-- Hoogle documentation, generated by Haddock -- See Hoogle, http://www.haskell.org/hoogle/ -- | A Microformats 2 parser. -- -- A parser for Microformats 2 -- (http:/microformats.orgwiki/microformats2), a simple way to -- describe structured information in HTML. @package microformats2-parser @version 1.0.1.9 module Data.Microformats2.Parser.Date data Date Date :: Int -> Int -> Int -> Date data HourType TwentyFourHour :: HourType AMHour :: HourType PMHour :: HourType data Time Time :: Int -> Int -> Int -> Time data DateTime DateTime :: Date -> Time -> DateTime data ZoneType Plus :: ZoneType Minus :: ZoneType data Zone Zone :: ZoneType -> Int -> Int -> Zone data TimeZone TimeZone :: Time -> Zone -> TimeZone data DateTimeZone DateTimeZone :: DateTime -> Zone -> DateTimeZone data DTPart DatePart :: Date -> DTPart TimePart :: Time -> DTPart ZonePart :: Zone -> DTPart TimeZonePart :: TimeZone -> DTPart DateTimePart :: DateTime -> DTPart DateTimeZonePart :: DateTimeZone -> DTPart isDatePart :: DTPart -> Bool isTimePart :: DTPart -> Bool isZonePart :: DTPart -> Bool isTimeZonePart :: DTPart -> Bool isDateTimePart :: DTPart -> Bool isDateTimeZonePart :: DTPart -> Bool parseDate :: Parser Date parseHourType :: Parser HourType parseTime :: Parser Time parseZone :: Parser Zone parseTimeZone :: Parser TimeZone parseDateTime :: Parser DateTime parseDateTimeZone :: Parser DateTimeZone parseDTPart :: Parser DTPart parseDTParts :: (Traversable φ, Monoid (φ DTPart)) => φ Text -> φ DTPart normalizeDTParts :: (Foldable φ) => φ DTPart -> Maybe DTPart instance GHC.Show.Show Data.Microformats2.Parser.Date.DTPart instance GHC.Show.Show Data.Microformats2.Parser.Date.DateTimeZone instance GHC.Show.Show Data.Microformats2.Parser.Date.TimeZone instance GHC.Show.Show Data.Microformats2.Parser.Date.Zone instance GHC.Show.Show Data.Microformats2.Parser.Date.DateTime instance GHC.Show.Show Data.Microformats2.Parser.Date.Time instance GHC.Show.Show Data.Microformats2.Parser.Date.Date module Data.Microformats2.Jf2 mf2ToJf2 :: Value -> Value module Data.Microformats2.Parser.Util if' :: Bool -> Maybe a -> Maybe a unless' :: Bool -> Maybe a -> Maybe a listToMaybeList :: [α] -> Maybe [α] stripQueryString :: Text -> Text groupBy' :: (Ord β) => (α -> β) -> [α] -> [(β, [α])] expandSnd :: Foldable φ => φ ([α], β) -> [(α, β)] resolveURI :: Maybe URI -> Text -> Text collapseWhitespace :: Text -> Text emptyVal :: Value -> Bool renderInner :: Element -> Text vsingleton :: Maybe Text -> Value extractVector :: Value -> Array mergeProps :: (τ, [(α, Value)]) -> (τ, Value) -- | Functors representing data structures that can be traversed from left -- to right. -- -- A definition of traverse must satisfy the following laws: -- --

naturality t . traverse f = -- traverse (t . f) for every applicative transformation -- t
identity traverse Identity = -- Identity
composition traverse (Compose . -- fmap g . f) = Compose . fmap (traverse g) . -- traverse f

-- -- A definition of sequenceA must satisfy the following laws: -- --

naturality t . sequenceA = -- sequenceA . fmap t for every applicative -- transformation t
identity sequenceA . fmap Identity -- = Identity
composition sequenceA . fmap -- Compose = Compose . fmap sequenceA . -- sequenceA

-- -- where an applicative transformation is a function -- --

--   t :: (Applicative f, Applicative g) => f a -> g a
--

-- -- preserving the Applicative operations, i.e. -- --

```
t (pure x) = pure x
```
```
t (x <*> y) = t x <*> t
--   y
```

-- -- and the identity functor Identity and composition of functors -- Compose are defined as -- --

--   newtype Identity a = Identity a
--   
--   instance Functor Identity where
--     fmap f (Identity x) = Identity (f x)
--   
--   instance Applicative Identity where
--     pure x = Identity x
--     Identity f <*> Identity x = Identity (f x)
--   
--   newtype Compose f g a = Compose (f (g a))
--   
--   instance (Functor f, Functor g) => Functor (Compose f g) where
--     fmap f (Compose x) = Compose (fmap (fmap f) x)
--   
--   instance (Applicative f, Applicative g) => Applicative (Compose f g) where
--     pure x = Compose (pure (pure x))
--     Compose f <*> Compose x = Compose ((<*>) <$> f <*> x)
--

-- -- (The naturality law is implied by parametricity.) -- -- Instances are similar to Functor, e.g. given a data type -- --

--   data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
--

-- -- a suitable instance would be -- --

--   instance Traversable Tree where
--      traverse f Empty = pure Empty
--      traverse f (Leaf x) = Leaf <$> f x
--      traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r
--

-- -- This is suitable even for abstract types, as the laws for -- <*> imply a form of associativity. -- -- The superclass instances should satisfy the following: -- --

In the Functor instance, fmap should be equivalent -- to traversal with the identity applicative functor -- (fmapDefault).
In the Foldable instance, foldMap should be -- equivalent to traversal with a constant applicative functor -- (foldMapDefault).

class (Functor t, Foldable t) => Traversable (t :: * -> *) -- | Map each element of a structure to an action, evaluate these actions -- from left to right, and collect the results. For a version that -- ignores the results see traverse_. traverse :: (Traversable t, Applicative f) => a -> f b -> t a -> f t b -- | The class of contravariant functors. -- -- Whereas in Haskell, one can think of a Functor as containing or -- producing values, a contravariant functor is a functor that can be -- thought of as consuming values. -- -- As an example, consider the type of predicate functions a -> -- Bool. One such predicate might be negative x = x < 0, -- which classifies integers as to whether they are negative. However, -- given this predicate, we can re-use it in other situations, providing -- we have a way to map values to integers. For instance, we can -- use the negative predicate on a person's bank balance to work -- out if they are currently overdrawn: -- --

--   newtype Predicate a = Predicate { getPredicate :: a -> Bool }
--   
--   instance Contravariant Predicate where
--     contramap f (Predicate p) = Predicate (p . f)
--                                            |   `- First, map the input...
--                                            `----- then apply the predicate.
--   
--   overdrawn :: Predicate Person
--   overdrawn = contramap personBankBalance negative
--

-- -- Any instance should be subject to the following laws: -- --

--   contramap id = id
--   contramap f . contramap g = contramap (g . f)
--

-- -- Note, that the second law follows from the free theorem of the type of -- contramap and the first law, so you need only check that the -- former condition holds. class Contravariant (f :: * -> *) contramap :: Contravariant f => a -> b -> f b -> f a -- | Replace all locations in the output with the same value. The default -- definition is contramap . const, but this may -- be overridden with a more efficient version. (>$) :: Contravariant f => b -> f b -> f a -- | Encode a Foldable as a JSON array. foldable :: (Foldable t, ToJSON a) => t a -> Encoding type GToJSON = GToJSON Value type GToEncoding = GToJSON Encoding -- | Helper function to use with liftToJSON, see -- listEncoding. listValue :: () => a -> Value -> [a] -> Value -- | Helper function to use with liftToEncoding. Useful when writing -- own ToJSON1 instances. -- --

--   newtype F a = F [a]
--   
--   -- This instance encodes String as an array of chars
--   instance ToJSON1 F where
--       liftToJSON     tj _ (F xs) = liftToJSON     tj (listValue    tj) xs
--       liftToEncoding te _ (F xs) = liftToEncoding te (listEncoding te) xs
--   
--   instance FromJSON1 F where
--       liftParseJSON p _ v = F <$> liftParseJSON p (listParser p) v
--

listEncoding :: () => a -> Encoding -> [a] -> Encoding -- | Lift the standard toEncoding function through the type -- constructor. toEncoding2 :: (ToJSON2 f, ToJSON a, ToJSON b) => f a b -> Encoding -- | Lift the standard toJSON function through the type constructor. toJSON2 :: (ToJSON2 f, ToJSON a, ToJSON b) => f a b -> Value -- | Lift the standard toEncoding function through the type -- constructor. toEncoding1 :: (ToJSON1 f, ToJSON a) => f a -> Encoding -- | Lift the standard toJSON function through the type constructor. toJSON1 :: (ToJSON1 f, ToJSON a) => f a -> Value -- | Contravariant map, as ToJSONKeyFunction is a contravariant -- functor. contramapToJSONKeyFunction :: () => b -> a -> ToJSONKeyFunction a -> ToJSONKeyFunction b -- | Helper for creating textual keys. -- --

--   instance ToJSONKey MyKey where
--       toJSONKey = toJSONKeyText myKeyToText
--         where
--           myKeyToText = Text.pack . show -- or showt from text-show
--

toJSONKeyText :: () => a -> Text -> ToJSONKeyFunction a -- | A configurable generic JSON encoder. This function applied to -- defaultOptions is used as the default for liftToEncoding -- when the type is an instance of Generic1. genericLiftToEncoding :: (Generic1 f, GToJSON Encoding One Rep1 f) => Options -> a -> Encoding -> [a] -> Encoding -> f a -> Encoding -- | A configurable generic JSON encoder. This function applied to -- defaultOptions is used as the default for toEncoding -- when the type is an instance of Generic. genericToEncoding :: (Generic a, GToJSON Encoding Zero Rep a) => Options -> a -> Encoding -- | A configurable generic JSON creator. This function applied to -- defaultOptions is used as the default for liftToJSON -- when the type is an instance of Generic1. genericLiftToJSON :: (Generic1 f, GToJSON Value One Rep1 f) => Options -> a -> Value -> [a] -> Value -> f a -> Value -- | A configurable generic JSON creator. This function applied to -- defaultOptions is used as the default for toJSON when -- the type is an instance of Generic. genericToJSON :: (Generic a, GToJSON Value Zero Rep a) => Options -> a -> Value -- | A ToArgs value either stores nothing (for ToJSON) or it -- stores the two function arguments that encode occurrences of the type -- parameter (for ToJSON1). data ToArgs res arity a [NoToArgs] :: ToArgs res Zero a [To1Args] :: ToArgs res One a -- | A type that can be converted to JSON. -- -- Instances in general must specify toJSON and -- should (but don't need to) specify toEncoding. -- -- An example type and instance: -- --

--   -- Allow ourselves to write Text literals.
--   {-# LANGUAGE OverloadedStrings #-}
--   
--   data Coord = Coord { x :: Double, y :: Double }
--   
--   instance ToJSON Coord where
--     toJSON (Coord x y) = object ["x" .= x, "y" .= y]
--   
--     toEncoding (Coord x y) = pairs ("x" .= x <> "y" .= y)
--

-- -- Instead of manually writing your ToJSON instance, there are two -- options to do it automatically: -- --

Data.Aeson.TH provides Template Haskell functions which -- will derive an instance at compile time. The generated instance is -- optimized for your type so it will probably be more efficient than the -- following option.
The compiler can provide a default generic implementation for -- toJSON.

-- -- To use the second, simply add a deriving Generic -- clause to your datatype and declare a ToJSON instance. If you -- require nothing other than defaultOptions, it is sufficient to -- write (and this is the only alternative where the default -- toJSON implementation is sufficient): -- --

--   {-# LANGUAGE DeriveGeneric #-}
--   
--   import GHC.Generics
--   
--   data Coord = Coord { x :: Double, y :: Double } deriving Generic
--   
--   instance ToJSON Coord where
--       toEncoding = genericToEncoding defaultOptions
--

-- -- If on the other hand you wish to customize the generic decoding, you -- have to implement both methods: -- --

--   customOptions = defaultOptions
--                   { fieldLabelModifier = map toUpper
--                   }
--   
--   instance ToJSON Coord where
--       toJSON     = genericToJSON customOptions
--       toEncoding = genericToEncoding customOptions
--

-- -- Previous versions of this library only had the toJSON method. -- Adding toEncoding had to reasons: -- --

toEncoding is more efficient for the common case that the output -- of toJSON is directly serialized to a ByteString. -- Further, expressing either method in terms of the other would be -- non-optimal.
The choice of defaults allows a smooth transition for existing -- users: Existing instances that do not define toEncoding still -- compile and have the correct semantics. This is ensured by making the -- default implementation of toEncoding use toJSON. This -- produces correct results, but since it performs an intermediate -- conversion to a Value, it will be less efficient than directly -- emitting an Encoding. (this also means that specifying nothing -- more than instance ToJSON Coord would be sufficient as a -- generically decoding instance, but there probably exists no good -- reason to not specify toEncoding in new instances.)

class ToJSON a -- | Convert a Haskell value to a JSON-friendly intermediate type. toJSON :: ToJSON a => a -> Value -- | Encode a Haskell value as JSON. -- -- The default implementation of this method creates an intermediate -- Value using toJSON. This provides source-level -- compatibility for people upgrading from older versions of this -- library, but obviously offers no performance advantage. -- -- To benefit from direct encoding, you must provide an -- implementation for this method. The easiest way to do so is by having -- your types implement Generic using the DeriveGeneric -- extension, and then have GHC generate a method body as follows. -- --

--   instance ToJSON Coord where
--       toEncoding = genericToEncoding defaultOptions
--

toEncoding :: ToJSON a => a -> Encoding toJSONList :: ToJSON a => [a] -> Value toEncodingList :: ToJSON a => [a] -> Encoding -- | A key-value pair for encoding a JSON object. class KeyValue kv (.=) :: (KeyValue kv, ToJSON v) => Text -> v -> kv -- | Typeclass for types that can be used as the key of a map-like -- container (like Map or HashMap). For example, since -- Text has a ToJSONKey instance and Char has a -- ToJSON instance, we can encode a value of type Map -- Text Char: -- --

--   >>> LBC8.putStrLn $ encode $ Map.fromList [("foo" :: Text, 'a')]
--   {"foo":"a"}
--

-- -- Since Int also has a ToJSONKey instance, we can -- similarly write: -- --

--   >>> LBC8.putStrLn $ encode $ Map.fromList [(5 :: Int, 'a')]
--   {"5":"a"}
--

-- -- JSON documents only accept strings as object keys. For any type from -- base that has a natural textual representation, it can be -- expected that its ToJSONKey instance will choose that -- representation. -- -- For data types that lack a natural textual representation, an -- alternative is provided. The map-like container is represented as a -- JSON array instead of a JSON object. Each value in the array is an -- array with exactly two values. The first is the key and the second is -- the value. -- -- For example, values of type '[Text]' cannot be encoded to a string, so -- a Map with keys of type '[Text]' is encoded as follows: -- --

--   >>> LBC8.putStrLn $ encode $ Map.fromList [(["foo","bar","baz" :: Text], 'a')]
--   [[["foo","bar","baz"],"a"]]
--

-- -- The default implementation of ToJSONKey chooses this method of -- encoding a key, using the ToJSON instance of the type. -- -- To use your own data type as the key in a map, all that is needed is -- to write a ToJSONKey (and possibly a FromJSONKey) -- instance for it. If the type cannot be trivially converted to and from -- Text, it is recommended that ToJSONKeyValue is used. -- Since the default implementations of the typeclass methods can build -- this from a ToJSON instance, there is nothing that needs to be -- written: -- --

--   data Foo = Foo { fooAge :: Int, fooName :: Text }
--     deriving (Eq,Ord,Generic)
--   instance ToJSON Foo
--   instance ToJSONKey Foo
--

-- -- That's it. We can now write: -- --

--   >>> let m = Map.fromList [(Foo 4 "bar",'a'),(Foo 6 "arg",'b')]
--   
--   >>> LBC8.putStrLn $ encode m
--   [[{"fooName":"bar","fooAge":4},"a"],[{"fooName":"arg","fooAge":6},"b"]]
--

-- -- The next case to consider is if we have a type that is a newtype -- wrapper around Text. The recommended approach is to use -- generalized newtype deriving: -- --

--   newtype RecordId = RecordId { getRecordId :: Text}
--     deriving (Eq,Ord,ToJSONKey)
--

-- -- Then we may write: -- --

--   >>> LBC8.putStrLn $ encode $ Map.fromList [(RecordId "abc",'a')]
--   {"abc":"a"}
--

-- -- Simple sum types are a final case worth considering. Suppose we have: -- --

--   data Color = Red | Green | Blue
--     deriving (Show,Read,Eq,Ord)
--

-- -- It is possible to get the ToJSONKey instance for free as we did -- with Foo. However, in this case, we have a natural way to go -- to and from Text that does not require any escape sequences. -- So, in this example, ToJSONKeyText will be used instead of -- ToJSONKeyValue. The Show instance can be used to help -- write ToJSONKey: -- --

--   instance ToJSONKey Color where
--     toJSONKey = ToJSONKeyText f g
--       where f = Text.pack . show
--             g = text . Text.pack . show
--             -- text function is from Data.Aeson.Encoding
--

-- -- The situation of needing to turning function a -> Text -- into a ToJSONKeyFunction is common enough that a special -- combinator is provided for it. The above instance can be rewritten as: -- --

--   instance ToJSONKey Color where
--     toJSONKey = toJSONKeyText (Text.pack . show)
--

-- -- The performance of the above instance can be improved by not using -- String as an intermediate step when converting to Text. -- One option for improving performance would be to use template haskell -- machinery from the text-show package. However, even with the -- approach, the Encoding (a wrapper around a bytestring builder) -- is generated by encoding the Text to a ByteString, an -- intermediate step that could be avoided. The fastest possible -- implementation would be: -- --

--   -- Assuming that OverloadedStrings is enabled
--   instance ToJSONKey Color where
--     toJSONKey = ToJSONKeyText f g
--       where f x = case x of {Red -> "Red";Green ->"Green";Blue -> "Blue"}
--             g x = case x of {Red -> text "Red";Green -> text "Green";Blue -> text "Blue"}
--             -- text function is from Data.Aeson.Encoding
--

-- -- This works because GHC can lift the encoded values out of the case -- statements, which means that they are only evaluated once. This -- approach should only be used when there is a serious need to maximize -- performance. class ToJSONKey a -- | Strategy for rendering the key for a map-like container. toJSONKey :: ToJSONKey a => ToJSONKeyFunction a -- | This is similar in spirit to the showsList method of -- Show. It makes it possible to give String keys special -- treatment without using OverlappingInstances. End users -- should always be able to use the default implementation of this -- method. toJSONKeyList :: ToJSONKey a => ToJSONKeyFunction [a] data ToJSONKeyFunction a -- | key is encoded to string, produces object ToJSONKeyText :: !a -> Text -> !a -> Encoding' Text -> ToJSONKeyFunction a -- | key is encoded to value, produces array ToJSONKeyValue :: !a -> Value -> !a -> Encoding -> ToJSONKeyFunction a -- | Lifting of the ToJSON class to unary type constructors. -- -- Instead of manually writing your ToJSON1 instance, there are -- two options to do it automatically: -- --

Data.Aeson.TH provides Template Haskell functions which -- will derive an instance at compile time. The generated instance is -- optimized for your type so it will probably be more efficient than the -- following option.
The compiler can provide a default generic implementation for -- toJSON1.

-- -- To use the second, simply add a deriving Generic1 -- clause to your datatype and declare a ToJSON1 instance for your -- datatype without giving definitions for liftToJSON or -- liftToEncoding. -- -- For example: -- --

--   {-# LANGUAGE DeriveGeneric #-}
--   
--   import GHC.Generics
--   
--   data Pair = Pair { pairFst :: a, pairSnd :: b } deriving Generic1
--   
--   instance ToJSON a => ToJSON1 (Pair a)
--

-- -- If the default implementation doesn't give exactly the results you -- want, you can customize the generic encoding with only a tiny amount -- of effort, using genericLiftToJSON and -- genericLiftToEncoding with your preferred Options: -- --

--   customOptions = defaultOptions
--                   { fieldLabelModifier = map toUpper
--                   }
--   
--   instance ToJSON a => ToJSON1 (Pair a) where
--       liftToJSON     = genericLiftToJSON customOptions
--       liftToEncoding = genericLiftToEncoding customOptions
--

-- -- See also ToJSON. class ToJSON1 (f :: * -> *) liftToJSON :: ToJSON1 f => a -> Value -> [a] -> Value -> f a -> Value liftToJSONList :: ToJSON1 f => a -> Value -> [a] -> Value -> [f a] -> Value liftToEncoding :: ToJSON1 f => a -> Encoding -> [a] -> Encoding -> f a -> Encoding liftToEncodingList :: ToJSON1 f => a -> Encoding -> [a] -> Encoding -> [f a] -> Encoding -- | Lifting of the ToJSON class to binary type constructors. -- -- Instead of manually writing your ToJSON2 instance, -- Data.Aeson.TH provides Template Haskell functions which will -- derive an instance at compile time. -- -- The compiler cannot provide a default generic implementation for -- liftToJSON2, unlike toJSON and liftToJSON. class ToJSON2 (f :: * -> * -> *) liftToJSON2 :: ToJSON2 f => a -> Value -> [a] -> Value -> b -> Value -> [b] -> Value -> f a b -> Value liftToJSONList2 :: ToJSON2 f => a -> Value -> [a] -> Value -> b -> Value -> [b] -> Value -> [f a b] -> Value liftToEncoding2 :: ToJSON2 f => a -> Encoding -> [a] -> Encoding -> b -> Encoding -> [b] -> Encoding -> f a b -> Encoding liftToEncodingList2 :: ToJSON2 f => a -> Encoding -> [a] -> Encoding -> b -> Encoding -> [b] -> Encoding -> [f a b] -> Encoding -- | Encode a series of key/value pairs, separated by commas. pairs :: Series -> Encoding -- | Make Encoding from Builder. -- -- Use with care! You have to make sure that the passed Builder is a -- valid JSON Encoding! unsafeToEncoding :: () => Builder -> Encoding' a -- | Acquire the underlying bytestring builder. fromEncoding :: Encoding' tag -> Builder -- | Often used synonym for Encoding'. type Encoding = Encoding' Value -- | A series of values that, when encoded, should be separated by commas. -- Since 0.11.0.0, the .= operator is overloaded to create -- either (Text, Value) or Series. You can use Series -- when encoding directly to a bytestring builder as in the following -- example: -- --

--   toEncoding (Person name age) = pairs ("name" .= name <> "age" .= age)
--

data Series -- | Helper for use in combination with .:? to provide default -- values for optional JSON object fields. -- -- This combinator is most useful if the key and value can be absent from -- an object without affecting its validity and we know a default value -- to assign in that case. If the key and value are mandatory, use -- .: instead. -- -- Example usage: -- --

--   v1 <- o .:? "opt_field_with_dfl" .!= "default_val"
--   v2 <- o .:  "mandatory_field"
--   v3 <- o .:? "opt_field2"
--

(.!=) :: () => Parser Maybe a -> a -> Parser a -- | Variant of .:! with explicit parser function. explicitParseFieldMaybe' :: () => Value -> Parser a -> Object -> Text -> Parser Maybe a -- | Variant of .:? with explicit parser function. explicitParseFieldMaybe :: () => Value -> Parser a -> Object -> Text -> Parser Maybe a -- | Variant of .: with explicit parser function. -- -- E.g. explicitParseField parseJSON1 :: -- (FromJSON1 f, FromJSON a) -> Object -> -- Text -> Parser (f a) explicitParseField :: () => Value -> Parser a -> Object -> Text -> Parser a -- | Function variant of .:!. parseFieldMaybe' :: FromJSON a => Object -> Text -> Parser Maybe a -- | Function variant of .:?. parseFieldMaybe :: FromJSON a => Object -> Text -> Parser Maybe a -- | Function variant of .:. parseField :: FromJSON a => Object -> Text -> Parser a -- | Retrieve the value associated with the given key of an Object. -- The result is Nothing if the key is not present or -- empty if the value cannot be converted to the desired type. -- -- This differs from .:? by attempting to parse Null the -- same as any other JSON value, instead of interpreting it as -- Nothing. (.:!) :: FromJSON a => Object -> Text -> Parser Maybe a -- | Retrieve the value associated with the given key of an Object. -- The result is Nothing if the key is not present or if its value -- is Null, or empty if the value cannot be converted to -- the desired type. -- -- This accessor is most useful if the key and value can be absent from -- an object without affecting its validity. If the key and value are -- mandatory, use .: instead. (.:?) :: FromJSON a => Object -> Text -> Parser Maybe a -- | Retrieve the value associated with the given key of an Object. -- The result is empty if the key is not present or the value -- cannot be converted to the desired type. -- -- This accessor is appropriate if the key and value must be -- present in an object for it to be valid. If the key and value are -- optional, use .:? instead. (.:) :: FromJSON a => Object -> Text -> Parser a -- | Convert a value from JSON, failing if the types do not match. fromJSON :: FromJSON a => Value -> Result a -- | Decode a nested JSON-encoded string. withEmbeddedJSON :: () => String -> Value -> Parser a -> Value -> Parser a -- | withBool expected f value applies f to the -- Bool when value is a Bool and fails using -- typeMismatch expected otherwise. withBool :: () => String -> Bool -> Parser a -> Value -> Parser a -- | withScientific expected f value applies f to -- the Scientific number when value is a Number -- and fails using typeMismatch expected otherwise. . -- Warning: If you are converting from a scientific to an -- unbounded type such as Integer you may want to add a -- restriction on the size of the exponent (see -- withBoundedScientific) to prevent malicious input from filling -- up the memory of the target system. withScientific :: () => String -> Scientific -> Parser a -> Value -> Parser a -- | withArray expected f value applies f to the -- Array when value is an Array and fails using -- typeMismatch expected otherwise. withArray :: () => String -> Array -> Parser a -> Value -> Parser a -- | withText expected f value applies f to the -- Text when value is a String and fails using -- typeMismatch expected otherwise. withText :: () => String -> Text -> Parser a -> Value -> Parser a -- | withObject expected f value applies f to the -- Object when value is an Object and fails using -- typeMismatch expected otherwise. withObject :: () => String -> Object -> Parser a -> Value -> Parser a -- | Helper function to use with liftParseJSON. See -- listEncoding. listParser :: () => Value -> Parser a -> Value -> Parser [a] -- | Lift the standard parseJSON function through the type -- constructor. parseJSON2 :: (FromJSON2 f, FromJSON a, FromJSON b) => Value -> Parser f a b -- | Lift the standard parseJSON function through the type -- constructor. parseJSON1 :: (FromJSON1 f, FromJSON a) => Value -> Parser f a -- | Fail parsing due to a type mismatch, with a descriptive message. -- -- Example usage: -- --

--   instance FromJSON Coord where
--     parseJSON (Object v) = {- type matches, life is good -}
--     parseJSON wat        = typeMismatch "Coord" wat
--

typeMismatch :: () => String -> Value -> Parser a -- | Same as fmap. Provided for the consistency with -- ToJSONKeyFunction. mapFromJSONKeyFunction :: () => a -> b -> FromJSONKeyFunction a -> FromJSONKeyFunction b -- | Semantically the same as coerceFromJSONKeyFunction = fmap coerce = -- coerce. -- -- See note on fromJSONKeyCoerce. coerceFromJSONKeyFunction :: Coercible a b => FromJSONKeyFunction a -> FromJSONKeyFunction b -- | Construct FromJSONKeyFunction for types coercible from -- Text. This conversion is still unsafe, as Hashable and -- Eq instances of a should be compatible with -- Text i.e. hash values should be equal for wrapped values as -- well. This property will always be maintained if the Hashable -- and Eq instances are derived with generalized newtype deriving. -- compatible with Text i.e. hash values be equal for wrapped -- values as well. -- -- On pre GHC 7.8 this is unconstrainted function. fromJSONKeyCoerce :: Coercible Text a => FromJSONKeyFunction a -- | A configurable generic JSON decoder. This function applied to -- defaultOptions is used as the default for liftParseJSON -- when the type is an instance of Generic1. genericLiftParseJSON :: (Generic1 f, GFromJSON One Rep1 f) => Options -> Value -> Parser a -> Value -> Parser [a] -> Value -> Parser f a -- | A configurable generic JSON decoder. This function applied to -- defaultOptions is used as the default for parseJSON when -- the type is an instance of Generic. genericParseJSON :: (Generic a, GFromJSON Zero Rep a) => Options -> Value -> Parser a -- | Class of generic representation types that can be converted from JSON. class GFromJSON arity (f :: * -> *) -- | This method (applied to defaultOptions) is used as the default -- generic implementation of parseJSON (if the arity is -- Zero) or liftParseJSON (if the arity is -- One). gParseJSON :: GFromJSON arity f => Options -> FromArgs arity a -> Value -> Parser f a -- | A FromArgs value either stores nothing (for FromJSON) or -- it stores the two function arguments that decode occurrences of the -- type parameter (for FromJSON1). data FromArgs arity a [NoFromArgs] :: FromArgs Zero a [From1Args] :: FromArgs One a -- | A type that can be converted from JSON, with the possibility of -- failure. -- -- In many cases, you can get the compiler to generate parsing code for -- you (see below). To begin, let's cover writing an instance by hand. -- -- There are various reasons a conversion could fail. For example, an -- Object could be missing a required key, an Array could -- be of the wrong size, or a value could be of an incompatible type. -- -- The basic ways to signal a failed conversion are as follows: -- --

empty and mzero work, but are terse and -- uninformative;
fail yields a custom error message;
typeMismatch produces an informative message for cases when -- the value encountered is not of the expected type.

-- -- An example type and instance using typeMismatch: -- --

--   -- Allow ourselves to write Text literals.
--   {-# LANGUAGE OverloadedStrings #-}
--   
--   data Coord = Coord { x :: Double, y :: Double }
--   
--   instance FromJSON Coord where
--       parseJSON (Object v) = Coord
--           <$> v .: "x"
--           <*> v .: "y"
--   
--       -- We do not expect a non-Object value here.
--       -- We could use mzero to fail, but typeMismatch
--       -- gives a much more informative error message.
--       parseJSON invalid    = typeMismatch "Coord" invalid
--

-- -- For this common case of only being concerned with a single type of -- JSON value, the functions withObject, withNumber, etc. -- are provided. Their use is to be preferred when possible, since they -- are more terse. Using withObject, we can rewrite the above -- instance (assuming the same language extension and data type) as: -- --

--   instance FromJSON Coord where
--       parseJSON = withObject "Coord" $ \v -> Coord
--           <$> v .: "x"
--           <*> v .: "y"
--

-- -- Instead of manually writing your FromJSON instance, there are -- two options to do it automatically: -- --

Data.Aeson.TH provides Template Haskell functions which -- will derive an instance at compile time. The generated instance is -- optimized for your type so it will probably be more efficient than the -- following option.
The compiler can provide a default generic implementation for -- parseJSON.

-- -- To use the second, simply add a deriving Generic -- clause to your datatype and declare a FromJSON instance for -- your datatype without giving a definition for parseJSON. -- -- For example, the previous example can be simplified to just: -- --

--   {-# LANGUAGE DeriveGeneric #-}
--   
--   import GHC.Generics
--   
--   data Coord = Coord { x :: Double, y :: Double } deriving Generic
--   
--   instance FromJSON Coord
--

-- -- The default implementation will be equivalent to parseJSON = -- genericParseJSON defaultOptions; If you need -- different options, you can customize the generic decoding by defining: -- --

--   customOptions = defaultOptions
--                   { fieldLabelModifier = map toUpper
--                   }
--   
--   instance FromJSON Coord where
--       parseJSON = genericParseJSON customOptions
--

class FromJSON a parseJSON :: FromJSON a => Value -> Parser a parseJSONList :: FromJSON a => Value -> Parser [a] -- | Read the docs for ToJSONKey first. This class is a conversion -- in the opposite direction. If you have a newtype wrapper around -- Text, the recommended way to define instances is with -- generalized newtype deriving: -- --

--   newtype SomeId = SomeId { getSomeId :: Text }
--     deriving (Eq,Ord,Hashable,FromJSONKey)
--

class FromJSONKey a -- | Strategy for parsing the key of a map-like container. fromJSONKey :: FromJSONKey a => FromJSONKeyFunction a -- | This is similar in spirit to the readList method of -- Read. It makes it possible to give String keys special -- treatment without using OverlappingInstances. End users -- should always be able to use the default implementation of this -- method. fromJSONKeyList :: FromJSONKey a => FromJSONKeyFunction [a] -- | This type is related to ToJSONKeyFunction. If -- FromJSONKeyValue is used in the FromJSONKey instance, -- then ToJSONKeyValue should be used in the ToJSONKey -- instance. The other three data constructors for this type all -- correspond to ToJSONKeyText. Strictly speaking, -- FromJSONKeyTextParser is more powerful than -- FromJSONKeyText, which is in turn more powerful than -- FromJSONKeyCoerce. For performance reasons, these exist as -- three options instead of one. data FromJSONKeyFunction a -- | uses coerce (unsafeCoerce in older GHCs) FromJSONKeyCoerce :: !CoerceText a -> FromJSONKeyFunction a -- | conversion from Text that always succeeds FromJSONKeyText :: !Text -> a -> FromJSONKeyFunction a -- | conversion from Text that may fail FromJSONKeyTextParser :: !Text -> Parser a -> FromJSONKeyFunction a -- | conversion for non-textual keys FromJSONKeyValue :: !Value -> Parser a -> FromJSONKeyFunction a -- | Lifting of the FromJSON class to unary type constructors. -- -- Instead of manually writing your FromJSON1 instance, there are -- two options to do it automatically: -- --

Data.Aeson.TH provides Template Haskell functions which -- will derive an instance at compile time. The generated instance is -- optimized for your type so it will probably be more efficient than the -- following option.
The compiler can provide a default generic implementation for -- liftParseJSON.

-- -- To use the second, simply add a deriving Generic1 -- clause to your datatype and declare a FromJSON1 instance for -- your datatype without giving a definition for liftParseJSON. -- -- For example: -- --

--   {-# LANGUAGE DeriveGeneric #-}
--   
--   import GHC.Generics
--   
--   data Pair a b = Pair { pairFst :: a, pairSnd :: b } deriving Generic1
--   
--   instance FromJSON a => FromJSON1 (Pair a)
--

-- -- If the default implementation doesn't give exactly the results you -- want, you can customize the generic decoding with only a tiny amount -- of effort, using genericLiftParseJSON with your preferred -- Options: -- --

--   customOptions = defaultOptions
--                   { fieldLabelModifier = map toUpper
--                   }
--   
--   instance FromJSON a => FromJSON1 (Pair a) where
--       liftParseJSON = genericLiftParseJSON customOptions
--

class FromJSON1 (f :: * -> *) liftParseJSON :: FromJSON1 f => Value -> Parser a -> Value -> Parser [a] -> Value -> Parser f a liftParseJSONList :: FromJSON1 f => Value -> Parser a -> Value -> Parser [a] -> Value -> Parser [f a] -- | Lifting of the FromJSON class to binary type constructors. -- -- Instead of manually writing your FromJSON2 instance, -- Data.Aeson.TH provides Template Haskell functions which will -- derive an instance at compile time. class FromJSON2 (f :: * -> * -> *) liftParseJSON2 :: FromJSON2 f => Value -> Parser a -> Value -> Parser [a] -> Value -> Parser b -> Value -> Parser [b] -> Value -> Parser f a b liftParseJSONList2 :: FromJSON2 f => Value -> Parser a -> Value -> Parser [a] -> Value -> Parser b -> Value -> Parser [b] -> Value -> Parser [f a b] -- | Better version of camelTo. Example where it works better: -- --

--   camelTo '_' 'CamelAPICase' == "camel_apicase"
--   camelTo2 '_' 'CamelAPICase' == "camel_api_case"
--

camelTo2 :: Char -> String -> String -- | Converts from CamelCase to another lower case, interspersing the -- character between all capital letters and their previous entries, -- except those capital letters that appear together, like API. -- -- For use by Aeson template haskell calls. -- --

--   camelTo '_' 'CamelCaseAPI' == "camel_case_api"
--

camelTo :: Char -> String -> String -- | Default TaggedObject SumEncoding options: -- --

--   defaultTaggedObject = TaggedObject
--                         { tagFieldName      = "tag"
--                         , contentsFieldName = "contents"
--                         }
--

defaultTaggedObject :: SumEncoding -- | Default encoding Options: -- --

--   Options
--   { fieldLabelModifier      = id
--   , constructorTagModifier  = id
--   , allNullaryToStringTag   = True
--   , omitNothingFields       = False
--   , sumEncoding             = defaultTaggedObject
--   , unwrapUnaryRecords      = False
--   , tagSingleConstructors   = False
--   }
--

defaultOptions :: Options -- | A handler function to handle previous errors and return to normal -- execution. parserCatchError :: () => Parser a -> JSONPath -> String -> Parser a -> Parser a -- | Throw a parser error with an additional path. parserThrowError :: () => JSONPath -> String -> Parser a -- | If the inner Parser failed, modify the failure message using -- the provided function. This allows you to create more descriptive -- error messages. For example: -- --

--   parseJSON (Object o) = modifyFailure
--       ("Parsing of the Foo value failed: " ++)
--       (Foo <$> o .: "someField")
--

-- -- Since 0.6.2.0 modifyFailure :: () => String -> String -> Parser a -> Parser a -- | Create a Value from a list of name/value Pairs. If -- duplicate keys arise, earlier keys and their associated values win. object :: [Pair] -> Value -- | Run a Parser with an Either result type. If the parse -- fails, the Left payload will contain an error message. parseEither :: () => a -> Parser b -> a -> Either String b -- | Run a Parser with a Maybe result type. parseMaybe :: () => a -> Parser b -> a -> Maybe b -- | Run a Parser. parse :: () => a -> Parser b -> a -> Result b -- | The empty object. emptyObject :: Value -- | The empty array. emptyArray :: Value -- | The result of running a Parser. data Result a Error :: String -> Result a Success :: a -> Result a -- | A JSON parser. N.B. This might not fit your usual understanding of -- "parser". Instead you might like to think of Parser as a "parse -- result", i.e. a parser to which the input has already been applied. data Parser a -- | A JSON "object" (key/value map). type Object = HashMap Text Value -- | A JSON "array" (sequence). type Array = Vector Value -- | A JSON value represented as a Haskell value. data Value Object :: !Object -> Value Array :: !Array -> Value String :: !Text -> Value Number :: !Scientific -> Value Bool :: !Bool -> Value Null :: Value -- | A newtype wrapper for UTCTime that uses the same non-standard -- serialization format as Microsoft .NET, whose System.DateTime -- type is by default serialized to JSON as in the following example: -- --

--   /Date(1302547608878)/
--

-- -- The number represents milliseconds since the Unix epoch. newtype DotNetTime DotNetTime :: UTCTime -> DotNetTime -- | Acquire the underlying value. [fromDotNetTime] :: DotNetTime -> UTCTime -- | A key/value pair for an Object. type Pair = (Text, Value) -- | Options that specify how to encode/decode your datatype to/from JSON. -- -- Options can be set using record syntax on defaultOptions with -- the fields below. data Options -- | Specifies how to encode constructors of a sum datatype. data SumEncoding -- | A constructor will be encoded to an object with a field -- tagFieldName which specifies the constructor tag (modified by -- the constructorTagModifier). If the constructor is a record the -- encoded record fields will be unpacked into this object. So make sure -- that your record doesn't have a field with the same label as the -- tagFieldName. Otherwise the tag gets overwritten by the encoded -- value of that field! If the constructor is not a record the encoded -- constructor contents will be stored under the contentsFieldName -- field. TaggedObject :: String -> String -> SumEncoding [tagFieldName] :: SumEncoding -> String [contentsFieldName] :: SumEncoding -> String -- | Constructor names won't be encoded. Instead only the contents of the -- constructor will be encoded as if the type had a single constructor. -- JSON encodings have to be disjoint for decoding to work properly. -- -- When decoding, constructors are tried in the order of definition. If -- some encodings overlap, the first one defined will succeed. -- -- Note: Nullary constructors are encoded as strings (using -- constructorTagModifier). Having a nullary constructor alongside -- a single field constructor that encodes to a string leads to -- ambiguity. -- -- Note: Only the last error is kept when decoding, so in the case -- of malformed JSON, only an error for the last constructor will be -- reported. UntaggedValue :: SumEncoding -- | A constructor will be encoded to an object with a single field named -- after the constructor tag (modified by the -- constructorTagModifier) which maps to the encoded contents of -- the constructor. ObjectWithSingleField :: SumEncoding -- | A constructor will be encoded to a 2-element array where the first -- element is the tag of the constructor (modified by the -- constructorTagModifier) and the second element the encoded -- contents of the constructor. TwoElemArray :: SumEncoding -- | A type-level indicator that ToJSON or FromJSON is -- being derived generically. data Zero -- | A type-level indicator that ToJSON1 or FromJSON1 is -- being derived generically. data One -- | A bifunctor is a type constructor that takes two type arguments and is -- a functor in both arguments. That is, unlike with -- Functor, a type constructor such as Either does not need -- to be partially applied for a Bifunctor instance, and the -- methods in this class permit mapping functions over the Left -- value or the Right value, or both at the same time. -- -- Formally, the class Bifunctor represents a bifunctor from -- Hask -> Hask. -- -- Intuitively it is a bifunctor where both the first and second -- arguments are covariant. -- -- You can define a Bifunctor by either defining bimap or -- by defining both first and second. -- -- If you supply bimap, you should ensure that: -- --

--   bimap id id ≡ id
--

-- -- If you supply first and second, ensure: -- --

--   first id ≡ id
--   second id ≡ id
--

-- -- If you supply both, you should also ensure: -- --

--   bimap f g ≡ first f . second g
--

-- -- These ensure by parametricity: -- --

--   bimap  (f . g) (h . i) ≡ bimap f h . bimap g i
--   first  (f . g) ≡ first  f . first  g
--   second (f . g) ≡ second f . second g
--

class Bifunctor (p :: * -> * -> *) -- | Map over both arguments at the same time. -- --

--   bimap f g ≡ first f . second g
--

-- --

Examples

-- --

--   >>> bimap toUpper (+1) ('j', 3)
--   ('J',4)
--

-- --

--   >>> bimap toUpper (+1) (Left 'j')
--   Left 'J'
--

-- --

--   >>> bimap toUpper (+1) (Right 3)
--   Right 4
--

bimap :: Bifunctor p => a -> b -> c -> d -> p a c -> p b d -- | Identity functor and monad. (a non-strict monad) newtype Identity a Identity :: a -> Identity a [runIdentity] :: Identity a -> a -- | The Const functor. newtype Const a (b :: k) :: forall k. () => * -> k -> * Const :: a -> Const a [getConst] :: Const a -> a -- | & is a reverse application operator. This provides -- notational convenience. Its precedence is one higher than that of the -- forward application operator $, which allows & to be -- nested in $. -- --

--   >>> 5 & (+1) & show
--   "6"
--

(&) :: () => a -> a -> b -> b infixl 1 & -- | Flipped version of <$>. -- --

--   (<&>) = flip fmap
--

-- --

Examples

-- -- Apply (+1) to a list, a Just and a Right: -- --

--   >>> Just 2 <&> (+1)
--   Just 3
--

-- --

--   >>> [1,2,3] <&> (+1)
--   [2,3,4]
--

-- --

--   >>> Right 3 <&> (+1)
--   Right 4
--

(<&>) :: Functor f => f a -> a -> b -> f b infixl 1 <&> -- | A class for types with a default value. class Default a -- | The default value for this type. def :: Default a => a parseLBS :: ByteString -> Document sinkDoc :: MonadThrow m => ConduitT ByteString o m Document -- | Formally, the class Profunctor represents a profunctor from -- Hask -> Hask. -- -- Intuitively it is a bifunctor where the first argument is -- contravariant and the second argument is covariant. -- -- You can define a Profunctor by either defining dimap or -- by defining both lmap and rmap. -- -- If you supply dimap, you should ensure that: -- --

--   dimap id id ≡ id
--

-- -- If you supply lmap and rmap, ensure: -- --

--   lmap id ≡ id
--   rmap id ≡ id
--

-- -- If you supply both, you should also ensure: -- --

--   dimap f g ≡ lmap f . rmap g
--

-- -- These ensure by parametricity: -- --

--   dimap (f . g) (h . i) ≡ dimap g h . dimap f i
--   lmap (f . g) ≡ lmap g . lmap f
--   rmap (f . g) ≡ rmap f . rmap g
--

class Profunctor (p :: * -> * -> *) -- | Map over both arguments at the same time. -- --

--   dimap f g ≡ lmap f . rmap g
--

dimap :: Profunctor p => a -> b -> c -> d -> p b c -> p a d -- | Map the first argument contravariantly. -- --

--   lmap f ≡ dimap f id
--

lmap :: Profunctor p => a -> b -> p b c -> p a c -- | Map the second argument covariantly. -- --

--   rmap ≡ dimap id
--

rmap :: Profunctor p => b -> c -> p a b -> p a c defaultFieldRules :: LensRules -- | Generate overloaded field accessors based on field names which are -- only prefixed with an underscore (e.g. _name), not -- additionally with the type name (e.g. _fooName). -- -- This might be the desired behaviour in case the -- DuplicateRecordFields language extension is used in order to -- get rid of the necessity to prefix each field name with the type name. -- -- As an example: -- --

