255-- 256-- However, two 'Functor' laws apply to a 'Setter': 257-- 258-- @ 259-- 'Control.Lens.Setter.over' l 'id' ≡ 'id' 260-- 'Control.Lens.Setter.over' l f '.' 'Control.Lens.Setter.over' l g ≡ 'Control.Lens.Setter.over' l (f '.' g) 261-- @ 262-- 263-- These can be stated more directly: 264-- 265-- @ 266-- l 'pure' ≡ 'pure' 267-- l f '.' 'untainted' '.' l g ≡ l (f '.' 'untainted' '.' g) 268-- @ 269-- 270-- You can compose a 'Setter' with a 'Lens' or a 'Traversal' using ('.') from the @Prelude@ 271-- and the result is always only a 'Setter' and nothing more. 272-- 273-- >>> over traverse f [a,b,c,d] 274-- [f a,f b,f c,f d] 275-- 276-- >>> over _1 f (a,b) 277-- (f a,b) 278-- 279-- >>> over (traverse._1) f [(a,b),(c,d)] 280-- [(f a,b),(f c,d)] 281-- 282-- >>> over both f (a,b) 283-- (f a,f b) 284-- 285-- >>> over (traverse.both) f [(a,b),(c,d)] 286-- [(f a,f b),(f c,f d)] 287type Setter s t a b = forall f. Settable f => (a -> f b) -> s -> f t 288 289-- | A 'Setter'' is just a 'Setter' that doesn't change the types. 290-- 291-- These are particularly common when talking about monomorphic containers. /e.g./ 292-- 293-- @ 294-- 'sets' Data.Text.map :: 'Setter'' 'Data.Text.Internal.Text' 'Char' 295-- @ 296-- 297-- @ 298-- type 'Setter'' = 'Simple' 'Setter' 299-- @ 300type Setter' s a = Setter s s a a 301 302-- | Every 'IndexedSetter' is a valid 'Setter'. 303-- 304-- The 'Setter' laws are still required to hold. 305type IndexedSetter i s t a b = forall f p. 306 (Indexable i p, Settable f) => p a (f b) -> s -> f t 307 308-- | @ 309-- type 'IndexedSetter'' i = 'Simple' ('IndexedSetter' i) 310-- @ 311type IndexedSetter' i s a = IndexedSetter i s s a a 312 313-- | An 'IndexPreservingSetter' can be composed with a 'IndexedSetter', 'IndexedTraversal' or 'IndexedLens' 314-- and leaves the index intact, yielding an 'IndexedSetter'. 315type IndexPreservingSetter s t a b = forall p f. (Conjoined p, Settable f) => p a (f b) -> p s (f t) 316 317-- | @ 318-- type 'IndexedPreservingSetter'' i = 'Simple' 'IndexedPreservingSetter' 319-- @ 320type IndexPreservingSetter' s a = IndexPreservingSetter s s a a 321 322----------------------------------------------------------------------------- 323-- Isomorphisms 324----------------------------------------------------------------------------- 325 326-- | Isomorphism families can be composed with another 'Lens' using ('.') and 'id'. 327-- 328-- Since every 'Iso' is both a valid 'Lens' and a valid 'Prism', the laws for those types 329-- imply the following laws for an 'Iso' 'f': 330-- 331-- @ 332-- f '.' 'Control.Lens.Iso.from' f ≡ 'id' 333-- 'Control.Lens.Iso.from' f '.' f ≡ 'id' 334-- @ 335-- 336-- Note: Composition with an 'Iso' is index- and measure- preserving. 337type Iso s t a b = forall p f. (Profunctor p, Functor f) => p a (f b) -> p s (f t) 338 339-- | @ 340-- type 'Iso'' = 'Control.Lens.Type.Simple' 'Iso' 341-- @ 342type Iso' s a = Iso s s a a 343 344------------------------------------------------------------------------------ 345-- Review Internals 346------------------------------------------------------------------------------ 347 348-- | This is a limited form of a 'Prism' that can only be used for 're' operations. 349-- 350-- Like with a 'Getter', there are no laws to state for a 'Review'. 351-- 352-- You can generate a 'Review' by using 'unto'. You can also use any 'Prism' or 'Iso' 353-- directly as a 'Review'. 354type Review t b = forall p f. (Choice p, Bifunctor p, Settable f) => Optic' p f t b 355 356-- | If you see this in a signature for a function, the function is expecting a 'Review' 357-- (in practice, this usually means a 'Prism'). 