-- | /Caution/: Improper use of this module can lead to unexpected behaviour if the preconditions of the functions are not met. module Lens.Family.Unchecked ( -- * Adapters -- | An adapter represents a isomorphism between two types or a parametric isomorphism between two families of types. -- For example we can build an adapter between the type families @'Either' a a@ and @('Bool', a)@ as follows: -- -- > timesTwo :: (Functor f, Functor g) => AdapterLike f g (Either a a) (Either b b) (Bool, a) (Bool b) -- > timesTwo f x = fmap yang . f . fmap yin -- > where -- > yin (True, a) = Left a -- > yin (False, a) = Right a -- > yang (Left a) = (True, a) -- > yang (Right a) = (False, a) -- -- /Note/: It is possible to adapters without even depending on @lens-family-core@ by expanding away the type synonym. -- -- > timesTwo :: (Functor f, Functor g) => (g (Either a a) -> f (Either b b)) -> g (Bool, a) -> f (Bool, b) -- -- The function 'adapter' can also be used to construct adapters from a pair of mutually inverse functions. -- * Lenses -- | A lens focuses on a field of record type. -- Lenses can be used to get and/or set the focused field. -- How to create a lens family is best illustrated by the common example of a field of a record: -- -- > data MyRecord a = MyRecord { _myA :: a, _myInt :: Int } -- > -- > -- The use of type variables a and b allow for polymorphic updates. -- > myA :: Functor f => LensLike f (MyRecord a) (MyRecord b) a b -- > myA f (MyRecord a i) = (\b -> MyRecord b i) <$> f a -- > -- > -- The field _myInt is monomorphic, so we can use a 'LensLike'' type. -- > -- However, the structure of the function is exactly the same as for LensLike. -- > myInt :: Functor f => LensLike' f (MyRecord a) Int -- > myInt f (MyRecord a i) = (\i' -> MyRecord a i') <$> f i -- -- See the @lens-family-th@ package to generate this sort of code using Template Haskell. -- -- /Note/: It is possible to build lenses without even depending on @lens-family-core@ by expanding away the type synonym. -- -- > myA :: Functor f => (a -> f b) -> (MyRecord a) -> f (MyRecord b) -- -- You can build lenses for more than just fields of records. -- Any value @l :: Functor f => LensLike f s t a b@ is well-defined when it satisfies the two van Laarhoven lens laws: -- -- * @l Identity === Identity@ -- -- * @l (Compose . fmap f . g) === Compose . fmap (l f) . (l g)@ -- -- The function 'lens' can also be used to construct lenses. -- The resulting lenses will be well-defined so long as their preconditions are satisfied. -- * Traversals -- | If you have zero or more fields of the same type of a record, a traversal can be used to refer to all of them in order. -- Multiple references are made by replacing the 'Functor' constraint of lenses with an 'Control.Applicative.Applicative' constraint. -- Consider the following example of a record with two 'Int' fields. -- -- > data MyRecord = MyRecord { _myA :: Int, _myB :: Int, _myC :: Bool } -- > -- > -- myInts is a traversal over both fields of MyRecord. -- > myInts :: Applicative f => LensLike' f MyRecord Int -- > myInts f (MyRecord a b c) = MyRecord <$> f a <*> f b <*> pure c -- -- If the record and the referenced fields are parametric, you can can build polymrphic traversals. -- Consider the following example of a record with two 'Maybe' fields. -- -- > data MyRecord a = MyRecord { _myA0 :: Maybe a, _myA1 :: Maybe a, myC :: Bool } -- > -- > -- myMaybes is a traversal over both fields of MyRecord. -- > myMaybes :: Applicative f => LensLike f (MyRecord a) (MyRecord b) (Maybe a) (Maybe b) -- > myMaybes f (MyRecord a0 a1 c) = MyRecord <$> f a0 <*> f a1 <*> pure c -- -- /Note/: It is possible to build traversals without even depending on @lens-family-core@ by expanding away the type synonym. -- -- > myMaybes :: Applicative f => (Maybe