--   data Foo a  = Foo { _x :: Int, _y :: a }
--   newtype Bar = Bar { _x :: Char }
--   makeFieldsNoPrefix ''Foo
--   makeFieldsNoPrefix ''Bar
--

-- -- will create classes -- --

--   class HasX s a | s -> a where
--     x :: Lens' s a
--   class HasY s a | s -> a where
--     y :: Lens' s a
--

-- -- together with instances -- --

--   instance HasX (Foo a) Int
--   instance HasY (Foo a) a where
--   instance HasX Bar Char where
--

-- -- For details, see classUnderscoreNoPrefixFields. -- --

--   makeFieldsNoPrefix = makeLensesWith classUnderscoreNoPrefixFields
--

makeFieldsNoPrefix :: Name -> DecsQ -- | Generate overloaded field accessors. -- -- e.g -- --

--   data Foo a = Foo { _fooX :: Int, _fooY :: a }
--   newtype Bar = Bar { _barX :: Char }
--   makeFields ''Foo
--   makeFields ''Bar
--

-- -- will create -- --

--   _fooXLens :: Lens' (Foo a) Int
--   _fooYLens :: Lens (Foo a) (Foo b) a b
--   class HasX s a | s -> a where
--     x :: Lens' s a
--   instance HasX (Foo a) Int where
--     x = _fooXLens
--   class HasY s a | s -> a where
--     y :: Lens' s a
--   instance HasY (Foo a) a where
--     y = _fooYLens
--   _barXLens :: Iso' Bar Char
--   instance HasX Bar Char where
--     x = _barXLens
--

-- -- For details, see camelCaseFields. -- --

--   makeFields = makeLensesWith defaultFieldRules
--

makeFields :: Name -> DecsQ -- | A FieldNamer for abbreviatedFields. abbreviatedNamer :: FieldNamer -- | Field rules fields in the form prefixFieldname or -- _prefixFieldname If you want all fields to be lensed, then there -- is no reason to use an _ before the prefix. If any of the -- record fields leads with an _ then it is assume a field -- without an _ should not have a lens created. -- -- Note that prefix may be any string of characters that are not -- uppercase letters. (In particular, it may be arbitrary string of -- lowercase letters and numbers) This is the behavior that -- defaultFieldRules had in lens 4.4 and earlier. abbreviatedFields :: LensRules -- | A FieldNamer for classUnderscoreNoPrefixFields. classUnderscoreNoPrefixNamer :: FieldNamer -- | Field rules for fields in the form _fieldname (the leading -- underscore is mandatory). -- -- Note: The primary difference to camelCaseFields is that -- for classUnderscoreNoPrefixFields the field names are not -- expected to be prefixed with the type name. This might be the desired -- behaviour when the DuplicateRecordFields extension is -- enabled. classUnderscoreNoPrefixFields :: LensRules -- | A FieldNamer for camelCaseFields. camelCaseNamer :: FieldNamer -- | Field rules for fields in the form prefixFieldname or -- _prefixFieldname If you want all fields to be lensed, then there -- is no reason to use an _ before the prefix. If any of the -- record fields leads with an _ then it is assume a field -- without an _ should not have a lens created. -- -- Note: The prefix must be the same as the typename -- (with the first letter lowercased). This is a change from lens -- versions before lens 4.5. If you want the old behaviour, use -- makeLensesWith abbreviatedFields camelCaseFields :: LensRules -- | A FieldNamer for underscoreFields. underscoreNamer :: FieldNamer -- | Field rules for fields in the form _prefix_fieldname underscoreFields :: LensRules -- | Build Wrapped instance for a given newtype makeWrapped :: Name -> DecsQ -- | Declare lenses for each records in the given declarations, using the -- specified LensRules. Any record syntax in the input will be -- stripped off. declareLensesWith :: LensRules -> DecsQ -> DecsQ -- |

--   declareFields = declareLensesWith defaultFieldRules
--

declareFields :: DecsQ -> DecsQ -- | Build Wrapped instance for each newtype. declareWrapped :: DecsQ -> DecsQ -- | Generate a Prism for each constructor of each data type. -- -- e.g. -- --

--   declarePrisms [d|
--     data Exp = Lit Int | Var String | Lambda{ bound::String, body::Exp }
--     |]
--

-- -- will create -- --

--   data Exp = Lit Int | Var String | Lambda { bound::String, body::Exp }
--   _Lit :: Prism' Exp Int
--   _Var :: Prism' Exp String
--   _Lambda :: Prism' Exp (String, Exp)
--

declarePrisms :: DecsQ -> DecsQ -- | Similar to makeClassyFor, but takes a declaration quote. declareClassyFor :: [(String, (String, String))] -> [(String, String)] -> DecsQ -> DecsQ -- | For each record in the declaration quote, make lenses and traversals -- for it, and create a class when the type has no arguments. All record -- syntax in the input will be stripped off. -- -- e.g. -- --

--   declareClassy [d|
--     data Foo = Foo { fooX, fooY :: Int }
--       deriving Show
--     |]
--

-- -- will create -- --

--   data Foo = Foo Int Int deriving Show
--   class HasFoo t where
--     foo :: Lens' t Foo
--   instance HasFoo Foo where foo = id
--   fooX, fooY :: HasFoo t => Lens' t Int
--

declareClassy :: DecsQ -> DecsQ -- | Similar to makeLensesFor, but takes a declaration quote. declareLensesFor :: [(String, String)] -> DecsQ -> DecsQ -- | Make lenses for all records in the given declaration quote. All record -- syntax in the input will be stripped off. -- -- e.g. -- --

--   declareLenses [d|
--     data Foo = Foo { fooX, fooY :: Int }
--       deriving Show
--     |]
--

-- -- will create -- --

--   data Foo = Foo Int Int deriving Show
--   fooX, fooY :: Lens' Foo Int
--

declareLenses :: DecsQ -> DecsQ -- | Build lenses with a custom configuration. makeLensesWith :: LensRules -> Name -> DecsQ -- | Derive lenses and traversals, using a named wrapper class, and -- specifying explicit pairings of (fieldName, traversalName). -- -- Example usage: -- --

--   makeClassyFor "HasFoo" "foo" [("_foo", "fooLens"), ("bar", "lbar")] ''Foo
--

makeClassyFor :: String -> String -> [(String, String)] -> Name -> DecsQ -- | Derive lenses and traversals, specifying explicit pairings of -- (fieldName, lensName). -- -- If you map multiple names to the same label, and it is present in the -- same constructor then this will generate a Traversal. -- -- e.g. -- --

--   makeLensesFor [("_foo", "fooLens"), ("baz", "lbaz")] ''Foo
--   makeLensesFor [("_barX", "bar"), ("_barY", "bar")] ''Bar
--

makeLensesFor :: [(String, String)] -> Name -> DecsQ -- | Make lenses and traversals for a type, and create a class when the -- type has no arguments. Works the same as makeClassy except that -- (a) it expects that record field names do not begin with an -- underscore, (b) all record fields are made into lenses, and (c) the -- resulting lens is prefixed with an underscore. makeClassy_ :: Name -> DecsQ -- | Make lenses and traversals for a type, and create a class when the -- type has no arguments. -- -- e.g. -- --

--   data Foo = Foo { _fooX, _fooY :: Int }
--   makeClassy ''Foo
--

-- -- will create -- --

--   class HasFoo t where
--     foo :: Lens' t Foo
--     fooX :: Lens' t Int
--     fooX = foo . go where go f (Foo x y) = (\x' -> Foo x' y) <$> f x
--     fooY :: Lens' t Int
--     fooY = foo . go where go f (Foo x y) = (\y' -> Foo x y') <$> f y
--   instance HasFoo Foo where
--     foo = id
--

-- --

--   makeClassy = makeLensesWith classyRules
--

makeClassy :: Name -> DecsQ -- | Build lenses (and traversals) with a sensible default configuration. -- -- e.g. -- --

--   data FooBar
--     = Foo { _x, _y :: Int }
--     | Bar { _x :: Int }
--   makeLenses ''FooBar
--

-- -- will create -- --

--   x :: Lens' FooBar Int
--   x f (Foo a b) = (\a' -> Foo a' b) <$> f a
--   x f (Bar a)   = Bar <$> f a
--   y :: Traversal' FooBar Int
--   y f (Foo a b) = (\b' -> Foo a  b') <$> f b
--   y _ c@(Bar _) = pure c
--

-- --

--   makeLenses = makeLensesWith lensRules
--

makeLenses :: Name -> DecsQ -- | A LensRules used by makeClassy_. classyRules_ :: LensRules -- | Rules for making lenses and traversals that precompose another -- Lens. classyRules :: LensRules -- | Create a FieldNamer from a mapping function. If the function -- returns [], it creates no lens for the field. mappingNamer :: String -> [String] -> FieldNamer -- | Create a FieldNamer from explicit pairings of (fieldName, -- lensName). lookingupNamer :: [(String, String)] -> FieldNamer -- | Construct a LensRules value for generating top-level -- definitions using the given map from field names to definition names. lensRulesFor :: [(String, String)] -> LensRules -- | A FieldNamer that strips the _ off of the field name, -- lowercases the name, and skips the field if it doesn't start with an -- '_'. underscoreNoPrefixNamer :: FieldNamer -- | Rules for making fairly simple partial lenses, ignoring the special -- cases for isomorphisms and traversals, and not making any classes. It -- uses underscoreNoPrefixNamer. lensRules :: LensRules -- | Lens' to access the option for naming "classy" lenses. lensClass :: Lens' LensRules ClassyNamer -- | Lens' to access the convention for naming fields in our -- LensRules. lensField :: Lens' LensRules FieldNamer -- | Create the class if the constructor is Simple and the -- lensClass rule matches. createClass :: Lens' LensRules Bool -- | Generate optics using lazy pattern matches. This can allow fields of -- an undefined value to be initialized with lenses: -- --

--   data Foo = Foo {_x :: Int, _y :: Bool}
--     deriving Show
--   
--   makeLensesWith (lensRules & generateLazyPatterns .~ True) ''Foo
--

-- --

--   > undefined & x .~ 8 & y .~ True
--   Foo {_x = 8, _y = True}
--

-- -- The downside of this flag is that it can lead to space-leaks and -- code-size/compile-time increases when generated for large records. By -- default this flag is turned off, and strict optics are generated. -- -- When using lazy optics the strict optic can be recovered by composing -- with $!: -- --

--   strictOptic = ($!) . lazyOptic
--

generateLazyPatterns :: Lens' LensRules Bool -- | Generate "updateable" optics when True. When False, -- Folds will be generated instead of Traversals and -- Getters will be generated instead of Lenses. This mode -- is intended to be used for types with invariants which must be -- maintained by "smart" constructors. generateUpdateableOptics :: Lens' LensRules Bool -- | Indicate whether or not to supply the signatures for the generated -- lenses. -- -- Disabling this can be useful if you want to provide a more restricted -- type signature or if you want to supply hand-written haddocks. generateSignatures :: Lens' LensRules Bool -- | Generate "simple" optics even when type-changing optics are possible. -- (e.g. Lens' instead of Lens) simpleLenses :: Lens' LensRules Bool -- | Rules to construct lenses for data fields. data LensRules -- | The rule to create function names of lenses for data fields. -- -- Although it's sometimes useful, you won't need the first two arguments -- most of the time. type FieldNamer = Name -> [Name] -> Name -> [DefName] -- | Name to give to generated field optics. data DefName -- | Simple top-level definiton name TopName :: Name -> DefName -- | makeFields-style class name and method name MethodName :: Name -> Name -> DefName -- | The optional rule to create a class and method around a monomorphic -- data type. If this naming convention is provided, it generates a -- "classy" lens. type ClassyNamer = Name -> Maybe (Name, Name) -- | Generate a Prism for each constructor of a data type and -- combine them into a single class. No Isos are created. Reviews are -- created for constructors with existentially quantified constructors -- and GADTs. -- -- e.g. -- --

--   data FooBarBaz a
--     = Foo Int
--     | Bar a
--     | Baz Int Char
--   makeClassyPrisms ''FooBarBaz
--

-- -- will create -- --

--   class AsFooBarBaz s a | s -> a where
--     _FooBarBaz :: Prism' s (FooBarBaz a)
--     _Foo :: Prism' s Int
--     _Bar :: Prism' s a
--     _Baz :: Prism' s (Int,Char)
--   
--     _Foo = _FooBarBaz . _Foo
--     _Bar = _FooBarBaz . _Bar
--     _Baz = _FooBarBaz . _Baz
--   
--   instance AsFooBarBaz (FooBarBaz a) a
--

-- -- Generate an As class of prisms. Names are selected by prefixing -- the constructor name with an underscore. Constructors with multiple -- fields will construct Prisms to tuples of those fields. makeClassyPrisms :: Name -> DecsQ -- | Generate a Prism for each constructor of a data type. Isos -- generated when possible. Reviews are created for constructors with -- existentially quantified constructors and GADTs. -- -- e.g. -- --

--   data FooBarBaz a
--     = Foo Int
--     | Bar a
--     | Baz Int Char
--   makePrisms ''FooBarBaz
--

-- -- will create -- --

--   _Foo :: Prism' (FooBarBaz a) Int
--   _Bar :: Prism (FooBarBaz a) (FooBarBaz b) a b
--   _Baz :: Prism' (FooBarBaz a) (Int, Char)
--

makePrisms :: Name -> DecsQ -- | An indexed version of at. -- --

--   >>> Map.fromList [(1,"world")] ^@. iat 1
--   (1,Just "world")
--

-- --

--   >>> iat 1 %@~ (\i x -> if odd i then Just "hello" else Nothing) $ Map.empty
--   fromList [(1,"hello")]
--

-- --

--   >>> iat 2 %@~ (\i x -> if odd i then Just "hello" else Nothing) $ Map.empty
--   fromList []
--

iat :: At m => Index m -> IndexedLens' Index m m Maybe IxValue m -- | Delete the value associated with a key in a Map-like container -- --

--   sans k = at k .~ Nothing
--

sans :: At m => Index m -> m -> m -- | A definition of ix for types with an At instance. This -- is the default if you don't specify a definition for ix. ixAt :: At m => Index m -> Traversal' m IxValue m -- | An indexed version of ix. -- --

--   >>> Seq.fromList [a,b,c,d] & iix 2 %@~ f'
--   fromList [a,b,f' 2 c,d]
--

-- --

--   >>> Seq.fromList [a,b,c,d] & iix 2 .@~ h
--   fromList [a,b,h 2,d]
--

-- --

--   >>> Seq.fromList [a,b,c,d] ^@? iix 2
--   Just (2,c)
--

-- --

--   >>> Seq.fromList [] ^@? iix 2
--   Nothing
--

iix :: Ixed m => Index m -> IndexedTraversal' Index m m IxValue m -- | An indexed version of contains. -- --

--   >>> IntSet.fromList [1,2,3,4] ^@. icontains 3
--   (3,True)
--

-- --

--   >>> IntSet.fromList [1,2,3,4] ^@. icontains 5
--   (5,False)
--

-- --

--   >>> IntSet.fromList [1,2,3,4] & icontains 3 %@~ \i x -> if odd i then not x else x
--   fromList [1,2,4]
--

-- --

--   >>> IntSet.fromList [1,2,3,4] & icontains 3 %@~ \i x -> if even i then not x else x
--   fromList [1,2,3,4]
--

icontains :: Contains m => Index m -> IndexedLens' Index m m Bool -- | This class provides a simple Lens that lets you view (and -- modify) information about whether or not a container contains a given -- Index. class Contains m -- |

--   >>> IntSet.fromList [1,2,3,4] ^. contains 3
--   True
--

-- --

--   >>> IntSet.fromList [1,2,3,4] ^. contains 5
--   False
--

-- --

--   >>> IntSet.fromList [1,2,3,4] & contains 3 .~ False
--   fromList [1,2,4]
--

contains :: Contains m => Index m -> Lens' m Bool -- | This provides a common notion of a value at an index that is shared by -- both Ixed and At. -- | Provides a simple Traversal lets you traverse the value -- at a given key in a Map or element at an ordinal position in a -- list or Seq. class Ixed m -- | NB: Setting the value of this Traversal will only set -- the value in at if it is already present. -- -- If you want to be able to insert missing values, you want -- at. -- --

--   >>> Seq.fromList [a,b,c,d] & ix 2 %~ f
--   fromList [a,b,f c,d]
--

-- --

--   >>> Seq.fromList [a,b,c,d] & ix 2 .~ e
--   fromList [a,b,e,d]
--

-- --

--   >>> Seq.fromList [a,b,c,d] ^? ix 2
--   Just c
--

-- --

--   >>> Seq.fromList [] ^? ix 2
--   Nothing
--

ix :: Ixed m => Index m -> Traversal' m IxValue m -- | At provides a Lens that can be used to read, write or -- delete the value associated with a key in a Map-like container -- on an ad hoc basis. -- -- An instance of At should satisfy: -- --

--   ix k ≡ at k . traverse
--

class Ixed m => At m -- |

--   >>> Map.fromList [(1,"world")] ^.at 1
--   Just "world"
--

-- --

--   >>> at 1 ?~ "hello" $ Map.empty
--   fromList [(1,"hello")]
--

-- -- Note: Map-like containers form a reasonable instance, -- but not Array-like ones, where you cannot satisfy the -- Lens laws. at :: At m => Index m -> Lens' m Maybe IxValue m -- | Extract each element of a (potentially monomorphic) container. -- -- Notably, when applied to a tuple, this generalizes both to -- arbitrary homogeneous tuples. -- --

--   >>> (1,2,3) & each *~ 10
--   (10,20,30)
--

-- -- It can also be used on monomorphic containers like Text or -- ByteString. -- --

--   >>> over each Char.toUpper ("hello"^.Text.packed)
--   "HELLO"
--

-- --

--   >>> ("hello","world") & each.each %~ Char.toUpper
--   ("HELLO","WORLD")
--

class Each s t a b | s -> a, t -> b, s b -> t, t a -> s each :: Each s t a b => Traversal s t a b -- | Implement plate operation for a type using its Generic -- instance. gplate :: (Generic a, GPlated a Rep a) => Traversal' a a -- | The original uniplate combinator, implemented in terms of -- Plated as a Lens. -- --

--   parts ≡ partsOf plate
--

-- -- The resulting Lens is safer to use as it ignores -- 'over-application' and deals gracefully with under-application, but it -- is only a proper Lens if you don't change the list -- length! parts :: Plated a => Lens' a [a] -- | Fold the immediate children of a Plated container. -- --

--   composOpFold z c f = foldrOf plate (c . f) z
--

composOpFold :: Plated a => b -> b -> b -> b -> a -> b -> a -> b -- | Perform a fold-like computation on each value, technically a -- paramorphism. -- --

--   para ≡ paraOf plate
--

para :: Plated a => a -> [r] -> r -> a -> r -- | Perform a fold-like computation on each value, technically a -- paramorphism. -- --

--   paraOf :: Fold a a -> (a -> [r] -> r) -> a -> r
--

paraOf :: () => Getting Endo [a] a a -> a -> [r] -> r -> a -> r -- | Extract one level of holes from a container in a region -- specified by one Traversal, using another. -- --

--   holesOnOf b l ≡ holesOf (b . l)
--

-- --

--   holesOnOf :: Iso' s a       -> Iso' a a                -> s -> [Pretext (->) a a s]
--   holesOnOf :: Lens' s a      -> Lens' a a               -> s -> [Pretext (->) a a s]
--   holesOnOf :: Traversal' s a -> Traversal' a a          -> s -> [Pretext (->) a a s]
--   holesOnOf :: Lens' s a      -> IndexedLens' i a a      -> s -> [Pretext (Indexed i) a a s]
--   holesOnOf :: Traversal' s a -> IndexedTraversal' i a a -> s -> [Pretext (Indexed i) a a s]
--

holesOnOf :: Conjoined p => LensLike Bazaar p r r s t a b -> Over p Bazaar p r r a b r r -> s -> [Pretext p r r t] -- | An alias for holesOf, provided for consistency with the other -- combinators. -- --

--   holesOn ≡ holesOf
--

-- --

--   holesOn :: Iso' s a                -> s -> [Pretext (->) a a s]
--   holesOn :: Lens' s a               -> s -> [Pretext (->) a a s]
--   holesOn :: Traversal' s a          -> s -> [Pretext (->) a a s]
--   holesOn :: IndexedLens' i s a      -> s -> [Pretext (Indexed i) a a s]
--   holesOn :: IndexedTraversal' i s a -> s -> [Pretext (Indexed i) a a s]
--

holesOn :: Conjoined p => Over p Bazaar p a a s t a a -> s -> [Pretext p a a t] -- | The one-level version of context. This extracts a list of the -- immediate children as editable contexts. -- -- Given a context you can use pos to see the values, peek -- at what the structure would be like with an edited result, or simply -- extract the original structure. -- --

--   propChildren x = children l x == map pos (holes l x)
--   propId x = all (== x) [extract w | w <- holes l x]
--

-- --

--   holes = holesOf plate
--

holes :: Plated a => a -> [Pretext ((->) :: * -> * -> *) a a a] -- | Return a list of all of the editable contexts for every location in -- the structure in an areas indicated by a user supplied -- Traversal, recursively using another user-supplied -- Traversal to walk each layer. -- --

--   contextsOnOf :: Traversal' s a -> Traversal' a a -> s -> [Context a a s]
--

contextsOnOf :: () => ATraversal s t a a -> ATraversal' a a -> s -> [Context a a t] -- | Return a list of all of the editable contexts for every location in -- the structure in an areas indicated by a user supplied -- Traversal, recursively using plate. -- --

--   contextsOn b ≡ contextsOnOf b plate
--

-- --

--   contextsOn :: Plated a => Traversal' s a -> s -> [Context a a s]
--

contextsOn :: Plated a => ATraversal s t a a -> s -> [Context a a t] -- | Return a list of all of the editable contexts for every location in -- the structure, recursively, using a user-specified Traversal to -- walk each layer. -- --

--   propUniverse l x = universeOf l x == map pos (contextsOf l x)
--   propId l x = all (== x) [extract w | w <- contextsOf l x]
--

-- --

--   contextsOf :: Traversal' a a -> a -> [Context a a a]
--

contextsOf :: () => ATraversal' a a -> a -> [Context a a a] -- | Return a list of all of the editable contexts for every location in -- the structure, recursively. -- --

--   propUniverse x = universe x == map pos (contexts x)
--   propId x = all (== x) [extract w | w <- contexts x]
--

-- --

--   contexts ≡ contextsOf plate
--

contexts :: Plated a => a -> [Context a a a] -- | Transform every element in a tree that lies in a region indicated by a -- supplied Traversal, walking with a user supplied -- Traversal in a bottom-up manner with a monadic effect. -- --

--   transformMOnOf :: Monad m => Traversal' s a -> Traversal' a a -> (a -> m a) -> s -> m s
--

transformMOnOf :: Monad m => LensLike WrappedMonad m s t a b -> LensLike WrappedMonad m a b a b -> b -> m b -> s -> m t -- | Transform every element in a tree using a user supplied -- Traversal in a bottom-up manner with a monadic effect. -- --

--   transformMOf :: Monad m => Traversal' a a -> (a -> m a) -> a -> m a
--

transformMOf :: Monad m => LensLike WrappedMonad m a b a b -> b -> m b -> a -> m b -- | Transform every element in the tree in a region indicated by a -- supplied Traversal, in a bottom-up manner, monadically. -- --

--   transformMOn :: (Monad m, Plated a) => Traversal' s a -> (a -> m a) -> s -> m s
--

transformMOn :: (Monad m, Plated a) => LensLike WrappedMonad m s t a a -> a -> m a -> s -> m t -- | Transform every element in the tree, in a bottom-up manner, -- monadically. transformM :: (Monad m, Plated a) => a -> m a -> a -> m a -- | Transform every element in a region indicated by a Setter by -- recursively applying another Setter in a bottom-up manner. -- --

--   transformOnOf :: Setter' s a -> Traversal' a a -> (a -> a) -> s -> s
--   transformOnOf :: Setter' s a -> Setter' a a    -> (a -> a) -> s -> s
--

transformOnOf :: () => ASetter s t a b -> ASetter a b a b -> b -> b -> s -> t -- | Transform every element by recursively applying a given Setter -- in a bottom-up manner. -- --

--   transformOf :: Traversal' a a -> (a -> a) -> a -> a
--   transformOf :: Setter' a a    -> (a -> a) -> a -> a
--

transformOf :: () => ASetter a b a b -> b -> b -> a -> b -- | Transform every element in the tree in a bottom-up manner over a -- region indicated by a Setter. -- --

--   transformOn :: Plated a => Traversal' s a -> (a -> a) -> s -> s
--   transformOn :: Plated a => Setter' s a    -> (a -> a) -> s -> s
--

transformOn :: Plated a => ASetter s t a a -> a -> a -> s -> t -- | Transform every element in the tree, in a bottom-up manner. -- -- For example, replacing negative literals with literals: -- --

--   negLits = transform $ \x -> case x of
--     Neg (Lit i) -> Lit (negate i)
--     _           -> x
--

transform :: Plated a => a -> a -> a -> a -- | Given a Fold that knows how to locate immediate children, fold -- all of the transitive descendants of a node, including itself that lie -- in a region indicated by another Fold. -- --

--   cosmosOnOf :: Fold s a -> Fold a a -> Fold s a
--

cosmosOnOf :: (Applicative f, Contravariant f) => LensLike' f s a -> LensLike' f a a -> LensLike' f s a -- | Given a Fold that knows how to find Plated parts of a -- container fold them and all of their descendants, recursively. -- --

--   cosmosOn :: Plated a => Fold s a -> Fold s a
--

cosmosOn :: (Applicative f, Contravariant f, Plated a) => LensLike' f s a -> LensLike' f s a -- | Given a Fold that knows how to locate immediate children, fold -- all of the transitive descendants of a node, including itself. -- --

--   cosmosOf :: Fold a a -> Fold a a
--

cosmosOf :: (Applicative f, Contravariant f) => LensLike' f a a -> LensLike' f a a -- | Fold over all transitive descendants of a Plated container, -- including itself. cosmos :: Plated a => Fold a a -- | Given a Fold that knows how to locate immediate children, -- retrieve all of the transitive descendants of a node, including itself -- that lie in a region indicated by another Fold. -- --

--   toListOf l ≡ universeOnOf l ignored
--

universeOnOf :: () => Getting [a] s a -> Getting [a] a a -> s -> [a] -- | Given a Fold that knows how to find Plated parts of a -- container retrieve them and all of their descendants, recursively. universeOn :: Plated a => Getting [a] s a -> s -> [a] -- | Given a Fold that knows how to locate immediate children, -- retrieve all of the transitive descendants of a node, including -- itself. -- --

--   universeOf :: Fold a a -> a -> [a]
--

universeOf :: () => Getting [a] a a -> a -> [a] -- | Retrieve all of the transitive descendants of a Plated -- container, including itself. universe :: Plated a => a -> [a] -- | Rewrite by applying a monadic rule everywhere inside of a structure -- located by a user-specified Traversal, using a user-specified -- Traversal for recursion. Ensures that the rule cannot be -- applied anywhere in the result. rewriteMOnOf :: Monad m => LensLike WrappedMonad m s t a b -> LensLike WrappedMonad m a b a b -> b -> m Maybe a -> s -> m t -- | Rewrite by applying a monadic rule everywhere inside of a structure -- located by a user-specified Traversal. Ensures that the rule -- cannot be applied anywhere in the result. rewriteMOn :: (Monad m, Plated a) => LensLike WrappedMonad m s t a a -> a -> m Maybe a -> s -> m t -- | Rewrite by applying a monadic rule everywhere you recursing with a -- user-specified Traversal. Ensures that the rule cannot be -- applied anywhere in the result. rewriteMOf :: Monad m => LensLike WrappedMonad m a b a b -> b -> m Maybe a -> a -> m b -- | Rewrite by applying a monadic rule everywhere you can. Ensures that -- the rule cannot be applied anywhere in the result. rewriteM :: (Monad m, Plated a) => a -> m Maybe a -> a -> m a -- | Rewrite recursively over part of a larger structure using a specified -- Setter. -- --

--   rewriteOnOf :: Iso' s a       -> Iso' a a       -> (a -> Maybe a) -> s -> s
--   rewriteOnOf :: Lens' s a      -> Lens' a a      -> (a -> Maybe a) -> s -> s
--   rewriteOnOf :: Traversal' s a -> Traversal' a a -> (a -> Maybe a) -> s -> s
--   rewriteOnOf :: Setter' s a    -> Setter' a a    -> (a -> Maybe a) -> s -> s
--

rewriteOnOf :: () => ASetter s t a b -> ASetter a b a b -> b -> Maybe a -> s -> t -- | Rewrite recursively over part of a larger structure. -- --

--   rewriteOn :: Plated a => Iso' s a       -> (a -> Maybe a) -> s -> s
--   rewriteOn :: Plated a => Lens' s a      -> (a -> Maybe a) -> s -> s
--   rewriteOn :: Plated a => Traversal' s a -> (a -> Maybe a) -> s -> s
--   rewriteOn :: Plated a => ASetter' s a   -> (a -> Maybe a) -> s -> s
--

rewriteOn :: Plated a => ASetter s t a a -> a -> Maybe a -> s -> t -- | Rewrite by applying a rule everywhere you can. Ensures that the rule -- cannot be applied anywhere in the result: -- --

--   propRewriteOf l r x = all (isNothing . r) (universeOf l (rewriteOf l r x))
--

-- -- Usually transformOf is more appropriate, but rewriteOf -- can give better compositionality. Given two single transformations -- f and g, you can construct a -> f a -- mplus g a which performs both rewrites until a fixed -- point. -- --

--   rewriteOf :: Iso' a a       -> (a -> Maybe a) -> a -> a
--   rewriteOf :: Lens' a a      -> (a -> Maybe a) -> a -> a
--   rewriteOf :: Traversal' a a -> (a -> Maybe a) -> a -> a
--   rewriteOf :: Setter' a a    -> (a -> Maybe a) -> a -> a
--

rewriteOf :: () => ASetter a b a b -> b -> Maybe a -> a -> b -- | Rewrite by applying a rule everywhere you can. Ensures that the rule -- cannot be applied anywhere in the result: -- --

--   propRewrite r x = all (isNothing . r) (universe (rewrite r x))
--

-- -- Usually transform is more appropriate, but rewrite can -- give better compositionality. Given two single transformations -- f and g, you can construct a -> f a -- mplus g a which performs both rewrites until a fixed -- point. rewrite :: Plated a => a -> Maybe a -> a -> a -- | Extract the immediate descendants of a Plated container. -- --

--   children ≡ toListOf plate
--

children :: Plated a => a -> [a] -- | Try to apply a traversal to all transitive descendants of a -- Plated container, but do not recurse through matching -- descendants. -- --

--   deep :: Plated s => Fold s a                 -> Fold s a
--   deep :: Plated s => IndexedFold s a          -> IndexedFold s a
--   deep :: Plated s => Traversal s s a b        -> Traversal s s a b
--   deep :: Plated s => IndexedTraversal s s a b -> IndexedTraversal s s a b
--

deep :: (Conjoined p, Applicative f, Plated s) => Traversing p f s s a b -> Over p f s s a b -- | Compose through a plate (...) :: (Applicative f, Plated c) => LensLike f s t c c -> Over p f c c a b -> Over p f s t a b infixr 9 ... -- | A Plated type is one where we know how to extract its immediate -- self-similar children. -- -- Example 1: -- --

--   import Control.Applicative
--   import Control.Lens
--   import Control.Lens.Plated
--   import Data.Data
--   import Data.Data.Lens (uniplate)
--

-- --

--   data Expr
--     = Val Int
--     | Neg Expr
--     | Add Expr Expr
--     deriving (Eq,Ord,Show,Read,Data,Typeable)
--

-- --

--   instance Plated Expr where
--     plate f (Neg e) = Neg <$> f e
--     plate f (Add a b) = Add <$> f a <*> f b
--     plate _ a = pure a
--

-- -- or -- --

--   instance Plated Expr where
--     plate = uniplate
--

-- -- Example 2: -- --

--   import Control.Applicative
--   import Control.Lens
--   import Control.Lens.Plated
--   import Data.Data
--   import Data.Data.Lens (uniplate)
--

-- --

--   data Tree a
--     = Bin (Tree a) (Tree a)
--     | Tip a
--     deriving (Eq,Ord,Show,Read,Data,Typeable)
--

-- --

--   instance Plated (Tree a) where
--     plate f (Bin l r) = Bin <$> f l <*> f r
--     plate _ t = pure t
--

-- -- or -- --

--   instance Data a => Plated (Tree a) where
--     plate = uniplate
--

-- -- Note the big distinction between these two implementations. -- -- The former will only treat children directly in this tree as -- descendents, the latter will treat trees contained in the values under -- the tips also as descendants! -- -- When in doubt, pick a Traversal and just use the various -- ...Of combinators rather than pollute Plated with -- orphan instances! -- -- If you want to find something unplated and non-recursive with -- biplate use the ...OnOf variant with ignored, -- though those usecases are much better served in most cases by using -- the existing Lens combinators! e.g. -- --

--   toListOf biplate ≡ universeOnOf biplate ignored
--

-- -- This same ability to explicitly pass the Traversal in question -- is why there is no analogue to uniplate's Biplate. -- -- Moreover, since we can allow custom traversals, we implement -- reasonable defaults for polymorphic data types, that only -- traverse into themselves, and not their polymorphic -- arguments. class Plated a -- | Traversal of the immediate children of this structure. -- -- If you're using GHC 7.2 or newer and your type has a Data -- instance, plate will default to uniplate and you can -- choose to not override it with your own definition. plate :: Plated a => Traversal' a a class GPlated a (g :: * -> *) -- | This type family is used by Zoom to describe the common effect -- type. -- | This type family is used by Magnify to describe the common -- effect type. -- | This class allows us to use zoom in, changing the State -- supplied by many different Monad transformers, potentially -- quite deep in a Monad transformer stack. class (MonadState s m, MonadState t n) => Zoom (m :: * -> *) (n :: * -> *) s t | m -> s, n -> t, m t -> n, n s -> m -- | Run a monadic action in a larger State than it was defined in, -- using a Lens' or Traversal'. -- -- This is commonly used to lift actions in a simpler State -- Monad into a State Monad with a larger -- State type. -- -- When applied to a Traversal' over multiple values, the actions -- for each target are executed sequentially and the results are -- aggregated. -- -- This can be used to edit pretty much any Monad transformer -- stack with a State in it! -- --

--   >>> flip State.evalState (a,b) $ zoom _1 $ use id
--   a
--

-- --

--   >>> flip State.execState (a,b) $ zoom _1 $ id .= c
--   (c,b)
--

-- --

--   >>> flip State.execState [(a,b),(c,d)] $ zoom traverse $ _2 %= f
--   [(a,f b),(c,f d)]
--

-- --

--   >>> flip State.runState [(a,b),(c,d)] $ zoom traverse $ _2 <%= f
--   (f b <> f d <> mempty,[(a,f b),(c,f d)])
--

-- --

--   >>> flip State.evalState (a,b) $ zoom both (use id)
--   a <> b
--

-- --

--   zoom :: Monad m             => Lens' s t      -> StateT t m a -> StateT s m a
--   zoom :: (Monad m, Monoid c) => Traversal' s t -> StateT t m c -> StateT s m c
--   zoom :: (Monad m, Monoid w)             => Lens' s t      -> RWST r w t m c -> RWST r w s m c
--   zoom :: (Monad m, Monoid w, Monoid c) => Traversal' s t -> RWST r w t m c -> RWST r w s m c
--   zoom :: (Monad m, Monoid w, Error e)  => Lens' s t      -> ErrorT e (RWST r w t m) c -> ErrorT e (RWST r w s m) c
--   zoom :: (Monad m, Monoid w, Monoid c, Error e) => Traversal' s t -> ErrorT e (RWST r w t m) c -> ErrorT e (RWST r w s m) c
--   ...
--

zoom :: Zoom m n s t => LensLike' Zoomed m c t s -> m c -> n c -- | This class allows us to use magnify part of the environment, -- changing the environment supplied by many different Monad -- transformers. Unlike zoom this can change the environment of a -- deeply nested Monad transformer. -- -- Also, unlike zoom, this can be used with any valid -- Getter, but cannot be used with a Traversal or -- Fold. class (Magnified m ~ Magnified n, MonadReader b m, MonadReader a n) => Magnify (m :: * -> *) (n :: * -> *) b a | m -> b, n -> a, m a -> n, n b -> m -- | Run a monadic action in a larger environment than it was defined in, -- using a Getter. -- -- This acts like local, but can in many cases change the type of -- the environment as well. -- -- This is commonly used to lift actions in a simpler Reader -- Monad into a Monad with a larger environment type. -- -- This can be used to edit pretty much any Monad transformer -- stack with an environment in it: -- --

--   >>> (1,2) & magnify _2 (+1)
--   3
--

-- --

--   >>> flip Reader.runReader (1,2) $ magnify _1 Reader.ask
--   1
--

-- --

--   >>> flip Reader.runReader (1,2,[10..20]) $ magnify (_3._tail) Reader.ask
--   [11,12,13,14,15,16,17,18,19,20]
--

-- --

--   magnify :: Getter s a -> (a -> r) -> s -> r
--   magnify :: Monoid r => Fold s a   -> (a -> r) -> s -> r
--

-- --

--   magnify :: Monoid w                 => Getter s t -> RWS t w st c -> RWS s w st c
--   magnify :: (Monoid w, Monoid c) => Fold s a   -> RWS a w st c -> RWS s w st c
--   ...
--

magnify :: Magnify m n b a => LensLike' Magnified m c a b -> m c -> n c -- | This combinator is based on ala' from Conor McBride's work on -- Epigram. -- -- As with _Wrapping, the user supplied function for the newtype -- is ignored. -- --

--   alaf :: Rewrapping s t => (Unwrapped s -> s) -> ((r ->  t) -> e -> s) -> (r -> Unwrapped t) -> e -> Unwrapped s
--

-- --

--   >>> alaf Sum foldMap Prelude.length ["hello","world"]
--   10
--

alaf :: (Functor f, Functor g, Rewrapping s t) => Unwrapped s -> s -> f t -> g s -> f Unwrapped t -> g Unwrapped s -- | This combinator is based on ala from Conor McBride's work on -- Epigram. -- -- As with _Wrapping, the user supplied function for the newtype -- is ignored. -- --

--   >>> ala Sum foldMap [1,2,3,4]
--   10
--

-- --

--   >>> ala All foldMap [True,True]
--   True
--

-- --

--   >>> ala All foldMap [True,False]
--   False
--

-- --

--   >>> ala Any foldMap [False,False]
--   False
--

-- --

--   >>> ala Any foldMap [True,False]
--   True
--

-- --

--   >>> ala Product foldMap [1,2,3,4]
--   24
--

-- -- You may want to think of this combinator as having the following, -- simpler, type. -- --

--   ala :: Rewrapping s t => (Unwrapped s -> s) -> ((Unwrapped t -> t) -> e -> s) -> e -> Unwrapped s
--

ala :: (Functor f, Rewrapping s t) => Unwrapped s -> s -> Unwrapped t -> t -> f s -> f Unwrapped s -- | This is a convenient version of _Unwrapped with an argument -- that's ignored. -- -- The user supplied function is ignored, merely its types are -- used. _Unwrapping :: Rewrapping s t => Unwrapped s -> s -> Iso Unwrapped t Unwrapped s t s -- | This is a convenient version of _Wrapped with an argument -- that's ignored. -- -- The user supplied function is ignored, merely its types are -- used. _Wrapping :: Rewrapping s t => Unwrapped s -> s -> Iso s t Unwrapped s Unwrapped t -- | This is a convenient version of _Wrapped with an argument -- that's ignored. -- -- The user supplied function is ignored, merely its type is used. _Unwrapping' :: Wrapped s => Unwrapped s -> s -> Iso' Unwrapped s s -- | This is a convenient version of _Wrapped with an argument -- that's ignored. -- -- The user supplied function is ignored, merely its type is used. _Wrapping' :: Wrapped s => Unwrapped s -> s -> Iso' s Unwrapped s -- | Given the constructor for a Wrapped type, return a -- deconstructor that is its inverse. -- -- Assuming the Wrapped instance is legal, these laws hold: -- --

--   op f . f ≡ id
--   f . op f ≡ id
--

-- --

--   >>> op Identity (Identity 4)
--   4
--

-- --

--   >>> op Const (Const "hello")
--   "hello"
--

op :: Wrapped s => Unwrapped s -> s -> s -> Unwrapped s _Unwrapped :: Rewrapping s t => Iso Unwrapped t Unwrapped s t s -- | Work under a newtype wrapper. -- --

--   >>> Const "hello" & _Wrapped %~ Prelude.length & getConst
--   5
--

-- --

--   _Wrapped   ≡ from _Unwrapped
--   _Unwrapped ≡ from _Wrapped
--

_Wrapped :: Rewrapping s t => Iso s t Unwrapped s Unwrapped t _Unwrapped' :: Wrapped s => Iso' Unwrapped s s -- | Implement the _Wrapped operation for a type using its -- Generic instance. _GWrapped' :: (Generic s, D1 d C1 c S1 s' Rec0 a ~ Rep s, Unwrapped s ~ GUnwrapped Rep s) => Iso' s Unwrapped s -- | Wrapped provides isomorphisms to wrap and unwrap newtypes or -- data types with one constructor. class Wrapped s where { type family Unwrapped s :: *; } -- | An isomorphism between s and a. -- -- If your type has a Generic instance, _Wrapped' will -- default to _GWrapped', and you can choose to not override it -- with your own definition. _Wrapped' :: Wrapped s => Iso' s Unwrapped s class Wrapped s => Rewrapped s t class (Rewrapped s t, Rewrapped t s) => Rewrapping s t -- | Attempt to extract the right-most element from a container, and a -- version of the container without that element. -- --

--   >>> unsnoc (LazyT.pack "hello!")
--   Just ("hello",'!')
--

-- --

--   >>> unsnoc (LazyT.pack "")
--   Nothing
--

-- --

--   >>> unsnoc (Seq.fromList [b,c,a])
--   Just (fromList [b,c],a)
--

-- --

--   >>> unsnoc (Seq.fromList [])
--   Nothing
--

unsnoc :: Snoc s s a a => s -> Maybe (s, a) -- | snoc an element onto the end of a container. -- --

--   >>> snoc (Seq.fromList []) a
--   fromList [a]
--

-- --

--   >>> snoc (Seq.fromList [b, c]) a
--   fromList [b,c,a]
--

-- --

--   >>> snoc (LazyT.pack "hello") '!'
--   "hello!"
--

snoc :: Snoc s s a a => s -> a -> s infixl 5 `snoc` -- | snoc an element onto the end of a container. -- -- This is an infix alias for snoc. -- --

--   >>> Seq.fromList [] |> a
--   fromList [a]
--

-- --

--   >>> Seq.fromList [b, c] |> a
--   fromList [b,c,a]
--

-- --

--   >>> LazyT.pack "hello" |> '!'
--   "hello!"
--

(|>) :: Snoc s s a a => s -> a -> s infixl 5 |> -- | A Traversal reading and writing to the last element of a -- non-empty container. -- --

--   >>> [a,b,c]^?!_last
--   c
--

-- --

--   >>> []^?_last
--   Nothing
--

-- --

--   >>> [a,b,c] & _last %~ f
--   [a,b,f c]
--

-- --

--   >>> [1,2]^?_last
--   Just 2
--

-- --

--   >>> [] & _last .~ 1
--   []
--

-- --

--   >>> [0] & _last .~ 2
--   [2]
--

-- --

--   >>> [0,1] & _last .~ 2
--   [0,2]
--

-- -- This Traversal is not limited to lists, however. We can also -- work with other containers, such as a Vector. -- --

--   >>> Vector.fromList "abcde" ^? _last
--   Just 'e'
--

-- --

--   >>> Vector.empty ^? _last
--   Nothing
--

-- --

--   >>> (Vector.fromList "abcde" & _last .~ 'Q') == Vector.fromList "abcdQ"
--   True
--

-- --

--   _last :: Traversal' [a] a
--   _last :: Traversal' (Seq a) a
--   _last :: Traversal' (Vector a) a
--

_last :: Snoc s s a a => Traversal' s a -- | A Traversal reading and replacing all but the a last element of -- a non-empty container. -- --

--   >>> [a,b,c,d]^?_init
--   Just [a,b,c]
--

-- --

--   >>> []^?_init
--   Nothing
--

-- --

--   >>> [a,b] & _init .~ [c,d,e]
--   [c,d,e,b]
--

-- --

--   >>> [] & _init .~ [a,b]
--   []
--

-- --

--   >>> [a,b,c,d] & _init.traverse %~ f
--   [f a,f b,f c,d]
--

-- --

--   >>> [1,2,3]^?_init
--   Just [1,2]
--

-- --

--   >>> [1,2,3,4]^?!_init
--   [1,2,3]
--

-- --

--   >>> "hello"^._init
--   "hell"
--

-- --

--   >>> ""^._init
--   ""
--

-- --

--   _init :: Traversal' [a] [a]
--   _init :: Traversal' (Seq a) (Seq a)
--   _init :: Traversal' (Vector a) (Vector a)
--

_init :: Snoc s s a a => Traversal' s s -- | A Traversal reading and writing to the tail of a -- non-empty container. -- --