358type AReview t b = Optic' Tagged Identity t b 359 360------------------------------------------------------------------------------ 361-- Prism Internals 362------------------------------------------------------------------------------ 363 364-- | A 'Prism' @l@ is a 'Traversal' that can also be turned 365-- around with 'Control.Lens.Review.re' to obtain a 'Getter' in the 366-- opposite direction. 367-- 368-- There are three laws that a 'Prism' should satisfy: 369-- 370-- First, if I 'Control.Lens.Review.re' or 'Control.Lens.Review.review' a value with a 'Prism' and then 'Control.Lens.Fold.preview' or use ('Control.Lens.Fold.^?'), I will get it back: 371-- 372-- @ 373-- 'Control.Lens.Fold.preview' l ('Control.Lens.Review.review' l b) ≡ 'Just' b 374-- @ 375-- 376-- Second, if you can extract a value @a@ using a 'Prism' @l@ from a value @s@, then the value @s@ is completely described by @l@ and @a@: 377-- 378-- @ 379-- 'Control.Lens.Fold.preview' l s ≡ 'Just' a ⟹ 'Control.Lens.Review.review' l a ≡ s 380-- @ 381-- 382-- Third, if you get non-match @t@, you can convert it result back to @s@: 383-- 384-- @ 385-- 'Control.Lens.Combinators.matching' l s ≡ 'Left' t ⟹ 'Control.Lens.Combinators.matching' l t ≡ 'Left' s 386-- @ 387-- 388-- The first two laws imply that the 'Traversal' laws hold for every 'Prism' and that we 'Data.Traversable.traverse' at most 1 element: 389-- 390-- @ 391-- 'Control.Lens.Fold.lengthOf' l x '<=' 1 392-- @ 393-- 394-- It may help to think of this as an 'Iso' that can be partial in one direction. 395-- 396-- Every 'Prism' is a valid 'Traversal'. 397-- 398-- Every 'Iso' is a valid 'Prism'. 399-- 400-- For example, you might have a @'Prism'' 'Integer' 'Numeric.Natural.Natural'@ allows you to always 401-- go from a 'Numeric.Natural.Natural' to an 'Integer', and provide you with tools to check if an 'Integer' is 402-- a 'Numeric.Natural.Natural' and/or to edit one if it is. 403-- 404-- 405-- @ 406-- 'nat' :: 'Prism'' 'Integer' 'Numeric.Natural.Natural' 407-- 'nat' = 'Control.Lens.Prism.prism' 'toInteger' '$' \\ i -> 408-- if i '<' 0 409-- then 'Left' i 410-- else 'Right' ('fromInteger' i) 411-- @ 412-- 413-- Now we can ask if an 'Integer' is a 'Numeric.Natural.Natural'. 414-- 415-- >>> 5^?nat 416-- Just 5 417-- 418-- >>> (-5)^?nat 419-- Nothing 420-- 421-- We can update the ones that are: 422-- 423-- >>> (-3,4) & both.nat *~ 2 424-- (-3,8) 425-- 426-- And we can then convert from a 'Numeric.Natural.Natural' to an 'Integer'. 427-- 428-- >>> 5 ^. re nat -- :: Natural 429-- 5 430-- 431-- Similarly we can use a 'Prism' to 'Data.Traversable.traverse' the 'Left' half of an 'Either': 432-- 433-- >>> Left "hello" & _Left %~ length 434-- Left 5 435-- 436-- or to construct an 'Either': 437-- 438-- >>> 5^.re _Left 439-- Left 5 440-- 441-- such that if you query it with the 'Prism', you will get your original input back. 442-- 443-- >>> 5^.re _Left ^? _Left 444-- Just 5 445-- 446-- Another interesting way to think of a 'Prism' is as the categorical dual of a 'Lens' 447-- -- a co-'Lens', so to speak. This is what permits the construction of 'Control.Lens.Prism.outside'. 448-- 449-- Note: Composition with a 'Prism' is index-preserving. 450type Prism s t a b = forall p f. (Choice p, Applicative f) => p a (f b) -> p s (f t) 451 452-- | A 'Simple' 'Prism'. 453type Prism' s a = Prism s s a a 454 455------------------------------------------------------------------------------- 456-- Equality 457------------------------------------------------------------------------------- 458 459-- | A witness that @(a ~ s, b ~ t)@. 