a -> f (Maybe b)) -> MyRecord a -> f (MyRecord b) -- > myMaybes f (MyRecord a0 a1 c) = MyRecord <$> f a0 <*> f a1 <*> pure c -- -- Unfortunately, there are no helper functions for making traversals. -- In most cases, you must make them by hand. -- -- Any value @t :: Applicative f => LensLike f s t a b@ is well-defined when it satisfies the two van Laarhoven traversal laws: -- -- * @t Identity === Identity@ -- -- * @t (Compose . fmap f . g) === Compose . fmap (t f) . (t g)@ -- -- 'Data.Traversable.traverse' is the canonical traversal for various containers. -- * Prisms -- | A prism focuses on a single variant of a type. -- They can be used to 'Lens.Family.matching' / 'Lens.Family.review' the focused variant. -- Consider the following example. -- -- > data MySum a = MyA a | MyB Int -- > -- > -- myA is a prism for the MyA variant of MySum -- > myA :: (Applicative f, Traversable g) => AdapterLike f g (MySum a) (MySum b) a b -- > myA f = either pure (fmap MyA . f) . traverse h -- > where -- > h (MyA a) = Right a -- > h (MyB n) = Left (MyB n) -- -- This prism can be used with 'Lens.Family.matching' via 'Lens.Family.under': -- -- @ 'Lens.Family.matching' ('Lens.Family.under' myA) :: MySum a -> Either (MySum b) a @ -- -- This prism can be used with 'Lens.Family.review' via 'Lens.Family.over': -- -- @ 'Lens.Family.review' ('Lens.Family.over' myA) :: a -> MySum a @ -- -- /Note/: It is possible to build prisms without even depending on @lens-family-core@ by expanding away the type synonym. -- -- > myA :: (Appicative f, Traversable g) => (g a -> f b) -> g (MySum a) -> f (MySum b) -- -- You can build prism for more than just constructors of sum types. -- Any value @p :: (Applicative f, Traversable g) => AdapterLike f g s t a b@ is well-defined when it satisfies the prism laws: -- -- * @matching (under p) (review (over p) b) === Right b@ -- -- * @(id ||| review (over p)) (matching (under p) s) === s@ -- -- * @left (match (under p)) (matching (under p) s) === left Left (matching (under p) s)@ -- -- The function 'prism' can also be used to construct prisms. -- The resulting prisms will be well-defined so long as their preconditions are satisfied. -- * Grates -- | A grate focuses on the contents of a representable functor. -- In other words, a grate focuses on the codomain of a function type or something isomorphic to a function type. -- They are used to lift operations on this codomain to operations on the larger structure via zipping. -- Consider the following example of a stream of 'Int's. -- -- > data IntStream = IntStream { hd :: Int, tl :: IntStream } -- > -- > -- myInts is a grate over the Ints of IntStream. -- > myInts :: Functor g => GrateLike' g IntStream Int -- > myInts f s = IntStream (f (hd <$> s)) (myInts f (tl <$> s)) -- -- If the contents are parametric, you can can build polymorphic grates. -- Consider the following example of a generic stream. -- -- > data Stream a = Stream { hd :: a, tl :: Stream a } -- > -- > -- myStream is a grate over the contents of a Stream. -- > myStream :: Functor g => GrateLike g (Stream a) (Stream b) a b -- > myStream f s = Stream (f (hd <$> s)) (myStream f (tl <$> s)) -- -- /Note/: It is possible to build grates without even depending on @lens-family-core@ by expanding away the type synonym. -- -- > myStream :: Functor g => (g (Stream a) -> Stream b) -> g a -> b -- -- Any value @t :: Functor g => GrateLike g s t a b@ is a well-defined grate when it satisfies the two van Laarhoven traversal laws: -- -- * @t runIdentity === runIdentity@ -- -- * @t (f . fmap g . runCompose) === (t f) . fmap (t g) . runCompose@ -- -- The function 'grate' can also be used to construct grates from graters. -- The resulting grates will be well-defined so long as the preconditions are satisfied. -- * Grids -- | A grid is both a