--   >>> [a,b] & _tail .~ [c,d,e]
--   [a,c,d,e]
--

-- --

--   >>> [] & _tail .~ [a,b]
--   []
--

-- --

--   >>> [a,b,c,d,e] & _tail.traverse %~ f
--   [a,f b,f c,f d,f e]
--

-- --

--   >>> [1,2] & _tail .~ [3,4,5]
--   [1,3,4,5]
--

-- --

--   >>> [] & _tail .~ [1,2]
--   []
--

-- --

--   >>> [a,b,c]^?_tail
--   Just [b,c]
--

-- --

--   >>> [1,2]^?!_tail
--   [2]
--

-- --

--   >>> "hello"^._tail
--   "ello"
--

-- --

--   >>> ""^._tail
--   ""
--

-- -- This isn't limited to lists. For instance you can also traverse -- the tail of a Seq. -- --

--   >>> Seq.fromList [a,b] & _tail .~ Seq.fromList [c,d,e]
--   fromList [a,c,d,e]
--

-- --

--   >>> Seq.fromList [a,b,c] ^? _tail
--   Just (fromList [b,c])
--

-- --

--   >>> Seq.fromList [] ^? _tail
--   Nothing
--

-- --

--   _tail :: Traversal' [a] [a]
--   _tail :: Traversal' (Seq a) (Seq a)
--   _tail :: Traversal' (Vector a) (Vector a)
--

_tail :: Cons s s a a => Traversal' s s -- | A Traversal reading and writing to the head of a -- non-empty container. -- --

--   >>> [a,b,c]^? _head
--   Just a
--

-- --

--   >>> [a,b,c] & _head .~ d
--   [d,b,c]
--

-- --

--   >>> [a,b,c] & _head %~ f
--   [f a,b,c]
--

-- --

--   >>> [] & _head %~ f
--   []
--

-- --

--   >>> [1,2,3]^?!_head
--   1
--

-- --

--   >>> []^?_head
--   Nothing
--

-- --

--   >>> [1,2]^?_head
--   Just 1
--

-- --

--   >>> [] & _head .~ 1
--   []
--

-- --

--   >>> [0] & _head .~ 2
--   [2]
--

-- --

--   >>> [0,1] & _head .~ 2
--   [2,1]
--

-- -- This isn't limited to lists. -- -- For instance you can also traverse the head of a Seq: -- --

--   >>> Seq.fromList [a,b,c,d] & _head %~ f
--   fromList [f a,b,c,d]
--

-- --

--   >>> Seq.fromList [] ^? _head
--   Nothing
--

-- --

--   >>> Seq.fromList [a,b,c,d] ^? _head
--   Just a
--

-- --

--   _head :: Traversal' [a] a
--   _head :: Traversal' (Seq a) a
--   _head :: Traversal' (Vector a) a
--

_head :: Cons s s a a => Traversal' s a -- | Attempt to extract the left-most element from a container, and a -- version of the container without that element. -- --

--   >>> uncons []
--   Nothing
--

-- --

--   >>> uncons [a, b, c]
--   Just (a,[b,c])
--

uncons :: Cons s s a a => s -> Maybe (a, s) -- | cons an element onto a container. -- --

--   >>> cons a []
--   [a]
--

-- --

--   >>> cons a [b, c]
--   [a,b,c]
--

-- --

--   >>> cons a (Seq.fromList [])
--   fromList [a]
--

-- --

--   >>> cons a (Seq.fromList [b, c])
--   fromList [a,b,c]
--

cons :: Cons s s a a => a -> s -> s infixr 5 `cons` -- | cons an element onto a container. -- -- This is an infix alias for cons. -- --

--   >>> a <| []
--   [a]
--

-- --

--   >>> a <| [b, c]
--   [a,b,c]
--

-- --

--   >>> a <| Seq.fromList []
--   fromList [a]
--

-- --

--   >>> a <| Seq.fromList [b, c]
--   fromList [a,b,c]
--

(<|) :: Cons s s a a => a -> s -> s infixr 5 <| infixr 5 :< infixl 5 :> -- | This class provides a way to attach or detach elements on the left -- side of a structure in a flexible manner. class Cons s t a b | s -> a, t -> b, s b -> t, t a -> s -- |

--   _Cons :: Prism [a] [b] (a, [a]) (b, [b])
--   _Cons :: Prism (Seq a) (Seq b) (a, Seq a) (b, Seq b)
--   _Cons :: Prism (Vector a) (Vector b) (a, Vector a) (b, Vector b)
--   _Cons :: Prism' String (Char, String)
--   _Cons :: Prism' Text (Char, Text)
--   _Cons :: Prism' ByteString (Word8, ByteString)
--

_Cons :: Cons s t a b => Prism s t (a, s) (b, t) -- | This class provides a way to attach or detach elements on the right -- side of a structure in a flexible manner. class Snoc s t a b | s -> a, t -> b, s b -> t, t a -> s -- |

--   _Snoc :: Prism [a] [b] ([a], a) ([b], b)
--   _Snoc :: Prism (Seq a) (Seq b) (Seq a, a) (Seq b, b)
--   _Snoc :: Prism (Vector a) (Vector b) (Vector a, a) (Vector b, b)
--   _Snoc :: Prism' String (String, Char)
--   _Snoc :: Prism' Text (Text, Char)
--   _Snoc :: Prism' ByteString (ByteString, Word8)
--

_Snoc :: Snoc s t a b => Prism s t (s, a) (t, b) class AsEmpty a -- |

--   >>> isn't _Empty [1,2,3]
--   True
--

_Empty :: AsEmpty a => Prism' a () -- | Data types that are representationally equal are isomorphic. -- -- This is only available on GHC 7.8+ coerced :: (Coercible s a, Coercible t b) => Iso s t a b -- | Lift an Iso into the second argument of a Bifunctor. -- This is essentially the same as mapping, but it takes a -- 'Bifunctor p' constraint instead of a 'Functor (p a)' one. -- --

--   seconding :: Bifunctor p => Iso s t a b -> Iso (p x s) (p y t) (p x a) (p y b)
--   seconding :: Bifunctor p => Iso' s a -> Iso' (p x s) (p x a)
--

seconding :: (Bifunctor f, Bifunctor g) => AnIso s t a b -> Iso f x s g y t f x a g y b -- | Lift an Iso into the first argument of a Bifunctor. -- --

--   firsting :: Bifunctor p => Iso s t a b -> Iso (p s x) (p t y) (p a x) (p b y)
--   firsting :: Bifunctor p => Iso' s a -> Iso' (p s x) (p a x)
--

firsting :: (Bifunctor f, Bifunctor g) => AnIso s t a b -> Iso f s x g t y f a x g b y -- | Lift two Isos into both arguments of a Bifunctor. -- --

--   bimapping :: Bifunctor p => Iso s t a b -> Iso s' t' a' b' -> Iso (p s s') (p t t') (p a a') (p b b')
--   bimapping :: Bifunctor p => Iso' s a -> Iso' s' a' -> Iso' (p s s') (p a a')
--

bimapping :: (Bifunctor f, Bifunctor g) => AnIso s t a b -> AnIso s' t' a' b' -> Iso f s s' g t t' f a a' g b b' -- | Lift an Iso covariantly into the right argument of a -- Profunctor. -- --

--   rmapping :: Profunctor p => Iso s t a b -> Iso (p x s) (p y t) (p x a) (p y b)
--   rmapping :: Profunctor p => Iso' s a -> Iso' (p x s) (p x a)
--

rmapping :: (Profunctor p, Profunctor q) => AnIso s t a b -> Iso p x s q y t p x a q y b -- | Lift an Iso contravariantly into the left argument of a -- Profunctor. -- --

--   lmapping :: Profunctor p => Iso s t a b -> Iso (p a x) (p b y) (p s x) (p t y)
--   lmapping :: Profunctor p => Iso' s a -> Iso' (p a x) (p s x)
--

lmapping :: (Profunctor p, Profunctor q) => AnIso s t a b -> Iso p a x q b y p s x q t y -- | Lift two Isos into both arguments of a Profunctor -- simultaneously. -- --

--   dimapping :: Profunctor p => Iso s t a b -> Iso s' t' a' b' -> Iso (p a s') (p b t') (p s a') (p t b')
--   dimapping :: Profunctor p => Iso' s a -> Iso' s' a' -> Iso' (p a s') (p s a')
--

dimapping :: (Profunctor p, Profunctor q) => AnIso s t a b -> AnIso s' t' a' b' -> Iso p a s' q b t' p s a' q t b' -- | Lift an Iso into a Contravariant functor. -- --

--   contramapping :: Contravariant f => Iso s t a b -> Iso (f a) (f b) (f s) (f t)
--   contramapping :: Contravariant f => Iso' s a -> Iso' (f a) (f s)
--

contramapping :: Contravariant f => AnIso s t a b -> Iso f a f b f s f t -- | This isomorphism can be used to inspect an IndexedTraversal to -- see how it associates the structure and it can also be used to bake -- the IndexedTraversal into a Magma so that you can -- traverse over it multiple times with access to the original indices. imagma :: () => Over Indexed i Molten i a b s t a b -> Iso s t' Magma i t b a Magma j t' c c -- | This isomorphism can be used to inspect a Traversal to see how -- it associates the structure and it can also be used to bake the -- Traversal into a Magma so that you can traverse over it -- multiple times. magma :: () => LensLike Mafic a b s t a b -> Iso s u Magma Int t b a Magma j u c c -- | Given a function that is its own inverse, this gives you an Iso -- using it in both directions. -- --

--   involuted ≡ join iso
--

-- --

--   >>> "live" ^. involuted reverse
--   "evil"
--

-- --

--   >>> "live" & involuted reverse %~ ('d':)
--   "lived"
--

involuted :: () => a -> a -> Iso' a a -- | An Iso between a list, ByteString, Text fragment, -- etc. and its reversal. -- --

--   >>> "live" ^. reversed
--   "evil"
--

-- --

--   >>> "live" & reversed %~ ('d':)
--   "lived"
--

reversed :: Reversing a => Iso' a a -- | An Iso between the strict variant of a structure and its lazy -- counterpart. -- --

--   lazy = from strict
--

-- -- See http://hackage.haskell.org/package/strict-base-types for an -- example use. lazy :: Strict lazy strict => Iso' strict lazy -- | The isomorphism for flipping a function. -- --

--   >>> ((,)^.flipped) 1 2
--   (2,1)
--

flipped :: (Profunctor p, Functor f) => p b -> a -> c f b' -> a' -> c' -> p a -> b -> c f a' -> b' -> c' -- | The canonical isomorphism for uncurrying and currying a function. -- --

--   uncurried = iso uncurry curry
--

-- --

--   uncurried = from curried
--

-- --

--   >>> ((+)^.uncurried) (1,2)
--   3
--

uncurried :: (Profunctor p, Functor f) => p (a, b) -> c f (d, e) -> f -> p a -> b -> c f d -> e -> f -- | The canonical isomorphism for currying and uncurrying a function. -- --

--   curried = iso curry uncurry
--

-- --

--   >>> (fst^.curried) 3 4
--   3
--

-- --

--   >>> view curried fst 3 4
--   3
--

curried :: (Profunctor p, Functor f) => p a -> b -> c f d -> e -> f -> p (a, b) -> c f (d, e) -> f -- | anon a p generalizes non a to take any -- value and a predicate. -- -- This function assumes that p a holds True and -- generates an isomorphism between Maybe (a | not (p -- a)) and a. -- --

--   >>> Map.empty & at "hello" . anon Map.empty Map.null . at "world" ?~ "!!!"
--   fromList [("hello",fromList [("world","!!!")])]
--

-- --

--   >>> fromList [("hello",fromList [("world","!!!")])] & at "hello" . anon Map.empty Map.null . at "world" .~ Nothing
--   fromList []
--

anon :: () => a -> a -> Bool -> Iso' Maybe a a -- | non' p generalizes non (p # ()) to -- take any unit Prism -- -- This function generates an isomorphism between Maybe (a | -- isn't p a) and a. -- --

--   >>> Map.singleton "hello" Map.empty & at "hello" . non' _Empty . at "world" ?~ "!!!"
--   fromList [("hello",fromList [("world","!!!")])]
--

-- --

--   >>> fromList [("hello",fromList [("world","!!!")])] & at "hello" . non' _Empty . at "world" .~ Nothing
--   fromList []
--

non' :: () => APrism' a () -> Iso' Maybe a a -- | If v is an element of a type a, and a' is -- a sans the element v, then non v is -- an isomorphism from Maybe a' to a. -- --

--   non ≡ non' . only
--

-- -- Keep in mind this is only a real isomorphism if you treat the domain -- as being Maybe (a sans v). -- -- This is practically quite useful when you want to have a Map -- where all the entries should have non-zero values. -- --

--   >>> Map.fromList [("hello",1)] & at "hello" . non 0 +~ 2
--   fromList [("hello",3)]
--

-- --

--   >>> Map.fromList [("hello",1)] & at "hello" . non 0 -~ 1
--   fromList []
--

-- --

--   >>> Map.fromList [("hello",1)] ^. at "hello" . non 0
--   1
--

-- --

--   >>> Map.fromList [] ^. at "hello" . non 0
--   0
--

-- -- This combinator is also particularly useful when working with nested -- maps. -- -- e.g. When you want to create the nested Map when it is -- missing: -- --

--   >>> Map.empty & at "hello" . non Map.empty . at "world" ?~ "!!!"
--   fromList [("hello",fromList [("world","!!!")])]
--

-- -- and when have deleting the last entry from the nested Map mean -- that we should delete its entry from the surrounding one: -- --

--   >>> fromList [("hello",fromList [("world","!!!")])] & at "hello" . non Map.empty . at "world" .~ Nothing
--   fromList []
--

-- -- It can also be used in reverse to exclude a given value: -- --

--   >>> non 0 # rem 10 4
--   Just 2
--

-- --

--   >>> non 0 # rem 10 5
--   Nothing
--

non :: Eq a => a -> Iso' Maybe a a -- | This can be used to lift any Iso into an arbitrary -- Functor. mapping :: (Functor f, Functor g) => AnIso s t a b -> Iso f s g t f a g b -- | This isomorphism can be used to convert to or from an instance of -- Enum. -- --

--   >>> LT^.from enum
--   0
--

-- --

--   >>> 97^.enum :: Char
--   'a'
--

-- -- Note: this is only an isomorphism from the numeric range actually used -- and it is a bit of a pleasant fiction, since there are questionable -- Enum instances for Double, and Float that exist -- solely for [1.0 .. 4.0] sugar and the instances for those and -- Integer don't cover all values in their range. enum :: Enum a => Iso' Int a -- | The opposite of working over a Setter is working -- under an isomorphism. -- --

--   under ≡ over . from
--

-- --

--   under :: Iso s t a b -> (t -> s) -> b -> a
--

under :: () => AnIso s t a b -> t -> s -> b -> a -- | Based on ala' from Conor McBride's work on Epigram. -- -- This version is generalized to accept any Iso, not just a -- newtype. -- -- For a version you pass the name of the newtype constructor -- to, see alaf. -- --

--   >>> auf (_Unwrapping Sum) (foldMapOf both) Prelude.length ("hello","world")
--   10
--

-- -- Mnemonically, the German auf plays a similar role to à -- la, and the combinator is au with an extra function -- argument: -- --

--   auf :: Iso s t a b -> ((r ->  a) -> e -> b) -> (r -> s) -> e -> t
--

-- -- but the signature is general. auf :: () => Optic Costar f g s t a b -> f a -> g b -> f s -> g t -- | Based on ala from Conor McBride's work on Epigram. -- -- This version is generalized to accept any Iso, not just a -- newtype. -- --

--   >>> au (_Wrapping Sum) foldMap [1,2,3,4]
--   10
--

-- -- You may want to think of this combinator as having the following, -- simpler type: -- --

--   au :: AnIso s t a b -> ((b -> t) -> e -> s) -> e -> a
--

au :: Functor f => AnIso s t a b -> b -> t -> f s -> f a -- | Convert from AnIso back to any Iso. -- -- This is useful when you need to store an isomorphism as a data type -- inside a container and later reconstitute it as an overloaded -- function. -- -- See cloneLens or cloneTraversal for more information on -- why you might want to do this. cloneIso :: () => AnIso s t a b -> Iso s t a b -- | Extract the two functions, one from s -> a and one from -- b -> t that characterize an Iso. withIso :: () => AnIso s t a b -> s -> a -> b -> t -> r -> r -- | Invert an isomorphism. -- --

--   from (from l) ≡ l
--

from :: () => AnIso s t a b -> Iso b a t s -- | Build a simple isomorphism from a pair of inverse functions. -- --

--   view (iso f g) ≡ f
--   view (from (iso f g)) ≡ g
--   over (iso f g) h ≡ g . h . f
--   over (from (iso f g)) h ≡ f . h . g
--

iso :: () => s -> a -> b -> t -> Iso s t a b -- | When you see this as an argument to a function, it expects an -- Iso. type AnIso s t a b = Exchange a b a Identity b -> Exchange a b s Identity t -- | A Simple AnIso. type AnIso' s a = AnIso s s a a -- | This class provides for symmetric bifunctors. class Bifunctor p => Swapped (p :: * -> * -> *) -- |

--   swapped . swapped ≡ id
--   first f . swapped = swapped . second f
--   second g . swapped = swapped . first g
--   bimap f g . swapped = swapped . bimap g f
--

-- --

--   >>> (1,2)^.swapped
--   (2,1)
--

swapped :: (Swapped p, Profunctor p, Functor f) => p p b a f p d c -> p p a b f p c d -- | Ad hoc conversion between "strict" and "lazy" versions of a structure, -- such as Text or ByteString. class Strict lazy strict | lazy -> strict, strict -> lazy strict :: Strict lazy strict => Iso' lazy strict -- | Composition with this isomorphism is occasionally useful when your -- Lens, Traversal or Iso has a constraint on an -- unused argument to force that argument to agree with the type of a -- used argument and avoid ScopedTypeVariables or other -- ugliness. simple :: () => p a f a -> p a f a -- | This is an adverb that can be used to modify many other Lens -- combinators to make them require simple lenses, simple traversals, -- simple prisms or simple isos as input. simply :: () => Optic' p f s a -> r -> Optic' p f s a -> r -- | Equality is symmetric. fromEq :: () => AnEquality s t a b -> Equality b a t s -- | We can use Equality to do substitution into anything. mapEq :: () => AnEquality s t a b -> f s -> f a -- | Substituting types with Equality. substEq :: () => AnEquality s t a b -> s ~ a -> t ~ b -> r -> r -- | Extract a witness of type Equality. runEq :: () => AnEquality s t a b -> Identical s t a b -- | Provides witness that (s ~ a, b ~ t) holds. data Identical (a :: k) (b :: k1) (s :: k) (t :: k1) :: forall k k1. () => k -> k1 -> k -> k1 -> * [Identical] :: Identical a b a b -- | When you see this as an argument to a function, it expects an -- Equality. type AnEquality (s :: k1) (t :: k2) (a :: k1) (b :: k2) = Identical a Proxy b a Proxy b -> Identical a Proxy b s Proxy t -- | A Simple AnEquality. type AnEquality' (s :: k2) (a :: k2) = AnEquality s s a a itraverseByOf :: () => IndexedTraversal i s t a b -> forall x. () => x -> f x -> forall x y. () => f x -> y -> f x -> f y -> i -> a -> f b -> s -> f t itraverseBy :: TraversableWithIndex i t => forall x. () => x -> f x -> forall x y. () => f x -> y -> f x -> f y -> i -> a -> f b -> t a -> f t b ifoldMapByOf :: () => IndexedFold i t a -> r -> r -> r -> r -> i -> a -> r -> t -> r ifoldMapBy :: FoldableWithIndex i t => r -> r -> r -> r -> i -> a -> r -> t a -> r -- | Generalizes mapAccumL to add access to the index. -- -- imapAccumLOf accumulates state from left to right. -- --

--   mapAccumLOf ≡ imapAccumL . const
--

imapAccumL :: TraversableWithIndex i t => i -> s -> a -> (s, b) -> s -> t a -> (s, t b) -- | Generalizes mapAccumR to add access to the index. -- -- imapAccumROf accumulates state from right to left. -- --

--   mapAccumR ≡ imapAccumR . const
--

imapAccumR :: TraversableWithIndex i t => i -> s -> a -> (s, b) -> s -> t a -> (s, t b) -- | Map each element of a structure to a monadic action, evaluate these -- actions from left to right, and collect the results, with access its -- position (and the arguments flipped). -- --

--   forM a ≡ iforM a . const
--   iforM ≡ flip imapM
--

iforM :: (TraversableWithIndex i t, Monad m) => t a -> i -> a -> m b -> m t b -- | Map each element of a structure to a monadic action, evaluate these -- actions from left to right, and collect the results, with access the -- index. -- -- When you don't need access to the index mapM is more liberal in -- what it can accept. -- --

--   mapM ≡ imapM . const
--

imapM :: (TraversableWithIndex i t, Monad m) => i -> a -> m b -> t a -> m t b -- | Traverse with an index (and the arguments flipped). -- --

--   for a ≡ ifor a . const
--   ifor ≡ flip itraverse
--

ifor :: (TraversableWithIndex i t, Applicative f) => t a -> i -> a -> f b -> f t b -- | Extract the key-value pairs from a structure. -- -- When you don't need access to the indices in the result, then -- toList is more flexible in what it accepts. -- --

--   toList ≡ map snd . itoList
--

itoList :: FoldableWithIndex i f => f a -> [(i, a)] -- | Monadic fold over the elements of a structure with an index, -- associating to the left. -- -- When you don't need access to the index then foldlM is more -- flexible in what it accepts. -- --

--   foldlM ≡ ifoldlM . const
--

ifoldlM :: (FoldableWithIndex i f, Monad m) => i -> b -> a -> m b -> b -> f a -> m b -- | Monadic fold right over the elements of a structure with an index. -- -- When you don't need access to the index then foldrM is more -- flexible in what it accepts. -- --

--   foldrM ≡ ifoldrM . const
--

ifoldrM :: (FoldableWithIndex i f, Monad m) => i -> a -> b -> m b -> b -> f a -> m b -- | Searches a container with a predicate that is also supplied the index, -- returning the left-most element of the structure matching the -- predicate, or Nothing if there is no such element. -- -- When you don't need access to the index then find is more -- flexible in what it accepts. -- --

--   find ≡ ifind . const
--

ifind :: FoldableWithIndex i f => i -> a -> Bool -> f a -> Maybe (i, a) -- | Concatenate the results of a function of the elements of an indexed -- container with access to the index. -- -- When you don't need access to the index then concatMap is more -- flexible in what it accepts. -- --

--   concatMap ≡ iconcatMap . const
--   iconcatMap ≡ ifoldMap
--

iconcatMap :: FoldableWithIndex i f => i -> a -> [b] -> f a -> [b] -- | Run monadic actions for each target of an IndexedFold or -- IndexedTraversal with access to the index, discarding the -- results (with the arguments flipped). -- --

--   iforM_ ≡ flip imapM_
--

-- -- When you don't need access to the index then forMOf_ is more -- flexible in what it accepts. -- --

--   forMOf_ l a ≡ iforMOf l a . const
--

iforM_ :: (FoldableWithIndex i t, Monad m) => t a -> i -> a -> m b -> m () -- | Run monadic actions for each target of an IndexedFold or -- IndexedTraversal with access to the index, discarding the -- results. -- -- When you don't need access to the index then mapMOf_ is more -- flexible in what it accepts. -- --

--   mapM_ ≡ imapM . const
--

imapM_ :: (FoldableWithIndex i t, Monad m) => i -> a -> m b -> t a -> m () -- | Traverse elements with access to the index i, discarding the -- results (with the arguments flipped). -- --

--   ifor_ ≡ flip itraverse_
--

-- -- When you don't need access to the index then for_ is more -- flexible in what it accepts. -- --

--   for_ a ≡ ifor_ a . const
--

ifor_ :: (FoldableWithIndex i t, Applicative f) => t a -> i -> a -> f b -> f () -- | Traverse elements with access to the index i, discarding the -- results. -- -- When you don't need access to the index then traverse_ is more -- flexible in what it accepts. -- --

--   traverse_ l = itraverse . const
--

itraverse_ :: (FoldableWithIndex i t, Applicative f) => i -> a -> f b -> t a -> f () -- | Determines whether no elements of the structure satisfy the predicate. -- --

--   none f ≡ not . any f
--

none :: Foldable f => a -> Bool -> f a -> Bool -- | Return whether or not none of the elements in a container satisfy a -- predicate, with access to the index i. -- -- When you don't need access to the index then none is more -- flexible in what it accepts. -- --

--   none ≡ inone . const
--   inone f ≡ not . iany f
--

inone :: FoldableWithIndex i f => i -> a -> Bool -> f a -> Bool -- | Return whether or not all elements in a container satisfy a predicate, -- with access to the index i. -- -- When you don't need access to the index then all is more -- flexible in what it accepts. -- --

--   all ≡ iall . const
--

iall :: FoldableWithIndex i f => i -> a -> Bool -> f a -> Bool -- | Return whether or not any element in a container satisfies a -- predicate, with access to the index i. -- -- When you don't need access to the index then any is more -- flexible in what it accepts. -- --

--   any ≡ iany . const
--

iany :: FoldableWithIndex i f => i -> a -> Bool -> f a -> Bool -- | This allows you to filter an IndexedFold, IndexedGetter, -- IndexedTraversal or IndexedLens based on an index. -- --

--   >>> ["hello","the","world","!!!"]^?traversed.index 2
--   Just "world"
--

index :: (Indexable i p, Eq i, Applicative f) => i -> Optical' p Indexed i f a a -- | This allows you to filter an IndexedFold, IndexedGetter, -- IndexedTraversal or IndexedLens based on a predicate on -- the indices. -- --

--   >>> ["hello","the","world","!!!"]^..traversed.indices even
--   ["hello","world"]
--

-- --

--   >>> over (traversed.indices (>0)) Prelude.reverse $ ["He","was","stressed","o_O"]
--   ["He","saw","desserts","O_o"]
--

indices :: (Indexable i p, Applicative f) => i -> Bool -> Optical' p Indexed i f a a -- | Composition of Indexed functions with a user supplied function -- for combining indices. icompose :: Indexable p c => i -> j -> p -> Indexed i s t -> r -> Indexed j a b -> s -> t -> c a b -> r -- | Composition of Indexed functions. -- -- Mnemonically, the < and > points to the fact -- that we want to preserve the indices. -- --

--   >>> let nestedMap = (fmap Map.fromList . Map.fromList) [(1, [(10, "one,ten"), (20, "one,twenty")]), (2, [(30, "two,thirty"), (40,"two,forty")])]
--   
--   >>> nestedMap^..(itraversed<.>itraversed).withIndex
--   [((1,10),"one,ten"),((1,20),"one,twenty"),((2,30),"two,thirty"),((2,40),"two,forty")]
--

(<.>) :: Indexable (i, j) p => Indexed i s t -> r -> Indexed j a b -> s -> t -> p a b -> r infixr 9 <.> -- | Remap the index. reindexed :: Indexable j p => i -> j -> Indexed i a b -> r -> p a b -> r -- | Use a value itself as its own index. This is essentially an indexed -- version of id. -- -- Note: When used to modify the value, this can break the index -- requirements assumed by indices and similar, so this is only -- properly an IndexedGetter, but it can be used as more. -- --

--   selfIndex :: IndexedGetter a a b
--

selfIndex :: Indexable a p => p a fb -> a -> fb -- | Compose a non-indexed function with an Indexed function. -- -- Mnemonically, the > points to the indexing we want to -- preserve. -- -- This is the same as (.). -- -- f . g (and f .> g) gives you the -- index of g unless g is index-preserving, like a -- Prism, Iso or Equality, in which case it'll pass -- through the index of f. -- --

--   >>> let nestedMap = (fmap Map.fromList . Map.fromList) [(1, [(10, "one,ten"), (20, "one,twenty")]), (2, [(30, "two,thirty"), (40,"two,forty")])]
--   
--   >>> nestedMap^..(itraversed.>itraversed).withIndex
--   [(10,"one,ten"),(20,"one,twenty"),(30,"two,thirty"),(40,"two,forty")]
--

(.>) :: () => st -> r -> kab -> st -> kab -> r infixr 9 .> -- | Compose an Indexed function with a non-indexed function. -- -- Mnemonically, the < points to the indexing we want to -- preserve. -- --

--   >>> let nestedMap = (fmap Map.fromList . Map.fromList) [(1, [(10, "one,ten"), (20, "one,twenty")]), (2, [(30, "two,thirty"), (40,"two,forty")])]
--   
--   >>> nestedMap^..(itraversed<.itraversed).withIndex
--   [(1,"one,ten"),(1,"one,twenty"),(2,"two,thirty"),(2,"two,forty")]
--

(<.) :: Indexable i p => Indexed i s t -> r -> a -> b -> s -> t -> p a b -> r infixr 9 <. -- | A Functor with an additional index. -- -- Instances must satisfy a modified form of the Functor laws: -- --

--   imap f . imap g ≡ imap (\i -> f i . g i)
--   imap (\_ a -> a) ≡ id
--

class Functor f => FunctorWithIndex i (f :: * -> *) | f -> i -- | Map with access to the index. imap :: FunctorWithIndex i f => i -> a -> b -> f a -> f b -- | The IndexedSetter for a FunctorWithIndex. -- -- If you don't need access to the index, then mapped is more -- flexible in what it accepts. imapped :: (FunctorWithIndex i f, Indexable i p, Settable f) => p a f b -> f a -> f f b -- | A container that supports folding with an additional index. class Foldable f => FoldableWithIndex i (f :: * -> *) | f -> i -- | Fold a container by mapping value to an arbitrary Monoid with -- access to the index i. -- -- When you don't need access to the index then foldMap is more -- flexible in what it accepts. -- --

--   foldMap ≡ ifoldMap . const
--

ifoldMap :: (FoldableWithIndex i f, Monoid m) => i -> a -> m -> f a -> m -- | The IndexedFold of a FoldableWithIndex container. -- -- ifolded . asIndex is a fold over the -- keys of a FoldableWithIndex. -- --

--   >>> Data.Map.fromList [(2, "hello"), (1, "world")]^..ifolded.asIndex
--   [1,2]
--

ifolded :: (FoldableWithIndex i f, Indexable i p, Contravariant f, Applicative f) => p a f a -> f a -> f f a -- | Right-associative fold of an indexed container with access to the -- index i. -- -- When you don't need access to the index then foldr is more -- flexible in what it accepts. -- --

--   foldr ≡ ifoldr . const
--

ifoldr :: FoldableWithIndex i f => i -> a -> b -> b -> b -> f a -> b -- | Left-associative fold of an indexed container with access to the index -- i. -- -- When you don't need access to the index then foldl is more -- flexible in what it accepts. -- --

--   foldl ≡ ifoldl . const
--

ifoldl :: FoldableWithIndex i f => i -> b -> a -> b -> b -> f a -> b -- | Strictly fold right over the elements of a structure with -- access to the index i. -- -- When you don't need access to the index then foldr' is more -- flexible in what it accepts. -- --

--   foldr' ≡ ifoldr' . const
--

ifoldr' :: FoldableWithIndex i f => i -> a -> b -> b -> b -> f a -> b -- | Fold over the elements of a structure with an index, associating to -- the left, but strictly. -- -- When you don't need access to the index then foldlOf' is more -- flexible in what it accepts. -- --

--   foldlOf' l ≡ ifoldlOf' l . const
--

ifoldl' :: FoldableWithIndex i f => i -> b -> a -> b -> b -> f a -> b -- | A Traversable with an additional index. -- -- An instance must satisfy a (modified) form of the Traversable -- laws: -- --

--   itraverse (const Identity) ≡ Identity
--   fmap (itraverse f) . itraverse g ≡ getCompose . itraverse (\i -> Compose . fmap (f i) . g i)
--

class (FunctorWithIndex i t, FoldableWithIndex i t, Traversable t) => TraversableWithIndex i (t :: * -> *) | t -> i -- | Traverse an indexed container. -- --

--   itraverse ≡ itraverseOf itraversed
--

itraverse :: (TraversableWithIndex i t, Applicative f) => i -> a -> f b -> t a -> f t b -- | The IndexedTraversal of a TraversableWithIndex -- container. itraversed :: (TraversableWithIndex i t, Indexable i p, Applicative f) => p a f b -> t a -> f t b -- | Reify a Lens so it can be stored safely in a container. newtype ReifiedLens s t a b Lens :: Lens s t a b -> ReifiedLens s t a b [runLens] :: ReifiedLens s t a b -> Lens s t a b -- |

--   type ReifiedLens' = Simple ReifiedLens
--

type ReifiedLens' s a = ReifiedLens s s a a -- | Reify an IndexedLens so it can be stored safely in a container. newtype ReifiedIndexedLens i s t a b IndexedLens :: IndexedLens i s t a b -> ReifiedIndexedLens i s t a b [runIndexedLens] :: ReifiedIndexedLens i s t a b -> IndexedLens i s t a b -- |

--   type ReifiedIndexedLens' i = Simple (ReifiedIndexedLens i)
--

type ReifiedIndexedLens' i s a = ReifiedIndexedLens i s s a a -- | Reify an IndexedTraversal so it can be stored safely in a -- container. newtype ReifiedIndexedTraversal i s t a b IndexedTraversal :: IndexedTraversal i s t a b -> ReifiedIndexedTraversal i s t a b [runIndexedTraversal] :: ReifiedIndexedTraversal i s t a b -> IndexedTraversal i s t a b -- |

--   type ReifiedIndexedTraversal' i = Simple (ReifiedIndexedTraversal i)
--

type ReifiedIndexedTraversal' i s a = ReifiedIndexedTraversal i s s a a -- | A form of Traversal that can be stored monomorphically in a -- container. newtype ReifiedTraversal s t a b Traversal :: Traversal s t a b -> ReifiedTraversal s t a b [runTraversal] :: ReifiedTraversal s t a b -> Traversal s t a b -- |

--   type ReifiedTraversal' = Simple ReifiedTraversal
--

type ReifiedTraversal' s a = ReifiedTraversal s s a a -- | Reify a Getter so it can be stored safely in a container. -- -- This can also be useful when combining getters in novel ways, as -- ReifiedGetter is isomorphic to '(->)' and provides similar -- instances. -- --

--   >>> ("hello","world","!!!")^.runGetter ((,) <$> Getter _2 <*> Getter (_1.to length))
--   ("world",5)
--

newtype ReifiedGetter s a Getter :: Getter s a -> ReifiedGetter s a [runGetter] :: ReifiedGetter s a -> Getter s a -- | Reify an IndexedGetter so it can be stored safely in a -- container. newtype ReifiedIndexedGetter i s a IndexedGetter :: IndexedGetter i s a -> ReifiedIndexedGetter i s a [runIndexedGetter] :: ReifiedIndexedGetter i s a -> IndexedGetter i s a -- | Reify a Fold so it can be stored safely in a container. -- -- This can also be useful for creatively combining folds as -- ReifiedFold s is isomorphic to ReaderT s [] -- and provides similar instances. -- --

--   >>> ("hello","world")^..runFold ((,) <$> Fold _2 <*> Fold both)
--   [("world","hello"),("world","world")]
--

newtype ReifiedFold s a Fold :: Fold s a -> ReifiedFold s a [runFold] :: ReifiedFold s a -> Fold s a newtype ReifiedIndexedFold i s a IndexedFold :: IndexedFold i s a -> ReifiedIndexedFold i s a [runIndexedFold] :: ReifiedIndexedFold i s a -> IndexedFold i s a -- | Reify a Setter so it can be stored safely in a container. newtype ReifiedSetter s t a b Setter :: Setter s t a b -> ReifiedSetter s t a b [runSetter] :: ReifiedSetter s t a b -> Setter s t a b -- |

--   type ReifiedSetter' = Simple ReifiedSetter
--

type ReifiedSetter' s a = ReifiedSetter s s a a -- | Reify an IndexedSetter so it can be stored safely in a -- container. newtype ReifiedIndexedSetter i s t a b IndexedSetter :: IndexedSetter i s t a b -> ReifiedIndexedSetter i s t a b [runIndexedSetter] :: ReifiedIndexedSetter i s t a b -> IndexedSetter i s t a b -- |

--   type ReifiedIndexedSetter' i = Simple (ReifiedIndexedSetter i)
--

type ReifiedIndexedSetter' i s a = ReifiedIndexedSetter i s s a a -- | Reify an Iso so it can be stored safely in a container. newtype ReifiedIso s t a b Iso :: Iso s t a b -> ReifiedIso s t a b [runIso] :: ReifiedIso s t a b -> Iso s t a b -- |

--   type ReifiedIso' = Simple ReifiedIso
--

type ReifiedIso' s a = ReifiedIso s s a a -- | Reify a Prism so it can be stored safely in a container. newtype ReifiedPrism s t a b Prism :: Prism s t a b -> ReifiedPrism s t a b [runPrism] :: ReifiedPrism s t a b -> Prism s t a b -- |

--   type ReifiedPrism' = Simple ReifiedPrism
--

type ReifiedPrism' s a = ReifiedPrism s s a a -- | This provides a breadth-first Traversal or Fold of the -- individual levels of any other Traversal or Fold via -- iterative deepening depth-first search. The levels are returned to you -- in a compressed format. -- -- This is similar to levels, but retains the index of the -- original IndexedTraversal, so you can access it when traversing -- the levels later on. -- --

--   >>> ["dog","cat"]^@..ilevels (traversed<.>traversed).itraversed
--   [((0,0),'d'),((0,1),'o'),((1,0),'c'),((0,2),'g'),((1,1),'a'),((1,2),'t')]
--

-- -- The resulting Traversal of the levels which is indexed by the -- depth of each Level. -- --

--   >>> ["dog","cat"]^@..ilevels (traversed<.>traversed)<.>itraversed
--   [((2,(0,0)),'d'),((3,(0,1)),'o'),((3,(1,0)),'c'),((4,(0,2)),'g'),((4,(1,1)),'a'),((5,(1,2)),'t')]
--

-- --

--   ilevels :: IndexedTraversal i s t a b      -> IndexedTraversal Int s t (Level i a) (Level i b)
--   ilevels :: IndexedFold i s a               -> IndexedFold Int s (Level i a)
--

-- -- Note: Internally this is implemented by using an illegal -- Applicative, as it extracts information in an order that -- violates the Applicative laws. ilevels :: Applicative f => Traversing Indexed i f s t a b -> IndexedLensLike Int f s t Level i a Level j b -- | This provides a breadth-first Traversal or Fold of the -- individual levels of any other Traversal or Fold -- via iterative deepening depth-first search. The levels are returned to -- you in a compressed format. -- -- This can permit us to extract the levels directly: -- --

--   >>> ["hello","world"]^..levels (traverse.traverse)
--   [Zero,Zero,One () 'h',Two 0 (One () 'e') (One () 'w'),Two 0 (One () 'l') (One () 'o'),Two 0 (One () 'l') (One () 'r'),Two 0 (One () 'o') (One () 'l'),One () 'd']
--

-- -- But we can also traverse them in turn: -- --

--   >>> ["hello","world"]^..levels (traverse.traverse).traverse
--   "hewlolrold"
--

-- -- We can use this to traverse to a fixed depth in the tree of -- (<*>) used in the Traversal: -- --

--   >>> ["hello","world"] & taking 4 (levels (traverse.traverse)).traverse %~ toUpper
--   ["HEllo","World"]
--

-- -- Or we can use it to traverse the first n elements in found in -- that Traversal regardless of the depth at which they were -- found. -- --

--   >>> ["hello","world"] & taking 4 (levels (traverse.traverse).traverse) %~ toUpper
--   ["HELlo","World"]
--

-- -- The resulting Traversal of the levels which is indexed -- by the depth of each Level. -- --

--   >>> ["dog","cat"]^@..levels (traverse.traverse) <. traverse
--   [(2,'d'),(3,'o'),(3,'c'),(4,'g'),(4,'a'),(5,'t')]
--

-- --

--   levels :: Traversal s t a b      -> IndexedTraversal Int s t (Level () a) (Level () b)
--   levels :: Fold s a               -> IndexedFold Int s (Level () a)
--

-- -- Note: Internally this is implemented by using an illegal -- Applicative, as it extracts information in an order that -- violates the Applicative laws. levels :: Applicative f => Traversing ((->) :: * -> * -> *) f s t a b -> IndexedLensLike Int f s t Level () a Level () b -- | Sequence a container using a specified Applicative. -- -- This is like traverseBy where the Traversable instance -- can be specified by any Traversal -- --

--   sequenceByOf traverse ≡ sequenceBy
--

sequenceByOf :: () => Traversal s t f b b -> forall x. () => x -> f x -> forall x y. () => f x -> y -> f x -> f y -> s -> f t -- | Traverse a container using a specified Applicative. -- -- This is like traverseBy where the Traversable instance -- can be specified by any Traversal -- --

--   traverseByOf traverse ≡ traverseBy
--

traverseByOf :: () => Traversal s t a b -> forall x. () => x -> f x -> forall x y. () => f x -> y -> f x -> f y -> a -> f b -> s -> f t -- | Fuse a Traversal by reassociating all of the -- (<*>) operations to the left and fusing all of -- the fmap calls into one. This is particularly useful when -- constructing a Traversal using operations from -- GHC.Generics. -- -- Given a pair of Traversals foo and bar, -- --

--   confusing (foo.bar) = foo.bar
--

-- -- However, foo and bar are each going to use the -- Applicative they are given. -- -- confusing exploits the Yoneda lemma to merge their -- separate uses of fmap into a single fmap. and it further -- exploits an interesting property of the right Kan lift (or -- Curried) to left associate all of the uses of -- (<*>) to make it possible to fuse together more -- fmaps. -- -- This is particularly effective when the choice of functor f -- is unknown at compile time or when the Traversal -- foo.bar in the above description is recursive or complex -- enough to prevent inlining. -- -- fusing is a version of this combinator suitable for fusing -- lenses. -- --

--   confusing :: Traversal s t a b -> Traversal s t a b
--

confusing :: Applicative f => LensLike Curried Yoneda f Yoneda f s t a b -> LensLike f s t a b -- | Try the second traversal. If it returns no entries, try again with all -- entries from the first traversal, recursively. -- --

--   deepOf :: Fold s s          -> Fold s a                   -> Fold s a
--   deepOf :: Traversal' s s    -> Traversal' s a             -> Traversal' s a
--   deepOf :: Traversal s t s t -> Traversal s t a b          -> Traversal s t a b
--   deepOf :: Fold s s          -> IndexedFold i s a          -> IndexedFold i s a
--   deepOf :: Traversal s t s t -> IndexedTraversal i s t a b -> IndexedTraversal i s t a b
--

deepOf :: (Conjoined p, Applicative f) => LensLike f s t s t -> Traversing p f s t a b -> Over p f s t a b -- | Try the first Traversal (or Fold), falling back on the -- second Traversal (or Fold) if it returns no entries. -- -- This is only a valid Traversal if the second Traversal -- is disjoint from the result of the first or returns exactly the same -- results. These conditions are trivially met when given a Lens, -- Iso, Getter, Prism or "affine" Traversal -- one -- that has 0 or 1 target. -- -- Mutatis mutandis for Fold. -- --

--   >>> [0,1,2,3] ^? failing (ix 1) (ix 2)
--   Just 1
--

-- --

--   >>> [0,1,2,3] ^? failing (ix 42) (ix 2)
--   Just 2
--

-- --

--   failing :: Traversal s t a b -> Traversal s t a b -> Traversal s t a b
--   failing :: Prism s t a b     -> Prism s t a b     -> Traversal s t a b
--   failing :: Fold s a          -> Fold s a          -> Fold s a
--

-- -- These cases are also supported, trivially, but are boring, because the -- left hand side always succeeds. -- --

--   failing :: Lens s t a b      -> Traversal s t a b -> Traversal s t a b
--   failing :: Iso s t a b       -> Traversal s t a b -> Traversal s t a b
--   failing :: Equality s t a b  -> Traversal s t a b -> Traversal s t a b
--   failing :: Getter s a        -> Fold s a          -> Fold s a
--

-- -- If both of the inputs are indexed, the result is also indexed, so you -- can apply this to a pair of indexed traversals or indexed folds, -- obtaining an indexed traversal or indexed fold. -- --

--   failing :: IndexedTraversal i s t a b -> IndexedTraversal i s t a b -> IndexedTraversal i s t a b
--   failing :: IndexedFold i s a          -> IndexedFold i s a          -> IndexedFold i s a
--

-- -- These cases are also supported, trivially, but are boring, because the -- left hand side always succeeds. -- --

--   failing :: IndexedLens i s t a b      -> IndexedTraversal i s t a b -> IndexedTraversal i s t a b
--   failing :: IndexedGetter i s a        -> IndexedGetter i s a        -> IndexedFold i s a
--

failing :: (Conjoined p, Applicative f) => Traversing p f s t a b -> Over p f s t a b -> Over p f s t a b infixl 5 `failing` -- | Try to map a function which uses the index over this -- IndexedTraversal, failing if the IndexedTraversal has no -- targets. -- --

--   ifailover :: Alternative m => IndexedTraversal i s t a b -> (i -> a -> b) -> s -> m t
--

ifailover :: Alternative m => Over Indexed i (,) Any s t a b -> i -> a -> b -> s -> m t -- | Try to map a function over this Traversal, failing if the -- Traversal has no targets. -- --