460-- 461-- Note: Composition with an 'Equality' is index-preserving. 462#if __GLASGOW_HASKELL__ >= 800 463type Equality (s :: k1) (t :: k2) (a :: k1) (b :: k2) = forall k3 (p :: k1 -> k3 -> Type) (f :: k2 -> k3) . 464#else 465type Equality (s :: k1) (t :: k2) (a :: k1) (b :: k2) = forall (p :: k1 -> * -> *) (f :: k2 -> *) . 466#endif 467 p a (f b) -> p s (f t) 468 469-- | A 'Simple' 'Equality'. 470type Equality' s a = Equality s s a a 471 472-- | Composable `asTypeOf`. Useful for constraining excess 473-- polymorphism, @foo . (id :: As Int) . bar@. 474type As a = Equality' a a 475 476------------------------------------------------------------------------------- 477-- Getters 478------------------------------------------------------------------------------- 479 480-- | A 'Getter' describes how to retrieve a single value in a way that can be 481-- composed with other 'LensLike' constructions. 482-- 483-- Unlike a 'Lens' a 'Getter' is read-only. Since a 'Getter' 484-- cannot be used to write back there are no 'Lens' laws that can be applied to 485-- it. In fact, it is isomorphic to an arbitrary function from @(s -> a)@. 486-- 487-- Moreover, a 'Getter' can be used directly as a 'Control.Lens.Fold.Fold', 488-- since it just ignores the 'Applicative'. 489type Getter s a = forall f. (Contravariant f, Functor f) => (a -> f a) -> s -> f s 490 491-- | Every 'IndexedGetter' is a valid 'Control.Lens.Fold.IndexedFold' and can be used for 'Control.Lens.Getter.Getting' like a 'Getter'. 492type IndexedGetter i s a = forall p f. (Indexable i p, Contravariant f, Functor f) => p a (f a) -> s -> f s 493 494-- | An 'IndexPreservingGetter' can be used as a 'Getter', but when composed with an 'IndexedTraversal', 495-- 'IndexedFold', or 'IndexedLens' yields an 'IndexedFold', 'IndexedFold' or 'IndexedGetter' respectively. 496type IndexPreservingGetter s a = forall p f. (Conjoined p, Contravariant f, Functor f) => p a (f a) -> p s (f s) 497 498-------------------------- 499-- Folds 500-------------------------- 501 502-- | A 'Fold' describes how to retrieve multiple values in a way that can be composed 503-- with other 'LensLike' constructions. 504-- 505-- A @'Fold' s a@ provides a structure with operations very similar to those of the 'Data.Foldable.Foldable' 506-- typeclass, see 'Control.Lens.Fold.foldMapOf' and the other 'Fold' combinators. 507-- 508-- By convention, if there exists a 'foo' method that expects a @'Data.Foldable.Foldable' (f a)@, then there should be a 509-- @fooOf@ method that takes a @'Fold' s a@ and a value of type @s@. 510-- 511-- A 'Getter' is a legal 'Fold' that just ignores the supplied 'Data.Monoid.Monoid'. 512-- 513-- Unlike a 'Control.Lens.Traversal.Traversal' a 'Fold' is read-only. Since a 'Fold' cannot be used to write back 514-- there are no 'Lens' laws that apply. 515type Fold s a = forall f. (Contravariant f, Applicative f) => (a -> f a) -> s -> f s 516 517-- | Every 'IndexedFold' is a valid 'Control.Lens.Fold.Fold' and can be used for 'Control.Lens.Getter.Getting'. 518type IndexedFold i s a = forall p f. (Indexable i p, Contravariant f, Applicative f) => p a (f a) -> s -> f s 519 520-- | An 'IndexPreservingFold' can be used as a 'Fold', but when composed with an 'IndexedTraversal', 521-- 'IndexedFold', or 'IndexedLens' yields an 'IndexedFold' respectively. 522type IndexPreservingFold s a = forall p f. (Conjoined p, Contravariant f, Applicative f) => p a (f a) -> p s (f s) 523 524-- | A relevant Fold (aka 'Fold1') has one or more targets. 