traversal and a grate. -- When you have a type that is isomorphic to a fixed and finite number of copies of another type, a grid can be used to zip or traverse them. -- Consider the following example of a record with exactly two 'Int' fields. -- -- > data MyRecord = MyRecord { _myA :: Int, _myB :: Int } -- > -- > -- myInts is a grid over both fields of MyRecord. -- > myInts :: (Applicative f, Functor g) => AdapterLike' f g MyRecord Int -- > myInts f r = MyRecord <$> f (_myA <$> r) <*> f (_myB <$> r) -- -- If the record and the referenced fields are parametric, you can can build polymorphic grids. -- Consider the following example of a record with exactly two 'Maybe' fields. -- -- > data MyRecord a = MyRecord { _myA0 :: Maybe a, _myA1 :: Maybe a } -- > -- > -- myMaybes is a traversal over both fields of MyRecord. -- > myMaybes :: (Applicative f, Functor g) => AdapterLike f g (MyRecord a) (MyRecord b) (Maybe a) (Maybe b) -- > myMaybes f r = MyRecord <$> f (_myA0 <$> r) <*> f (_myA1 <$> r) -- -- A grid is converted into a grate by using the 'Lens.Family.over' function, and it is converted to a traversal by using the 'Lens.Family.under' function. -- -- /Note/: It is possible to build grids without even depending on @lens-family-core@ by expanding away the type synonym. -- -- > myMaybes :: (Applicative f, Functor g) => (g (Maybe a) -> f (Maybe b)) -> g (MyRecord a) -> f (MyRecord b) -- -- Unfortunately, there are no helper functions for making grids. -- In most cases, you must make them by hand. -- * Documentation adapter , lens , prism , grate , setting , resetting -- * Types , AdapterLike, AdapterLike' , LensLike, LensLike' , GrateLike, GrateLike' , Identical ) where import Lens.Family.Identical type AdapterLike f g s t a b = (g a -> f b) -> (g s -> f t) type AdapterLike' f g s a = (g a -> f a) -> (g s -> f s) type LensLike f s t a b = (a -> f b) -> (s -> f t) type LensLike' f s a = (a -> f a) -> (s -> f s) type GrateLike g s t a b = (g a -> b) -> (g s -> t) type GrateLike' g s a = (g a -> a) -> (g s -> s) adapter :: (Functor f, Functor g) => (s -> a) -- ^ yin -> (b -> t) -- ^ yang -> AdapterLike f g s t a b -- ^ @ -- adapter :: (s -> a) -> (b -> t) -> Adapter s t a b -- @ -- -- Build an adapter from an isomorphism family. -- -- /Caution/: In order for the generated adapter family to be well-defined, you must ensure that the two isomorphism laws hold: -- -- * @yin . yang === id@ -- -- * @yang . yin === id@ adapter :: (s -> a) -> (b -> t) -> AdapterLike f g s t a b adapter s -> a yin b -> t yang g a -> f b f g s s = b -> t yang (b -> t) -> f b -> f t forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b <$> g a -> f b f (s -> a yin (s -> a) -> g s -> g a forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b <$> g s s) lens :: Functor f => (s -> a) -- ^ getter -> (s -> b -> t) -- ^ setter -> LensLike f s t a b -- ^ @ -- lens :: (s -> a) -> (s -> b -> t) -> Lens s t a b -- @ -- -- Build a lens from a @getter@ and @setter@ family. -- -- /Caution/: In order for the generated lens family to be well-defined, you must ensure that the three lens laws hold: -- -- * @getter (setter s a) === a@ -- -- * @setter s (getter s) === s@ -- -- * @setter (setter s a1) a2 === setter s a2@ lens :: (s -> a) -> (s -> b -> t) -> LensLike f s t a b lens s -> a getter s -> b -> t setter a -> f b f s s = s -> b -> t setter s s (b -> t) -> f b -> f t forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b <$> a -> f b f (s -> a getter s s) grate :: Functor g => (((s -> a) -> b) -> t) -- ^ grater -> GrateLike g s t a b -- ^ @ -- grate :: (((s -> a) -> b) -> t) -> Grate s t a b -- @ -- -- Build a grate from a @grater@ family. -- -- /Caution/: In order for the generated grate family to be well-defined, you must ensure that the two grater laws hold: -- -- * @grater ($ s) === s@ -- -- * @grater (\k -> h (k . grater)) === grater (\k -> h ($ k))@ -- -- Note: The grater laws are that of an algebra for the parameterised continuation monad, `Lens.Family.PCont`. grate :: (((s -> a) -> b) -> t) -> GrateLike g s t a b grate ((s -> a) -> b) -> t grater g a -> b f g s s = ((s -> a) -> b) -> t grater (((s -> a) -> b) -> t) -> ((s -> a) -> b) -> t forall a b. (a -> b) -> a -> b $ \s -> a h -> g a -> b f (s -> a h (s -> a) -> g s -> g a forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b <$> g s s) prism :: (Applicative f, Traversable g) => (s -> Either t a) -- ^ matcher -> (b -> t) -- ^ reviewer -> AdapterLike f g s t a b -- ^ @ -- prism :: (s -> Either t a) -> (b -> t) -> Prism s t a b -- @ -- -- Build a prism from a @matcher@ and @reviewer@ family. -- -- /Caution/: In order for the generated prism family to be well-defined, you must ensure that the three prism laws hold: -- -- * @matcher (reviewer b) === Right b@ -- -- * @(id ||| reviewer) (matcher s) === s@ -- -- * @left matcher (matcher s) === left Left (matcher s)@ prism :: (s -> Either t a) -> (b -> t) -> AdapterLike f g s t a b prism s -> Either t a matcher b -> t reviewer g a -> f b f g s s = (t -> f t) -> (g a -> f t) -> Either t (g a) -> f t forall a c b. (a -> c) -> (b -> c) -> Either a b -> c either t -> f t forall (f :: * -> *) a. Applicative f => a -> f a pure ((b -> t) -> f b -> f t forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b fmap b -> t reviewer (f b -> f t) -> (g a -> f b) -> g a -> f t forall b c a. (b -> c) -> (a -> b) -> a -> c . g a -> f b f) (Either t (g a) -> f t) -> Either t (g a) -> f t forall a b. (a -> b) -> a -> b $ (s -> Either t a) -> g s -> Either t (g a) forall (t :: * -> *) (f :: * -> *) a b. (Traversable t, Applicative f) => (a -> f b) -> t a -> f (t b) traverse s -> Either t a matcher g s s -- | 'setting' promotes a \"semantic editor combinator\" to a modify-only lens. -- To demote a lens to a semantic edit combinator, use the section @(l %~)@ or @over l@ from "Lens.Family". -- -- >>> [("The",0),("quick",1),("brown",1),("fox",2)] & setting map . fstL %~ length -- [(3,0),(5,1),(5,1),(3,2)] -- -- /Caution/: In order for the generated family to be well-defined, you must ensure that the two functors laws hold: -- -- * @sec id === id@ -- -- * @sec f . sec g === sec (f . g)@ setting :: Identical f => ((a -> b) -> s -> t) -- ^ sec (semantic editor combinator) -> LensLike f s t a b setting :: ((a -> b) -> s -> t) -> LensLike f s t a b setting (a -> b) -> s -> t sec a -> f b f = t -> f t forall (f :: * -> *) a. Applicative f => a -> f a pure (t -> f t) -> (s -> t) -> s -> f t forall b c a. (b -> c) -> (a -> b) -> a -> c . (a -> b) -> s -> t sec (f b -> b forall (f :: * -> *) a. Identical f => f a -> a extract (f b -> b) -> (a -> f b) -> a -> b forall b c a. (b -> c) -> (a -> b) -> a -> c . a -> f b f) -- | 'resetting' promotes a \"semantic editor combinator\" to a form of grate that can only lift unary functions. -- To demote a grate to a semantic edit combinator, use @under l@ from "Lens.Family". -- -- /Caution/: In order for the generated family to be well-defined, you must ensure that the two functors laws hold: -- -- * @sec id === id@ -- -- * @sec f . sec g === sec (f . g)@ resetting :: Identical g => ((a -> b) -> s -> t) -- ^ sec (semantic editor combinator) -> GrateLike g s t a b resetting :: ((a -> b) -> s -> t) -> GrateLike g s t a b resetting (a -> b) -> s -> t sec g a -> b f = (a -> b) -> s -> t sec (g a -> b f (g a -> b) -> (a -> g a) -> a -> b forall b c a. (b -> c) -> (a -> b) -> a -> c . a -> g a forall (f :: * -> *) a. Applicative f => a -> f a pure) (s -> t) -> (g s -> s) -> g s -> t forall b c a. (b -> c) -> (a -> b) -> a -> c . g s -> s forall (f :: * -> *) a. Identical f => f a -> a extract