--   >>> failover (element 3) (*2) [1,2] :: Maybe [Int]
--   Nothing
--

-- --

--   >>> failover _Left (*2) (Right 4) :: Maybe (Either Int Int)
--   Nothing
--

-- --

--   >>> failover _Right (*2) (Right 4) :: Maybe (Either Int Int)
--   Just (Right 8)
--

-- --

--   failover :: Alternative m => Traversal s t a b -> (a -> b) -> s -> m t
--

failover :: Alternative m => LensLike (,) Any s t a b -> a -> b -> s -> m t -- | Traverse elements of a Traversable container where their -- ordinal positions match a predicate. -- --

--   elements ≡ elementsOf traverse
--

elements :: Traversable t => Int -> Bool -> IndexedTraversal' Int t a a -- | Traverse (or fold) selected elements of a Traversal (or -- Fold) where their ordinal positions match a predicate. -- --

--   elementsOf :: Traversal' s a -> (Int -> Bool) -> IndexedTraversal' Int s a
--   elementsOf :: Fold s a       -> (Int -> Bool) -> IndexedFold Int s a
--

elementsOf :: Applicative f => LensLike Indexing f s t a a -> Int -> Bool -> IndexedLensLike Int f s t a a -- | Traverse the nth element of a Traversable container. -- --

--   element ≡ elementOf traverse
--

element :: Traversable t => Int -> IndexedTraversal' Int t a a -- | Traverse the nth elementOf a Traversal, -- Lens or Iso if it exists. -- --

--   >>> [[1],[3,4]] & elementOf (traverse.traverse) 1 .~ 5
--   [[1],[5,4]]
--

-- --

--   >>> [[1],[3,4]] ^? elementOf (folded.folded) 1
--   Just 3
--

-- --

--   >>> timingOut $ ['a'..] ^?! elementOf folded 5
--   'f'
--

-- --

--   >>> timingOut $ take 10 $ elementOf traverse 3 .~ 16 $ [0..]
--   [0,1,2,16,4,5,6,7,8,9]
--

-- --

--   elementOf :: Traversal' s a -> Int -> IndexedTraversal' Int s a
--   elementOf :: Fold s a       -> Int -> IndexedFold Int s a
--

elementOf :: Applicative f => LensLike Indexing f s t a a -> Int -> IndexedLensLike Int f s t a a -- | This is the trivial empty Traversal. -- --

--   ignored :: IndexedTraversal i s s a b
--

-- --

--   ignored ≡ const pure
--

-- --

--   >>> 6 & ignored %~ absurd
--   6
--

ignored :: Applicative f => pafb -> s -> f s -- | Traverse any Traversable container. This is an -- IndexedTraversal that is indexed by ordinal position. traversed64 :: Traversable f => IndexedTraversal Int64 f a f b a b -- | Traverse any Traversable1 container. This is an -- IndexedTraversal1 that is indexed by ordinal position. traversed1 :: Traversable1 f => IndexedTraversal1 Int f a f b a b -- | Traverse any Traversable container. This is an -- IndexedTraversal that is indexed by ordinal position. traversed :: Traversable f => IndexedTraversal Int f a f b a b -- | Generalizes mapAccumL to an arbitrary IndexedTraversal -- with access to the index. -- -- imapAccumLOf accumulates state from left to right. -- --

--   mapAccumLOf l ≡ imapAccumLOf l . const
--

-- --

--   imapAccumLOf :: IndexedLens i s t a b      -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
--   imapAccumLOf :: IndexedTraversal i s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
--

imapAccumLOf :: () => Over Indexed i State acc s t a b -> i -> acc -> a -> (acc, b) -> acc -> s -> (acc, t) -- | Generalizes mapAccumR to an arbitrary IndexedTraversal -- with access to the index. -- -- imapAccumROf accumulates state from right to left. -- --

--   mapAccumROf l ≡ imapAccumROf l . const
--

-- --

--   imapAccumROf :: IndexedLens i s t a b      -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
--   imapAccumROf :: IndexedTraversal i s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
--

imapAccumROf :: () => Over Indexed i Backwards State acc s t a b -> i -> acc -> a -> (acc, b) -> acc -> s -> (acc, t) -- | Map each element of a structure targeted by a Lens to a monadic -- action, evaluate these actions from left to right, and collect the -- results, with access its position (and the arguments flipped). -- --

--   forMOf l a ≡ iforMOf l a . const
--   iforMOf ≡ flip . imapMOf
--

-- --

--   iforMOf :: Monad m => IndexedLens i s t a b      -> s -> (i -> a -> m b) -> m t
--   iforMOf :: Monad m => IndexedTraversal i s t a b -> s -> (i -> a -> m b) -> m t
--

iforMOf :: () => Indexed i a WrappedMonad m b -> s -> WrappedMonad m t -> s -> i -> a -> m b -> m t -- | Map each element of a structure targeted by a Lens to a monadic -- action, evaluate these actions from left to right, and collect the -- results, with access its position. -- -- When you don't need access to the index mapMOf is more liberal -- in what it can accept. -- --

--   mapMOf l ≡ imapMOf l . const
--

-- --

--   imapMOf :: Monad m => IndexedLens       i s t a b -> (i -> a -> m b) -> s -> m t
--   imapMOf :: Monad m => IndexedTraversal  i s t a b -> (i -> a -> m b) -> s -> m t
--   imapMOf :: Bind  m => IndexedTraversal1 i s t a b -> (i -> a -> m b) -> s -> m t
--

imapMOf :: () => Over Indexed i WrappedMonad m s t a b -> i -> a -> m b -> s -> m t -- | Traverse with an index (and the arguments flipped). -- --

--   forOf l a ≡ iforOf l a . const
--   iforOf ≡ flip . itraverseOf
--

-- --

--   iforOf :: Functor f     => IndexedLens i s t a b       -> s -> (i -> a -> f b) -> f t
--   iforOf :: Applicative f => IndexedTraversal i s t a b  -> s -> (i -> a -> f b) -> f t
--   iforOf :: Apply f       => IndexedTraversal1 i s t a b -> s -> (i -> a -> f b) -> f t
--

iforOf :: () => Indexed i a f b -> s -> f t -> s -> i -> a -> f b -> f t -- | Traversal with an index. -- -- NB: When you don't need access to the index then you can just -- apply your IndexedTraversal directly as a function! -- --

--   itraverseOf ≡ withIndex
--   traverseOf l = itraverseOf l . const = id
--

-- --

--   itraverseOf :: Functor f     => IndexedLens i s t a b       -> (i -> a -> f b) -> s -> f t
--   itraverseOf :: Applicative f => IndexedTraversal i s t a b  -> (i -> a -> f b) -> s -> f t
--   itraverseOf :: Apply f       => IndexedTraversal1 i s t a b -> (i -> a -> f b) -> s -> f t
--

itraverseOf :: () => Indexed i a f b -> s -> f t -> i -> a -> f b -> s -> f t -- | Clone an IndexedTraversal1 yielding an IndexedTraversal1 -- with the same index. cloneIndexedTraversal1 :: () => AnIndexedTraversal1 i s t a b -> IndexedTraversal1 i s t a b -- | Clone a Traversal1 yielding an IndexPreservingTraversal1 -- that passes through whatever index it is composed with. cloneIndexPreservingTraversal1 :: () => ATraversal1 s t a b -> IndexPreservingTraversal1 s t a b -- | A Traversal1 is completely characterized by its behavior on a -- Bazaar1. cloneTraversal1 :: () => ATraversal1 s t a b -> Traversal1 s t a b -- | Clone an IndexedTraversal yielding an IndexedTraversal -- with the same index. cloneIndexedTraversal :: () => AnIndexedTraversal i s t a b -> IndexedTraversal i s t a b -- | Clone a Traversal yielding an IndexPreservingTraversal -- that passes through whatever index it is composed with. cloneIndexPreservingTraversal :: () => ATraversal s t a b -> IndexPreservingTraversal s t a b -- | A Traversal is completely characterized by its behavior on a -- Bazaar. -- -- Cloning a Traversal is one way to make sure you aren't given -- something weaker, such as a Fold and can be used as a way to -- pass around traversals that have to be monomorphic in f. -- -- Note: This only accepts a proper Traversal (or Lens). To -- clone a Lens as such, use cloneLens. -- -- Note: It is usually better to use ReifiedTraversal and -- runTraversal than to cloneTraversal. The former can -- execute at full speed, while the latter needs to round trip through -- the Bazaar. -- --

--   >>> let foo l a = (view (getting (cloneTraversal l)) a, set (cloneTraversal l) 10 a)
--   
--   >>> foo both ("hello","world")
--   ("helloworld",(10,10))
--

-- --

--   cloneTraversal :: LensLike (Bazaar (->) a b) s t a b -> Traversal s t a b
--

cloneTraversal :: () => ATraversal s t a b -> Traversal s t a b -- | Visit all but the first n targets of a Traversal, -- Fold, Getter or Lens. -- --

--   >>> ("hello","world") ^? dropping 1 both
--   Just "world"
--

-- -- Dropping works on infinite traversals as well: -- --

--   >>> [1..] ^? dropping 1 folded
--   Just 2
--

-- --

--   dropping :: Int -> Traversal' s a                   -> Traversal' s a
--   dropping :: Int -> Lens' s a                        -> Traversal' s a
--   dropping :: Int -> Iso' s a                         -> Traversal' s a
--   dropping :: Int -> Prism' s a                       -> Traversal' s a
--   dropping :: Int -> Getter s a                       -> Fold s a
--   dropping :: Int -> Fold s a                         -> Fold s a
--   dropping :: Int -> IndexedTraversal' i s a          -> IndexedTraversal' i s a
--   dropping :: Int -> IndexedLens' i s a               -> IndexedTraversal' i s a
--   dropping :: Int -> IndexedGetter i s a              -> IndexedFold i s a
--   dropping :: Int -> IndexedFold i s a                -> IndexedFold i s a
--

dropping :: (Conjoined p, Applicative f) => Int -> Over p Indexing f s t a a -> Over p f s t a a -- | Visit the first n targets of a Traversal, Fold, -- Getter or Lens. -- --

--   >>> [("hello","world"),("!!!","!!!")]^.. taking 2 (traverse.both)
--   ["hello","world"]
--

-- --

--   >>> timingOut $ [1..] ^.. taking 3 traverse
--   [1,2,3]
--

-- --

--   >>> over (taking 5 traverse) succ "hello world"
--   "ifmmp world"
--

-- --

--   taking :: Int -> Traversal' s a                   -> Traversal' s a
--   taking :: Int -> Lens' s a                        -> Traversal' s a
--   taking :: Int -> Iso' s a                         -> Traversal' s a
--   taking :: Int -> Prism' s a                       -> Traversal' s a
--   taking :: Int -> Getter s a                       -> Fold s a
--   taking :: Int -> Fold s a                         -> Fold s a
--   taking :: Int -> IndexedTraversal' i s a          -> IndexedTraversal' i s a
--   taking :: Int -> IndexedLens' i s a               -> IndexedTraversal' i s a
--   taking :: Int -> IndexedGetter i s a              -> IndexedFold i s a
--   taking :: Int -> IndexedFold i s a                -> IndexedFold i s a
--

taking :: (Conjoined p, Applicative f) => Int -> Traversing p f s t a a -> Over p f s t a a -- | Apply a different Traversal or Fold to each side of a -- Bitraversable container. -- --

--   beside :: Traversal s t a b                -> Traversal s' t' a b                -> Traversal (r s s') (r t t') a b
--   beside :: IndexedTraversal i s t a b       -> IndexedTraversal i s' t' a b       -> IndexedTraversal i (r s s') (r t t') a b
--   beside :: IndexPreservingTraversal s t a b -> IndexPreservingTraversal s' t' a b -> IndexPreservingTraversal (r s s') (r t t') a b
--

-- --

--   beside :: Traversal s t a b                -> Traversal s' t' a b                -> Traversal (s,s') (t,t') a b
--   beside :: Lens s t a b                     -> Lens s' t' a b                     -> Traversal (s,s') (t,t') a b
--   beside :: Fold s a                         -> Fold s' a                          -> Fold (s,s') a
--   beside :: Getter s a                       -> Getter s' a                        -> Fold (s,s') a
--

-- --

--   beside :: IndexedTraversal i s t a b       -> IndexedTraversal i s' t' a b       -> IndexedTraversal i (s,s') (t,t') a b
--   beside :: IndexedLens i s t a b            -> IndexedLens i s' t' a b            -> IndexedTraversal i (s,s') (t,t') a b
--   beside :: IndexedFold i s a                -> IndexedFold i s' a                 -> IndexedFold i (s,s') a
--   beside :: IndexedGetter i s a              -> IndexedGetter i s' a               -> IndexedFold i (s,s') a
--

-- --

--   beside :: IndexPreservingTraversal s t a b -> IndexPreservingTraversal s' t' a b -> IndexPreservingTraversal (s,s') (t,t') a b
--   beside :: IndexPreservingLens s t a b      -> IndexPreservingLens s' t' a b      -> IndexPreservingTraversal (s,s') (t,t') a b
--   beside :: IndexPreservingFold s a          -> IndexPreservingFold s' a           -> IndexPreservingFold (s,s') a
--   beside :: IndexPreservingGetter s a        -> IndexPreservingGetter s' a         -> IndexPreservingFold (s,s') a
--

-- --

--   >>> ("hello",["world","!!!"])^..beside id traverse
--   ["hello","world","!!!"]
--

beside :: (Representable q, Applicative Rep q, Applicative f, Bitraversable r) => Optical p q f s t a b -> Optical p q f s' t' a b -> Optical p q f r s s' r t t' a b -- | Traverse both parts of a Bitraversable1 container with matching -- types. -- -- Usually that type will be a pair. -- --

--   both1 :: Traversal1 (a, a)       (b, b)       a b
--   both1 :: Traversal1 (Either a a) (Either b b) a b
--

both1 :: Bitraversable1 r => Traversal1 r a a r b b a b -- | Traverse both parts of a Bitraversable container with matching -- types. -- -- Usually that type will be a pair. -- --

--   >>> (1,2) & both *~ 10
--   (10,20)
--

-- --

--   >>> over both length ("hello","world")
--   (5,5)
--

-- --

--   >>> ("hello","world")^.both
--   "helloworld"
--

-- --

--   both :: Traversal (a, a)       (b, b)       a b
--   both :: Traversal (Either a a) (Either b b) a b
--

both :: Bitraversable r => Traversal r a a r b b a b -- | The one-level version of contextsOf. This extracts a list of -- the immediate children according to a given Traversal as -- editable contexts. -- -- Given a context you can use pos to see the values, peek -- at what the structure would be like with an edited result, or simply -- extract the original structure. -- --

--   propChildren l x = toListOf l x == map pos (holesOf l x)
--   propId l x = all (== x) [extract w | w <- holesOf l x]
--

-- --

--   holesOf :: Iso' s a                -> s -> [Pretext' (->) a s]
--   holesOf :: Lens' s a               -> s -> [Pretext' (->) a s]
--   holesOf :: Traversal' s a          -> s -> [Pretext' (->) a s]
--   holesOf :: IndexedLens' i s a      -> s -> [Pretext' (Indexed i) a s]
--   holesOf :: IndexedTraversal' i s a -> s -> [Pretext' (Indexed i) a s]
--

holesOf :: Conjoined p => Over p Bazaar p a a s t a a -> s -> [Pretext p a a t] -- | This converts a Traversal that you "know" will target only one -- element to a Lens. It can also be used to transform a -- Fold into a Getter. -- -- The resulting Lens or Getter will be partial if the -- Traversal targets nothing or more than one element. -- --

--   >>> Left (ErrorCall "unsafeSingular: empty traversal") <- try (evaluate ([] & unsafeSingular traverse .~ 0)) :: IO (Either ErrorCall [Integer])
--

-- --

--   unsafeSingular :: Traversal s t a b          -> Lens s t a b
--   unsafeSingular :: Fold s a                   -> Getter s a
--   unsafeSingular :: IndexedTraversal i s t a b -> IndexedLens i s t a b
--   unsafeSingular :: IndexedFold i s a          -> IndexedGetter i s a
--

unsafeSingular :: (HasCallStack, Conjoined p, Functor f) => Traversing p f s t a b -> Over p f s t a b -- | This converts a Traversal that you "know" will target one or -- more elements to a Lens. It can also be used to transform a -- non-empty Fold into a Getter. -- -- The resulting Lens or Getter will be partial if the -- supplied Traversal returns no results. -- --

--   >>> [1,2,3] ^. singular _head
--   1
--

-- --

--   >>> Left (ErrorCall "singular: empty traversal") <- try (evaluate ([] ^. singular _head)) :: IO (Either ErrorCall ())
--

-- --

--   >>> Left 4 ^. singular _Left
--   4
--

-- --

--   >>> [1..10] ^. singular (ix 7)
--   8
--

-- --

--   >>> [] & singular traverse .~ 0
--   []
--

-- --

--   singular :: Traversal s t a a          -> Lens s t a a
--   singular :: Fold s a                   -> Getter s a
--   singular :: IndexedTraversal i s t a a -> IndexedLens i s t a a
--   singular :: IndexedFold i s a          -> IndexedGetter i s a
--

singular :: (HasCallStack, Conjoined p, Functor f) => Traversing p f s t a a -> Over p f s t a a iunsafePartsOf' :: () => Over Indexed i Bazaar Indexed i a b s t a b -> IndexedLens [i] s t [a] [b] unsafePartsOf' :: () => ATraversal s t a b -> Lens s t [a] [b] -- | An indexed version of unsafePartsOf that receives the entire -- list of indices as its index. iunsafePartsOf :: (Indexable [i] p, Functor f) => Traversing Indexed i f s t a b -> Over p f s t [a] [b] -- | unsafePartsOf turns a Traversal into a uniplate -- (or biplate) family. -- -- If you do not need the types of s and t to be -- different, it is recommended that you use partsOf. -- -- It is generally safer to traverse with the Bazaar rather than -- use this combinator. However, it is sometimes convenient. -- -- This is unsafe because if you don't supply at least as many -- b's as you were given a's, then the reconstruction -- of t will result in an error! -- -- When applied to a Fold the result is merely a Getter -- (and becomes safe). -- --

--   unsafePartsOf :: Iso s t a b       -> Lens s t [a] [b]
--   unsafePartsOf :: Lens s t a b      -> Lens s t [a] [b]
--   unsafePartsOf :: Traversal s t a b -> Lens s t [a] [b]
--   unsafePartsOf :: Fold s a          -> Getter s [a]
--   unsafePartsOf :: Getter s a        -> Getter s [a]
--

unsafePartsOf :: Functor f => Traversing ((->) :: * -> * -> *) f s t a b -> LensLike f s t [a] [b] -- | A type-restricted version of ipartsOf that can only be used -- with an IndexedTraversal. ipartsOf' :: (Indexable [i] p, Functor f) => Over Indexed i Bazaar' Indexed i a s t a a -> Over p f s t [a] [a] -- | A type-restricted version of partsOf that can only be used with -- a Traversal. partsOf' :: () => ATraversal s t a a -> Lens s t [a] [a] -- | An indexed version of partsOf that receives the entire list of -- indices as its index. ipartsOf :: (Indexable [i] p, Functor f) => Traversing Indexed i f s t a a -> Over p f s t [a] [a] -- | partsOf turns a Traversal into a Lens that -- resembles an early version of the uniplate (or biplate) -- type. -- -- Note: You should really try to maintain the invariant of the -- number of children in the list. -- --

--   >>> (a,b,c) & partsOf each .~ [x,y,z]
--   (x,y,z)
--

-- -- Any extras will be lost. If you do not supply enough, then the -- remainder will come from the original structure. -- --

--   >>> (a,b,c) & partsOf each .~ [w,x,y,z]
--   (w,x,y)
--

-- --

--   >>> (a,b,c) & partsOf each .~ [x,y]
--   (x,y,c)
--

-- --

--   >>> ('b', 'a', 'd', 'c') & partsOf each %~ sort
--   ('a','b','c','d')
--

-- -- So technically, this is only a Lens if you do not change the -- number of results it returns. -- -- When applied to a Fold the result is merely a Getter. -- --

--   partsOf :: Iso' s a       -> Lens' s [a]
--   partsOf :: Lens' s a      -> Lens' s [a]
--   partsOf :: Traversal' s a -> Lens' s [a]
--   partsOf :: Fold s a       -> Getter s [a]
--   partsOf :: Getter s a     -> Getter s [a]
--

partsOf :: Functor f => Traversing ((->) :: * -> * -> *) f s t a a -> LensLike f s t [a] [a] -- | This IndexedTraversal allows you to traverse the -- individual stores in a Bazaar with access to their indices. iloci :: (Indexable i p, Applicative f) => p a f b -> Bazaar Indexed i a c s -> f Bazaar Indexed i b c s -- | This Traversal allows you to traverse the individual -- stores in a Bazaar. loci :: Applicative f => a -> f b -> Bazaar ((->) :: * -> * -> *) a c s -> f Bazaar ((->) :: * -> * -> *) b c s -- | This permits the use of scanl1 over an arbitrary -- Traversal or Lens. -- --

--   scanl1 ≡ scanl1Of traverse
--

-- --

--   scanl1Of :: Iso s t a a       -> (a -> a -> a) -> s -> t
--   scanl1Of :: Lens s t a a      -> (a -> a -> a) -> s -> t
--   scanl1Of :: Traversal s t a a -> (a -> a -> a) -> s -> t
--

scanl1Of :: () => LensLike State Maybe a s t a a -> a -> a -> a -> s -> t -- | This permits the use of scanr1 over an arbitrary -- Traversal or Lens. -- --

--   scanr1 ≡ scanr1Of traverse
--

-- --

--   scanr1Of :: Iso s t a a       -> (a -> a -> a) -> s -> t
--   scanr1Of :: Lens s t a a      -> (a -> a -> a) -> s -> t
--   scanr1Of :: Traversal s t a a -> (a -> a -> a) -> s -> t
--

scanr1Of :: () => LensLike Backwards State Maybe a s t a a -> a -> a -> a -> s -> t -- | This generalizes mapAccumL to an arbitrary Traversal. -- --

--   mapAccumL ≡ mapAccumLOf traverse
--

-- -- mapAccumLOf accumulates State from left to right. -- --

--   mapAccumLOf :: Iso s t a b       -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
--   mapAccumLOf :: Lens s t a b      -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
--   mapAccumLOf :: Traversal s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
--

-- --

--   mapAccumLOf :: LensLike (State acc) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
--   mapAccumLOf l f acc0 s = swap (runState (l (a -> state (acc -> swap (f acc a))) s) acc0)
--

mapAccumLOf :: () => LensLike State acc s t a b -> acc -> a -> (acc, b) -> acc -> s -> (acc, t) -- | This generalizes mapAccumR to an arbitrary Traversal. -- --

--   mapAccumR ≡ mapAccumROf traverse
--

-- -- mapAccumROf accumulates State from right to left. -- --

--   mapAccumROf :: Iso s t a b       -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
--   mapAccumROf :: Lens s t a b      -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
--   mapAccumROf :: Traversal s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
--

-- --

--   mapAccumROf :: LensLike (Backwards (State acc)) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
--

mapAccumROf :: () => LensLike Backwards State acc s t a b -> acc -> a -> (acc, b) -> acc -> s -> (acc, t) -- | This generalizes transpose to an arbitrary Traversal. -- -- Note: transpose handles ragged inputs more intelligently, but -- for non-ragged inputs: -- --

--   >>> transposeOf traverse [[1,2,3],[4,5,6]]
--   [[1,4],[2,5],[3,6]]
--

-- --

--   transpose ≡ transposeOf traverse
--

-- -- Since every Lens is a Traversal, we can use this as a -- form of monadic strength as well: -- --

--   transposeOf _2 :: (b, [a]) -> [(b, a)]
--

transposeOf :: () => LensLike ZipList s t [a] a -> s -> [t] -- | Sequence the (monadic) effects targeted by a Lens in a -- container from left to right. -- --

--   >>> sequenceOf each ([1,2],[3,4],[5,6])
--   [(1,3,5),(1,3,6),(1,4,5),(1,4,6),(2,3,5),(2,3,6),(2,4,5),(2,4,6)]
--

-- --

--   sequence ≡ sequenceOf traverse
--   sequenceOf l ≡ mapMOf l id
--   sequenceOf l ≡ unwrapMonad . l WrapMonad
--

-- --

--   sequenceOf :: Monad m => Iso s t (m b) b       -> s -> m t
--   sequenceOf :: Monad m => Lens s t (m b) b      -> s -> m t
--   sequenceOf :: Monad m => Traversal s t (m b) b -> s -> m t
--

sequenceOf :: () => LensLike WrappedMonad m s t m b b -> s -> m t -- | forMOf is a flipped version of mapMOf, consistent with -- the definition of forM. -- --

--   >>> forMOf both (1,3) $ \x -> [x, x + 1]
--   [(1,3),(1,4),(2,3),(2,4)]
--

-- --

--   forM ≡ forMOf traverse
--   forMOf l ≡ flip (mapMOf l)
--   iforMOf l s ≡ forM l s . Indexed
--

-- --

--   forMOf :: Monad m => Iso s t a b       -> s -> (a -> m b) -> m t
--   forMOf :: Monad m => Lens s t a b      -> s -> (a -> m b) -> m t
--   forMOf :: Monad m => Traversal s t a b -> s -> (a -> m b) -> m t
--

forMOf :: () => LensLike WrappedMonad m s t a b -> s -> a -> m b -> m t -- | Map each element of a structure targeted by a Lens to a monadic -- action, evaluate these actions from left to right, and collect the -- results. -- --

--   >>> mapMOf both (\x -> [x, x + 1]) (1,3)
--   [(1,3),(1,4),(2,3),(2,4)]
--

-- --

--   mapM ≡ mapMOf traverse
--   imapMOf l ≡ forM l . Indexed
--

-- --

--   mapMOf :: Monad m => Iso s t a b       -> (a -> m b) -> s -> m t
--   mapMOf :: Monad m => Lens s t a b      -> (a -> m b) -> s -> m t
--   mapMOf :: Monad m => Traversal s t a b -> (a -> m b) -> s -> m t
--

mapMOf :: () => LensLike WrappedMonad m s t a b -> a -> m b -> s -> m t -- | Evaluate each action in the structure from left to right, and collect -- the results. -- --

--   >>> sequenceAOf both ([1,2],[3,4])
--   [(1,3),(1,4),(2,3),(2,4)]
--

-- --

--   sequenceA ≡ sequenceAOf traverse ≡ traverse id
--   sequenceAOf l ≡ traverseOf l id ≡ l id
--

-- --

--   sequenceAOf :: Functor f => Iso s t (f b) b       -> s -> f t
--   sequenceAOf :: Functor f => Lens s t (f b) b      -> s -> f t
--   sequenceAOf :: Applicative f => Traversal s t (f b) b -> s -> f t
--

sequenceAOf :: () => LensLike f s t f b b -> s -> f t -- | A version of traverseOf with the arguments flipped, such that: -- --

--   >>> forOf each (1,2,3) print
--   1
--   2
--   3
--   ((),(),())
--

-- -- This function is only provided for consistency, flip is -- strictly more general. -- --

--   forOf ≡ flip
--   forOf ≡ flip . traverseOf
--

-- --

--   for ≡ forOf traverse
--   ifor l s ≡ for l s . Indexed
--

-- --

--   forOf :: Functor f => Iso s t a b -> s -> (a -> f b) -> f t
--   forOf :: Functor f => Lens s t a b -> s -> (a -> f b) -> f t
--   forOf :: Applicative f => Traversal s t a b -> s -> (a -> f b) -> f t
--

forOf :: () => LensLike f s t a b -> s -> a -> f b -> f t -- | Map each element of a structure targeted by a Lens or -- Traversal, evaluate these actions from left to right, and -- collect the results. -- -- This function is only provided for consistency, id is strictly -- more general. -- --

--   >>> traverseOf each print (1,2,3)
--   1
--   2
--   3
--   ((),(),())
--

-- --

--   traverseOf ≡ id
--   itraverseOf l ≡ traverseOf l . Indexed
--   itraverseOf itraversed ≡ itraverse
--

-- -- This yields the obvious law: -- --

--   traverse ≡ traverseOf traverse
--

-- --

--   traverseOf :: Functor f     => Iso s t a b        -> (a -> f b) -> s -> f t
--   traverseOf :: Functor f     => Lens s t a b       -> (a -> f b) -> s -> f t
--   traverseOf :: Apply f       => Traversal1 s t a b -> (a -> f b) -> s -> f t
--   traverseOf :: Applicative f => Traversal s t a b  -> (a -> f b) -> s -> f t
--

traverseOf :: () => LensLike f s t a b -> a -> f b -> s -> f t -- | When you see this as an argument to a function, it expects a -- Traversal. type ATraversal s t a b = LensLike Bazaar ((->) :: * -> * -> *) a b s t a b -- |

--   type ATraversal' = Simple ATraversal
--

type ATraversal' s a = ATraversal s s a a -- | When you see this as an argument to a function, it expects a -- Traversal1. type ATraversal1 s t a b = LensLike Bazaar1 ((->) :: * -> * -> *) a b s t a b -- |

--   type ATraversal1' = Simple ATraversal1
--

type ATraversal1' s a = ATraversal1 s s a a -- | When you see this as an argument to a function, it expects an -- IndexedTraversal. type AnIndexedTraversal i s t a b = Over Indexed i Bazaar Indexed i a b s t a b -- | When you see this as an argument to a function, it expects an -- IndexedTraversal1. type AnIndexedTraversal1 i s t a b = Over Indexed i Bazaar1 Indexed i a b s t a b -- |

--   type AnIndexedTraversal' = Simple (AnIndexedTraversal i)
--

type AnIndexedTraversal' i s a = AnIndexedTraversal i s s a a -- |

--   type AnIndexedTraversal1' = Simple (AnIndexedTraversal1 i)
--

type AnIndexedTraversal1' i s a = AnIndexedTraversal1 i s s a a -- | When you see this as an argument to a function, it expects -- --

to be indexed if p is an instance of Indexed -- i,
to be unindexed if p is (->),
a Traversal if f is Applicative,
a Getter if f is only a Functor and -- Contravariant,
a Lens if f is only a Functor,
a Fold if f is Applicative and -- Contravariant.

type Traversing (p :: * -> * -> *) (f :: * -> *) s t a b = Over p BazaarT p f a b s t a b type Traversing1 (p :: * -> * -> *) (f :: * -> *) s t a b = Over p BazaarT1 p f a b s t a b -- |

--   type Traversing' f = Simple (Traversing f)
--

type Traversing' (p :: * -> * -> *) (f :: * -> *) s a = Traversing p f s s a a type Traversing1' (p :: * -> * -> *) (f :: * -> *) s a = Traversing1 p f s s a a -- | Allows IndexedTraversal the value at the smallest index. class Ord k => TraverseMin k (m :: * -> *) | m -> k -- | IndexedTraversal of the element with the smallest index. traverseMin :: (TraverseMin k m, Indexable k p, Applicative f) => p v f v -> m v -> f m v -- | Allows IndexedTraversal of the value at the largest index. class Ord k => TraverseMax k (m :: * -> *) | m -> k -- | IndexedTraversal of the element at the largest index. traverseMax :: (TraverseMax k m, Indexable k p, Applicative f) => p v f v -> m v -> f m v -- | Fold a value using a specified Fold and Monoid -- operations. This is like foldMapBy where the Foldable -- instance can be manually specified. -- --

--   foldMapByOf folded ≡ foldMapBy
--

-- --

--   foldMapByOf :: Getter s a     -> (r -> r -> r) -> r -> (a -> r) -> s -> r
--   foldMapByOf :: Fold s a       -> (r -> r -> r) -> r -> (a -> r) -> s -> r
--   foldMapByOf :: Traversal' s a -> (r -> r -> r) -> r -> (a -> r) -> s -> r
--   foldMapByOf :: Lens' s a      -> (r -> r -> r) -> r -> (a -> r) -> s -> r
--   foldMapByOf :: Iso' s a       -> (r -> r -> r) -> r -> (a -> r) -> s -> r
--

-- --

--   >>> foldMapByOf both (+) 0 length ("hello","world")
--   10
--

foldMapByOf :: () => Fold s a -> r -> r -> r -> r -> a -> r -> s -> r -- | Fold a value using a specified Fold and Monoid -- operations. This is like foldBy where the Foldable -- instance can be manually specified. -- --

--   foldByOf folded ≡ foldBy
--

-- --

--   foldByOf :: Getter s a     -> (a -> a -> a) -> a -> s -> a
--   foldByOf :: Fold s a       -> (a -> a -> a) -> a -> s -> a
--   foldByOf :: Lens' s a      -> (a -> a -> a) -> a -> s -> a
--   foldByOf :: Traversal' s a -> (a -> a -> a) -> a -> s -> a
--   foldByOf :: Iso' s a       -> (a -> a -> a) -> a -> s -> a
--

-- --

--   >>> foldByOf both (++) [] ("hello","world")
--   "helloworld"
--

foldByOf :: () => Fold s a -> a -> a -> a -> a -> s -> a -- | Obtain an IndexedFold by dropping elements from another -- IndexedFold, IndexedLens, IndexedGetter or -- IndexedTraversal while a predicate holds. -- --

--   idroppingWhile :: (i -> a -> Bool) -> IndexedFold i s a          -> IndexedFold i s a
--   idroppingWhile :: (i -> a -> Bool) -> IndexedTraversal' i s a    -> IndexedFold i s a -- see notes
--   idroppingWhile :: (i -> a -> Bool) -> IndexedLens' i s a         -> IndexedFold i s a -- see notes
--   idroppingWhile :: (i -> a -> Bool) -> IndexedGetter i s a        -> IndexedFold i s a
--

-- -- Note: As with droppingWhile applying idroppingWhile to -- an IndexedLens or IndexedTraversal will still allow you -- to use it as a pseudo-IndexedTraversal, but if you change the -- value of the first target to one where the predicate returns -- True, then you will break the Traversal laws and -- Traversal fusion will no longer be sound. idroppingWhile :: (Indexable i p, Profunctor q, Applicative f) => i -> a -> Bool -> Optical Indexed i q Compose State Bool f s t a a -> Optical p q f s t a a -- | Obtain an IndexedFold by taking elements from another -- IndexedFold, IndexedLens, IndexedGetter or -- IndexedTraversal while a predicate holds. -- --

--   itakingWhile :: (i -> a -> Bool) -> IndexedFold i s a          -> IndexedFold i s a
--   itakingWhile :: (i -> a -> Bool) -> IndexedTraversal' i s a    -> IndexedFold i s a
--   itakingWhile :: (i -> a -> Bool) -> IndexedLens' i s a         -> IndexedFold i s a
--   itakingWhile :: (i -> a -> Bool) -> IndexedGetter i s a        -> IndexedFold i s a
--

-- -- Note: Applying itakingWhile to an IndexedLens or -- IndexedTraversal will still allow you to use it as a -- pseudo-IndexedTraversal, but if you change the value of any -- target to one where the predicate returns False, then you will -- break the Traversal laws and Traversal fusion will no -- longer be sound. itakingWhile :: (Indexable i p, Profunctor q, Contravariant f, Applicative f) => i -> a -> Bool -> Optical' Indexed i q (Const Endo f s :: * -> *) s a -> Optical' p q f s a -- | Filter an IndexedFold or IndexedGetter, obtaining an -- IndexedFold. -- --

--   >>> [0,0,0,5,5,5]^..traversed.ifiltered (\i a -> i <= a)
--   [0,5,5,5]
--

-- -- Compose with ifiltered to filter another IndexedLens, -- IndexedIso, IndexedGetter, IndexedFold (or -- IndexedTraversal) with access to both the value and the index. -- -- Note: As with filtered, this is not a legal -- IndexedTraversal, unless you are very careful not to invalidate -- the predicate on the target! ifiltered :: (Indexable i p, Applicative f) => i -> a -> Bool -> Optical' p Indexed i f a a -- | Retrieve the indices of the values targeted by a IndexedFold or -- IndexedTraversal which satisfy a predicate. -- --

--   findIndices ≡ findIndicesOf folded
--

-- --

--   findIndicesOf :: IndexedFold i s a       -> (a -> Bool) -> s -> [i]
--   findIndicesOf :: IndexedTraversal' i s a -> (a -> Bool) -> s -> [i]
--

findIndicesOf :: () => IndexedGetting i Endo [i] s a -> a -> Bool -> s -> [i] -- | Retrieve the index of the first value targeted by a IndexedFold -- or IndexedTraversal which satisfies a predicate. -- --

--   findIndex ≡ findIndexOf folded
--

-- --

--   findIndexOf :: IndexedFold i s a       -> (a -> Bool) -> s -> Maybe i
--   findIndexOf :: IndexedTraversal' i s a -> (a -> Bool) -> s -> Maybe i
--

findIndexOf :: () => IndexedGetting i First i s a -> a -> Bool -> s -> Maybe i -- | Retrieve the indices of the values targeted by a IndexedFold or -- IndexedTraversal which are equal to a given value. -- --

--   elemIndices ≡ elemIndicesOf folded
--

-- --

--   elemIndicesOf :: Eq a => IndexedFold i s a       -> a -> s -> [i]
--   elemIndicesOf :: Eq a => IndexedTraversal' i s a -> a -> s -> [i]
--

elemIndicesOf :: Eq a => IndexedGetting i Endo [i] s a -> a -> s -> [i] -- | Retrieve the index of the first value targeted by a IndexedFold -- or IndexedTraversal which is equal to a given value. -- --

--   elemIndex ≡ elemIndexOf folded
--

-- --

--   elemIndexOf :: Eq a => IndexedFold i s a       -> a -> s -> Maybe i
--   elemIndexOf :: Eq a => IndexedTraversal' i s a -> a -> s -> Maybe i
--

elemIndexOf :: Eq a => IndexedGetting i First i s a -> a -> s -> Maybe i -- | Perform an *UNSAFE* head (with index) of an IndexedFold -- or IndexedTraversal assuming that it is there. -- --

--   (^@?!) :: s -> IndexedGetter i s a     -> (i, a)
--   (^@?!) :: s -> IndexedFold i s a       -> (i, a)
--   (^@?!) :: s -> IndexedLens' i s a      -> (i, a)
--   (^@?!) :: s -> IndexedTraversal' i s a -> (i, a)
--

(^@?!) :: HasCallStack => s -> IndexedGetting i Endo (i, a) s a -> (i, a) infixl 8 ^@?! -- | Perform a safe head (with index) of an IndexedFold or -- IndexedTraversal or retrieve Just the index and result -- from an IndexedGetter or IndexedLens. -- -- When using a IndexedTraversal as a partial IndexedLens, -- or an IndexedFold as a partial IndexedGetter this can be -- a convenient way to extract the optional value. -- --

--   (^@?) :: s -> IndexedGetter i s a     -> Maybe (i, a)
--   (^@?) :: s -> IndexedFold i s a       -> Maybe (i, a)
--   (^@?) :: s -> IndexedLens' i s a      -> Maybe (i, a)
--   (^@?) :: s -> IndexedTraversal' i s a -> Maybe (i, a)
--

(^@?) :: () => s -> IndexedGetting i Endo Maybe (i, a) s a -> Maybe (i, a) infixl 8 ^@? -- | An infix version of itoListOf. (^@..) :: () => s -> IndexedGetting i Endo [(i, a)] s a -> [(i, a)] infixl 8 ^@.. -- | Extract the key-value pairs from a structure. -- -- When you don't need access to the indices in the result, then -- toListOf is more flexible in what it accepts. -- --

--   toListOf l ≡ map snd . itoListOf l
--

-- --

--   itoListOf :: IndexedGetter i s a     -> s -> [(i,a)]
--   itoListOf :: IndexedFold i s a       -> s -> [(i,a)]
--   itoListOf :: IndexedLens' i s a      -> s -> [(i,a)]
--   itoListOf :: IndexedTraversal' i s a -> s -> [(i,a)]
--

itoListOf :: () => IndexedGetting i Endo [(i, a)] s a -> s -> [(i, a)] -- | Monadic fold over the elements of a structure with an index, -- associating to the left. -- -- When you don't need access to the index then foldlMOf is more -- flexible in what it accepts. -- --

--   foldlMOf l ≡ ifoldlMOf l . const
--

-- --

--   ifoldlMOf :: Monad m => IndexedGetter i s a     -> (i -> r -> a -> m r) -> r -> s -> m r
--   ifoldlMOf :: Monad m => IndexedFold i s a       -> (i -> r -> a -> m r) -> r -> s -> m r
--   ifoldlMOf :: Monad m => IndexedLens' i s a      -> (i -> r -> a -> m r) -> r -> s -> m r
--   ifoldlMOf :: Monad m => IndexedTraversal' i s a -> (i -> r -> a -> m r) -> r -> s -> m r
--

ifoldlMOf :: Monad m => IndexedGetting i Endo r -> m r s a -> i -> r -> a -> m r -> r -> s -> m r -- | Monadic fold right over the elements of a structure with an index. -- -- When you don't need access to the index then foldrMOf is more -- flexible in what it accepts. -- --

--   foldrMOf l ≡ ifoldrMOf l . const
--

-- --

--   ifoldrMOf :: Monad m => IndexedGetter i s a     -> (i -> a -> r -> m r) -> r -> s -> m r
--   ifoldrMOf :: Monad m => IndexedFold i s a       -> (i -> a -> r -> m r) -> r -> s -> m r
--   ifoldrMOf :: Monad m => IndexedLens' i s a      -> (i -> a -> r -> m r) -> r -> s -> m r
--   ifoldrMOf :: Monad m => IndexedTraversal' i s a -> (i -> a -> r -> m r) -> r -> s -> m r
--

ifoldrMOf :: Monad m => IndexedGetting i Dual Endo r -> m r s a -> i -> a -> r -> m r -> r -> s -> m r -- | Fold over the elements of a structure with an index, associating to -- the left, but strictly. -- -- When you don't need access to the index then foldlOf' is more -- flexible in what it accepts. -- --

--   foldlOf' l ≡ ifoldlOf' l . const
--

-- --

--   ifoldlOf' :: IndexedGetter i s a       -> (i -> r -> a -> r) -> r -> s -> r
--   ifoldlOf' :: IndexedFold i s a         -> (i -> r -> a -> r) -> r -> s -> r
--   ifoldlOf' :: IndexedLens' i s a        -> (i -> r -> a -> r) -> r -> s -> r
--   ifoldlOf' :: IndexedTraversal' i s a   -> (i -> r -> a -> r) -> r -> s -> r
--

ifoldlOf' :: () => IndexedGetting i Endo r -> r s a -> i -> r -> a -> r -> r -> s -> r -- | Strictly fold right over the elements of a structure with an -- index. -- -- When you don't need access to the index then foldrOf' is more -- flexible in what it accepts. -- --

--   foldrOf' l ≡ ifoldrOf' l . const
--

-- --

--   ifoldrOf' :: IndexedGetter i s a     -> (i -> a -> r -> r) -> r -> s -> r
--   ifoldrOf' :: IndexedFold i s a       -> (i -> a -> r -> r) -> r -> s -> r
--   ifoldrOf' :: IndexedLens' i s a      -> (i -> a -> r -> r) -> r -> s -> r
--   ifoldrOf' :: IndexedTraversal' i s a -> (i -> a -> r -> r) -> r -> s -> r
--

ifoldrOf' :: () => IndexedGetting i Dual Endo r -> r s a -> i -> a -> r -> r -> r -> s -> r -- | The ifindMOf function takes an IndexedFold or -- IndexedTraversal, a monadic predicate that is also supplied the -- index, a structure and returns in the monad the left-most element of -- the structure matching the predicate, or Nothing if there is no -- such element. -- -- When you don't need access to the index then findMOf is more -- flexible in what it accepts. -- --

--   findMOf l ≡ ifindMOf l . const
--

-- --

--   ifindMOf :: Monad m => IndexedGetter i s a     -> (i -> a -> m Bool) -> s -> m (Maybe a)
--   ifindMOf :: Monad m => IndexedFold i s a       -> (i -> a -> m Bool) -> s -> m (Maybe a)
--   ifindMOf :: Monad m => IndexedLens' i s a      -> (i -> a -> m Bool) -> s -> m (Maybe a)
--   ifindMOf :: Monad m => IndexedTraversal' i s a -> (i -> a -> m Bool) -> s -> m (Maybe a)
--

ifindMOf :: Monad m => IndexedGetting i Endo m Maybe a s a -> i -> a -> m Bool -> s -> m Maybe a -- | The ifindOf function takes an IndexedFold or -- IndexedTraversal, a predicate that is also supplied the index, -- a structure and returns the left-most element of the structure -- matching the predicate, or Nothing if there is no such element. -- -- When you don't need access to the index then findOf is more -- flexible in what it accepts. -- --

--   findOf l ≡ ifindOf l . const
--

-- --

--   ifindOf :: IndexedGetter i s a     -> (i -> a -> Bool) -> s -> Maybe a
--   ifindOf :: IndexedFold i s a       -> (i -> a -> Bool) -> s -> Maybe a
--   ifindOf :: IndexedLens' i s a      -> (i -> a -> Bool) -> s -> Maybe a
--   ifindOf :: IndexedTraversal' i s a -> (i -> a -> Bool) -> s -> Maybe a
--

ifindOf :: () => IndexedGetting i Endo Maybe a s a -> i -> a -> Bool -> s -> Maybe a -- | Concatenate the results of a function of the elements of an -- IndexedFold or IndexedTraversal with access to the -- index. -- -- When you don't need access to the index then concatMapOf is -- more flexible in what it accepts. -- --