525type Fold1 s a = forall f. (Contravariant f, Apply f) => (a -> f a) -> s -> f s 526type IndexedFold1 i s a = forall p f. (Indexable i p, Contravariant f, Apply f) => p a (f a) -> s -> f s 527type IndexPreservingFold1 s a = forall p f. (Conjoined p, Contravariant f, Apply f) => p a (f a) -> p s (f s) 528 529------------------------------------------------------------------------------- 530-- Simple Overloading 531------------------------------------------------------------------------------- 532 533-- | A 'Simple' 'Lens', 'Simple' 'Traversal', ... can 534-- be used instead of a 'Lens','Traversal', ... 535-- whenever the type variables don't change upon setting a value. 536-- 537-- @ 538-- 'Data.Complex.Lens._imagPart' :: 'Simple' 'Lens' ('Data.Complex.Complex' a) a 539-- 'Control.Lens.Traversal.traversed' :: 'Simple' ('IndexedTraversal' 'Int') [a] a 540-- @ 541-- 542-- Note: To use this alias in your own code with @'LensLike' f@ or 543-- 'Setter', you may have to turn on @LiberalTypeSynonyms@. 544-- 545-- This is commonly abbreviated as a \"prime\" marker, /e.g./ 'Lens'' = 'Simple' 'Lens'. 546type Simple f s a = f s s a a 547 548------------------------------------------------------------------------------- 549-- Optics 550------------------------------------------------------------------------------- 551 552-- | A valid 'Optic' @l@ should satisfy the laws: 553-- 554-- @ 555-- l 'pure' ≡ 'pure' 556-- l ('Procompose' f g) = 'Procompose' (l f) (l g) 557-- @ 558-- 559-- This gives rise to the laws for 'Equality', 'Iso', 'Prism', 'Lens', 560-- 'Traversal', 'Traversal1', 'Setter', 'Fold', 'Fold1', and 'Getter' as well 561-- along with their index-preserving variants. 562-- 563-- @ 564-- type 'LensLike' f s t a b = 'Optic' (->) f s t a b 565-- @ 566type Optic p f s t a b = p a (f b) -> p s (f t) 567 568-- | @ 569-- type 'Optic'' p f s a = 'Simple' ('Optic' p f) s a 570-- @ 571type Optic' p f s a = Optic p f s s a a 572 573-- | @ 574-- type 'LensLike' f s t a b = 'Optical' (->) (->) f s t a b 575-- @ 576-- 577-- @ 578-- type 'Over' p f s t a b = 'Optical' p (->) f s t a b 579-- @ 580-- 581-- @ 582-- type 'Optic' p f s t a b = 'Optical' p p f s t a b 583-- @ 584type Optical p q f s t a b = p a (f b) -> q s (f t) 585 586-- | @ 587-- type 'Optical'' p q f s a = 'Simple' ('Optical' p q f) s a 588-- @ 589type Optical' p q f s a = Optical p q f s s a a 590 591 592-- | Many combinators that accept a 'Lens' can also accept a 593-- 'Traversal' in limited situations. 594-- 595-- They do so by specializing the type of 'Functor' that they require of the 596-- caller. 597-- 598-- If a function accepts a @'LensLike' f s t a b@ for some 'Functor' @f@, 599-- then they may be passed a 'Lens'. 600-- 601-- Further, if @f@ is an 'Applicative', they may also be passed a 602-- 'Traversal'. 603type LensLike f s t a b = (a -> f b) -> s -> f t 604 605-- | @ 606-- type 'LensLike'' f = 'Simple' ('LensLike' f) 607-- @ 608type LensLike' f s a = LensLike f s s a a 609 610-- | Convenient alias for constructing indexed lenses and their ilk. 611type IndexedLensLike i f s t a b = forall p. Indexable i p => p a (f b) -> s -> f t 612 613-- | Convenient alias for constructing simple indexed lenses and their ilk. 614type IndexedLensLike' i f s a = IndexedLensLike i f s s a a 615 616-- | This is a convenient alias for use when you need to consume either indexed or non-indexed lens-likes based on context. 617type Over p f s t a b = p a (f b) -> s -> f t 618 619-- | This is a convenient alias for use when you need to consume either indexed or non-indexed lens-likes based on context. 620-- 621-- @ 622-- type 'Over'' p f = 'Simple' ('Over' p f) 623-- @ 624type Over' p f s a = Over p f s s a a 625