--   concatMapOf l ≡ iconcatMapOf l . const
--   iconcatMapOf ≡ ifoldMapOf
--

-- --

--   iconcatMapOf :: IndexedGetter i s a     -> (i -> a -> [r]) -> s -> [r]
--   iconcatMapOf :: IndexedFold i s a       -> (i -> a -> [r]) -> s -> [r]
--   iconcatMapOf :: IndexedLens' i s a      -> (i -> a -> [r]) -> s -> [r]
--   iconcatMapOf :: IndexedTraversal' i s a -> (i -> a -> [r]) -> s -> [r]
--

iconcatMapOf :: () => IndexedGetting i [r] s a -> i -> a -> [r] -> s -> [r] -- | Run monadic actions for each target of an IndexedFold or -- IndexedTraversal with access to the index, discarding the -- results (with the arguments flipped). -- --

--   iforMOf_ ≡ flip . imapMOf_
--

-- -- When you don't need access to the index then forMOf_ is more -- flexible in what it accepts. -- --

--   forMOf_ l a ≡ iforMOf l a . const
--

-- --

--   iforMOf_ :: Monad m => IndexedGetter i s a     -> s -> (i -> a -> m r) -> m ()
--   iforMOf_ :: Monad m => IndexedFold i s a       -> s -> (i -> a -> m r) -> m ()
--   iforMOf_ :: Monad m => IndexedLens' i s a      -> s -> (i -> a -> m r) -> m ()
--   iforMOf_ :: Monad m => IndexedTraversal' i s a -> s -> (i -> a -> m r) -> m ()
--

iforMOf_ :: Monad m => IndexedGetting i Sequenced r m s a -> s -> i -> a -> m r -> m () -- | Run monadic actions for each target of an IndexedFold or -- IndexedTraversal with access to the index, discarding the -- results. -- -- When you don't need access to the index then mapMOf_ is more -- flexible in what it accepts. -- --

--   mapMOf_ l ≡ imapMOf l . const
--

-- --

--   imapMOf_ :: Monad m => IndexedGetter i s a     -> (i -> a -> m r) -> s -> m ()
--   imapMOf_ :: Monad m => IndexedFold i s a       -> (i -> a -> m r) -> s -> m ()
--   imapMOf_ :: Monad m => IndexedLens' i s a      -> (i -> a -> m r) -> s -> m ()
--   imapMOf_ :: Monad m => IndexedTraversal' i s a -> (i -> a -> m r) -> s -> m ()
--

imapMOf_ :: Monad m => IndexedGetting i Sequenced r m s a -> i -> a -> m r -> s -> m () -- | Traverse the targets of an IndexedFold or -- IndexedTraversal with access to the index, discarding the -- results (with the arguments flipped). -- --

--   iforOf_ ≡ flip . itraverseOf_
--

-- -- When you don't need access to the index then forOf_ is more -- flexible in what it accepts. -- --

--   forOf_ l a ≡ iforOf_ l a . const
--

-- --

--   iforOf_ :: Functor f     => IndexedGetter i s a     -> s -> (i -> a -> f r) -> f ()
--   iforOf_ :: Applicative f => IndexedFold i s a       -> s -> (i -> a -> f r) -> f ()
--   iforOf_ :: Functor f     => IndexedLens' i s a      -> s -> (i -> a -> f r) -> f ()
--   iforOf_ :: Applicative f => IndexedTraversal' i s a -> s -> (i -> a -> f r) -> f ()
--

iforOf_ :: Functor f => IndexedGetting i Traversed r f s a -> s -> i -> a -> f r -> f () -- | Traverse the targets of an IndexedFold or -- IndexedTraversal with access to the i, discarding the -- results. -- -- When you don't need access to the index then traverseOf_ is -- more flexible in what it accepts. -- --

--   traverseOf_ l ≡ itraverseOf l . const
--

-- --

--   itraverseOf_ :: Functor f     => IndexedGetter i s a     -> (i -> a -> f r) -> s -> f ()
--   itraverseOf_ :: Applicative f => IndexedFold i s a       -> (i -> a -> f r) -> s -> f ()
--   itraverseOf_ :: Functor f     => IndexedLens' i s a      -> (i -> a -> f r) -> s -> f ()
--   itraverseOf_ :: Applicative f => IndexedTraversal' i s a -> (i -> a -> f r) -> s -> f ()
--

itraverseOf_ :: Functor f => IndexedGetting i Traversed r f s a -> i -> a -> f r -> s -> f () -- | Return whether or not none of the elements viewed through an -- IndexedFold or IndexedTraversal satisfy a predicate, -- with access to the i. -- -- When you don't need access to the index then noneOf is more -- flexible in what it accepts. -- --

--   noneOf l ≡ inoneOf l . const
--

-- --

--   inoneOf :: IndexedGetter i s a     -> (i -> a -> Bool) -> s -> Bool
--   inoneOf :: IndexedFold i s a       -> (i -> a -> Bool) -> s -> Bool
--   inoneOf :: IndexedLens' i s a      -> (i -> a -> Bool) -> s -> Bool
--   inoneOf :: IndexedTraversal' i s a -> (i -> a -> Bool) -> s -> Bool
--

inoneOf :: () => IndexedGetting i Any s a -> i -> a -> Bool -> s -> Bool -- | Return whether or not all elements viewed through an -- IndexedFold or IndexedTraversal satisfy a predicate, -- with access to the i. -- -- When you don't need access to the index then allOf is more -- flexible in what it accepts. -- --

--   allOf l ≡ iallOf l . const
--

-- --

--   iallOf :: IndexedGetter i s a     -> (i -> a -> Bool) -> s -> Bool
--   iallOf :: IndexedFold i s a       -> (i -> a -> Bool) -> s -> Bool
--   iallOf :: IndexedLens' i s a      -> (i -> a -> Bool) -> s -> Bool
--   iallOf :: IndexedTraversal' i s a -> (i -> a -> Bool) -> s -> Bool
--

iallOf :: () => IndexedGetting i All s a -> i -> a -> Bool -> s -> Bool -- | Return whether or not any element viewed through an IndexedFold -- or IndexedTraversal satisfy a predicate, with access to the -- i. -- -- When you don't need access to the index then anyOf is more -- flexible in what it accepts. -- --

--   anyOf l ≡ ianyOf l . const
--

-- --

--   ianyOf :: IndexedGetter i s a     -> (i -> a -> Bool) -> s -> Bool
--   ianyOf :: IndexedFold i s a       -> (i -> a -> Bool) -> s -> Bool
--   ianyOf :: IndexedLens' i s a      -> (i -> a -> Bool) -> s -> Bool
--   ianyOf :: IndexedTraversal' i s a -> (i -> a -> Bool) -> s -> Bool
--

ianyOf :: () => IndexedGetting i Any s a -> i -> a -> Bool -> s -> Bool -- | Left-associative fold of the parts of a structure that are viewed -- through an IndexedFold or IndexedTraversal with access -- to the i. -- -- When you don't need access to the index then foldlOf is more -- flexible in what it accepts. -- --

--   foldlOf l ≡ ifoldlOf l . const
--

-- --

--   ifoldlOf :: IndexedGetter i s a     -> (i -> r -> a -> r) -> r -> s -> r
--   ifoldlOf :: IndexedFold i s a       -> (i -> r -> a -> r) -> r -> s -> r
--   ifoldlOf :: IndexedLens' i s a      -> (i -> r -> a -> r) -> r -> s -> r
--   ifoldlOf :: IndexedTraversal' i s a -> (i -> r -> a -> r) -> r -> s -> r
--

ifoldlOf :: () => IndexedGetting i Dual Endo r s a -> i -> r -> a -> r -> r -> s -> r -- | Right-associative fold of parts of a structure that are viewed through -- an IndexedFold or IndexedTraversal with access to the -- i. -- -- When you don't need access to the index then foldrOf is more -- flexible in what it accepts. -- --

--   foldrOf l ≡ ifoldrOf l . const
--

-- --

--   ifoldrOf :: IndexedGetter i s a     -> (i -> a -> r -> r) -> r -> s -> r
--   ifoldrOf :: IndexedFold i s a       -> (i -> a -> r -> r) -> r -> s -> r
--   ifoldrOf :: IndexedLens' i s a      -> (i -> a -> r -> r) -> r -> s -> r
--   ifoldrOf :: IndexedTraversal' i s a -> (i -> a -> r -> r) -> r -> s -> r
--

ifoldrOf :: () => IndexedGetting i Endo r s a -> i -> a -> r -> r -> r -> s -> r -- | Fold an IndexedFold or IndexedTraversal by mapping -- indices and values to an arbitrary Monoid with access to the -- i. -- -- When you don't need access to the index then foldMapOf is more -- flexible in what it accepts. -- --

--   foldMapOf l ≡ ifoldMapOf l . const
--

-- --

--   ifoldMapOf ::             IndexedGetter i s a     -> (i -> a -> m) -> s -> m
--   ifoldMapOf :: Monoid m => IndexedFold i s a       -> (i -> a -> m) -> s -> m
--   ifoldMapOf ::             IndexedLens' i s a      -> (i -> a -> m) -> s -> m
--   ifoldMapOf :: Monoid m => IndexedTraversal' i s a -> (i -> a -> m) -> s -> m
--

ifoldMapOf :: () => IndexedGetting i m s a -> i -> a -> m -> s -> m -- | This allows you to traverse the elements of a pretty much any -- LensLike construction in the opposite order. -- -- This will preserve indexes on Indexed types and will give you -- the elements of a (finite) Fold or Traversal in the -- opposite order. -- -- This has no practical impact on a Getter, Setter, -- Lens or Iso. -- -- NB: To write back through an Iso, you want to use -- from. Similarly, to write back through an Prism, you -- want to use re. backwards :: (Profunctor p, Profunctor q) => Optical p q Backwards f s t a b -> Optical p q f s t a b -- | Retrieve a function of the first index and value targeted by an -- IndexedFold or IndexedTraversal (or a function of -- Just the index and result from an IndexedGetter or -- IndexedLens) into the current state. -- --

--   ipreuses = uses . ipre
--

-- --

--   ipreuses :: MonadState s m => IndexedGetter i s a     -> (i -> a -> r) -> m (Maybe r)
--   ipreuses :: MonadState s m => IndexedFold i s a       -> (i -> a -> r) -> m (Maybe r)
--   ipreuses :: MonadState s m => IndexedLens' i s a      -> (i -> a -> r) -> m (Maybe r)
--   ipreuses :: MonadState s m => IndexedTraversal' i s a -> (i -> a -> r) -> m (Maybe r)
--

ipreuses :: MonadState s m => IndexedGetting i First r s a -> i -> a -> r -> m Maybe r -- | Retrieve a function of the first value targeted by a Fold or -- Traversal (or Just the result from a Getter or -- Lens) into the current state. -- --

--   preuses = uses . pre
--

-- --

--   preuses :: MonadState s m => Getter s a     -> (a -> r) -> m (Maybe r)
--   preuses :: MonadState s m => Fold s a       -> (a -> r) -> m (Maybe r)
--   preuses :: MonadState s m => Lens' s a      -> (a -> r) -> m (Maybe r)
--   preuses :: MonadState s m => Iso' s a       -> (a -> r) -> m (Maybe r)
--   preuses :: MonadState s m => Traversal' s a -> (a -> r) -> m (Maybe r)
--

preuses :: MonadState s m => Getting First r s a -> a -> r -> m Maybe r -- | Retrieve the first index and value targeted by an IndexedFold -- or IndexedTraversal (or Just the index and result from -- an IndexedGetter or IndexedLens) into the current state. -- --

--   ipreuse = use . ipre
--

-- --

--   ipreuse :: MonadState s m => IndexedGetter i s a     -> m (Maybe (i, a))
--   ipreuse :: MonadState s m => IndexedFold i s a       -> m (Maybe (i, a))
--   ipreuse :: MonadState s m => IndexedLens' i s a      -> m (Maybe (i, a))
--   ipreuse :: MonadState s m => IndexedTraversal' i s a -> m (Maybe (i, a))
--

ipreuse :: MonadState s m => IndexedGetting i First (i, a) s a -> m Maybe (i, a) -- | Retrieve the first value targeted by a Fold or Traversal -- (or Just the result from a Getter or Lens) into -- the current state. -- --

--   preuse = use . pre
--

-- --

--   preuse :: MonadState s m => Getter s a     -> m (Maybe a)
--   preuse :: MonadState s m => Fold s a       -> m (Maybe a)
--   preuse :: MonadState s m => Lens' s a      -> m (Maybe a)
--   preuse :: MonadState s m => Iso' s a       -> m (Maybe a)
--   preuse :: MonadState s m => Traversal' s a -> m (Maybe a)
--

preuse :: MonadState s m => Getting First a s a -> m Maybe a -- | Retrieve a function of the first index and value targeted by an -- IndexedFold or IndexedTraversal (or Just the -- result from an IndexedGetter or IndexedLens). See also -- (^@?). -- --

--   ipreviews = views . ipre
--

-- -- This is usually applied in the Reader Monad (->) -- s. -- --

--   ipreviews :: IndexedGetter i s a     -> (i -> a -> r) -> s -> Maybe r
--   ipreviews :: IndexedFold i s a       -> (i -> a -> r) -> s -> Maybe r
--   ipreviews :: IndexedLens' i s a      -> (i -> a -> r) -> s -> Maybe r
--   ipreviews :: IndexedTraversal' i s a -> (i -> a -> r) -> s -> Maybe r
--

-- -- However, it may be useful to think of its full generality when working -- with a Monad transformer stack: -- --

--   ipreviews :: MonadReader s m => IndexedGetter i s a     -> (i -> a -> r) -> m (Maybe r)
--   ipreviews :: MonadReader s m => IndexedFold i s a       -> (i -> a -> r) -> m (Maybe r)
--   ipreviews :: MonadReader s m => IndexedLens' i s a      -> (i -> a -> r) -> m (Maybe r)
--   ipreviews :: MonadReader s m => IndexedTraversal' i s a -> (i -> a -> r) -> m (Maybe r)
--

ipreviews :: MonadReader s m => IndexedGetting i First r s a -> i -> a -> r -> m Maybe r -- | Retrieve a function of the first value targeted by a Fold or -- Traversal (or Just the result from a Getter or -- Lens). -- -- This is usually applied in the Reader Monad (->) -- s. previews :: MonadReader s m => Getting First r s a -> a -> r -> m Maybe r -- | Retrieve the first index and value targeted by a Fold or -- Traversal (or Just the result from a Getter or -- Lens). See also (^@?). -- --

--   ipreview = view . ipre
--

-- -- This is usually applied in the Reader Monad (->) -- s. -- --

--   ipreview :: IndexedGetter i s a     -> s -> Maybe (i, a)
--   ipreview :: IndexedFold i s a       -> s -> Maybe (i, a)
--   ipreview :: IndexedLens' i s a      -> s -> Maybe (i, a)
--   ipreview :: IndexedTraversal' i s a -> s -> Maybe (i, a)
--

-- -- However, it may be useful to think of its full generality when working -- with a Monad transformer stack: -- --

--   ipreview :: MonadReader s m => IndexedGetter s a     -> m (Maybe (i, a))
--   ipreview :: MonadReader s m => IndexedFold s a       -> m (Maybe (i, a))
--   ipreview :: MonadReader s m => IndexedLens' s a      -> m (Maybe (i, a))
--   ipreview :: MonadReader s m => IndexedTraversal' s a -> m (Maybe (i, a))
--

ipreview :: MonadReader s m => IndexedGetting i First (i, a) s a -> m Maybe (i, a) -- | Retrieve the first value targeted by a Fold or Traversal -- (or Just the result from a Getter or Lens). See -- also (^?). -- --

--   listToMaybe . toList ≡ preview folded
--

-- -- This is usually applied in the Reader Monad (->) -- s. -- --

--   preview = view . pre
--

-- --

--   preview :: Getter s a     -> s -> Maybe a
--   preview :: Fold s a       -> s -> Maybe a
--   preview :: Lens' s a      -> s -> Maybe a
--   preview :: Iso' s a       -> s -> Maybe a
--   preview :: Traversal' s a -> s -> Maybe a
--

-- -- However, it may be useful to think of its full generality when working -- with a Monad transformer stack: -- --

--   preview :: MonadReader s m => Getter s a     -> m (Maybe a)
--   preview :: MonadReader s m => Fold s a       -> m (Maybe a)
--   preview :: MonadReader s m => Lens' s a      -> m (Maybe a)
--   preview :: MonadReader s m => Iso' s a       -> m (Maybe a)
--   preview :: MonadReader s m => Traversal' s a -> m (Maybe a)
--

preview :: MonadReader s m => Getting First a s a -> m Maybe a -- | This converts an IndexedFold to an IndexPreservingGetter -- that returns the first index and element, if they exist, as a -- Maybe. -- --

--   ipre :: IndexedGetter i s a     -> IndexPreservingGetter s (Maybe (i, a))
--   ipre :: IndexedFold i s a       -> IndexPreservingGetter s (Maybe (i, a))
--   ipre :: IndexedTraversal' i s a -> IndexPreservingGetter s (Maybe (i, a))
--   ipre :: IndexedLens' i s a      -> IndexPreservingGetter s (Maybe (i, a))
--

ipre :: () => IndexedGetting i First (i, a) s a -> IndexPreservingGetter s Maybe (i, a) -- | This converts a Fold to a IndexPreservingGetter that -- returns the first element, if it exists, as a Maybe. -- --

--   pre :: Getter s a     -> IndexPreservingGetter s (Maybe a)
--   pre :: Fold s a       -> IndexPreservingGetter s (Maybe a)
--   pre :: Traversal' s a -> IndexPreservingGetter s (Maybe a)
--   pre :: Lens' s a      -> IndexPreservingGetter s (Maybe a)
--   pre :: Iso' s a       -> IndexPreservingGetter s (Maybe a)
--   pre :: Prism' s a     -> IndexPreservingGetter s (Maybe a)
--

pre :: () => Getting First a s a -> IndexPreservingGetter s Maybe a -- | Check to see if this Fold or Traversal has no matches. -- --

--   >>> hasn't _Left (Right 12)
--   True
--

-- --

--   >>> hasn't _Left (Left 12)
--   False
--

hasn't :: () => Getting All s a -> s -> Bool -- | Check to see if this Fold or Traversal matches 1 or more -- entries. -- --

--   >>> has (element 0) []
--   False
--

-- --

--   >>> has _Left (Left 12)
--   True
--

-- --

--   >>> has _Right (Left 12)
--   False
--

-- -- This will always return True for a Lens or -- Getter. -- --

--   >>> has _1 ("hello","world")
--   True
--

-- --

--   has :: Getter s a     -> s -> Bool
--   has :: Fold s a       -> s -> Bool
--   has :: Iso' s a       -> s -> Bool
--   has :: Lens' s a      -> s -> Bool
--   has :: Traversal' s a -> s -> Bool
--

has :: () => Getting Any s a -> s -> Bool -- | Monadic fold over the elements of a structure, associating to the -- left, i.e. from left to right. -- --

--   foldlM ≡ foldlMOf folded
--

-- --

--   foldlMOf :: Monad m => Getter s a     -> (r -> a -> m r) -> r -> s -> m r
--   foldlMOf :: Monad m => Fold s a       -> (r -> a -> m r) -> r -> s -> m r
--   foldlMOf :: Monad m => Iso' s a       -> (r -> a -> m r) -> r -> s -> m r
--   foldlMOf :: Monad m => Lens' s a      -> (r -> a -> m r) -> r -> s -> m r
--   foldlMOf :: Monad m => Traversal' s a -> (r -> a -> m r) -> r -> s -> m r
--

foldlMOf :: Monad m => Getting Endo r -> m r s a -> r -> a -> m r -> r -> s -> m r -- | Monadic fold over the elements of a structure, associating to the -- right, i.e. from right to left. -- --

--   foldrM ≡ foldrMOf folded
--

-- --

--   foldrMOf :: Monad m => Getter s a     -> (a -> r -> m r) -> r -> s -> m r
--   foldrMOf :: Monad m => Fold s a       -> (a -> r -> m r) -> r -> s -> m r
--   foldrMOf :: Monad m => Iso' s a       -> (a -> r -> m r) -> r -> s -> m r
--   foldrMOf :: Monad m => Lens' s a      -> (a -> r -> m r) -> r -> s -> m r
--   foldrMOf :: Monad m => Traversal' s a -> (a -> r -> m r) -> r -> s -> m r
--

foldrMOf :: Monad m => Getting Dual Endo r -> m r s a -> a -> r -> m r -> r -> s -> m r -- | A variant of foldlOf' that has no base case and thus may only -- be applied to folds and structures such that the fold views at least -- one element of the structure. -- --

--   foldl1Of' l f ≡ foldl1' f . toListOf l
--

-- --

--   foldl1Of' :: Getter s a     -> (a -> a -> a) -> s -> a
--   foldl1Of' :: Fold s a       -> (a -> a -> a) -> s -> a
--   foldl1Of' :: Iso' s a       -> (a -> a -> a) -> s -> a
--   foldl1Of' :: Lens' s a      -> (a -> a -> a) -> s -> a
--   foldl1Of' :: Traversal' s a -> (a -> a -> a) -> s -> a
--

foldl1Of' :: HasCallStack => Getting Endo Endo Maybe a s a -> a -> a -> a -> s -> a -- | A variant of foldrOf' that has no base case and thus may only -- be applied to folds and structures such that the fold views at least -- one element of the structure. -- --

--   foldr1Of l f ≡ foldr1 f . toListOf l
--

-- --

--   foldr1Of' :: Getter s a     -> (a -> a -> a) -> s -> a
--   foldr1Of' :: Fold s a       -> (a -> a -> a) -> s -> a
--   foldr1Of' :: Iso' s a       -> (a -> a -> a) -> s -> a
--   foldr1Of' :: Lens' s a      -> (a -> a -> a) -> s -> a
--   foldr1Of' :: Traversal' s a -> (a -> a -> a) -> s -> a
--

foldr1Of' :: HasCallStack => Getting Dual Endo Endo Maybe a s a -> a -> a -> a -> s -> a -- | Fold over the elements of a structure, associating to the left, but -- strictly. -- --

--   foldl' ≡ foldlOf' folded
--

-- --

--   foldlOf' :: Getter s a     -> (r -> a -> r) -> r -> s -> r
--   foldlOf' :: Fold s a       -> (r -> a -> r) -> r -> s -> r
--   foldlOf' :: Iso' s a       -> (r -> a -> r) -> r -> s -> r
--   foldlOf' :: Lens' s a      -> (r -> a -> r) -> r -> s -> r
--   foldlOf' :: Traversal' s a -> (r -> a -> r) -> r -> s -> r
--

foldlOf' :: () => Getting Endo Endo r s a -> r -> a -> r -> r -> s -> r -- | Strictly fold right over the elements of a structure. -- --

--   foldr' ≡ foldrOf' folded
--

-- --

--   foldrOf' :: Getter s a     -> (a -> r -> r) -> r -> s -> r
--   foldrOf' :: Fold s a       -> (a -> r -> r) -> r -> s -> r
--   foldrOf' :: Iso' s a       -> (a -> r -> r) -> r -> s -> r
--   foldrOf' :: Lens' s a      -> (a -> r -> r) -> r -> s -> r
--   foldrOf' :: Traversal' s a -> (a -> r -> r) -> r -> s -> r
--

foldrOf' :: () => Getting Dual Endo Endo r s a -> a -> r -> r -> r -> s -> r -- | A variant of foldlOf that has no base case and thus may only be -- applied to lenses and structures such that the Lens views at -- least one element of the structure. -- --

--   >>> foldl1Of each (+) (1,2,3,4)
--   10
--

-- --

--   foldl1Of l f ≡ foldl1 f . toListOf l
--   foldl1 ≡ foldl1Of folded
--

-- --

--   foldl1Of :: Getter s a     -> (a -> a -> a) -> s -> a
--   foldl1Of :: Fold s a       -> (a -> a -> a) -> s -> a
--   foldl1Of :: Iso' s a       -> (a -> a -> a) -> s -> a
--   foldl1Of :: Lens' s a      -> (a -> a -> a) -> s -> a
--   foldl1Of :: Traversal' s a -> (a -> a -> a) -> s -> a
--

foldl1Of :: HasCallStack => Getting Dual Endo Maybe a s a -> a -> a -> a -> s -> a -- | A variant of foldrOf that has no base case and thus may only be -- applied to lenses and structures such that the Lens views at -- least one element of the structure. -- --

--   >>> foldr1Of each (+) (1,2,3,4)
--   10
--

-- --

--   foldr1Of l f ≡ foldr1 f . toListOf l
--   foldr1 ≡ foldr1Of folded
--

-- --

--   foldr1Of :: Getter s a     -> (a -> a -> a) -> s -> a
--   foldr1Of :: Fold s a       -> (a -> a -> a) -> s -> a
--   foldr1Of :: Iso' s a       -> (a -> a -> a) -> s -> a
--   foldr1Of :: Lens' s a      -> (a -> a -> a) -> s -> a
--   foldr1Of :: Traversal' s a -> (a -> a -> a) -> s -> a
--

foldr1Of :: HasCallStack => Getting Endo Maybe a s a -> a -> a -> a -> s -> a -- | The lookupOf function takes a Fold (or Getter, -- Traversal, Lens, Iso, etc.), a key, and a -- structure containing key/value pairs. It returns the first value -- corresponding to the given key. This function generalizes -- lookup to work on an arbitrary Fold instead of lists. -- --

--   >>> lookupOf folded 4 [(2, 'a'), (4, 'b'), (4, 'c')]
--   Just 'b'
--

-- --

--   >>> lookupOf each 2 [(2, 'a'), (4, 'b'), (4, 'c')]
--   Just 'a'
--

-- --

--   lookupOf :: Eq k => Fold s (k,v) -> k -> s -> Maybe v
--

lookupOf :: Eq k => Getting Endo Maybe v s (k, v) -> k -> s -> Maybe v -- | The findMOf function takes a Lens (or Getter, -- Iso, Fold, or Traversal), a monadic predicate and -- a structure and returns in the monad the leftmost element of the -- structure matching the predicate, or Nothing if there is no -- such element. -- --

--   >>> findMOf each ( \x -> print ("Checking " ++ show x) >> return (even x)) (1,3,4,6)
--   "Checking 1"
--   "Checking 3"
--   "Checking 4"
--   Just 4
--

-- --

--   >>> findMOf each ( \x -> print ("Checking " ++ show x) >> return (even x)) (1,3,5,7)
--   "Checking 1"
--   "Checking 3"
--   "Checking 5"
--   "Checking 7"
--   Nothing
--

-- --

--   findMOf :: (Monad m, Getter s a)     -> (a -> m Bool) -> s -> m (Maybe a)
--   findMOf :: (Monad m, Fold s a)       -> (a -> m Bool) -> s -> m (Maybe a)
--   findMOf :: (Monad m, Iso' s a)       -> (a -> m Bool) -> s -> m (Maybe a)
--   findMOf :: (Monad m, Lens' s a)      -> (a -> m Bool) -> s -> m (Maybe a)
--   findMOf :: (Monad m, Traversal' s a) -> (a -> m Bool) -> s -> m (Maybe a)
--

-- --

--   findMOf folded :: (Monad m, Foldable f) => (a -> m Bool) -> f a -> m (Maybe a)
--   ifindMOf l ≡ findMOf l . Indexed
--

-- -- A simpler version that didn't permit indexing, would be: -- --

--   findMOf :: Monad m => Getting (Endo (m (Maybe a))) s a -> (a -> m Bool) -> s -> m (Maybe a)
--   findMOf l p = foldrOf l (a y -> p a >>= x -> if x then return (Just a) else y) $ return Nothing
--

findMOf :: Monad m => Getting Endo m Maybe a s a -> a -> m Bool -> s -> m Maybe a -- | The findOf function takes a Lens (or Getter, -- Iso, Fold, or Traversal), a predicate and a -- structure and returns the leftmost element of the structure matching -- the predicate, or Nothing if there is no such element. -- --

--   >>> findOf each even (1,3,4,6)
--   Just 4
--

-- --

--   >>> findOf folded even [1,3,5,7]
--   Nothing
--

-- --

--   findOf :: Getter s a     -> (a -> Bool) -> s -> Maybe a
--   findOf :: Fold s a       -> (a -> Bool) -> s -> Maybe a
--   findOf :: Iso' s a       -> (a -> Bool) -> s -> Maybe a
--   findOf :: Lens' s a      -> (a -> Bool) -> s -> Maybe a
--   findOf :: Traversal' s a -> (a -> Bool) -> s -> Maybe a
--

-- --

--   find ≡ findOf folded
--   ifindOf l ≡ findOf l . Indexed
--

-- -- A simpler version that didn't permit indexing, would be: -- --

--   findOf :: Getting (Endo (Maybe a)) s a -> (a -> Bool) -> s -> Maybe a
--   findOf l p = foldrOf l (a y -> if p a then Just a else y) Nothing
--

findOf :: () => Getting Endo Maybe a s a -> a -> Bool -> s -> Maybe a -- | Obtain the minimum element (if any) targeted by a Fold, -- Traversal, Lens, Iso or Getter according -- to a user supplied Ordering. -- -- In the interest of efficiency, This operation has semantics more -- strict than strictly necessary. -- --

--   >>> minimumByOf traverse (compare `on` length) ["mustard","relish","ham"]
--   Just "ham"
--

-- --

--   minimumBy cmp ≡ fromMaybe (error "empty") . minimumByOf folded cmp
--

-- --

--   minimumByOf :: Getter s a     -> (a -> a -> Ordering) -> s -> Maybe a
--   minimumByOf :: Fold s a       -> (a -> a -> Ordering) -> s -> Maybe a
--   minimumByOf :: Iso' s a       -> (a -> a -> Ordering) -> s -> Maybe a
--   minimumByOf :: Lens' s a      -> (a -> a -> Ordering) -> s -> Maybe a
--   minimumByOf :: Traversal' s a -> (a -> a -> Ordering) -> s -> Maybe a
--

minimumByOf :: () => Getting Endo Endo Maybe a s a -> a -> a -> Ordering -> s -> Maybe a -- | Obtain the maximum element (if any) targeted by a Fold, -- Traversal, Lens, Iso, or Getter according -- to a user supplied Ordering. -- --

--   >>> maximumByOf traverse (compare `on` length) ["mustard","relish","ham"]
--   Just "mustard"
--

-- -- In the interest of efficiency, This operation has semantics more -- strict than strictly necessary. -- --

--   maximumBy cmp ≡ fromMaybe (error "empty") . maximumByOf folded cmp
--

-- --

--   maximumByOf :: Getter s a     -> (a -> a -> Ordering) -> s -> Maybe a
--   maximumByOf :: Fold s a       -> (a -> a -> Ordering) -> s -> Maybe a
--   maximumByOf :: Iso' s a       -> (a -> a -> Ordering) -> s -> Maybe a
--   maximumByOf :: Lens' s a      -> (a -> a -> Ordering) -> s -> Maybe a
--   maximumByOf :: Traversal' s a -> (a -> a -> Ordering) -> s -> Maybe a
--

maximumByOf :: () => Getting Endo Endo Maybe a s a -> a -> a -> Ordering -> s -> Maybe a -- | Obtain the minimum element targeted by a Fold1 or -- Traversal1. -- --

--   >>> minimum1Of traverse1 (1 :| [2..10])
--   1
--

-- --

--   minimum1Of :: Ord a => Getter s a      -> s -> a
--   minimum1Of :: Ord a => Fold1 s a       -> s -> a
--   minimum1Of :: Ord a => Iso' s a        -> s -> a
--   minimum1Of :: Ord a => Lens' s a       -> s -> a
--   minimum1Of :: Ord a => Traversal1' s a -> s -> a
--

minimum1Of :: Ord a => Getting Min a s a -> s -> a -- | Obtain the minimum element (if any) targeted by a Fold or -- Traversal safely. -- -- Note: minimumOf on a valid Iso, Lens or -- Getter will always return Just a value. -- --

--   >>> minimumOf traverse [1..10]
--   Just 1
--

-- --

--   >>> minimumOf traverse []
--   Nothing
--

-- --

--   >>> minimumOf (folded.filtered even) [1,4,3,6,7,9,2]
--   Just 2
--

-- --

--   minimum ≡ fromMaybe (error "empty") . minimumOf folded
--

-- -- In the interest of efficiency, This operation has semantics more -- strict than strictly necessary. rmap getMin -- (foldMapOf l Min) has lazier semantics but could -- leak memory. -- --

--   minimumOf :: Ord a => Getter s a     -> s -> Maybe a
--   minimumOf :: Ord a => Fold s a       -> s -> Maybe a
--   minimumOf :: Ord a => Iso' s a       -> s -> Maybe a
--   minimumOf :: Ord a => Lens' s a      -> s -> Maybe a
--   minimumOf :: Ord a => Traversal' s a -> s -> Maybe a
--

minimumOf :: Ord a => Getting Endo Endo Maybe a s a -> s -> Maybe a -- | Obtain the maximum element targeted by a Fold1 or -- Traversal1. -- --

--   >>> maximum1Of traverse1 (1 :| [2..10])
--   10
--

-- --

--   maximum1Of :: Ord a => Getter s a      -> s -> a
--   maximum1Of :: Ord a => Fold1 s a       -> s -> a
--   maximum1Of :: Ord a => Iso' s a        -> s -> a
--   maximum1Of :: Ord a => Lens' s a       -> s -> a
--   maximum1Of :: Ord a => Traversal1' s a -> s -> a
--

maximum1Of :: Ord a => Getting Max a s a -> s -> a -- | Obtain the maximum element (if any) targeted by a Fold or -- Traversal safely. -- -- Note: maximumOf on a valid Iso, Lens or -- Getter will always return Just a value. -- --

--   >>> maximumOf traverse [1..10]
--   Just 10
--

-- --

--   >>> maximumOf traverse []
--   Nothing
--

-- --

--   >>> maximumOf (folded.filtered even) [1,4,3,6,7,9,2]
--   Just 6
--

-- --

--   maximum ≡ fromMaybe (error "empty") . maximumOf folded
--

-- -- In the interest of efficiency, This operation has semantics more -- strict than strictly necessary. rmap getMax -- (foldMapOf l Max) has lazier semantics but could -- leak memory. -- --

--   maximumOf :: Ord a => Getter s a     -> s -> Maybe a
--   maximumOf :: Ord a => Fold s a       -> s -> Maybe a
--   maximumOf :: Ord a => Iso' s a       -> s -> Maybe a
--   maximumOf :: Ord a => Lens' s a      -> s -> Maybe a
--   maximumOf :: Ord a => Traversal' s a -> s -> Maybe a
--

maximumOf :: Ord a => Getting Endo Endo Maybe a s a -> s -> Maybe a -- | Returns True if this Fold or Traversal has any -- targets in the given container. -- -- A more "conversational" alias for this combinator is has. -- -- Note: notNullOf on a valid Iso, Lens or -- Getter should always return True. -- --

--   not . null ≡ notNullOf folded
--

-- -- This may be rather inefficient compared to the not . -- null check of many containers. -- --

--   >>> notNullOf _1 (1,2)
--   True
--

-- --

--   >>> notNullOf traverse [1..10]
--   True
--

-- --

--   >>> notNullOf folded []
--   False
--

-- --

--   >>> notNullOf (element 20) [1..10]
--   False
--

-- --

--   notNullOf (folded . _1 . folded) :: (Foldable f, Foldable g) => f (g a, b) -> Bool
--

-- --

--   notNullOf :: Getter s a     -> s -> Bool
--   notNullOf :: Fold s a       -> s -> Bool
--   notNullOf :: Iso' s a       -> s -> Bool
--   notNullOf :: Lens' s a      -> s -> Bool
--   notNullOf :: Traversal' s a -> s -> Bool
--

notNullOf :: () => Getting Any s a -> s -> Bool -- | Returns True if this Fold or Traversal has no -- targets in the given container. -- -- Note: nullOf on a valid Iso, Lens or -- Getter should always return False. -- --

--   null ≡ nullOf folded
--

-- -- This may be rather inefficient compared to the null check of -- many containers. -- --

--   >>> nullOf _1 (1,2)
--   False
--

-- --

--   >>> nullOf ignored ()
--   True
--

-- --

--   >>> nullOf traverse []
--   True
--

-- --

--   >>> nullOf (element 20) [1..10]
--   True
--

-- --

--   nullOf (folded . _1 . folded) :: (Foldable f, Foldable g) => f (g a, b) -> Bool
--

-- --

--   nullOf :: Getter s a     -> s -> Bool
--   nullOf :: Fold s a       -> s -> Bool
--   nullOf :: Iso' s a       -> s -> Bool
--   nullOf :: Lens' s a      -> s -> Bool
--   nullOf :: Traversal' s a -> s -> Bool
--

nullOf :: () => Getting All s a -> s -> Bool -- | Retrieve the Last entry of a Fold1 or Traversal1 -- or retrieve the result from a Getter or Lens.o -- --

--   >>> last1Of traverse1 (1 :| [2..10])
--   10
--

-- --

--   >>> last1Of both1 (1,2)
--   2
--

-- --

--   last1Of :: Getter s a      -> s -> Maybe a
--   last1Of :: Fold1 s a       -> s -> Maybe a
--   last1Of :: Lens' s a       -> s -> Maybe a
--   last1Of :: Iso' s a        -> s -> Maybe a
--   last1Of :: Traversal1' s a -> s -> Maybe a
--

last1Of :: () => Getting Last a s a -> s -> a -- | Retrieve the Last entry of a Fold or Traversal or -- retrieve Just the result from a Getter or Lens. -- -- The answer is computed in a manner that leaks space less than -- ala Last . foldMapOf and gives -- you back access to the outermost Just constructor more quickly, -- but may have worse constant factors. -- --

--   >>> lastOf traverse [1..10]
--   Just 10
--

-- --

--   >>> lastOf both (1,2)
--   Just 2
--

-- --

--   >>> lastOf ignored ()
--   Nothing
--

-- --

--   lastOf :: Getter s a     -> s -> Maybe a
--   lastOf :: Fold s a       -> s -> Maybe a
--   lastOf :: Lens' s a      -> s -> Maybe a
--   lastOf :: Iso' s a       -> s -> Maybe a
--   lastOf :: Traversal' s a -> s -> Maybe a
--

lastOf :: () => Getting Rightmost a s a -> s -> Maybe a -- | Retrieve the First entry of a Fold1 or Traversal1 -- or the result from a Getter or Lens. -- --

--   >>> first1Of traverse1 (1 :| [2..10])
--   1
--

-- --

--   >>> first1Of both1 (1,2)
--   1
--

-- -- Note: this is different from ^.. -- --

--   >>> first1Of traverse1 ([1,2] :| [[3,4],[5,6]])
--   [1,2]
--

-- --

--   >>> ([1,2] :| [[3,4],[5,6]]) ^. traverse1
--   [1,2,3,4,5,6]
--

-- --

--   first1Of :: Getter s a      -> s -> a
--   first1Of :: Fold1 s a       -> s -> a
--   first1Of :: Lens' s a       -> s -> a
--   first1Of :: Iso' s a        -> s -> a
--   first1Of :: Traversal1' s a -> s -> a
--

first1Of :: () => Getting First a s a -> s -> a -- | Retrieve the First entry of a Fold or Traversal -- or retrieve Just the result from a Getter or -- Lens. -- -- The answer is computed in a manner that leaks space less than -- ala First . foldMapOf and gives -- you back access to the outermost Just constructor more quickly, -- but may have worse constant factors. -- -- Note: this could been named headOf. -- --

--   >>> firstOf traverse [1..10]
--   Just 1
--

-- --

--   >>> firstOf both (1,2)
--   Just 1
--

-- --

--   >>> firstOf ignored ()
--   Nothing
--

-- --

--   firstOf :: Getter s a     -> s -> Maybe a
--   firstOf :: Fold s a       -> s -> Maybe a
--   firstOf :: Lens' s a      -> s -> Maybe a
--   firstOf :: Iso' s a       -> s -> Maybe a
--   firstOf :: Traversal' s a -> s -> Maybe a
--

firstOf :: () => Getting Leftmost a s a -> s -> Maybe a -- | Perform an *UNSAFE* head of a Fold or Traversal -- assuming that it is there. -- --

--   >>> Left 4 ^?! _Left
--   4
--

-- --

--   >>> "world" ^?! ix 3
--   'l'
--

-- --

--   (^?!) :: s -> Getter s a     -> a
--   (^?!) :: s -> Fold s a       -> a
--   (^?!) :: s -> Lens' s a      -> a
--   (^?!) :: s -> Iso' s a       -> a
--   (^?!) :: s -> Traversal' s a -> a
--

(^?!) :: HasCallStack => s -> Getting Endo a s a -> a infixl 8 ^?! -- | Perform a safe head of a Fold or Traversal or -- retrieve Just the result from a Getter or Lens. -- -- When using a Traversal as a partial Lens, or a -- Fold as a partial Getter this can be a convenient way to -- extract the optional value. -- -- Note: if you get stack overflows due to this, you may want to use -- firstOf instead, which can deal more gracefully with heavily -- left-biased trees. -- --

--   >>> Left 4 ^?_Left
--   Just 4
--

-- --

--   >>> Right 4 ^?_Left
--   Nothing
--

-- --

--   >>> "world" ^? ix 3
--   Just 'l'
--

-- --

--   >>> "world" ^? ix 20
--   Nothing
--

-- --

--   (^?) ≡ flip preview
--

-- --

--   (^?) :: s -> Getter s a     -> Maybe a
--   (^?) :: s -> Fold s a       -> Maybe a
--   (^?) :: s -> Lens' s a      -> Maybe a
--   (^?) :: s -> Iso' s a       -> Maybe a
--   (^?) :: s -> Traversal' s a -> Maybe a
--

(^?) :: () => s -> Getting First a s a -> Maybe a infixl 8 ^? -- | Calculate the number of targets there are for a Fold in a given -- container. -- -- Note: This can be rather inefficient for large containers and -- just like length, this will not terminate for infinite folds. -- --

--   length ≡ lengthOf folded
--

-- --

--   >>> lengthOf _1 ("hello",())
--   1
--

-- --

--   >>> lengthOf traverse [1..10]
--   10
--

-- --

--   >>> lengthOf (traverse.traverse) [[1,2],[3,4],[5,6]]
--   6
--

-- --

--   lengthOf (folded . folded) :: (Foldable f, Foldable g) => f (g a) -> Int
--

-- --

--   lengthOf :: Getter s a     -> s -> Int
--   lengthOf :: Fold s a       -> s -> Int
--   lengthOf :: Lens' s a      -> s -> Int
--   lengthOf :: Iso' s a       -> s -> Int
--   lengthOf :: Traversal' s a -> s -> Int
--

lengthOf :: () => Getting Endo Endo Int s a -> s -> Int -- | Concatenate all of the lists targeted by a Fold into a longer -- list. -- --

--   >>> concatOf both ("pan","ama")
--   "panama"
--

-- --

--   concat ≡ concatOf folded
--   concatOf ≡ view
--

-- --

--   concatOf :: Getter s [r]     -> s -> [r]
--   concatOf :: Fold s [r]       -> s -> [r]
--   concatOf :: Iso' s [r]       -> s -> [r]
--   concatOf :: Lens' s [r]      -> s -> [r]
--   concatOf :: Traversal' s [r] -> s -> [r]
--

concatOf :: () => Getting [r] s [r] -> s -> [r] -- | Map a function over all the targets of a Fold of a container -- and concatenate the resulting lists. -- --

--   >>> concatMapOf both (\x -> [x, x + 1]) (1,3)
--   [1,2,3,4]
--

-- --

--   concatMap ≡ concatMapOf folded
--

-- --

--   concatMapOf :: Getter s a     -> (a -> [r]) -> s -> [r]
--   concatMapOf :: Fold s a       -> (a -> [r]) -> s -> [r]
--   concatMapOf :: Lens' s a      -> (a -> [r]) -> s -> [r]
--   concatMapOf :: Iso' s a       -> (a -> [r]) -> s -> [r]
--   concatMapOf :: Traversal' s a -> (a -> [r]) -> s -> [r]
--

concatMapOf :: () => Getting [r] s a -> a -> [r] -> s -> [r] -- | Does the element not occur anywhere within a given Fold of the -- structure? -- --

--   >>> notElemOf each 'd' ('a','b','c')
--   True
--

-- --

--   >>> notElemOf each 'a' ('a','b','c')
--   False
--

-- --

--   notElem ≡ notElemOf folded
--

-- --

--   notElemOf :: Eq a => Getter s a     -> a -> s -> Bool
--   notElemOf :: Eq a => Fold s a       -> a -> s -> Bool
--   notElemOf :: Eq a => Iso' s a       -> a -> s -> Bool
--   notElemOf :: Eq a => Lens' s a      -> a -> s -> Bool
--   notElemOf :: Eq a => Traversal' s a -> a -> s -> Bool
--   notElemOf :: Eq a => Prism' s a     -> a -> s -> Bool
--

notElemOf :: Eq a => Getting All s a -> a -> s -> Bool -- | Does the element occur anywhere within a given Fold of the -- structure? -- --

--   >>> elemOf both "hello" ("hello","world")
--   True
--

-- --

--   elem ≡ elemOf folded
--

-- --

--   elemOf :: Eq a => Getter s a     -> a -> s -> Bool
--   elemOf :: Eq a => Fold s a       -> a -> s -> Bool
--   elemOf :: Eq a => Lens' s a      -> a -> s -> Bool
--   elemOf :: Eq a => Iso' s a       -> a -> s -> Bool
--   elemOf :: Eq a => Traversal' s a -> a -> s -> Bool
--   elemOf :: Eq a => Prism' s a     -> a -> s -> Bool
--

elemOf :: Eq a => Getting Any s a -> a -> s -> Bool -- | The sum of a collection of actions, generalizing concatOf. -- --

--   >>> msumOf both ("hello","world")
--   "helloworld"
--

-- --

--   >>> msumOf each (Nothing, Just "hello", Nothing)
--   Just "hello"
--

-- --

--   msum ≡ msumOf folded
--

-- --

--   msumOf :: MonadPlus m => Getter s (m a)     -> s -> m a
--   msumOf :: MonadPlus m => Fold s (m a)       -> s -> m a
--   msumOf :: MonadPlus m => Lens' s (m a)      -> s -> m a
--   msumOf :: MonadPlus m => Iso' s (m a)       -> s -> m a
--   msumOf :: MonadPlus m => Traversal' s (m a) -> s -> m a
--   msumOf :: MonadPlus m => Prism' s (m a)     -> s -> m a
--

msumOf :: MonadPlus m => Getting Endo m a s m a -> s -> m a -- | The sum of a collection of actions, generalizing concatOf. -- --

--   >>> asumOf both ("hello","world")
--   "helloworld"
--

-- --

--   >>> asumOf each (Nothing, Just "hello", Nothing)
--   Just "hello"
--

-- --

--   asum ≡ asumOf folded
--

-- --

--   asumOf :: Alternative f => Getter s (f a)     -> s -> f a
--   asumOf :: Alternative f => Fold s (f a)       -> s -> f a
--   asumOf :: Alternative f => Lens' s (f a)      -> s -> f a
--   asumOf :: Alternative f => Iso' s (f a)       -> s -> f a
--   asumOf :: Alternative f => Traversal' s (f a) -> s -> f a
--   asumOf :: Alternative f => Prism' s (f a)     -> s -> f a
--

asumOf :: Alternative f => Getting Endo f a s f a -> s -> f a -- | Evaluate each monadic action referenced by a Fold on the -- structure from left to right, and ignore the results. -- --

--   >>> sequenceOf_ both (putStrLn "hello",putStrLn "world")
--   hello
--   world
--

-- --

--   sequence_ ≡ sequenceOf_ folded
--

-- --

--   sequenceOf_ :: Monad m => Getter s (m a)     -> s -> m ()
--   sequenceOf_ :: Monad m => Fold s (m a)       -> s -> m ()
--   sequenceOf_ :: Monad m => Lens' s (m a)      -> s -> m ()
--   sequenceOf_ :: Monad m => Iso' s (m a)       -> s -> m ()
--   sequenceOf_ :: Monad m => Traversal' s (m a) -> s -> m ()
--   sequenceOf_ :: Monad m => Prism' s (m a)     -> s -> m ()
--

sequenceOf_ :: Monad m => Getting Sequenced a m s m a -> s -> m () -- | forMOf_ is mapMOf_ with two of its arguments flipped. -- --

--   >>> forMOf_ both ("hello","world") putStrLn
--   hello
--   world
--

-- --

--   forM_ ≡ forMOf_ folded
--

-- --

--   forMOf_ :: Monad m => Getter s a     -> s -> (a -> m r) -> m ()
--   forMOf_ :: Monad m => Fold s a       -> s -> (a -> m r) -> m ()
--   forMOf_ :: Monad m => Lens' s a      -> s -> (a -> m r) -> m ()
--   forMOf_ :: Monad m => Iso' s a       -> s -> (a -> m r) -> m ()
--   forMOf_ :: Monad m => Traversal' s a -> s -> (a -> m r) -> m ()
--   forMOf_ :: Monad m => Prism' s a     -> s -> (a -> m r) -> m ()
--

forMOf_ :: Monad m => Getting Sequenced r m s a -> s -> a -> m r -> m () -- | Map each target of a Fold on a structure to a monadic action, -- evaluate these actions from left to right, and ignore the results. -- --

--   >>> mapMOf_ both putStrLn ("hello","world")
--   hello
--   world
--

-- --

--   mapM_ ≡ mapMOf_ folded
--

-- --

--   mapMOf_ :: Monad m => Getter s a     -> (a -> m r) -> s -> m ()
--   mapMOf_ :: Monad m => Fold s a       -> (a -> m r) -> s -> m ()
--   mapMOf_ :: Monad m => Lens' s a      -> (a -> m r) -> s -> m ()
--   mapMOf_ :: Monad m => Iso' s a       -> (a -> m r) -> s -> m ()
--   mapMOf_ :: Monad m => Traversal' s a -> (a -> m r) -> s -> m ()
--   mapMOf_ :: Monad m => Prism' s a     -> (a -> m r) -> s -> m ()
--

mapMOf_ :: Monad m => Getting Sequenced r m s a -> a -> m r -> s -> m () -- | See sequenceAOf_ and traverse1Of_. -- --

--   sequence1Of_ :: Apply f => Fold1 s (f a) -> s -> f ()
--

sequence1Of_ :: Functor f => Getting TraversedF a f s f a -> s -> f () -- | See forOf_ and traverse1Of_. -- --

--   >>> for1Of_ both1 ("abc", "bcd") (\ks -> Map.fromList [ (k, ()) | k <- ks ])
--   fromList [('b',()),('c',())]
--

-- --

--   for1Of_ :: Apply f => Fold1 s a -> s -> (a -> f r) -> f ()
--

for1Of_ :: Functor f => Getting TraversedF r f s a -> s -> a -> f r -> f () -- | Traverse over all of the targets of a Fold1, computing an -- Apply based answer. -- -- As long as you have Applicative or Functor effect you -- are better using traverseOf_. The traverse1Of_ is useful -- only when you have genuine Apply effect. -- --

--   >>> traverse1Of_ both1 (\ks -> Map.fromList [ (k, ()) | k <- ks ]) ("abc", "bcd")
--   fromList [('b',()),('c',())]
--

-- --

--   traverse1Of_ :: Apply f => Fold1 s a -> (a -> f r) -> s -> f ()
--

traverse1Of_ :: Functor f => Getting TraversedF r f s a -> a -> f r -> s -> f () -- | Evaluate each action in observed by a Fold on a structure from -- left to right, ignoring the results. -- --

--   sequenceA_ ≡ sequenceAOf_ folded
--

-- --

--   >>> sequenceAOf_ both (putStrLn "hello",putStrLn "world")
--   hello
--   world
--

-- --

--   sequenceAOf_ :: Functor f     => Getter s (f a)     -> s -> f ()
--   sequenceAOf_ :: Applicative f => Fold s (f a)       -> s -> f ()
--   sequenceAOf_ :: Functor f     => Lens' s (f a)      -> s -> f ()
--   sequenceAOf_ :: Functor f     => Iso' s (f a)       -> s -> f ()
--   sequenceAOf_ :: Applicative f => Traversal' s (f a) -> s -> f ()
--   sequenceAOf_ :: Applicative f => Prism' s (f a)     -> s -> f ()
--

sequenceAOf_ :: Functor f => Getting Traversed a f s f a -> s -> f () -- | Traverse over all of the targets of a Fold (or Getter), -- computing an Applicative (or Functor)-based answer, but -- unlike forOf do not construct a new structure. forOf_ -- generalizes for_ to work over any Fold. -- -- When passed a Getter, forOf_ can work over any -- Functor, but when passed a Fold, forOf_ requires -- an Applicative. -- --

--   for_ ≡ forOf_ folded
--

-- --

--   >>> forOf_ both ("hello","world") putStrLn
--   hello
--   world
--

-- -- The rather specific signature of forOf_ allows it to be used as -- if the signature was any of: -- --

--   iforOf_ l s ≡ forOf_ l s . Indexed
--

-- --

--   forOf_ :: Functor f     => Getter s a     -> s -> (a -> f r) -> f ()
--   forOf_ :: Applicative f => Fold s a       -> s -> (a -> f r) -> f ()
--   forOf_ :: Functor f     => Lens' s a      -> s -> (a -> f r) -> f ()
--   forOf_ :: Functor f     => Iso' s a       -> s -> (a -> f r) -> f ()
--   forOf_ :: Applicative f => Traversal' s a -> s -> (a -> f r) -> f ()
--   forOf_ :: Applicative f => Prism' s a     -> s -> (a -> f r) -> f ()
--

forOf_ :: Functor f => Getting Traversed r f s a -> s -> a -> f r -> f () -- | Traverse over all of the targets of a Fold (or Getter), -- computing an Applicative (or Functor)-based answer, but -- unlike traverseOf do not construct a new structure. -- traverseOf_ generalizes traverse_ to work over any -- Fold. -- -- When passed a Getter, traverseOf_ can work over any -- Functor, but when passed a Fold, traverseOf_ -- requires an Applicative. -- --

--   >>> traverseOf_ both putStrLn ("hello","world")
--   hello
--   world
--

-- --

--   traverse_ ≡ traverseOf_ folded
--

-- --

--   traverseOf_ _2 :: Functor f => (c -> f r) -> (d, c) -> f ()
--   traverseOf_ _Left :: Applicative f => (a -> f b) -> Either a c -> f ()
--

-- --

--   itraverseOf_ l ≡ traverseOf_ l . Indexed
--

-- -- The rather specific signature of traverseOf_ allows it to be -- used as if the signature was any of: -- --

--   traverseOf_ :: Functor f     => Getter s a     -> (a -> f r) -> s -> f ()
--   traverseOf_ :: Applicative f => Fold s a       -> (a -> f r) -> s -> f ()
--   traverseOf_ :: Functor f     => Lens' s a      -> (a -> f r) -> s -> f ()
--   traverseOf_ :: Functor f     => Iso' s a       -> (a -> f r) -> s -> f ()
--   traverseOf_ :: Applicative f => Traversal' s a -> (a -> f r) -> s -> f ()
--   traverseOf_ :: Applicative f => Prism' s a     -> (a -> f r) -> s -> f ()
--

traverseOf_ :: Functor f => Getting Traversed r f s a -> a -> f r -> s -> f () -- | Calculate the Sum of every number targeted by a Fold. -- --

--   >>> sumOf both (5,6)
--   11
--   
--   >>> sumOf folded [1,2,3,4]
--   10
--   
--   >>> sumOf (folded.both) [(1,2),(3,4)]
--   10
--   
--   >>> import Data.Data.Lens
--   
--   >>> sumOf biplate [(1::Int,[]),(2,[(3::Int,4::Int)])] :: Int
--   10
--

-- --

--   sum ≡ sumOf folded
--

-- -- This operation may be more strict than you would expect. If you want a -- lazier version use ala Sum . -- foldMapOf -- --

--   sumOf _1 :: Num a => (a, b) -> a
--   sumOf (folded . _1) :: (Foldable f, Num a) => f (a, b) -> a
--

-- --

--   sumOf :: Num a => Getter s a     -> s -> a
--   sumOf :: Num a => Fold s a       -> s -> a
--   sumOf :: Num a => Lens' s a      -> s -> a
--   sumOf :: Num a => Iso' s a       -> s -> a
--   sumOf :: Num a => Traversal' s a -> s -> a
--   sumOf :: Num a => Prism' s a     -> s -> a
--

sumOf :: Num a => Getting Endo Endo a s a -> s -> a -- | Calculate the Product of every number targeted by a -- Fold. -- --

--   >>> productOf both (4,5)
--   20
--   
--   >>> productOf folded [1,2,3,4,5]
--   120
--

-- --

--   product ≡ productOf folded
--

-- -- This operation may be more strict than you would expect. If you want a -- lazier version use ala Product . -- foldMapOf -- --

--   productOf :: Num a => Getter s a     -> s -> a
--   productOf :: Num a => Fold s a       -> s -> a
--   productOf :: Num a => Lens' s a      -> s -> a
--   productOf :: Num a => Iso' s a       -> s -> a
--   productOf :: Num a => Traversal' s a -> s -> a
--   productOf :: Num a => Prism' s a     -> s -> a
--

productOf :: Num a => Getting Endo Endo a s a -> s -> a -- | Returns True only if no targets of a Fold satisfy a -- predicate. -- --

--   >>> noneOf each (is _Nothing) (Just 3, Just 4, Just 5)
--   True
--   
--   >>> noneOf (folded.folded) (<10) [[13,99,20],[3,71,42]]
--   False
--

-- --

--   inoneOf l = noneOf l . Indexed
--

-- --

--   noneOf :: Getter s a     -> (a -> Bool) -> s -> Bool
--   noneOf :: Fold s a       -> (a -> Bool) -> s -> Bool
--   noneOf :: Lens' s a      -> (a -> Bool) -> s -> Bool
--   noneOf :: Iso' s a       -> (a -> Bool) -> s -> Bool
--   noneOf :: Traversal' s a -> (a -> Bool) -> s -> Bool
--   noneOf :: Prism' s a     -> (a -> Bool) -> s -> Bool
--

noneOf :: () => Getting Any s a -> a -> Bool -> s -> Bool -- | Returns True if every target of a Fold satisfies a -- predicate. -- --

--   >>> allOf both (>=3) (4,5)
--   True
--   
--   >>> allOf folded (>=2) [1..10]
--   False
--

-- --

--   all ≡ allOf folded
--

-- --

--   iallOf l = allOf l . Indexed
--

-- --

--   allOf :: Getter s a     -> (a -> Bool) -> s -> Bool
--   allOf :: Fold s a       -> (a -> Bool) -> s -> Bool
--   allOf :: Lens' s a      -> (a -> Bool) -> s -> Bool
--   allOf :: Iso' s a       -> (a -> Bool) -> s -> Bool
--   allOf :: Traversal' s a -> (a -> Bool) -> s -> Bool
--   allOf :: Prism' s a     -> (a -> Bool) -> s -> Bool
--

allOf :: () => Getting All s a -> a -> Bool -> s -> Bool -- | Returns True if any target of a Fold satisfies a -- predicate. -- --

--   >>> anyOf both (=='x') ('x','y')
--   True
--   
--   >>> import Data.Data.Lens
--   
--   >>> anyOf biplate (== "world") (((),2::Int),"hello",("world",11::Int))
--   True
--

-- --

--   any ≡ anyOf folded
--

-- --

--   ianyOf l ≡ anyOf l . Indexed
--

-- --

--   anyOf :: Getter s a     -> (a -> Bool) -> s -> Bool
--   anyOf :: Fold s a       -> (a -> Bool) -> s -> Bool
--   anyOf :: Lens' s a      -> (a -> Bool) -> s -> Bool
--   anyOf :: Iso' s a       -> (a -> Bool) -> s -> Bool
--   anyOf :: Traversal' s a -> (a -> Bool) -> s -> Bool
--   anyOf :: Prism' s a     -> (a -> Bool) -> s -> Bool
--

anyOf :: () => Getting Any s a -> a -> Bool -> s -> Bool -- | Returns True if any target of a Fold is True. -- --

--   >>> orOf both (True,False)
--   True
--   
--   >>> orOf both (False,False)
--   False
--

-- --

--   or ≡ orOf folded
--

-- --

--   orOf :: Getter s Bool     -> s -> Bool
--   orOf :: Fold s Bool       -> s -> Bool
--   orOf :: Lens' s Bool      -> s -> Bool
--   orOf :: Iso' s Bool       -> s -> Bool
--   orOf :: Traversal' s Bool -> s -> Bool
--   orOf :: Prism' s Bool     -> s -> Bool
--

orOf :: () => Getting Any s Bool -> s -> Bool -- | Returns True if every target of a Fold is True. -- --

--   >>> andOf both (True,False)
--   False
--   
--   >>> andOf both (True,True)
--   True
--

-- --

--   and ≡ andOf folded
--

-- --

--   andOf :: Getter s Bool     -> s -> Bool
--   andOf :: Fold s Bool       -> s -> Bool
--   andOf :: Lens' s Bool      -> s -> Bool
--   andOf :: Iso' s Bool       -> s -> Bool
--   andOf :: Traversal' s Bool -> s -> Bool
--   andOf :: Prism' s Bool     -> s -> Bool
--

andOf :: () => Getting All s Bool -> s -> Bool -- | A convenient infix (flipped) version of toListOf. -- --

--   >>> [[1,2],[3]]^..id
--   [[[1,2],[3]]]
--   
--   >>> [[1,2],[3]]^..traverse
--   [[1,2],[3]]
--   
--   >>> [[1,2],[3]]^..traverse.traverse
--   [1,2,3]
--

-- --

--   >>> (1,2)^..both
--   [1,2]
--

-- --

--   toList xs ≡ xs ^.. folded
--   (^..) ≡ flip toListOf
--

-- --

--   (^..) :: s -> Getter s a     -> a :: s -> Fold s a       -> a :: s -> Lens' s a      -> a :: s -> Iso' s a       -> a :: s -> Traversal' s a -> a :: s -> Prism' s a     -> [a]
--

(^..) :: () => s -> Getting Endo [a] s a -> [a] infixl 8 ^.. -- | Extract a NonEmpty of the targets of Fold1. -- --

--   >>> toNonEmptyOf both1 ("hello", "world")
--   "hello" :| ["world"]
--

-- --

--   toNonEmptyOf :: Getter s a      -> s -> NonEmpty a
--   toNonEmptyOf :: Fold1 s a       -> s -> NonEmpty a
--   toNonEmptyOf :: Lens' s a       -> s -> NonEmpty a
--   toNonEmptyOf :: Iso' s a        -> s -> NonEmpty a
--   toNonEmptyOf :: Traversal1' s a -> s -> NonEmpty a
--   toNonEmptyOf :: Prism' s a      -> s -> NonEmpty a
--

toNonEmptyOf :: () => Getting NonEmptyDList a s a -> s -> NonEmpty a -- | Extract a list of the targets of a Fold. See also (^..). -- --

--   toList ≡ toListOf folded
--   (^..) ≡ flip toListOf
--

toListOf :: () => Getting Endo [a] s a -> s -> [a] -- | Left-associative fold of the parts of a structure that are viewed -- through a Lens, Getter, Fold or Traversal. -- --

--   foldl ≡ foldlOf folded
--

-- --

--   foldlOf :: Getter s a     -> (r -> a -> r) -> r -> s -> r
--   foldlOf :: Fold s a       -> (r -> a -> r) -> r -> s -> r
--   foldlOf :: Lens' s a      -> (r -> a -> r) -> r -> s -> r
--   foldlOf :: Iso' s a       -> (r -> a -> r) -> r -> s -> r
--   foldlOf :: Traversal' s a -> (r -> a -> r) -> r -> s -> r
--   foldlOf :: Prism' s a     -> (r -> a -> r) -> r -> s -> r
--

foldlOf :: () => Getting Dual Endo r s a -> r -> a -> r -> r -> s -> r -- | Right-associative fold of parts of a structure that are viewed through -- a Lens, Getter, Fold or Traversal. -- --

--   foldr ≡ foldrOf folded
--

-- --

--   foldrOf :: Getter s a     -> (a -> r -> r) -> r -> s -> r
--   foldrOf :: Fold s a       -> (a -> r -> r) -> r -> s -> r
--   foldrOf :: Lens' s a      -> (a -> r -> r) -> r -> s -> r
--   foldrOf :: Iso' s a       -> (a -> r -> r) -> r -> s -> r
--   foldrOf :: Traversal' s a -> (a -> r -> r) -> r -> s -> r
--   foldrOf :: Prism' s a     -> (a -> r -> r) -> r -> s -> r
--

-- --

--   ifoldrOf l ≡ foldrOf l . Indexed
--

-- --

--   foldrOf :: Getting (Endo r) s a -> (a -> r -> r) -> r -> s -> r
--

foldrOf :: () => Getting Endo r s a -> a -> r -> r -> r -> s -> r -- | Combine the elements of a structure viewed through a Lens, -- Getter, Fold or Traversal using a monoid. -- --

--   >>> foldOf (folded.folded) [[Sum 1,Sum 4],[Sum 8, Sum 8],[Sum 21]]
--   Sum {getSum = 42}
--

-- --

--   fold = foldOf folded
--

-- --

--   foldOf ≡ view
--

-- --

--   foldOf ::             Getter s m     -> s -> m
--   foldOf :: Monoid m => Fold s m       -> s -> m
--   foldOf ::             Lens' s m      -> s -> m
--   foldOf ::             Iso' s m       -> s -> m
--   foldOf :: Monoid m => Traversal' s m -> s -> m
--   foldOf :: Monoid m => Prism' s m     -> s -> m
--

foldOf :: () => Getting a s a -> s -> a -- | Map each part of a structure viewed through a Lens, -- Getter, Fold or Traversal to a monoid and combine -- the results. -- --

--   >>> foldMapOf (folded . both . _Just) Sum [(Just 21, Just 21)]
--   Sum {getSum = 42}
--

-- --

--   foldMap = foldMapOf folded
--

-- --

--   foldMapOf ≡ views
--   ifoldMapOf l = foldMapOf l . Indexed
--

-- --

--   foldMapOf ::                Getter s a      -> (a -> r) -> s -> r
--   foldMapOf :: Monoid r    => Fold s a        -> (a -> r) -> s -> r
--   foldMapOf :: Semigroup r => Fold1 s a       -> (a -> r) -> s -> r
--   foldMapOf ::                Lens' s a       -> (a -> r) -> s -> r
--   foldMapOf ::                Iso' s a        -> (a -> r) -> s -> r
--   foldMapOf :: Monoid r    => Traversal' s a  -> (a -> r) -> s -> r
--   foldMapOf :: Semigroup r => Traversal1' s a -> (a -> r) -> s -> r
--   foldMapOf :: Monoid r    => Prism' s a      -> (a -> r) -> s -> r
--

-- --

--   foldMapOf :: Getting r s a -> (a -> r) -> s -> r
--

foldMapOf :: () => Getting r s a -> a -> r -> s -> r -- | A Fold over the individual lines of a String. -- --

--   lined :: Fold String String
--   lined :: Traversal' String String
--

-- --

--   lined :: IndexedFold Int String String
--   lined :: IndexedTraversal' Int String String
--

-- -- Note: This function type-checks as a Traversal but it doesn't -- satisfy the laws. It's only valid to use it when you don't insert any -- newline characters while traversing, and if your original -- String contains only isolated newline characters. lined :: Applicative f => IndexedLensLike' Int f String String -- | A Fold over the individual words of a String. -- --

--   worded :: Fold String String
--   worded :: Traversal' String String
--

-- --

--   worded :: IndexedFold Int String String
--   worded :: IndexedTraversal' Int String String
--

-- -- Note: This function type-checks as a Traversal but it doesn't -- satisfy the laws. It's only valid to use it when you don't insert any -- whitespace characters while traversing, and if your original -- String contains only isolated space characters (and no other -- characters that count as space, such as non-breaking spaces). worded :: Applicative f => IndexedLensLike' Int f String String -- | Obtain a Fold by dropping elements from another Fold, -- Lens, Iso, Getter or Traversal while a -- predicate holds. -- --

--   dropWhile p ≡ toListOf (droppingWhile p folded)
--

-- --

--   >>> toListOf (droppingWhile (<=3) folded) [1..6]
--   [4,5,6]
--

-- --

--   >>> toListOf (droppingWhile (<=3) folded) [1,6,1]
--   [6,1]
--

-- --

--   droppingWhile :: (a -> Bool) -> Fold s a                         -> Fold s a
--   droppingWhile :: (a -> Bool) -> Getter s a                       -> Fold s a
--   droppingWhile :: (a -> Bool) -> Traversal' s a                   -> Fold s a                -- see notes
--   droppingWhile :: (a -> Bool) -> Lens' s a                        -> Fold s a                -- see notes
--   droppingWhile :: (a -> Bool) -> Prism' s a                       -> Fold s a                -- see notes
--   droppingWhile :: (a -> Bool) -> Iso' s a                         -> Fold s a                -- see notes
--

-- --

--   droppingWhile :: (a -> Bool) -> IndexPreservingTraversal' s a    -> IndexPreservingFold s a -- see notes
--   droppingWhile :: (a -> Bool) -> IndexPreservingLens' s a         -> IndexPreservingFold s a -- see notes
--   droppingWhile :: (a -> Bool) -> IndexPreservingGetter s a        -> IndexPreservingFold s a
--   droppingWhile :: (a -> Bool) -> IndexPreservingFold s a          -> IndexPreservingFold s a
--

-- --

--   droppingWhile :: (a -> Bool) -> IndexedTraversal' i s a          -> IndexedFold i s a       -- see notes
--   droppingWhile :: (a -> Bool) -> IndexedLens' i s a               -> IndexedFold i s a       -- see notes
--   droppingWhile :: (a -> Bool) -> IndexedGetter i s a              -> IndexedFold i s a
--   droppingWhile :: (a -> Bool) -> IndexedFold i s a                -> IndexedFold i s a
--

-- -- Note: Many uses of this combinator will yield something that meets the -- types, but not the laws of a valid Traversal or -- IndexedTraversal. The Traversal and -- IndexedTraversal laws are only satisfied if the new values you -- assign to the first target also does not pass the predicate! Otherwise -- subsequent traversals will visit fewer elements and Traversal -- fusion is not sound. -- -- So for any traversal t and predicate p, -- droppingWhile p t may not be lawful, but -- (dropping 1 . droppingWhile p) t is. For -- example: -- --

--   >>> let l  :: Traversal' [Int] Int; l  = droppingWhile (<= 1) traverse
--   
--   >>> let l' :: Traversal' [Int] Int; l' = dropping 1 l
--

-- -- l is not a lawful setter because over l f . -- over l g ≢ over l (f . g): -- --

--   >>> [1,2,3] & l .~ 0 & l .~ 4
--   [1,0,0]
--   
--   >>> [1,2,3] & l .~ 4
--   [1,4,4]
--

-- -- l' on the other hand behaves lawfully: -- --

--   >>> [1,2,3] & l' .~ 0 & l' .~ 4
--   [1,2,4]
--   
--   >>> [1,2,3] & l' .~ 4
--   [1,2,4]
--

droppingWhile :: (Conjoined p, Profunctor q, Applicative f) => a -> Bool -> Optical p q Compose State Bool f s t a a -> Optical p q f s t a a -- | Obtain a Fold by taking elements from another Fold, -- Lens, Iso, Getter or Traversal while a -- predicate holds. -- --

--   takeWhile p ≡ toListOf (takingWhile p folded)
--

-- --

--   >>> timingOut $ toListOf (takingWhile (<=3) folded) [1..]
--   [1,2,3]
--

-- --

--   takingWhile :: (a -> Bool) -> Fold s a                         -> Fold s a
--   takingWhile :: (a -> Bool) -> Getter s a                       -> Fold s a
--   takingWhile :: (a -> Bool) -> Traversal' s a                   -> Fold s a -- * See note below
--   takingWhile :: (a -> Bool) -> Lens' s a                        -> Fold s a -- * See note below
--   takingWhile :: (a -> Bool) -> Prism' s a                       -> Fold s a -- * See note below
--   takingWhile :: (a -> Bool) -> Iso' s a                         -> Fold s a -- * See note below
--   takingWhile :: (a -> Bool) -> IndexedTraversal' i s a          -> IndexedFold i s a -- * See note below
--   takingWhile :: (a -> Bool) -> IndexedLens' i s a               -> IndexedFold i s a -- * See note below
--   takingWhile :: (a -> Bool) -> IndexedFold i s a                -> IndexedFold i s a
--   takingWhile :: (a -> Bool) -> IndexedGetter i s a              -> IndexedFold i s a
--

-- -- Note: When applied to a Traversal, takingWhile -- yields something that can be used as if it were a Traversal, -- but which is not a Traversal per the laws, unless you are -- careful to ensure that you do not invalidate the predicate when -- writing back through it. takingWhile :: (Conjoined p, Applicative f) => a -> Bool -> Over p TakingWhile p f a a s t a a -> Over p f s t a a -- | Obtain an Fold that can be composed with to filter another -- Lens, Iso, Getter, Fold (or -- Traversal). -- -- Note: This is not a legal Traversal, unless you are very -- careful not to invalidate the predicate on the target. -- -- Note: This is also not a legal Prism, unless you are -- very careful not to inject a value that matches the predicate. -- -- As a counter example, consider that given evens = filtered -- even the second Traversal law is violated: -- --

--   over evens succ . over evens succ /= over evens (succ . succ)
--

-- -- So, in order for this to qualify as a legal Traversal you can -- only use it for actions that preserve the result of the predicate! -- --

--   >>> [1..10]^..folded.filtered even
--   [2,4,6,8,10]
--

-- -- This will preserve an index if it is present. filtered :: (Choice p, Applicative f) => a -> Bool -> Optic' p f a a -- | x ^. iterated f returns an infinite -- Fold1 of repeated applications of f to x. -- --

--   toListOf (iterated f) a ≡ iterate f a
--

-- --

--   iterated :: (a -> a) -> Fold1 a a
--

iterated :: Apply f => a -> a -> LensLike' f a a -- | Build a Fold that unfolds its values from a seed. -- --

--   unfoldr ≡ toListOf . unfolded
--

-- --

--   >>> 10^..unfolded (\b -> if b == 0 then Nothing else Just (b, b-1))
--   [10,9,8,7,6,5,4,3,2,1]
--

unfolded :: () => b -> Maybe (a, b) -> Fold b a -- | Transform a non-empty Fold into a Fold1 that loops over -- its elements over and over. -- --

--   >>> timingOut $ [1,2,3]^..taking 7 (cycled traverse)
--   [1,2,3,1,2,3,1]
--

-- --

--   cycled :: Fold1 s a -> Fold1 s a
--

cycled :: Apply f => LensLike f s t a b -> LensLike f s t a b -- | A Fold that replicates its input n times. -- --

--   replicate n ≡ toListOf (replicated n)
--

-- --

--   >>> 5^..replicated 20
--   [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
--

replicated :: () => Int -> Fold a a -- | Form a Fold1 by repeating the input forever. -- --

--   repeat ≡ toListOf repeated
--

-- --

--   >>> timingOut $ 5^..taking 20 repeated
--   [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
--

-- --

--   repeated :: Fold1 a a
--

repeated :: Apply f => LensLike' f a a -- | Obtain a Fold from any Foldable indexed by ordinal -- position. folded64 :: Foldable f => IndexedFold Int64 f a a -- | Obtain a Fold from any Foldable indexed by ordinal -- position. -- --

--   >>> Just 3^..folded
--   [3]
--

-- --

--   >>> Nothing^..folded
--   []
--

-- --

--   >>> [(1,2),(3,4)]^..folded.both
--   [1,2,3,4]
--

folded :: Foldable f => IndexedFold Int f a a -- | Obtain FoldWithIndex by lifting ifoldr like function. ifoldring :: (Indexable i p, Contravariant f, Applicative f) => i -> a -> f a -> f a -> f a -> s -> f a -> Over p f s t a b -- | Obtain a Fold by lifting foldr like function. -- --

--   >>> [1,2,3,4]^..foldring foldr
--   [1,2,3,4]
--

foldring :: (Contravariant f, Applicative f) => a -> f a -> f a -> f a -> s -> f a -> LensLike f s t a b ifolding :: (Foldable f, Indexable i p, Contravariant g, Applicative g) => s -> f (i, a) -> Over p g s t a b -- | Obtain a Fold by lifting an operation that returns a -- Foldable result. -- -- This can be useful to lift operations from Data.List and -- elsewhere into a Fold. -- --

--   >>> [1,2,3,4]^..folding tail
--   [2,3,4]
--

folding :: Foldable f => s -> f a -> Fold s a -- | This is an improper prism for text formatting based on Read and -- Show. -- -- This Prism is "improper" in the sense that it normalizes the -- text formatting, but round tripping is idempotent given sane -- 'Read'/'Show' instances. -- --

--   >>> _Show # 2
--   "2"
--

-- --

--   >>> "EQ" ^? _Show :: Maybe Ordering
--   Just EQ
--

-- --

--   _Show ≡ prism' show readMaybe
--

_Show :: (Read a, Show a) => Prism' String a -- | This Prism compares for approximate equality with a given value -- and a predicate for testing, an example where the value is the empty -- list and the predicate checks that a list is empty (same as -- _Empty with the AsEmpty list instance): -- --

--   >>> nearly [] null # ()
--   []
--   
--   >>> [1,2,3,4] ^? nearly [] null
--   Nothing
--

-- --

--   nearly [] null :: Prism' [a] ()
--

-- -- To comply with the Prism laws the arguments you supply to -- nearly a p are somewhat constrained. -- -- We assume p x holds iff x ≡ a. Under that assumption -- then this is a valid Prism. -- -- This is useful when working with a type where you can test equality -- for only a subset of its values, and the prism selects such a value. nearly :: () => a -> a -> Bool -> Prism' a () -- | This Prism compares for exact equality with a given value. -- --

--   >>> only 4 # ()
--   4
--

-- --

--   >>> 5 ^? only 4
--   Nothing
--

only :: Eq a => a -> Prism' a () -- | Void is a logically uninhabited data type. -- -- This is a Prism that will always fail to match. _Void :: (Choice p, Applicative f) => p a f Void -> p s f s -- | This Prism provides the Traversal of a Nothing in -- a Maybe. -- --

--   >>> Nothing ^? _Nothing
--   Just ()
--

-- --

--   >>> Just () ^? _Nothing
--   Nothing
--

-- -- But you can turn it around and use it to construct Nothing as -- well: -- --

--   >>> _Nothing # ()
--   Nothing
--

_Nothing :: (Choice p, Applicative f) => p () f () -> p Maybe a f Maybe a -- | This Prism provides a Traversal for tweaking the target -- of the value of Just in a Maybe. -- --

--   >>> over _Just (+1) (Just 2)
--   Just 3
--

-- -- Unlike traverse this is a Prism, and so you can use it -- to inject as well: -- --

--   >>> _Just # 5
--   Just 5
--

-- --

--   >>> 5^.re _Just
--   Just 5
--

-- -- Interestingly, -- --

--   m ^? _Just ≡ m
--

-- --

--   >>> Just x ^? _Just
--   Just x
--

-- --

--   >>> Nothing ^? _Just
--   Nothing
--

_Just :: (Choice p, Applicative f) => p a f b -> p Maybe a f Maybe b -- | This Prism provides a Traversal for tweaking the -- Right half of an Either: -- --

--   >>> over _Right (+1) (Left 2)
--   Left 2
--

-- --

--   >>> over _Right (+1) (Right 2)
--   Right 3
--

-- --

--   >>> Right "hello" ^._Right
--   "hello"
--

-- --

--   >>> Left "hello" ^._Right :: [Double]
--   []
--

-- -- It also can be turned around to obtain the embedding into the -- Right half of an Either: -- --

--   >>> _Right # 5
--   Right 5
--

-- --

--   >>> 5^.re _Right
--   Right 5
--

_Right :: (Choice p, Applicative f) => p a f b -> p Either c a f Either c b -- | This Prism provides a Traversal for tweaking the -- Left half of an Either: -- --

--   >>> over _Left (+1) (Left 2)
--   Left 3
--

-- --

--   >>> over _Left (+1) (Right 2)
--   Right 2
--

-- --

--   >>> Right 42 ^._Left :: String
--   ""
--

-- --

--   >>> Left "hello" ^._Left
--   "hello"
--

-- -- It also can be turned around to obtain the embedding into the -- Left half of an Either: -- --

--   >>> _Left # 5
--   Left 5
--

-- --

--   >>> 5^.re _Left
--   Left 5
--

_Left :: (Choice p, Applicative f) => p a f b -> p Either a c f Either b c -- | Retrieve the value targeted by a Prism or return the original -- value while allowing the type to change if it does not match. -- --

--   >>> matching _Just (Just 12)
--   Right 12
--

-- --

--   >>> matching _Just (Nothing :: Maybe Int) :: Either (Maybe Bool) Int
--   Left Nothing
--

matching :: () => APrism s t a b -> s -> Either t a -- | Check to see if this Prism doesn't match. -- --

--   >>> isn't _Left (Right 12)
--   True
--

-- --

--   >>> isn't _Left (Left 12)
--   False
--

-- --

--   >>> isn't _Empty []
--   False
--

isn't :: () => APrism s t a b -> s -> Bool -- | lift a Prism through a Traversable functor, -- giving a Prism that matches only if all the elements of the container -- match the Prism. -- --

--   >>> [Left 1, Right "foo", Left 4, Right "woot"]^..below _Right
--   []
--

-- --

--   >>> [Right "hail hydra!", Right "foo", Right "blah", Right "woot"]^..below _Right
--   [["hail hydra!","foo","blah","woot"]]
--

below :: Traversable f => APrism' s a -> Prism' f s f a -- | Use a Prism to work over part of a structure. aside :: () => APrism s t a b -> Prism (e, s) (e, t) (e, a) (e, b) -- | Given a pair of prisms, project sums. -- -- Viewing a Prism as a co-Lens, this combinator can be -- seen to be dual to alongside. without :: () => APrism s t a b -> APrism u v c d -> Prism Either s u Either t v Either a c Either b d -- | Use a Prism as a kind of first-class pattern. -- --

--   outside :: Prism s t a b -> Lens (t -> r) (s -> r) (b -> r) (a -> r)
--

outside :: Representable p => APrism s t a b -> Lens p t r p s r p b r p a r -- | This is usually used to build a Prism', when you have to use an -- operation like cast which already returns a Maybe. prism' :: () => b -> s -> s -> Maybe a -> Prism s s a b -- | Build a Prism. -- -- Either t a is used instead of Maybe a -- to permit the types of s and t to differ. prism :: () => b -> t -> s -> Either t a -> Prism s t a b -- | Clone a Prism so that you can reuse the same monomorphically -- typed Prism for different purposes. -- -- See cloneLens and cloneTraversal for examples of why you -- might want to do this. clonePrism :: () => APrism s t a b -> Prism s t a b -- | Convert APrism to the pair of functions that characterize it. withPrism :: () => APrism s t a b -> b -> t -> s -> Either t a -> r -> r -- | If you see this in a signature for a function, the function is -- expecting a Prism. type APrism s t a b = Market a b a Identity b -> Market a b s Identity t -- |

--   type APrism' = Simple APrism
--

type APrism' s a = APrism s s a a -- | This can be used to turn an Iso or Prism around and -- use the current state through it the other way, applying a -- function. -- --

--   reuses ≡ uses . re
--   reuses (unto f) g ≡ gets (g . f)
--

-- --

--   >>> evalState (reuses _Left isLeft) (5 :: Int)
--   True
--

-- --

--   reuses :: MonadState a m => Prism' s a -> (s -> r) -> m r
--   reuses :: MonadState a m => Iso' s a   -> (s -> r) -> m r
--

reuses :: MonadState b m => AReview t b -> t -> r -> m r -- | This can be used to turn an Iso or Prism around and -- use a value (or the current environment) through it the other -- way. -- --

--   reuse ≡ use . re
--   reuse . unto ≡ gets
--

-- --

--   >>> evalState (reuse _Left) 5
--   Left 5
--

-- --

--   >>> evalState (reuse (unto succ)) 5
--   6
--

-- --

--   reuse :: MonadState a m => Prism' s a -> m s
--   reuse :: MonadState a m => Iso' s a   -> m s
--

reuse :: MonadState b m => AReview t b -> m t -- | This can be used to turn an Iso or Prism around and -- view a value (or the current environment) through it the other -- way, applying a function. -- --

--   reviews ≡ views . re
--   reviews (unto f) g ≡ g . f
--

-- --

--   >>> reviews _Left isRight "mustard"
--   False
--

-- --

--   >>> reviews (unto succ) (*2) 3
--   8
--

-- -- Usually this function is used in the (->) Monad -- with a Prism or Iso, in which case it may be useful to -- think of it as having one of these more restricted type signatures: -- --

--   reviews :: Iso' s a   -> (s -> r) -> a -> r
--   reviews :: Prism' s a -> (s -> r) -> a -> r
--

-- -- However, when working with a Monad transformer stack, it is -- sometimes useful to be able to review the current environment, -- in which case it may be beneficial to think of it as having one of -- these slightly more liberal type signatures: -- --

--   reviews :: MonadReader a m => Iso' s a   -> (s -> r) -> m r
--   reviews :: MonadReader a m => Prism' s a -> (s -> r) -> m r
--

reviews :: MonadReader b m => AReview t b -> t -> r -> m r -- | An infix alias for review. -- --

--   unto f # x ≡ f x
--   l # x ≡ x ^. re l
--

-- -- This is commonly used when using a Prism as a smart -- constructor. -- --

--   >>> _Left # 4
--   Left 4
--

-- -- But it can be used for any Prism -- --

--   >>> base 16 # 123
--   "7b"
--

-- --

--   (#) :: Iso'      s a -> a -> s
--   (#) :: Prism'    s a -> a -> s
--   (#) :: Review    s a -> a -> s
--   (#) :: Equality' s a -> a -> s
--

(#) :: () => AReview t b -> b -> t infixr 8 # -- | This can be used to turn an Iso or Prism around and -- view a value (or the current environment) through it the other -- way. -- --

--   review ≡ view . re
--   review . unto ≡ id
--

-- --

--   >>> review _Left "mustard"
--   Left "mustard"
--

-- --

--   >>> review (unto succ) 5
--   6
--

-- -- Usually review is used in the (->) Monad -- with a Prism or Iso, in which case it may be useful to -- think of it as having one of these more restricted type signatures: -- --

--   review :: Iso' s a   -> a -> s
--   review :: Prism' s a -> a -> s
--

--   review :: MonadReader a m => Iso' s a   -> m s
--   review :: MonadReader a m => Prism' s a -> m s
--

review :: MonadReader b m => AReview t b -> m t -- | Turn a Getter around to get a Review -- --

--   un = unto . view
--   unto = un . to
--

-- --

--   >>> un (to length) # [1,2,3]
--   3
--

un :: (Profunctor p, Bifunctor p, Functor f) => Getting a s a -> Optic' p f a s -- | An analogue of to for review. -- --

--   unto :: (b -> t) -> Review' t b
--

-- --

--   unto = un . to
--

unto :: (Profunctor p, Bifunctor p, Functor f) => b -> t -> Optic p f s t a b -- | Coerce a Getter-compatible Optical to an -- Optical'. This is useful when using a Traversal that is -- not simple as a Getter or a Fold. -- --

--   getting :: Traversal s t a b          -> Fold s a
--   getting :: Lens s t a b               -> Getter s a
--   getting :: IndexedTraversal i s t a b -> IndexedFold i s a
--   getting :: IndexedLens i s t a b      -> IndexedGetter i s a
--

getting :: (Profunctor p, Profunctor q, Functor f, Contravariant f) => Optical p q f s t a b -> Optical' p q f s a -- | View the index and value of an IndexedGetter or -- IndexedLens. -- -- This is the same operation as iview with the arguments flipped. -- -- The fixity and semantics are such that subsequent field accesses can -- be performed with (.). -- --

--   (^@.) :: s -> IndexedGetter i s a -> (i, a)
--   (^@.) :: s -> IndexedLens' i s a  -> (i, a)
--

-- -- The result probably doesn't have much meaning when applied to an -- IndexedFold. (^@.) :: () => s -> IndexedGetting i (i, a) s a -> (i, a) infixl 8 ^@. -- | Use a function of the index and value of an IndexedGetter into -- the current state. -- -- When applied to an IndexedFold the result will be a monoidal -- summary instead of a single answer. iuses :: MonadState s m => IndexedGetting i r s a -> i -> a -> r -> m r -- | Use the index and value of an IndexedGetter into the current -- state as a pair. -- -- When applied to an IndexedFold the result will most likely be a -- nonsensical monoidal summary of the indices tupled with a monoidal -- summary of the values and probably not whatever it is you wanted. iuse :: MonadState s m => IndexedGetting i (i, a) s a -> m (i, a) -- | View a function of the index and value of an IndexedGetter into -- the current environment. -- -- When applied to an IndexedFold the result will be a monoidal -- summary instead of a single answer. -- --

--   iviews ≡ ifoldMapOf
--

iviews :: MonadReader s m => IndexedGetting i r s a -> i -> a -> r -> m r -- | View the index and value of an IndexedGetter into the current -- environment as a pair. -- -- When applied to an IndexedFold the result will most likely be a -- nonsensical monoidal summary of the indices tupled with a monoidal -- summary of the values and probably not whatever it is you wanted. iview :: MonadReader s m => IndexedGetting i (i, a) s a -> m (i, a) -- | This is a generalized form of listen that only extracts the -- portion of the log that is focused on by a Getter. If given a -- Fold or a Traversal then a monoidal summary of the parts -- of the log that are visited will be returned. -- --

--   ilistenings :: MonadWriter w m             => IndexedGetter w u     -> (i -> u -> v) -> m a -> m (a, v)
--   ilistenings :: MonadWriter w m             => IndexedLens' w u      -> (i -> u -> v) -> m a -> m (a, v)
--   ilistenings :: (MonadWriter w m, Monoid v) => IndexedFold w u       -> (i -> u -> v) -> m a -> m (a, v)
--   ilistenings :: (MonadWriter w m, Monoid v) => IndexedTraversal' w u -> (i -> u -> v) -> m a -> m (a, v)
--

ilistenings :: MonadWriter w m => IndexedGetting i v w u -> i -> u -> v -> m a -> m (a, v) -- | This is a generalized form of listen that only extracts the -- portion of the log that is focused on by a Getter. If given a -- Fold or a Traversal then a monoidal summary of the parts -- of the log that are visited will be returned. -- --

--   listenings :: MonadWriter w m             => Getter w u     -> (u -> v) -> m a -> m (a, v)
--   listenings :: MonadWriter w m             => Lens' w u      -> (u -> v) -> m a -> m (a, v)
--   listenings :: MonadWriter w m             => Iso' w u       -> (u -> v) -> m a -> m (a, v)
--   listenings :: (MonadWriter w m, Monoid v) => Fold w u       -> (u -> v) -> m a -> m (a, v)
--   listenings :: (MonadWriter w m, Monoid v) => Traversal' w u -> (u -> v) -> m a -> m (a, v)
--   listenings :: (MonadWriter w m, Monoid v) => Prism' w u     -> (u -> v) -> m a -> m (a, v)
--

listenings :: MonadWriter w m => Getting v w u -> u -> v -> m a -> m (a, v) -- | This is a generalized form of listen that only extracts the -- portion of the log that is focused on by a Getter. If given a -- Fold or a Traversal then a monoidal summary of the parts -- of the log that are visited will be returned. -- --

--   ilistening :: MonadWriter w m             => IndexedGetter i w u     -> m a -> m (a, (i, u))
--   ilistening :: MonadWriter w m             => IndexedLens' i w u      -> m a -> m (a, (i, u))
--   ilistening :: (MonadWriter w m, Monoid u) => IndexedFold i w u       -> m a -> m (a, (i, u))
--   ilistening :: (MonadWriter w m, Monoid u) => IndexedTraversal' i w u -> m a -> m (a, (i, u))
--

ilistening :: MonadWriter w m => IndexedGetting i (i, u) w u -> m a -> m (a, (i, u)) -- | This is a generalized form of listen that only extracts the -- portion of the log that is focused on by a Getter. If given a -- Fold or a Traversal then a monoidal summary of the parts -- of the log that are visited will be returned. -- --

--   listening :: MonadWriter w m             => Getter w u     -> m a -> m (a, u)
--   listening :: MonadWriter w m             => Lens' w u      -> m a -> m (a, u)
--   listening :: MonadWriter w m             => Iso' w u       -> m a -> m (a, u)
--   listening :: (MonadWriter w m, Monoid u) => Fold w u       -> m a -> m (a, u)
--   listening :: (MonadWriter w m, Monoid u) => Traversal' w u -> m a -> m (a, u)
--   listening :: (MonadWriter w m, Monoid u) => Prism' w u     -> m a -> m (a, u)
--

listening :: MonadWriter w m => Getting u w u -> m a -> m (a, u) -- | Use the target of a Lens, Iso or Getter in the -- current state, or use a summary of a Fold or Traversal -- that points to a monoidal value. -- --

--   >>> evalState (uses _1 length) ("hello","world")
--   5
--

-- --

--   uses :: MonadState s m             => Getter s a     -> (a -> r) -> m r
--   uses :: (MonadState s m, Monoid r) => Fold s a       -> (a -> r) -> m r
--   uses :: MonadState s m             => Lens' s a      -> (a -> r) -> m r
--   uses :: MonadState s m             => Iso' s a       -> (a -> r) -> m r
--   uses :: (MonadState s m, Monoid r) => Traversal' s a -> (a -> r) -> m r
--

-- --

--   uses :: MonadState s m => Getting r s t a b -> (a -> r) -> m r
--

uses :: MonadState s m => LensLike' (Const r :: * -> *) s a -> a -> r -> m r -- | Use the target of a Lens, Iso, or Getter in the -- current state, or use a summary of a Fold or Traversal -- that points to a monoidal value. -- --

--   >>> evalState (use _1) (a,b)
--   a
--

-- --

--   >>> evalState (use _1) ("hello","world")
--   "hello"
--

-- --

--   use :: MonadState s m             => Getter s a     -> m a
--   use :: (MonadState s m, Monoid r) => Fold s r       -> m r
--   use :: MonadState s m             => Iso' s a       -> m a
--   use :: MonadState s m             => Lens' s a      -> m a
--   use :: (MonadState s m, Monoid r) => Traversal' s r -> m r
--

use :: MonadState s m => Getting a s a -> m a -- | View the value pointed to by a Getter or Lens or the -- result of folding over all the results of a Fold or -- Traversal that points at a monoidal values. -- -- This is the same operation as view with the arguments flipped. -- -- The fixity and semantics are such that subsequent field accesses can -- be performed with (.). -- --

--   >>> (a,b)^._2
--   b
--

-- --

--   >>> ("hello","world")^._2
--   "world"
--

-- --

--   >>> import Data.Complex
--   
--   >>> ((0, 1 :+ 2), 3)^._1._2.to magnitude
--   2.23606797749979
--

-- --

--   (^.) ::             s -> Getter s a     -> a
--   (^.) :: Monoid m => s -> Fold s m       -> m
--   (^.) ::             s -> Iso' s a       -> a
--   (^.) ::             s -> Lens' s a      -> a
--   (^.) :: Monoid m => s -> Traversal' s m -> m
--

(^.) :: () => s -> Getting a s a -> a infixl 8 ^. -- | View a function of the value pointed to by a Getter or -- Lens or the result of folding over the result of mapping the -- targets of a Fold or Traversal. -- --

--   views l f ≡ view (l . to f)
--

-- --

--   >>> views (to f) g a
--   g (f a)
--

-- --

--   >>> views _2 length (1,"hello")
--   5
--

-- -- As views is commonly used to access the target of a -- Getter or obtain a monoidal summary of the targets of a -- Fold, It may be useful to think of it as having one of these -- more restricted signatures: -- --

--   views ::             Getter s a     -> (a -> r) -> s -> r
--   views :: Monoid m => Fold s a       -> (a -> m) -> s -> m
--   views ::             Iso' s a       -> (a -> r) -> s -> r
--   views ::             Lens' s a      -> (a -> r) -> s -> r
--   views :: Monoid m => Traversal' s a -> (a -> m) -> s -> m
--

-- -- In a more general setting, such as when working with a Monad -- transformer stack you can use: -- --

--   views :: MonadReader s m             => Getter s a     -> (a -> r) -> m r
--   views :: (MonadReader s m, Monoid r) => Fold s a       -> (a -> r) -> m r
--   views :: MonadReader s m             => Iso' s a       -> (a -> r) -> m r
--   views :: MonadReader s m             => Lens' s a      -> (a -> r) -> m r
--   views :: (MonadReader s m, Monoid r) => Traversal' s a -> (a -> r) -> m r
--

-- --

--   views :: MonadReader s m => Getting r s a -> (a -> r) -> m r
--

views :: MonadReader s m => LensLike' (Const r :: * -> *) s a -> a -> r -> m r -- | View the value pointed to by a Getter, Iso or -- Lens or the result of folding over all the results of a -- Fold or Traversal that points at a monoidal value. -- --

--   view . to ≡ id
--

-- --

--   >>> view (to f) a
--   f a
--

-- --

--   >>> view _2 (1,"hello")
--   "hello"
--

-- --

--   >>> view (to succ) 5
--   6
--

-- --

--   >>> view (_2._1) ("hello",("world","!!!"))
--   "world"
--

-- -- As view is commonly used to access the target of a -- Getter or obtain a monoidal summary of the targets of a -- Fold, It may be useful to think of it as having one of these -- more restricted signatures: -- --

--   view ::             Getter s a     -> s -> a
--   view :: Monoid m => Fold s m       -> s -> m
--   view ::             Iso' s a       -> s -> a
--   view ::             Lens' s a      -> s -> a
--   view :: Monoid m => Traversal' s m -> s -> m
--

-- -- In a more general setting, such as when working with a Monad -- transformer stack you can use: -- --

--   view :: MonadReader s m             => Getter s a     -> m a
--   view :: (MonadReader s m, Monoid a) => Fold s a       -> m a
--   view :: MonadReader s m             => Iso' s a       -> m a
--   view :: MonadReader s m             => Lens' s a      -> m a
--   view :: (MonadReader s m, Monoid a) => Traversal' s a -> m a
--

view :: MonadReader s m => Getting a s a -> m a -- |

--   ilike :: i -> a -> IndexedGetter i s a
--

ilike :: (Indexable i p, Contravariant f, Functor f) => i -> a -> Over' p f s a -- | Build an constant-valued (index-preserving) Getter from an -- arbitrary Haskell value. -- --

--   like a . like b ≡ like b
--   a ^. like b ≡ b
--   a ^. like b ≡ a ^. to (const b)
--

-- -- This can be useful as a second case failing a Fold -- e.g. foo failing like 0 -- --

--   like :: a -> IndexPreservingGetter s a
--

like :: (Profunctor p, Contravariant f, Functor f) => a -> Optic' p f s a -- |

--   ito :: (s -> (i, a)) -> IndexedGetter i s a
--

ito :: (Indexable i p, Contravariant f) => s -> (i, a) -> Over' p f s a -- | Build an (index-preserving) Getter from an arbitrary Haskell -- function. -- --

--   to f . to g ≡ to (g . f)
--

-- --

--   a ^. to f ≡ f a
--

-- --

--   >>> a ^.to f
--   f a
--

-- --

--   >>> ("hello","world")^.to snd
--   "world"
--

-- --

--   >>> 5^.to succ
--   6
--

-- --

--   >>> (0, -5)^._2.to abs
--   5
--

-- --

--   to :: (s -> a) -> IndexPreservingGetter s a
--

to :: (Profunctor p, Contravariant f) => s -> a -> Optic' p f s a -- | When you see this in a type signature it indicates that you can pass -- the function a Lens, Getter, Traversal, -- Fold, Prism, Iso, or one of the indexed variants, -- and it will just "do the right thing". -- -- Most Getter combinators are able to be used with both a -- Getter or a Fold in limited situations, to do so, they -- need to be monomorphic in what we are going to extract with -- Const. To be compatible with Lens, Traversal and -- Iso we also restricted choices of the irrelevant t and -- b parameters. -- -- If a function accepts a Getting r s a, then when -- r is a Monoid, then you can pass a Fold (or -- Traversal), otherwise you can only pass this a Getter or -- Lens. type Getting r s a = a -> Const r a -> s -> Const r s -- | Used to consume an IndexedFold. type IndexedGetting i m s a = Indexed i a Const m a -> s -> Const m s -- | This is a convenient alias used when consuming (indexed) getters and -- (indexed) folds in a highly general fashion. type Accessing (p :: * -> * -> *) m s a = p a Const m a -> s -> Const m s -- | Strict version of _19 _19' :: Field19 s t a b => Lens s t a b -- | Strict version of _18 _18' :: Field18 s t a b => Lens s t a b -- | Strict version of _17 _17' :: Field17 s t a b => Lens s t a b -- | Strict version of _16 _16' :: Field16 s t a b => Lens s t a b -- | Strict version of _15 _15' :: Field15 s t a b => Lens s t a b -- | Strict version of _14 _14' :: Field14 s t a b => Lens s t a b -- | Strict version of _13 _13' :: Field13 s t a b => Lens s t a b -- | Strict version of _12 _12' :: Field12 s t a b => Lens s t a b -- | Strict version of _11 _11' :: Field11 s t a b => Lens s t a b -- | Strict version of _10 _10' :: Field10 s t a b => Lens s t a b -- | Strict version of _9 _9' :: Field9 s t a b => Lens s t a b -- | Strict version of _8 _8' :: Field8 s t a b => Lens s t a b -- | Strict version of _7 _7' :: Field7 s t a b => Lens s t a b -- | Strict version of _6 _6' :: Field6 s t a b => Lens s t a b -- | Strict version of _5 _5' :: Field5 s t a b => Lens s t a b -- | Strict version of _4 _4' :: Field4 s t a b => Lens s t a b -- | Strict version of _3 _3' :: Field3 s t a b => Lens s t a b -- | Strict version of _2 _2' :: Field2 s t a b => Lens s t a b -- | Strict version of _1 _1' :: Field1 s t a b => Lens s t a b -- | Provides access to 1st field of a tuple. class Field1 s t a b | s -> a, t -> b, s b -> t, t a -> s -- | Access the 1st field of a tuple (and possibly change its type). -- --

--   >>> (1,2)^._1
--   1
--

-- --

--   >>> _1 .~ "hello" $ (1,2)
--   ("hello",2)
--

-- --

--   >>> (1,2) & _1 .~ "hello"
--   ("hello",2)
--

-- --

--   >>> _1 putStrLn ("hello","world")
--   hello
--   ((),"world")
--

-- -- This can also be used on larger tuples as well: -- --

--   >>> (1,2,3,4,5) & _1 +~ 41
--   (42,2,3,4,5)
--

-- --

--   _1 :: Lens (a,b) (a',b) a a'
--   _1 :: Lens (a,b,c) (a',b,c) a a'
--   _1 :: Lens (a,b,c,d) (a',b,c,d) a a'
--   ...
--   _1 :: Lens (a,b,c,d,e,f,g,h,i) (a',b,c,d,e,f,g,h,i) a a'
--

_1 :: Field1 s t a b => Lens s t a b -- | Provides access to the 2nd field of a tuple. class Field2 s t a b | s -> a, t -> b, s b -> t, t a -> s -- | Access the 2nd field of a tuple. -- --

--   >>> _2 .~ "hello" $ (1,(),3,4)
--   (1,"hello",3,4)
--

-- --

--   >>> (1,2,3,4) & _2 *~ 3
--   (1,6,3,4)
--

-- --

--   >>> _2 print (1,2)
--   2
--   (1,())
--

-- --

--   anyOf _2 :: (s -> Bool) -> (a, s) -> Bool
--   traverse . _2 :: (Applicative f, Traversable t) => (a -> f b) -> t (s, a) -> f (t (s, b))
--   foldMapOf (traverse . _2) :: (Traversable t, Monoid m) => (s -> m) -> t (b, s) -> m
--

_2 :: Field2 s t a b => Lens s t a b -- | Provides access to the 3rd field of a tuple. class Field3 s t a b | s -> a, t -> b, s b -> t, t a -> s -- | Access the 3rd field of a tuple. _3 :: Field3 s t a b => Lens s t a b -- | Provide access to the 4th field of a tuple. class Field4 s t a b | s -> a, t -> b, s b -> t, t a -> s -- | Access the 4th field of a tuple. _4 :: Field4 s t a b => Lens s t a b -- | Provides access to the 5th field of a tuple. class Field5 s t a b | s -> a, t -> b, s b -> t, t a -> s -- | Access the 5th field of a tuple. _5 :: Field5 s t a b => Lens s t a b -- | Provides access to the 6th element of a tuple. class Field6 s t a b | s -> a, t -> b, s b -> t, t a -> s -- | Access the 6th field of a tuple. _6 :: Field6 s t a b => Lens s t a b -- | Provide access to the 7th field of a tuple. class Field7 s t a b | s -> a, t -> b, s b -> t, t a -> s -- | Access the 7th field of a tuple. _7 :: Field7 s t a b => Lens s t a b -- | Provide access to the 8th field of a tuple. class Field8 s t a b | s -> a, t -> b, s b -> t, t a -> s -- | Access the 8th field of a tuple. _8 :: Field8 s t a b => Lens s t a b -- | Provides access to the 9th field of a tuple. class Field9 s t a b | s -> a, t -> b, s b -> t, t a -> s -- | Access the 9th field of a tuple. _9 :: Field9 s t a b => Lens s t a b -- | Provides access to the 10th field of a tuple. class Field10 s t a b | s -> a, t -> b, s b -> t, t a -> s -- | Access the 10th field of a tuple. _10 :: Field10 s t a b => Lens s t a b -- | Provides access to the 11th field of a tuple. class Field11 s t a b | s -> a, t -> b, s b -> t, t a -> s -- | Access the 11th field of a tuple. _11 :: Field11 s t a b => Lens s t a b -- | Provides access to the 12th field of a tuple. class Field12 s t a b | s -> a, t -> b, s b -> t, t a -> s -- | Access the 12th field of a tuple. _12 :: Field12 s t a b => Lens s t a b -- | Provides access to the 13th field of a tuple. class Field13 s t a b | s -> a, t -> b, s b -> t, t a -> s -- | Access the 13th field of a tuple. _13 :: Field13 s t a b => Lens s t a b -- | Provides access to the 14th field of a tuple. class Field14 s t a b | s -> a, t -> b, s b -> t, t a -> s -- | Access the 14th field of a tuple. _14 :: Field14 s t a b => Lens s t a b -- | Provides access to the 15th field of a tuple. class Field15 s t a b | s -> a, t -> b, s b -> t, t a -> s -- | Access the 15th field of a tuple. _15 :: Field15 s t a b => Lens s t a b -- | Provides access to the 16th field of a tuple. class Field16 s t a b | s -> a, t -> b, s b -> t, t a -> s -- | Access the 16th field of a tuple. _16 :: Field16 s t a b => Lens s t a b -- | Provides access to the 17th field of a tuple. class Field17 s t a b | s -> a, t -> b, s b -> t, t a -> s -- | Access the 17th field of a tuple. _17 :: Field17 s t a b => Lens s t a b -- | Provides access to the 18th field of a tuple. class Field18 s t a b | s -> a, t -> b, s b -> t, t a -> s -- | Access the 18th field of a tuple. _18 :: Field18 s t a b => Lens s t a b -- | Provides access to the 19th field of a tuple. class Field19 s t a b | s -> a, t -> b, s b -> t, t a -> s -- | Access the 19th field of a tuple. _19 :: Field19 s t a b => Lens s t a b -- | Fuse a composition of lenses using Yoneda to provide -- fmap fusion. -- -- In general, given a pair of lenses foo and bar -- --

--   fusing (foo.bar) = foo.bar
--

-- -- however, foo and bar are either going to fmap -- internally or they are trivial. -- -- fusing exploits the Yoneda lemma to merge these separate -- uses into a single fmap. -- -- This is particularly effective when the choice of functor f -- is unknown at compile time or when the Lens foo.bar in -- the above description is recursive or complex enough to prevent -- inlining. -- --

--   fusing :: Lens s t a b -> Lens s t a b
--

fusing :: Functor f => LensLike Yoneda f s t a b -> LensLike f s t a b -- | We can always retrieve a () from any type. -- --

--   >>> "hello"^.united
--   ()
--

-- --

--   >>> "hello" & united .~ ()
--   "hello"
--

united :: Functor f => () -> f () -> a -> f a -- | There is a field for every type in the Void. Very zen. -- --

--   >>> [] & mapped.devoid +~ 1
--   []
--

-- --

--   >>> Nothing & mapped.devoid %~ abs
--   Nothing
--

-- --

--   devoid :: Lens' Void a
--

devoid :: () => Over p f Void Void a b -- | A version of (<.=) that works on ALens. (<#=) :: MonadState s m => ALens s s a b -> b -> m b infix 4 <#= -- | A version of (<.~) that works on ALens. -- --

--   >>> ("hello","there") & _2 <#~ "world"
--   ("world",("hello","world"))
--

(<#~) :: () => ALens s t a b -> b -> s -> (b, t) infixr 4 <#~ -- | A version of (%%=) that works on ALens. (#%%=) :: MonadState s m => ALens s s a b -> a -> (r, b) -> m r infix 4 #%%= -- | A version of (<%=) that works on ALens. (<#%=) :: MonadState s m => ALens s s a b -> a -> b -> m b infix 4 <#%= -- | A version of (<%~) that works on ALens. -- --

--   >>> ("hello","world") & _2 <#%~ length
--   (5,("hello",5))
--

(<#%~) :: () => ALens s t a b -> a -> b -> s -> (b, t) infixr 4 <#%~ -- | A version of (%=) that works on ALens. (#%=) :: MonadState s m => ALens s s a b -> a -> b -> m () infix 4 #%= -- | A version of (.=) that works on ALens. (#=) :: MonadState s m => ALens s s a b -> b -> m () infix 4 #= -- | A version of (%%~) that works on ALens. -- --

--   >>> ("hello","world") & _2 #%%~ \x -> (length x, x ++ "!")
--   (5,("hello","world!"))
--

(#%%~) :: Functor f => ALens s t a b -> a -> f b -> s -> f t infixr 4 #%%~ -- | A version of (%~) that works on ALens. -- --

--   >>> ("hello","world") & _2 #%~ length
--   ("hello",5)
--

(#%~) :: () => ALens s t a b -> a -> b -> s -> t infixr 4 #%~ -- | A version of (.~) that works on ALens. -- --

--   >>> ("hello","there") & _2 #~ "world"
--   ("hello","world")
--

(#~) :: () => ALens s t a b -> b -> s -> t infixr 4 #~ -- | A version of set that works on ALens. -- --

--   >>> storing _2 "world" ("hello","there")
--   ("hello","world")
--

storing :: () => ALens s t a b -> b -> s -> t -- | A version of (^.) that works on ALens. -- --

--   >>> ("hello","world")^#_2
--   "world"
--

(^#) :: () => s -> ALens s t a b -> a infixl 8 ^# -- | Adjust the target of an IndexedLens returning the old value, or -- adjust all of the targets of an IndexedTraversal within the -- current state, and return a monoidal summary of the old values. -- --

--   (<<%@=) :: MonadState s m                 => IndexedLens i s s a b      -> (i -> a -> b) -> m a
--   (<<%@=) :: (MonadState s m, Monoid b) => IndexedTraversal i s s a b -> (i -> a -> b) -> m a
--

(<<%@=) :: MonadState s m => Over Indexed i (,) a s s a b -> i -> a -> b -> m a infix 4 <<%@= -- | Adjust the target of an IndexedLens returning the intermediate -- result, or adjust all of the targets of an IndexedTraversal -- within the current state, and return a monoidal summary of the -- intermediate results. -- --

--   (<%@=) :: MonadState s m                 => IndexedLens i s s a b      -> (i -> a -> b) -> m b
--   (<%@=) :: (MonadState s m, Monoid b) => IndexedTraversal i s s a b -> (i -> a -> b) -> m b
--

(<%@=) :: MonadState s m => Over Indexed i (,) b s s a b -> i -> a -> b -> m b infix 4 <%@= -- | Adjust the target of an IndexedLens returning a supplementary -- result, or adjust all of the targets of an IndexedTraversal -- within the current state, and return a monoidal summary of the -- supplementary results. -- --

--   l %%@= f ≡ state (l %%@~ f)
--

-- --

--   (%%@=) :: MonadState s m                 => IndexedLens i s s a b      -> (i -> a -> (r, b)) -> s -> m r
--   (%%@=) :: (MonadState s m, Monoid r) => IndexedTraversal i s s a b -> (i -> a -> (r, b)) -> s -> m r
--

(%%@=) :: MonadState s m => Over Indexed i (,) r s s a b -> i -> a -> (r, b) -> m r infix 4 %%@= -- | Adjust the target of an IndexedLens returning a supplementary -- result, or adjust all of the targets of an IndexedTraversal and -- return a monoidal summary of the supplementary results and the answer. -- --

--   (%%@~) ≡ withIndex
--

-- --

--   (%%@~) :: Functor f => IndexedLens i s t a b      -> (i -> a -> f b) -> s -> f t
--   (%%@~) :: Applicative f => IndexedTraversal i s t a b -> (i -> a -> f b) -> s -> f t
--

-- -- In particular, it is often useful to think of this function as having -- one of these even more restricted type signatures: -- --

--   (%%@~) ::             IndexedLens i s t a b      -> (i -> a -> (r, b)) -> s -> (r, t)
--   (%%@~) :: Monoid r => IndexedTraversal i s t a b -> (i -> a -> (r, b)) -> s -> (r, t)
--

(%%@~) :: () => Over Indexed i f s t a b -> i -> a -> f b -> s -> f t infixr 4 %%@~ -- | Adjust the target of an IndexedLens returning the old value, or -- adjust all of the targets of an IndexedTraversal and return a -- monoidal summary of the old values along with the answer. -- --

--   (<<%@~) ::             IndexedLens i s t a b      -> (i -> a -> b) -> s -> (a, t)
--   (<<%@~) :: Monoid a => IndexedTraversal i s t a b -> (i -> a -> b) -> s -> (a, t)
--

(<<%@~) :: () => Over Indexed i (,) a s t a b -> i -> a -> b -> s -> (a, t) infixr 4 <<%@~ -- | Adjust the target of an IndexedLens returning the intermediate -- result, or adjust all of the targets of an IndexedTraversal and -- return a monoidal summary along with the answer. -- --

--   l <%~ f ≡ l <%@~ const f
--

-- -- When you do not need access to the index then (<%~) is more -- liberal in what it can accept. -- -- If you do not need the intermediate result, you can use (%@~) -- or even (%~). -- --

--   (<%@~) ::             IndexedLens i s t a b      -> (i -> a -> b) -> s -> (b, t)
--   (<%@~) :: Monoid b => IndexedTraversal i s t a b -> (i -> a -> b) -> s -> (b, t)
--

(<%@~) :: () => Over Indexed i (,) b s t a b -> i -> a -> b -> s -> (b, t) infixr 4 <%@~ -- | over for Arrows. -- -- Unlike over, overA can't accept a simple Setter, -- but requires a full lens, or close enough. -- --

--   >>> overA _1 ((+1) *** (+2)) ((1,2),6)
--   ((2,4),6)
--

-- --

--   overA :: Arrow ar => Lens s t a b -> ar a b -> ar s t
--

overA :: Arrow ar => LensLike Context a b s t a b -> ar a b -> ar s t -- | mappend a monoidal value onto the end of the target of a -- Lens into your Monad's state and return the result. -- -- When you do not need the result of the operation, (<>=) -- is more flexible. (<<>=) :: (MonadState s m, Monoid r) => LensLike' (,) r s r -> r -> m r infix 4 <<>= -- | mappend a monoidal value onto the end of the target of a -- Lens and return the result. -- -- When you do not need the result of the operation, (<>~) -- is more flexible. (<<>~) :: Monoid m => LensLike (,) m s t m m -> m -> s -> (m, t) infixr 4 <<>~ -- | Run a monadic action, and set the target of Lens to its result. -- --

--   (<<~) :: MonadState s m => Iso s s a b   -> m b -> m b
--   (<<~) :: MonadState s m => Lens s s a b  -> m b -> m b
--

-- -- NB: This is limited to taking an actual Lens than admitting a -- Traversal because there are potential loss of state issues -- otherwise. (<<~) :: MonadState s m => ALens s s a b -> m b -> m b infixr 2 <<~ -- | Modify the target of a Lens into your Monad's state by -- mappending a value and return the old value that was -- replaced. -- -- When you do not need the result of the operation, (<>=) -- is more flexible. -- --

--   (<<<>=) :: (MonadState s m, Monoid r) => Lens' s r -> r -> m r
--   (<<<>=) :: (MonadState s m, Monoid r) => Iso' s r -> r -> m r
--

(<<<>=) :: (MonadState s m, Monoid r) => LensLike' (,) r s r -> r -> m r infix 4 <<<>= -- | Modify the target of a Lens into your Monad's state by -- taking its logical && with a value and return the -- old value that was replaced. -- -- When you do not need the result of the operation, (&&=) -- is more flexible. -- --

--   (<<&&=) :: MonadState s m => Lens' s Bool -> Bool -> m Bool
--   (<<&&=) :: MonadState s m => Iso' s Bool -> Bool -> m Bool
--

(<<&&=) :: MonadState s m => LensLike' (,) Bool s Bool -> Bool -> m Bool infix 4 <<&&= -- | Modify the target of a Lens into your Monad's state by -- taking its logical || with a value and return the old -- value that was replaced. -- -- When you do not need the result of the operation, (||=) is more -- flexible. -- --

--   (<<||=) :: MonadState s m => Lens' s Bool -> Bool -> m Bool
--   (<<||=) :: MonadState s m => Iso' s Bool -> Bool -> m Bool
--

(<<||=) :: MonadState s m => LensLike' (,) Bool s Bool -> Bool -> m Bool infix 4 <<||= -- | Modify the target of a Lens into your Monad's state by -- raising it by an arbitrary power and return the old value that -- was replaced. -- -- When you do not need the result of the operation, (**=) is more -- flexible. -- --

--   (<<**=) :: (MonadState s m, Floating a) => Lens' s a -> a -> m a
--   (<<**=) :: (MonadState s m, Floating a) => Iso' s a -> a -> m a
--

(<<**=) :: (MonadState s m, Floating a) => LensLike' (,) a s a -> a -> m a infix 4 <<**= -- | Modify the target of a Lens into your Monad's state by -- raising it by an integral power and return the old value that -- was replaced. -- -- When you do not need the result of the operation, (^^=) is more -- flexible. -- --

--   (<<^^=) :: (MonadState s m, Fractional a, Integral e) => Lens' s a -> e -> m a
--   (<<^^=) :: (MonadState s m, Fractional a, Integral e) => Iso' s a -> e -> m a
--

(<<^^=) :: (MonadState s m, Fractional a, Integral e) => LensLike' (,) a s a -> e -> m a infix 4 <<^^= -- | Modify the target of a Lens into your Monad's state by -- raising it by a non-negative power and return the old value -- that was replaced. -- -- When you do not need the result of the operation, (^=) is more -- flexible. -- --

--   (<<^=) :: (MonadState s m, Num a, Integral e) => Lens' s a -> e -> m a
--   (<<^=) :: (MonadState s m, Num a, Integral e) => Iso' s a -> a -> m a
--

(<<^=) :: (MonadState s m, Num a, Integral e) => LensLike' (,) a s a -> e -> m a infix 4 <<^= -- | Modify the target of a Lens into your Monads state by -- dividing by a value and return the old value that was replaced. -- -- When you do not need the result of the operation, (//=) is more -- flexible. -- --

--   (<<//=) :: (MonadState s m, Fractional a) => Lens' s a -> a -> m a
--   (<<//=) :: (MonadState s m, Fractional a) => Iso' s a -> a -> m a
--

(< LensLike' (,) a s a -> a -> m a infix 4 <Lens into your Monad's state by -- multipling a value and return the old value that was replaced. -- -- When you do not need the result of the operation, (*=) is more -- flexible. -- --

--   (<<*=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
--   (<<*=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a
--

(<<*=) :: (MonadState s m, Num a) => LensLike' (,) a s a -> a -> m a infix 4 <<*= -- | Modify the target of a Lens into your Monad's state by -- subtracting a value and return the old value that was replaced. -- -- When you do not need the result of the operation, (-=) is more -- flexible. -- --

--   (<<-=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
--   (<<-=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a
--

(<<-=) :: (MonadState s m, Num a) => LensLike' (,) a s a -> a -> m a infix 4 <<-= -- | Modify the target of a Lens into your Monad's state by -- adding a value and return the old value that was replaced. -- -- When you do not need the result of the operation, (+=) is more -- flexible. -- --

--   (<<+=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
--   (<<+=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a
--

(<<+=) :: (MonadState s m, Num a) => LensLike' (,) a s a -> a -> m a infix 4 <<+= -- | Replace the target of a Lens into your Monad's state -- with Just a user supplied value and return the old value -- that was replaced. -- -- When applied to a Traversal, this will return a monoidal -- summary of all of the old values present. -- -- When you do not need the result of the operation, (?=) is more -- flexible. -- --

--   (<<?=) :: MonadState s m             => Lens s t a (Maybe b)      -> b -> m a
--   (<<?=) :: MonadState s m             => Iso s t a (Maybe b)       -> b -> m a
--   (<<?=) :: (MonadState s m, Monoid a) => Traversal s t a (Maybe b) -> b -> m a
--

(< LensLike (,) a s s a Maybe b -> b -> m a infix 4 <Lens into your Monad's state -- with a user supplied value and return the old value that was -- replaced. -- -- When applied to a Traversal, this will return a monoidal -- summary of all of the old values present. -- -- When you do not need the result of the operation, (.=) is more -- flexible. -- --

--   (<<.=) :: MonadState s m             => Lens' s a      -> a -> m a
--   (<<.=) :: MonadState s m             => Iso' s a       -> a -> m a
--   (<<.=) :: (MonadState s m, Monoid a) => Traversal' s a -> a -> m a
--

(<<.=) :: MonadState s m => LensLike (,) a s s a b -> b -> m a infix 4 <<.= -- | Modify the target of a Lens into your Monad's state by -- a user supplied function and return the old value that was -- replaced. -- -- When applied to a Traversal, this will return a monoidal -- summary of all of the old values present. -- -- When you do not need the result of the operation, (%=) is more -- flexible. -- --

--   (<<%=) :: MonadState s m             => Lens' s a      -> (a -> a) -> m a
--   (<<%=) :: MonadState s m             => Iso' s a       -> (a -> a) -> m a
--   (<<%=) :: (MonadState s m, Monoid a) => Traversal' s a -> (a -> a) -> m a
--

-- --

--   (<<%=) :: MonadState s m => LensLike ((,)a) s s a b -> (a -> b) -> m a
--

(<<%=) :: (Strong p, MonadState s m) => Over p (,) a s s a b -> p a b -> m a infix 4 <<%= -- | Logically && a Boolean valued Lens into your -- Monad's state and return the result. -- -- When you do not need the result of the operation, (&&=) -- is more flexible. -- --

--   (<&&=) :: MonadState s m => Lens' s Bool -> Bool -> m Bool
--   (<&&=) :: MonadState s m => Iso' s Bool  -> Bool -> m Bool
--

(<&&=) :: MonadState s m => LensLike' (,) Bool s Bool -> Bool -> m Bool infix 4 <&&= -- | Logically || a Boolean valued Lens into your -- Monad's state and return the result. -- -- When you do not need the result of the operation, (||=) is more -- flexible. -- --

--   (<||=) :: MonadState s m => Lens' s Bool -> Bool -> m Bool
--   (<||=) :: MonadState s m => Iso' s Bool  -> Bool -> m Bool
--

(<||=) :: MonadState s m => LensLike' (,) Bool s Bool -> Bool -> m Bool infix 4 <||= -- | Raise the target of a floating-point valued Lens into your -- Monad's state to an arbitrary power and return the result. -- -- When you do not need the result of the operation, (**=) is more -- flexible. -- --

--   (<**=) :: (MonadState s m, Floating a) => Lens' s a -> a -> m a
--   (<**=) :: (MonadState s m, Floating a) => Iso' s a -> a -> m a
--

(<**=) :: (MonadState s m, Floating a) => LensLike' (,) a s a -> a -> m a infix 4 <**= -- | Raise the target of a fractionally valued Lens into your -- Monad's state to an Integral power and return the -- result. -- -- When you do not need the result of the operation, (^^=) is more -- flexible. -- --

--   (<^^=) :: (MonadState s m, Fractional b, Integral e) => Lens' s a -> e -> m a
--   (<^^=) :: (MonadState s m, Fractional b, Integral e) => Iso' s a  -> e -> m a
--

(<^^=) :: (MonadState s m, Fractional a, Integral e) => LensLike' (,) a s a -> e -> m a infix 4 <^^= -- | Raise the target of a numerically valued Lens into your -- Monad's state to a non-negative Integral power and -- return the result. -- -- When you do not need the result of the operation, (^=) is more -- flexible. -- --

--   (<^=) :: (MonadState s m, Num a, Integral e) => Lens' s a -> e -> m a
--   (<^=) :: (MonadState s m, Num a, Integral e) => Iso' s a -> e -> m a
--

(<^=) :: (MonadState s m, Num a, Integral e) => LensLike' (,) a s a -> e -> m a infix 4 <^= -- | Divide the target of a fractionally valued Lens into your -- Monad's state and return the result. -- -- When you do not need the result of the division, (//=) is more -- flexible. -- --

--   (<//=) :: (MonadState s m, Fractional a) => Lens' s a -> a -> m a
--   (<//=) :: (MonadState s m, Fractional a) => Iso' s a -> a -> m a
--

( LensLike' (,) a s a -> a -> m a infix 4 Lens into your -- Monad's state and return the result. -- -- When you do not need the result of the multiplication, (*=) is -- more flexible. -- --

--   (<*=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
--   (<*=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a
--

(<*=) :: (MonadState s m, Num a) => LensLike' (,) a s a -> a -> m a infix 4 <*= -- | Subtract from the target of a numerically valued Lens into your -- Monad's state and return the result. -- -- When you do not need the result of the subtraction, (-=) is -- more flexible. -- --

--   (<-=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
--   (<-=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a
--

(<-=) :: (MonadState s m, Num a) => LensLike' (,) a s a -> a -> m a infix 4 <-= -- | Add to the target of a numerically valued Lens into your -- Monad's state and return the result. -- -- When you do not need the result of the addition, (+=) is more -- flexible. -- --

--   (<+=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
--   (<+=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a
--

(<+=) :: (MonadState s m, Num a) => LensLike' (,) a s a -> a -> m a infix 4 <+= -- | Modify the target of a Lens into your Monad's state by -- a user supplied function and return the result. -- -- When applied to a Traversal, it this will return a monoidal -- summary of all of the intermediate results. -- -- When you do not need the result of the operation, (%=) is more -- flexible. -- --

--   (<%=) :: MonadState s m             => Lens' s a      -> (a -> a) -> m a
--   (<%=) :: MonadState s m             => Iso' s a       -> (a -> a) -> m a
--   (<%=) :: (MonadState s m, Monoid a) => Traversal' s a -> (a -> a) -> m a
--

(<%=) :: MonadState s m => LensLike (,) b s s a b -> a -> b -> m b infix 4 <%= -- | Modify the target of a monoidally valued Lens by -- mappending a new value and return the old value. -- -- When you do not need the old value, (<>~) is more -- flexible. -- --

--   >>> (Sum a,b) & _1 <<<>~ Sum c
--   (Sum {getSum = a},(Sum {getSum = a + c},b))
--

-- --

--   >>> _2 <<<>~ ", 007" $ ("James", "Bond")
--   ("Bond",("James","Bond, 007"))
--

-- --

--   (<<<>~) :: Monoid r => Lens' s r -> r -> s -> (r, s)
--   (<<<>~) :: Monoid r => Iso' s r -> r -> s -> (r, s)
--

(<<<>~) :: Monoid r => LensLike' (,) r s r -> r -> s -> (r, s) infixr 4 <<<>~ -- | Logically && the target of a Bool-valued -- Lens and return the old value. -- -- When you do not need the old value, (&&~) is more -- flexible. -- --

--   >>> (False,6) & _1 <<&&~ True
--   (False,(False,6))
--

-- --

--   >>> ("hello",True) & _2 <<&&~ False
--   (True,("hello",False))
--

-- --

--   (<<&&~) :: Lens' s Bool -> Bool -> s -> (Bool, s)
--   (<<&&~) :: Iso' s Bool -> Bool -> s -> (Bool, s)
--

(<<&&~) :: () => LensLike' (,) Bool s Bool -> Bool -> s -> (Bool, s) infixr 4 <<&&~ -- | Logically || the target of a Bool-valued Lens and -- return the old value. -- -- When you do not need the old value, (||~) is more flexible. -- --

--   >>> (False,6) & _1 <<||~ True
--   (False,(True,6))
--

-- --

--   >>> ("hello",True) & _2 <<||~ False
--   (True,("hello",True))
--

-- --

--   (<<||~) :: Lens' s Bool -> Bool -> s -> (Bool, s)
--   (<<||~) :: Iso' s Bool -> Bool -> s -> (Bool, s)
--

(<<||~) :: () => LensLike' (,) Bool s Bool -> Bool -> s -> (Bool, s) infixr 4 <<||~ -- | Raise the target of a floating-point valued Lens to an -- arbitrary power and return the old value. -- -- When you do not need the old value, (**~) is more flexible. -- --

--   >>> (a,b) & _1 <<**~ c
--   (a,(a**c,b))
--

-- --

--   >>> (a,b) & _2 <<**~ c
--   (b,(a,b**c))
--

-- --

--   (<<**~) :: Floating a => Lens' s a -> a -> s -> (a, s)
--   (<<**~) :: Floating a => Iso' s a -> a -> s -> (a, s)
--

(<<**~) :: Floating a => LensLike' (,) a s a -> a -> s -> (a, s) infixr 4 <<**~ -- | Raise the target of a fractionally valued Lens to an integral -- power and return the old value. -- -- When you do not need the old value, (^^~) is more flexible. -- --

--   (<<^^~) :: (Fractional a, Integral e) => Lens' s a -> e -> s -> (a, s)
--   (<<^^~) :: (Fractional a, Integral e) => Iso' s a -> e -> S -> (a, s)
--

(<<^^~) :: (Fractional a, Integral e) => LensLike' (,) a s a -> e -> s -> (a, s) infixr 4 <<^^~ -- | Raise the target of a numerically valued Lens to a non-negative -- power and return the old value. -- -- When you do not need the old value, (^~) is more flexible. -- --

--   (<<^~) :: (Num a, Integral e) => Lens' s a -> e -> s -> (a, s)
--   (<<^~) :: (Num a, Integral e) => Iso' s a -> e -> s -> (a, s)
--

(<<^~) :: (Num a, Integral e) => LensLike' (,) a s a -> e -> s -> (a, s) infixr 4 <<^~ -- | Divide the target of a numerically valued Lens and return the -- old value. -- -- When you do not need the old value, (//~) is more flexible. -- --

--   >>> (a,b) & _1 <<//~ c
--   (a,(a / c,b))
--

-- --

--   >>> ("Hawaii",10) & _2 <<//~ 2
--   (10.0,("Hawaii",5.0))
--

-- --

--   (<<//~) :: Fractional a => Lens' s a -> a -> s -> (a, s)
--   (<<//~) :: Fractional a => Iso' s a -> a -> s -> (a, s)
--

(< LensLike' (,) a s a -> a -> s -> (a, s) infixr 4 <Lens and return the -- old value. -- -- When you do not need the old value, (-~) is more flexible. -- --

--   >>> (a,b) & _1 <<*~ c
--   (a,(a * c,b))
--

-- --

--   >>> (a,b) & _2 <<*~ c
--   (b,(a,b * c))
--

-- --

--   (<<*~) :: Num a => Lens' s a -> a -> s -> (a, s)
--   (<<*~) :: Num a => Iso' s a -> a -> s -> (a, s)
--

(<<*~) :: Num a => LensLike' (,) a s a -> a -> s -> (a, s) infixr 4 <<*~ -- | Decrement the target of a numerically valued Lens and return -- the old value. -- -- When you do not need the old value, (-~) is more flexible. -- --

--   >>> (a,b) & _1 <<-~ c
--   (a,(a - c,b))
--

-- --

--   >>> (a,b) & _2 <<-~ c
--   (b,(a,b - c))
--

-- --

--   (<<-~) :: Num a => Lens' s a -> a -> s -> (a, s)
--   (<<-~) :: Num a => Iso' s a -> a -> s -> (a, s)
--

(<<-~) :: Num a => LensLike' (,) a s a -> a -> s -> (a, s) infixr 4 <<-~ -- | Increment the target of a numerically valued Lens and return -- the old value. -- -- When you do not need the old value, (+~) is more flexible. -- --

--   >>> (a,b) & _1 <<+~ c
--   (a,(a + c,b))
--

-- --

--   >>> (a,b) & _2 <<+~ c
--   (b,(a,b + c))
--

-- --

--   (<<+~) :: Num a => Lens' s a -> a -> s -> (a, s)
--   (<<+~) :: Num a => Iso' s a -> a -> s -> (a, s)
--

(<<+~) :: Num a => LensLike' (,) a s a -> a -> s -> (a, s) infixr 4 <<+~ -- | Replace the target of a Lens with a Just value, but -- return the old value. -- -- If you do not need the old value (?~) is more flexible. -- --

--   >>> import Data.Map as Map
--   
--   >>> _2.at "hello" <<?~ "world" $ (42,Map.fromList [("goodnight","gracie")])
--   (Nothing,(42,fromList [("goodnight","gracie"),("hello","world")]))
--

-- --

--   (<<?~) :: Iso s t a (Maybe b)       -> b -> s -> (a, t)
--   (<<?~) :: Lens s t a (Maybe b)      -> b -> s -> (a, t)
--   (<<?~) :: Traversal s t a (Maybe b) -> b -> s -> (a, t)
--

(< LensLike (,) a s t a Maybe b -> b -> s -> (a, t) infixr 4 <Lens, but return the old value. -- -- When you do not need the old value, (.~) is more flexible. -- --

--   (<<.~) ::             Lens s t a b      -> b -> s -> (a, t)
--   (<<.~) ::             Iso s t a b       -> b -> s -> (a, t)
--   (<<.~) :: Monoid a => Traversal s t a b -> b -> s -> (a, t)
--

(<<.~) :: () => LensLike (,) a s t a b -> b -> s -> (a, t) infixr 4 <<.~ -- | Modify the target of a Lens, but return the old value. -- -- When you do not need the old value, (%~) is more flexible. -- --

--   (<<%~) ::             Lens s t a b      -> (a -> b) -> s -> (a, t)
--   (<<%~) ::             Iso s t a b       -> (a -> b) -> s -> (a, t)
--   (<<%~) :: Monoid a => Traversal s t a b -> (a -> b) -> s -> (a, t)
--

(<<%~) :: () => LensLike (,) a s t a b -> a -> b -> s -> (a, t) infixr 4 <<%~ -- | Logically && a Boolean valued Lens and return -- the result. -- -- When you do not need the result of the operation, (&&~) -- is more flexible. -- --

--   (<&&~) :: Lens' s Bool -> Bool -> s -> (Bool, s)
--   (<&&~) :: Iso' s Bool  -> Bool -> s -> (Bool, s)
--

(<&&~) :: () => LensLike (,) Bool s t Bool Bool -> Bool -> s -> (Bool, t) infixr 4 <&&~ -- | Logically || a Boolean valued Lens and return the -- result. -- -- When you do not need the result of the operation, (||~) is more -- flexible. -- --

--   (<||~) :: Lens' s Bool -> Bool -> s -> (Bool, s)
--   (<||~) :: Iso' s Bool  -> Bool -> s -> (Bool, s)
--

(<||~) :: () => LensLike (,) Bool s t Bool Bool -> Bool -> s -> (Bool, t) infixr 4 <||~ -- | Raise the target of a floating-point valued Lens to an -- arbitrary power and return the result. -- -- When you do not need the result of the operation, (**~) is more -- flexible. -- --

--   (<**~) :: Floating a => Lens' s a -> a -> s -> (a, s)
--   (<**~) :: Floating a => Iso' s a  -> a -> s -> (a, s)
--

(<**~) :: Floating a => LensLike (,) a s t a a -> a -> s -> (a, t) infixr 4 <**~ -- | Raise the target of a fractionally valued Lens to an -- Integral power and return the result. -- -- When you do not need the result of the operation, (^^~) is more -- flexible. -- --

--   (<^^~) :: (Fractional a, Integral e) => Lens' s a -> e -> s -> (a, s)
--   (<^^~) :: (Fractional a, Integral e) => Iso' s a -> e -> s -> (a, s)
--

(<^^~) :: (Fractional a, Integral e) => LensLike (,) a s t a a -> e -> s -> (a, t) infixr 4 <^^~ -- | Raise the target of a numerically valued Lens to a non-negative -- Integral power and return the result. -- -- When you do not need the result of the operation, (^~) is more -- flexible. -- --

--   (<^~) :: (Num a, Integral e) => Lens' s a -> e -> s -> (a, s)
--   (<^~) :: (Num a, Integral e) => Iso' s a -> e -> s -> (a, s)
--

(<^~) :: (Num a, Integral e) => LensLike (,) a s t a a -> e -> s -> (a, t) infixr 4 <^~ -- | Divide the target of a fractionally valued Lens and return the -- result. -- -- When you do not need the result of the division, (//~) is more -- flexible. -- --

--   (<//~) :: Fractional a => Lens' s a -> a -> s -> (a, s)
--   (<//~) :: Fractional a => Iso'  s a -> a -> s -> (a, s)
--

( LensLike (,) a s t a a -> a -> s -> (a, t) infixr 4 Lens and return the -- result. -- -- When you do not need the result of the multiplication, (*~) is -- more flexible. -- --

--   (<*~) :: Num a => Lens' s a -> a -> s -> (a, s)
--   (<*~) :: Num a => Iso'  s a -> a -> s -> (a, s)
--

(<*~) :: Num a => LensLike (,) a s t a a -> a -> s -> (a, t) infixr 4 <*~ -- | Decrement the target of a numerically valued Lens and return -- the result. -- -- When you do not need the result of the subtraction, (-~) is -- more flexible. -- --

--   (<-~) :: Num a => Lens' s a -> a -> s -> (a, s)
--   (<-~) :: Num a => Iso' s a  -> a -> s -> (a, s)
--

(<-~) :: Num a => LensLike (,) a s t a a -> a -> s -> (a, t) infixr 4 <-~ -- | Increment the target of a numerically valued Lens and return -- the result. -- -- When you do not need the result of the addition, (+~) is more -- flexible. -- --

--   (<+~) :: Num a => Lens' s a -> a -> s -> (a, s)
--   (<+~) :: Num a => Iso' s a  -> a -> s -> (a, s)
--

(<+~) :: Num a => LensLike (,) a s t a a -> a -> s -> (a, t) infixr 4 <+~ -- | Modify the target of a Lens and return the result. -- -- When you do not need the result of the operation, (%~) is more -- flexible. -- --

--   (<%~) ::             Lens s t a b      -> (a -> b) -> s -> (b, t)
--   (<%~) ::             Iso s t a b       -> (a -> b) -> s -> (b, t)
--   (<%~) :: Monoid b => Traversal s t a b -> (a -> b) -> s -> (b, t)
--

(<%~) :: () => LensLike (,) b s t a b -> a -> b -> s -> (b, t) infixr 4 <%~ -- | Clone an IndexedLens as an IndexedLens with the same -- index. cloneIndexedLens :: () => AnIndexedLens i s t a b -> IndexedLens i s t a b -- | Clone a Lens as an IndexedPreservingLens that just -- passes through whatever index is on any IndexedLens, -- IndexedFold, IndexedGetter or IndexedTraversal it -- is composed with. cloneIndexPreservingLens :: () => ALens s t a b -> IndexPreservingLens s t a b -- | Cloning a Lens is one way to make sure you aren't given -- something weaker, such as a Traversal and can be used as a way -- to pass around lenses that have to be monomorphic in f. -- -- Note: This only accepts a proper Lens. -- --

--   >>> let example l x = set (cloneLens l) (x^.cloneLens l + 1) x in example _2 ("hello",1,"you")
--   ("hello",2,"you")
--

cloneLens :: () => ALens s t a b -> Lens s t a b -- | This Lens lets you view the current pos of -- any indexed store comonad and seek to a new position. This -- reduces the API for working these instances to a single Lens. -- --

--   ipos w ≡ w ^. locus
--   iseek s w ≡ w & locus .~ s
--   iseeks f w ≡ w & locus %~ f
--

-- --

--   locus :: Lens' (Context' a s) a
--   locus :: Conjoined p => Lens' (Pretext' p a s) a
--   locus :: Conjoined p => Lens' (PretextT' p g a s) a
--

locus :: IndexedComonadStore p => Lens p a c s p b c s a b -- | alongside makes a Lens from two other lenses or a -- Getter from two other getters by executing them on their -- respective halves of a product. -- --

--   >>> (Left a, Right b)^.alongside chosen chosen
--   (a,b)
--

-- --

--   >>> (Left a, Right b) & alongside chosen chosen .~ (c,d)
--   (Left c,Right d)
--

-- --

--   alongside :: Lens   s t a b -> Lens   s' t' a' b' -> Lens   (s,s') (t,t') (a,a') (b,b')
--   alongside :: Getter s   a   -> Getter s'    a'    -> Getter (s,s')        (a,a')
--

alongside :: () => LensLike AlongsideLeft f b' s t a b -> LensLike AlongsideRight f t s' t' a' b' -> LensLike f (s, s') (t, t') (a, a') (b, b') -- | This is a Lens that updates either side of an Either, -- where both sides have the same type. -- --

--   chosen ≡ choosing id id
--

-- --

--   >>> Left a^.chosen
--   a
--

-- --

--   >>> Right a^.chosen
--   a
--

-- --

--   >>> Right "hello"^.chosen
--   "hello"
--

-- --

--   >>> Right a & chosen *~ b
--   Right (a * b)
--

-- --

--   chosen :: Lens (Either a a) (Either b b) a b
--   chosen f (Left a)  = Left <$> f a
--   chosen f (Right a) = Right <$> f a
--

chosen :: (Conjoined p, Functor f) => p a f b -> p Either a a f Either b b -- | Merge two lenses, getters, setters, folds or traversals. -- --

--   chosen ≡ choosing id id
--

-- --

--   choosing :: Getter s a     -> Getter s' a     -> Getter (Either s s') a
--   choosing :: Fold s a       -> Fold s' a       -> Fold (Either s s') a
--   choosing :: Lens' s a      -> Lens' s' a      -> Lens' (Either s s') a
--   choosing :: Traversal' s a -> Traversal' s' a -> Traversal' (Either s s') a
--   choosing :: Setter' s a    -> Setter' s' a    -> Setter' (Either s s') a
--

choosing :: Functor f => LensLike f s t a b -> LensLike f s' t' a b -> LensLike f Either s s' Either t t' a b -- | Lift a Lens so it can run under a function (or other -- corepresentable profunctor). -- --

--   inside :: Lens s t a b -> Lens (e -> s) (e -> t) (e -> a) (e -> b)
--

-- --

--   >>> (\x -> (x-1,x+1)) ^. inside _1 $ 5
--   4
--

-- --

--   >>> runState (modify (1:) >> modify (2:)) ^. (inside _2) $ []
--   [2,1]
--

inside :: Corepresentable p => ALens s t a b -> Lens p e s p e t p e a p e b -- | This is convenient to flip argument order of composite -- functions defined as: -- --

--   fab ?? a = fmap ($ a) fab
--

-- -- For the Functor instance f = ((->) r) you can -- reason about this function as if the definition was (??) ≡ -- flip: -- --

--   >>> (h ?? x) a
--   h a x
--

-- --

--   >>> execState ?? [] $ modify (1:)
--   [1]
--

-- --

--   >>> over _2 ?? ("hello","world") $ length
--   ("hello",5)
--

-- --

--   >>> over ?? length ?? ("hello","world") $ _2
--   ("hello",5)
--

(??) :: Functor f => f a -> b -> a -> f b infixl 1 ?? -- | Modify the target of a Lens in the current state returning some -- extra information of type r or modify all targets of a -- Traversal in the current state, extracting extra information of -- type r and return a monoidal summary of the changes. -- --

--   >>> runState (_1 %%= \x -> (f x, g x)) (a,b)
--   (f a,(g a,b))
--

-- --

--   (%%=) ≡ (state .)
--

-- -- It may be useful to think of (%%=), instead, as having either -- of the following more restricted type signatures: -- --

--   (%%=) :: MonadState s m             => Iso s s a b       -> (a -> (r, b)) -> m r
--   (%%=) :: MonadState s m             => Lens s s a b      -> (a -> (r, b)) -> m r
--   (%%=) :: (MonadState s m, Monoid r) => Traversal s s a b -> (a -> (r, b)) -> m r
--

(%%=) :: MonadState s m => Over p (,) r s s a b -> p a (r, b) -> m r infix 4 %%= -- | (%%~) can be used in one of two scenarios: -- -- When applied to a Lens, it can edit the target of the -- Lens in a structure, extracting a functorial result. -- -- When applied to a Traversal, it can edit the targets of the -- traversals, extracting an applicative summary of its actions. -- --

--   >>> [66,97,116,109,97,110] & each %%~ \a -> ("na", chr a)
--   ("nananananana","Batman")
--

-- -- For all that the definition of this combinator is just: -- --

--   (%%~) ≡ id
--

-- -- It may be beneficial to think about it as if it had these even more -- restricted types, however: -- --

--   (%%~) :: Functor f =>     Iso s t a b       -> (a -> f b) -> s -> f t
--   (%%~) :: Functor f =>     Lens s t a b      -> (a -> f b) -> s -> f t
--   (%%~) :: Applicative f => Traversal s t a b -> (a -> f b) -> s -> f t
--

-- -- When applied to a Traversal, it can edit the targets of the -- traversals, extracting a supplemental monoidal summary of its actions, -- by choosing f = ((,) m) -- --

--   (%%~) ::             Iso s t a b       -> (a -> (r, b)) -> s -> (r, t)
--   (%%~) ::             Lens s t a b      -> (a -> (r, b)) -> s -> (r, t)
--   (%%~) :: Monoid m => Traversal s t a b -> (a -> (m, b)) -> s -> (m, t)
--

(%%~) :: () => LensLike f s t a b -> a -> f b -> s -> f t infixr 4 %%~ -- | This can be used to chain lens operations using op= syntax -- rather than op~ syntax for simple non-type-changing cases. -- --

--   >>> (10,20) & _1 .~ 30 & _2 .~ 40
--   (30,40)
--

-- --

--   >>> (10,20) &~ do _1 .= 30; _2 .= 40
--   (30,40)
--

-- -- This does not support type-changing assignment, e.g. -- --

--   >>> (10,20) & _1 .~ "hello"
--   ("hello",20)
--

(&~) :: () => s -> State s a -> s infixl 1 &~ -- | Build an IndexedLens from a Getter and a Setter. ilens :: () => s -> (i, a) -> s -> b -> t -> IndexedLens i s t a b -- | Build an index-preserving Lens from a Getter and a -- Setter. iplens :: () => s -> a -> s -> b -> t -> IndexPreservingLens s t a b -- | Build a Lens from a getter and a setter. -- --

--   lens :: Functor f => (s -> a) -> (s -> b -> t) -> (a -> f b) -> s -> f t
--

-- --

--   >>> s ^. lens getter setter
--   getter s
--

-- --

--   >>> s & lens getter setter .~ b
--   setter s b
--

-- --

--   >>> s & lens getter setter %~ f
--   setter s (f (getter s))
--

-- --

--   lens :: (s -> a) -> (s -> a -> s) -> Lens' s a
--

lens :: () => s -> a -> s -> b -> t -> Lens s t a b -- | When you see this as an argument to a function, it expects a -- Lens. -- -- This type can also be used when you need to store a Lens in a -- container, since it is rank-1. You can turn them back into a -- Lens with cloneLens, or use it directly with combinators -- like storing and (^#). type ALens s t a b = LensLike Pretext ((->) :: * -> * -> *) a b s t a b -- |

--   type ALens' = Simple ALens
--

type ALens' s a = ALens s s a a -- | When you see this as an argument to a function, it expects an -- IndexedLens type AnIndexedLens i s t a b = Optical Indexed i ((->) :: * -> * -> *) Pretext Indexed i a b s t a b -- |

--   type AnIndexedLens' = Simple (AnIndexedLens i)
--

type AnIndexedLens' i s a = AnIndexedLens i s s a a -- | Map with index. (Deprecated alias for iover). -- -- When you do not need access to the index, then mapOf is more -- liberal in what it can accept. -- --

--   mapOf l ≡ imapOf l . const
--

-- --

--   imapOf :: IndexedSetter i s t a b    -> (i -> a -> b) -> s -> t
--   imapOf :: IndexedLens i s t a b      -> (i -> a -> b) -> s -> t
--   imapOf :: IndexedTraversal i s t a b -> (i -> a -> b) -> s -> t
--

imapOf :: () => AnIndexedSetter i s t a b -> i -> a -> b -> s -> t -- | mapOf is a deprecated alias for over. mapOf :: () => ASetter s t a b -> a -> b -> s -> t -- | Run an arrow command and use the output to set all the targets of a -- Lens, Setter or Traversal to the result. -- -- assignA can be used very similarly to (<~), except -- that the type of the object being modified can change; for example: -- --

--   runKleisli action ((), (), ()) where
--     action =      assignA _1 (Kleisli (const getVal1))
--              >>> assignA _2 (Kleisli (const getVal2))
--              >>> assignA _3 (Kleisli (const getVal3))
--     getVal1 :: Either String Int
--     getVal1 = ...
--     getVal2 :: Either String Bool
--     getVal2 = ...
--     getVal3 :: Either String Char
--     getVal3 = ...
--

-- -- has the type Either String (Int, Bool, -- Char) -- --

--   assignA :: Arrow p => Iso s t a b       -> p s b -> p s t
--   assignA :: Arrow p => Lens s t a b      -> p s b -> p s t
--   assignA :: Arrow p => Traversal s t a b -> p s b -> p s t
--   assignA :: Arrow p => Setter s t a b    -> p s b -> p s t
--

assignA :: Arrow p => ASetter s t a b -> p s b -> p s t -- | Replace every target in the current state of an IndexedSetter, -- IndexedLens or IndexedTraversal with access to the -- index. -- -- When you do not need access to the index then (.=) is more -- liberal in what it can accept. -- --

--   l .= b ≡ l .@= const b
--

-- --

--   (.@=) :: MonadState s m => IndexedSetter i s s a b    -> (i -> b) -> m ()
--   (.@=) :: MonadState s m => IndexedLens i s s a b      -> (i -> b) -> m ()
--   (.@=) :: MonadState s m => IndexedTraversal i s t a b -> (i -> b) -> m ()
--

(.@=) :: MonadState s m => AnIndexedSetter i s s a b -> i -> b -> m () infix 4 .@= -- | This is an alias for (%@=). imodifying :: MonadState s m => AnIndexedSetter i s s a b -> i -> a -> b -> m () -- | Adjust every target in the current state of an IndexedSetter, -- IndexedLens or IndexedTraversal with access to the -- index. -- -- When you do not need access to the index then (%=) is more -- liberal in what it can accept. -- --

--   l %= f ≡ l %@= const f
--

-- --

--   (%@=) :: MonadState s m => IndexedSetter i s s a b    -> (i -> a -> b) -> m ()
--   (%@=) :: MonadState s m => IndexedLens i s s a b      -> (i -> a -> b) -> m ()
--   (%@=) :: MonadState s m => IndexedTraversal i s t a b -> (i -> a -> b) -> m ()
--

(%@=) :: MonadState s m => AnIndexedSetter i s s a b -> i -> a -> b -> m () infix 4 %@= -- | Replace every target of an IndexedSetter, IndexedLens or -- IndexedTraversal with access to the index. -- --

--   (.@~) ≡ iset
--

-- -- When you do not need access to the index then (.~) is more -- liberal in what it can accept. -- --

--   l .~ b ≡ l .@~ const b
--

-- --

--   (.@~) :: IndexedSetter i s t a b    -> (i -> b) -> s -> t
--   (.@~) :: IndexedLens i s t a b      -> (i -> b) -> s -> t
--   (.@~) :: IndexedTraversal i s t a b -> (i -> b) -> s -> t
--

(.@~) :: () => AnIndexedSetter i s t a b -> i -> b -> s -> t infixr 4 .@~ -- | Adjust every target of an IndexedSetter, IndexedLens or -- IndexedTraversal with access to the index. -- --

--   (%@~) ≡ iover
--

-- -- When you do not need access to the index then (%~) is more -- liberal in what it can accept. -- --

--   l %~ f ≡ l %@~ const f
--

-- --

--   (%@~) :: IndexedSetter i s t a b    -> (i -> a -> b) -> s -> t
--   (%@~) :: IndexedLens i s t a b      -> (i -> a -> b) -> s -> t
--   (%@~) :: IndexedTraversal i s t a b -> (i -> a -> b) -> s -> t
--

(%@~) :: () => AnIndexedSetter i s t a b -> i -> a -> b -> s -> t infixr 4 %@~ -- | Build an IndexedSetter from an imap-like function. -- -- Your supplied function f is required to satisfy: -- --

--   f id ≡ id
--   f g . f h ≡ f (g . h)
--

-- -- Equational reasoning: -- --

--   isets . iover ≡ id
--   iover . isets ≡ id
--

-- -- Another way to view isets is that it takes a "semantic editor -- combinator" which has been modified to carry an index and transforms -- it into a IndexedSetter. isets :: () => i -> a -> b -> s -> t -> IndexedSetter i s t a b -- | Set with index. Equivalent to iover with the current value -- ignored. -- -- When you do not need access to the index, then set is more -- liberal in what it can accept. -- --

--   set l ≡ iset l . const
--

-- --

--   iset :: IndexedSetter i s t a b    -> (i -> b) -> s -> t
--   iset :: IndexedLens i s t a b      -> (i -> b) -> s -> t
--   iset :: IndexedTraversal i s t a b -> (i -> b) -> s -> t
--

iset :: () => AnIndexedSetter i s t a b -> i -> b -> s -> t -- | Map with index. This is an alias for imapOf. -- -- When you do not need access to the index, then over is more -- liberal in what it can accept. -- --

--   over l ≡ iover l . const
--   iover l ≡ over l . Indexed
--

-- --

--   iover :: IndexedSetter i s t a b    -> (i -> a -> b) -> s -> t
--   iover :: IndexedLens i s t a b      -> (i -> a -> b) -> s -> t
--   iover :: IndexedTraversal i s t a b -> (i -> a -> b) -> s -> t
--

iover :: () => AnIndexedSetter i s t a b -> i -> a -> b -> s -> t -- | This is a generalization of censor that alows you to -- censor just a portion of the resulting MonadWriter, with -- access to the index of an IndexedSetter. icensoring :: MonadWriter w m => IndexedSetter i w w u v -> i -> u -> v -> m a -> m a -- | This is a generalization of censor that alows you to -- censor just a portion of the resulting MonadWriter. censoring :: MonadWriter w m => Setter w w u v -> u -> v -> m a -> m a -- | This is a generalization of pass that alows you to modify just -- a portion of the resulting MonadWriter with access to the index -- of an IndexedSetter. ipassing :: MonadWriter w m => IndexedSetter i w w u v -> m (a, i -> u -> v) -> m a -- | This is a generalization of pass that alows you to modify just -- a portion of the resulting MonadWriter. passing :: MonadWriter w m => Setter w w u v -> m (a, u -> v) -> m a -- | Write to a fragment of a larger Writer format. scribe :: (MonadWriter t m, Monoid s) => ASetter s t a b -> b -> m () -- | Modify the target(s) of a Lens', Iso, Setter or -- Traversal by mappending a value. -- --

--   >>> execState (do _1 <>= Sum c; _2 <>= Product d) (Sum a,Product b)
--   (Sum {getSum = a + c},Product {getProduct = b * d})
--

-- --

--   >>> execState (both <>= "!!!") ("hello","world")
--   ("hello!!!","world!!!")
--

-- --

--   (<>=) :: (MonadState s m, Monoid a) => Setter' s a -> a -> m ()
--   (<>=) :: (MonadState s m, Monoid a) => Iso' s a -> a -> m ()
--   (<>=) :: (MonadState s m, Monoid a) => Lens' s a -> a -> m ()
--   (<>=) :: (MonadState s m, Monoid a) => Traversal' s a -> a -> m ()
--

(<>=) :: (MonadState s m, Monoid a) => ASetter' s a -> a -> m () infix 4 <>= -- | Modify the target of a monoidally valued by mappending another -- value. -- --

--   >>> (Sum a,b) & _1 <>~ Sum c
--   (Sum {getSum = a + c},b)
--

-- --

--   >>> (Sum a,Sum b) & both <>~ Sum c
--   (Sum {getSum = a + c},Sum {getSum = b + c})
--

-- --

--   >>> both <>~ "!!!" $ ("hello","world")
--   ("hello!!!","world!!!")
--

-- --

--   (<>~) :: Monoid a => Setter s t a a    -> a -> s -> t
--   (<>~) :: Monoid a => Iso s t a a       -> a -> s -> t
--   (<>~) :: Monoid a => Lens s t a a      -> a -> s -> t
--   (<>~) :: Monoid a => Traversal s t a a -> a -> s -> t
--

(<>~) :: Monoid a => ASetter s t a a -> a -> s -> t infixr 4 <>~ -- | Set Just a value with pass-through -- -- This is useful for chaining assignment without round-tripping through -- your Monad stack. -- --

--   do x <- at "foo" <?= ninety_nine_bottles_of_beer_on_the_wall
--

-- -- If you do not need a copy of the intermediate result, then using l -- ?= d will avoid unused binding warnings. -- --

--   (<?=) :: MonadState s m => Setter s s a (Maybe b)    -> b -> m b
--   (<?=) :: MonadState s m => Iso s s a (Maybe b)       -> b -> m b
--   (<?=) :: MonadState s m => Lens s s a (Maybe b)      -> b -> m b
--   (<?=) :: MonadState s m => Traversal s s a (Maybe b) -> b -> m b
--

( ASetter s s a Maybe b -> b -> m b infix 4 Monad stack. -- --

--   do x <- _2 <.= ninety_nine_bottles_of_beer_on_the_wall
--

-- -- If you do not need a copy of the intermediate result, then using l -- .= d will avoid unused binding warnings. -- --

--   (<.=) :: MonadState s m => Setter s s a b    -> b -> m b
--   (<.=) :: MonadState s m => Iso s s a b       -> b -> m b
--   (<.=) :: MonadState s m => Lens s s a b      -> b -> m b
--   (<.=) :: MonadState s m => Traversal s s a b -> b -> m b
--

(<.=) :: MonadState s m => ASetter s s a b -> b -> m b infix 4 <.= -- | Run a monadic action, and set all of the targets of a Lens, -- Setter or Traversal to its result. -- --

--   (<~) :: MonadState s m => Iso s s a b       -> m b -> m ()
--   (<~) :: MonadState s m => Lens s s a b      -> m b -> m ()
--   (<~) :: MonadState s m => Traversal s s a b -> m b -> m ()
--   (<~) :: MonadState s m => Setter s s a b    -> m b -> m ()
--

-- -- As a reasonable mnemonic, this lets you store the result of a monadic -- action in a Lens rather than in a local variable. -- --

--   do foo <- bar
--      ...
--

-- -- will store the result in a variable, while -- --

--   do foo <~ bar
--      ...
--

-- -- will store the result in a Lens, Setter, or -- Traversal. (<~) :: MonadState s m => ASetter s s a b -> m b -> m () infixr 2 <~ -- | Modify the target(s) of a Lens', 'Iso, Setter or -- Traversal by taking their logical || with a value. -- --

--   >>> execState (do _1 ||= True; _2 ||= False; _3 ||= True; _4 ||= False) (True,True,False,False)
--   (True,True,True,False)
--

-- --

--   (||=) :: MonadState s m => Setter' s Bool    -> Bool -> m ()
--   (||=) :: MonadState s m => Iso' s Bool       -> Bool -> m ()
--   (||=) :: MonadState s m => Lens' s Bool      -> Bool -> m ()
--   (||=) :: MonadState s m => Traversal' s Bool -> Bool -> m ()
--

(||=) :: MonadState s m => ASetter' s Bool -> Bool -> m () infix 4 ||= -- | Modify the target(s) of a Lens', Iso, Setter or -- Traversal by taking their logical && with a -- value. -- --

--   >>> execState (do _1 &&= True; _2 &&= False; _3 &&= True; _4 &&= False) (True,True,False,False)
--   (True,False,False,False)
--

-- --

--   (&&=) :: MonadState s m => Setter' s Bool    -> Bool -> m ()
--   (&&=) :: MonadState s m => Iso' s Bool       -> Bool -> m ()
--   (&&=) :: MonadState s m => Lens' s Bool      -> Bool -> m ()
--   (&&=) :: MonadState s m => Traversal' s Bool -> Bool -> m ()
--

(&&=) :: MonadState s m => ASetter' s Bool -> Bool -> m () infix 4 &&= -- | Raise the target(s) of a numerically valued Lens, Setter -- or Traversal to an arbitrary power -- --

--   >>> execState (do _1 **= c; _2 **= d) (a,b)
--   (a**c,b**d)
--

-- --

--   (**=) ::  (MonadState s m, Floating a) => Setter' s a    -> a -> m ()
--   (**=) ::  (MonadState s m, Floating a) => Iso' s a       -> a -> m ()
--   (**=) ::  (MonadState s m, Floating a) => Lens' s a      -> a -> m ()
--   (**=) ::  (MonadState s m, Floating a) => Traversal' s a -> a -> m ()
--

(**=) :: (MonadState s m, Floating a) => ASetter' s a -> a -> m () infix 4 **= -- | Raise the target(s) of a numerically valued Lens, Setter -- or Traversal to an integral power. -- --

--   (^^=) ::  (MonadState s m, Fractional a, Integral e) => Setter' s a    -> e -> m ()
--   (^^=) ::  (MonadState s m, Fractional a, Integral e) => Iso' s a       -> e -> m ()
--   (^^=) ::  (MonadState s m, Fractional a, Integral e) => Lens' s a      -> e -> m ()
--   (^^=) ::  (MonadState s m, Fractional a, Integral e) => Traversal' s a -> e -> m ()
--

(^^=) :: (MonadState s m, Fractional a, Integral e) => ASetter' s a -> e -> m () infix 4 ^^= -- | Raise the target(s) of a numerically valued Lens, Setter -- or Traversal to a non-negative integral power. -- --

--   (^=) ::  (MonadState s m, Num a, Integral e) => Setter' s a    -> e -> m ()
--   (^=) ::  (MonadState s m, Num a, Integral e) => Iso' s a       -> e -> m ()
--   (^=) ::  (MonadState s m, Num a, Integral e) => Lens' s a      -> e -> m ()
--   (^=) ::  (MonadState s m, Num a, Integral e) => Traversal' s a -> e -> m ()
--

(^=) :: (MonadState s m, Num a, Integral e) => ASetter' s a -> e -> m () infix 4 ^= -- | Modify the target(s) of a Lens', Iso, Setter or -- Traversal by dividing by a value. -- --

--   >>> execState (do _1 //= c; _2 //= d) (a,b)
--   (a / c,b / d)
--

-- --

--   (//=) :: (MonadState s m, Fractional a) => Setter' s a    -> a -> m ()
--   (//=) :: (MonadState s m, Fractional a) => Iso' s a       -> a -> m ()
--   (//=) :: (MonadState s m, Fractional a) => Lens' s a      -> a -> m ()
--   (//=) :: (MonadState s m, Fractional a) => Traversal' s a -> a -> m ()
--

(//=) :: (MonadState s m, Fractional a) => ASetter' s a -> a -> m () infix 4 //= -- | Modify the target(s) of a Lens', Iso, Setter or -- Traversal by multiplying by value. -- --

--   >>> execState (do _1 *= c; _2 *= d) (a,b)
--   (a * c,b * d)
--

-- --

--   (*=) :: (MonadState s m, Num a) => Setter' s a    -> a -> m ()
--   (*=) :: (MonadState s m, Num a) => Iso' s a       -> a -> m ()
--   (*=) :: (MonadState s m, Num a) => Lens' s a      -> a -> m ()
--   (*=) :: (MonadState s m, Num a) => Traversal' s a -> a -> m ()
--

(*=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m () infix 4 *= -- | Modify the target(s) of a Lens', Iso, Setter or -- Traversal by subtracting a value. -- --

--   >>> execState (do _1 -= c; _2 -= d) (a,b)
--   (a - c,b - d)
--

-- --

--   (-=) :: (MonadState s m, Num a) => Setter' s a    -> a -> m ()
--   (-=) :: (MonadState s m, Num a) => Iso' s a       -> a -> m ()
--   (-=) :: (MonadState s m, Num a) => Lens' s a      -> a -> m ()
--   (-=) :: (MonadState s m, Num a) => Traversal' s a -> a -> m ()
--

(-=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m () infix 4 -= -- | Modify the target(s) of a Lens', Iso, Setter or -- Traversal by adding a value. -- -- Example: -- --

--   fresh :: MonadState Int m => m Int
--   fresh = do
--     id += 1
--     use id
--

-- --

--   >>> execState (do _1 += c; _2 += d) (a,b)
--   (a + c,b + d)
--

-- --

--   >>> execState (do _1.at 1.non 0 += 10) (Map.fromList [(2,100)],"hello")
--   (fromList [(1,10),(2,100)],"hello")
--

-- --

--   (+=) :: (MonadState s m, Num a) => Setter' s a    -> a -> m ()
--   (+=) :: (MonadState s m, Num a) => Iso' s a       -> a -> m ()
--   (+=) :: (MonadState s m, Num a) => Lens' s a      -> a -> m ()
--   (+=) :: (MonadState s m, Num a) => Traversal' s a -> a -> m ()
--

(+=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m () infix 4 += -- | Replace the target of a Lens or all of the targets of a -- Setter or Traversal in our monadic state with -- Just a new value, irrespective of the old. -- --

--   >>> execState (do at 1 ?= a; at 2 ?= b) Map.empty
--   fromList [(1,a),(2,b)]
--

-- --

--   >>> execState (do _1 ?= b; _2 ?= c) (Just a, Nothing)
--   (Just b,Just c)
--

-- --

--   (?=) :: MonadState s m => Iso' s (Maybe a)       -> a -> m ()
--   (?=) :: MonadState s m => Lens' s (Maybe a)      -> a -> m ()
--   (?=) :: MonadState s m => Traversal' s (Maybe a) -> a -> m ()
--   (?=) :: MonadState s m => Setter' s (Maybe a)    -> a -> m ()
--

(?=) :: MonadState s m => ASetter s s a Maybe b -> b -> m () infix 4 ?= -- | This is an alias for (%=). modifying :: MonadState s m => ASetter s s a b -> a -> b -> m () -- | Map over the target of a Lens or all of the targets of a -- Setter or Traversal in our monadic state. -- --

--   >>> execState (do _1 %= f;_2 %= g) (a,b)
--   (f a,g b)
--

-- --

--   >>> execState (do both %= f) (a,b)
--   (f a,f b)
--

-- --

--   (%=) :: MonadState s m => Iso' s a       -> (a -> a) -> m ()
--   (%=) :: MonadState s m => Lens' s a      -> (a -> a) -> m ()
--   (%=) :: MonadState s m => Traversal' s a -> (a -> a) -> m ()
--   (%=) :: MonadState s m => Setter' s a    -> (a -> a) -> m ()
--

-- --

--   (%=) :: MonadState s m => ASetter s s a b -> (a -> b) -> m ()
--

(%=) :: MonadState s m => ASetter s s a b -> a -> b -> m () infix 4 %= -- | Replace the target of a Lens or all of the targets of a -- Setter or Traversal in our monadic state with a new -- value, irrespective of the old. -- -- This is an alias for (.=). -- --

--   >>> execState (do assign _1 c; assign _2 d) (a,b)
--   (c,d)
--

-- --

--   >>> execState (both .= c) (a,b)
--   (c,c)
--

-- --

--   assign :: MonadState s m => Iso' s a       -> a -> m ()
--   assign :: MonadState s m => Lens' s a      -> a -> m ()
--   assign :: MonadState s m => Traversal' s a -> a -> m ()
--   assign :: MonadState s m => Setter' s a    -> a -> m ()
--

assign :: MonadState s m => ASetter s s a b -> b -> m () -- | Logically && the target(s) of a Bool-valued -- Lens or Setter. -- --

--   >>> both &&~ True $ (False, True)
--   (False,True)
--

-- --

--   >>> both &&~ False $ (False, True)
--   (False,False)
--

-- --

--   (&&~) :: Setter' s Bool    -> Bool -> s -> s
--   (&&~) :: Iso' s Bool       -> Bool -> s -> s
--   (&&~) :: Lens' s Bool      -> Bool -> s -> s
--   (&&~) :: Traversal' s Bool -> Bool -> s -> s
--

(&&~) :: () => ASetter s t Bool Bool -> Bool -> s -> t infixr 4 &&~ -- | Logically || the target(s) of a Bool-valued Lens -- or Setter. -- --

--   >>> both ||~ True $ (False,True)
--   (True,True)
--

-- --

--   >>> both ||~ False $ (False,True)
--   (False,True)
--

-- --

--   (||~) :: Setter' s Bool    -> Bool -> s -> s
--   (||~) :: Iso' s Bool       -> Bool -> s -> s
--   (||~) :: Lens' s Bool      -> Bool -> s -> s
--   (||~) :: Traversal' s Bool -> Bool -> s -> s
--

(||~) :: () => ASetter s t Bool Bool -> Bool -> s -> t infixr 4 ||~ -- | Raise the target(s) of a floating-point valued Lens, -- Setter or Traversal to an arbitrary power. -- --

--   >>> (a,b) & _1 **~ c
--   (a**c,b)
--

-- --

--   >>> (a,b) & both **~ c
--   (a**c,b**c)
--

-- --

--   >>> _2 **~ 10 $ (3,2)
--   (3,1024.0)
--

-- --

--   (**~) :: Floating a => Setter' s a    -> a -> s -> s
--   (**~) :: Floating a => Iso' s a       -> a -> s -> s
--   (**~) :: Floating a => Lens' s a      -> a -> s -> s
--   (**~) :: Floating a => Traversal' s a -> a -> s -> s
--

(**~) :: Floating a => ASetter s t a a -> a -> s -> t infixr 4 **~ -- | Raise the target(s) of a fractionally valued Lens, -- Setter or Traversal to an integral power. -- --

--   >>> (1,2) & _2 ^^~ (-1)
--   (1,0.5)
--

-- --

--   (^^~) :: (Fractional a, Integral e) => Setter' s a    -> e -> s -> s
--   (^^~) :: (Fractional a, Integral e) => Iso' s a       -> e -> s -> s
--   (^^~) :: (Fractional a, Integral e) => Lens' s a      -> e -> s -> s
--   (^^~) :: (Fractional a, Integral e) => Traversal' s a -> e -> s -> s
--

(^^~) :: (Fractional a, Integral e) => ASetter s t a a -> e -> s -> t infixr 4 ^^~ -- | Raise the target(s) of a numerically valued Lens, Setter -- or Traversal to a non-negative integral power. -- --

--   >>> (1,3) & _2 ^~ 2
--   (1,9)
--

-- --

--   (^~) :: (Num a, Integral e) => Setter' s a    -> e -> s -> s
--   (^~) :: (Num a, Integral e) => Iso' s a       -> e -> s -> s
--   (^~) :: (Num a, Integral e) => Lens' s a      -> e -> s -> s
--   (^~) :: (Num a, Integral e) => Traversal' s a -> e -> s -> s
--

(^~) :: (Num a, Integral e) => ASetter s t a a -> e -> s -> t infixr 4 ^~ -- | Divide the target(s) of a numerically valued Lens, Iso, -- Setter or Traversal. -- --

--   >>> (a,b) & _1 //~ c
--   (a / c,b)
--

-- --

--   >>> (a,b) & both //~ c
--   (a / c,b / c)
--

-- --

--   >>> ("Hawaii",10) & _2 //~ 2
--   ("Hawaii",5.0)
--

-- --

--   (//~) :: Fractional a => Setter' s a    -> a -> s -> s
--   (//~) :: Fractional a => Iso' s a       -> a -> s -> s
--   (//~) :: Fractional a => Lens' s a      -> a -> s -> s
--   (//~) :: Fractional a => Traversal' s a -> a -> s -> s
--

(//~) :: Fractional a => ASetter s t a a -> a -> s -> t infixr 4 //~ -- | Decrement the target(s) of a numerically valued Lens, -- Iso, Setter or Traversal. -- --

--   >>> (a,b) & _1 -~ c
--   (a - c,b)
--

-- --

--   >>> (a,b) & both -~ c
--   (a - c,b - c)
--

-- --

--   >>> _1 -~ 2 $ (1,2)
--   (-1,2)
--

-- --

--   >>> mapped.mapped -~ 1 $ [[4,5],[6,7]]
--   [[3,4],[5,6]]
--

-- --

--   (-~) :: Num a => Setter' s a    -> a -> s -> s
--   (-~) :: Num a => Iso' s a       -> a -> s -> s
--   (-~) :: Num a => Lens' s a      -> a -> s -> s
--   (-~) :: Num a => Traversal' s a -> a -> s -> s
--

(-~) :: Num a => ASetter s t a a -> a -> s -> t infixr 4 -~ -- | Multiply the target(s) of a numerically valued Lens, -- Iso, Setter or Traversal. -- --

--   >>> (a,b) & _1 *~ c
--   (a * c,b)
--

-- --

--   >>> (a,b) & both *~ c
--   (a * c,b * c)
--

-- --

--   >>> (1,2) & _2 *~ 4
--   (1,8)
--

-- --

--   >>> Just 24 & mapped *~ 2
--   Just 48
--

-- --

--   (*~) :: Num a => Setter' s a    -> a -> s -> s
--   (*~) :: Num a => Iso' s a       -> a -> s -> s
--   (*~) :: Num a => Lens' s a      -> a -> s -> s
--   (*~) :: Num a => Traversal' s a -> a -> s -> s
--

(*~) :: Num a => ASetter s t a a -> a -> s -> t infixr 4 *~ -- | Increment the target(s) of a numerically valued Lens, -- Setter or Traversal. -- --

--   >>> (a,b) & _1 +~ c
--   (a + c,b)
--

-- --

--   >>> (a,b) & both +~ c
--   (a + c,b + c)
--

-- --

--   >>> (1,2) & _2 +~ 1
--   (1,3)
--

-- --

--   >>> [(a,b),(c,d)] & traverse.both +~ e
--   [(a + e,b + e),(c + e,d + e)]
--

-- --

--   (+~) :: Num a => Setter' s a    -> a -> s -> s
--   (+~) :: Num a => Iso' s a       -> a -> s -> s
--   (+~) :: Num a => Lens' s a      -> a -> s -> s
--   (+~) :: Num a => Traversal' s a -> a -> s -> s
--

(+~) :: Num a => ASetter s t a a -> a -> s -> t infixr 4 +~ -- | Set to Just a value with pass-through. -- -- This is mostly present for consistency, but may be useful for for -- chaining assignments. -- -- If you do not need a copy of the intermediate result, then using l -- ?~ d directly is a good idea. -- --

--   >>> import Data.Map as Map
--   
--   >>> _2.at "hello" <?~ "world" $ (42,Map.fromList [("goodnight","gracie")])
--   ("world",(42,fromList [("goodnight","gracie"),("hello","world")]))
--

-- --

--   (<?~) :: Setter s t a (Maybe b)    -> b -> s -> (b, t)
--   (<?~) :: Iso s t a (Maybe b)       -> b -> s -> (b, t)
--   (<?~) :: Lens s t a (Maybe b)      -> b -> s -> (b, t)
--   (<?~) :: Traversal s t a (Maybe b) -> b -> s -> (b, t)
--

( ASetter s t a Maybe b -> b -> s -> (b, t) infixr 4 l -- .~ t directly is a good idea. -- --

--   >>> (a,b) & _1 <.~ c
--   (c,(c,b))
--

-- --

--   >>> ("good","morning","vietnam") & _3 <.~ "world"
--   ("world",("good","morning","world"))
--

-- --

--   >>> (42,Map.fromList [("goodnight","gracie")]) & _2.at "hello" <.~ Just "world"
--   (Just "world",(42,fromList [("goodnight","gracie"),("hello","world")]))
--

-- --

--   (<.~) :: Setter s t a b    -> b -> s -> (b, t)
--   (<.~) :: Iso s t a b       -> b -> s -> (b, t)
--   (<.~) :: Lens s t a b      -> b -> s -> (b, t)
--   (<.~) :: Traversal s t a b -> b -> s -> (b, t)
--

(<.~) :: () => ASetter s t a b -> b -> s -> (b, t) infixr 4 <.~ -- | Set the target of a Lens, Traversal or Setter to -- Just a value. -- --

--   l ?~ t ≡ set l (Just t)
--

-- --

--   >>> Nothing & id ?~ a
--   Just a
--

-- --

--   >>> Map.empty & at 3 ?~ x
--   fromList [(3,x)]
--

-- --

--   (?~) :: Setter s t a (Maybe b)    -> b -> s -> t
--   (?~) :: Iso s t a (Maybe b)       -> b -> s -> t
--   (?~) :: Lens s t a (Maybe b)      -> b -> s -> t
--   (?~) :: Traversal s t a (Maybe b) -> b -> s -> t
--

(?~) :: () => ASetter s t a Maybe b -> b -> s -> t infixr 4 ?~ -- | Replace the target of a Lens or all of the targets of a -- Setter or Traversal with a constant value. -- -- This is an infix version of set, provided for consistency with -- (.=). -- --

--   f <$ a ≡ mapped .~ f $ a
--

-- --

--   >>> (a,b,c,d) & _4 .~ e
--   (a,b,c,e)
--

-- --

--   >>> (42,"world") & _1 .~ "hello"
--   ("hello","world")
--

-- --

--   >>> (a,b) & both .~ c
--   (c,c)
--

-- --

--   (.~) :: Setter s t a b    -> b -> s -> t
--   (.~) :: Iso s t a b       -> b -> s -> t
--   (.~) :: Lens s t a b      -> b -> s -> t
--   (.~) :: Traversal s t a b -> b -> s -> t
--

(.~) :: () => ASetter s t a b -> b -> s -> t infixr 4 .~ -- | Modifies the target of a Lens or all of the targets of a -- Setter or Traversal with a user supplied function. -- -- This is an infix version of over. -- --

--   fmap f ≡ mapped %~ f
--   fmapDefault f ≡ traverse %~ f
--

-- --

--   >>> (a,b,c) & _3 %~ f
--   (a,b,f c)
--

-- --

--   >>> (a,b) & both %~ f
--   (f a,f b)
--

-- --

--   >>> _2 %~ length $ (1,"hello")
--   (1,5)
--

-- --

--   >>> traverse %~ f $ [a,b,c]
--   [f a,f b,f c]
--

-- --

--   >>> traverse %~ even $ [1,2,3]
--   [False,True,False]
--

-- --

--   >>> traverse.traverse %~ length $ [["hello","world"],["!!!"]]
--   [[5,5],[3]]
--

-- --

--   (%~) :: Setter s t a b    -> (a -> b) -> s -> t
--   (%~) :: Iso s t a b       -> (a -> b) -> s -> t
--   (%~) :: Lens s t a b      -> (a -> b) -> s -> t
--   (%~) :: Traversal s t a b -> (a -> b) -> s -> t
--

(%~) :: () => ASetter s t a b -> a -> b -> s -> t infixr 4 %~ -- | Replace the target of a Lens or all of the targets of a -- Setter' or Traversal with a constant value, without -- changing its type. -- -- This is a type restricted version of set, which retains the -- type of the original. -- --

--   >>> set' mapped x [a,b,c,d]
--   [x,x,x,x]
--

-- --

--   >>> set' _2 "hello" (1,"world")
--   (1,"hello")
--

-- --

--   >>> set' mapped 0 [1,2,3,4]
--   [0,0,0,0]
--

-- -- Note: Attempting to adjust set' a Fold or Getter -- will fail at compile time with an relatively nice error message. -- --

--   set' :: Setter' s a    -> a -> s -> s
--   set' :: Iso' s a       -> a -> s -> s
--   set' :: Lens' s a      -> a -> s -> s
--   set' :: Traversal' s a -> a -> s -> s
--

set' :: () => ASetter' s a -> a -> s -> s -- | Replace the target of a Lens or all of the targets of a -- Setter or Traversal with a constant value. -- --

--   (<$) ≡ set mapped
--

-- --

--   >>> set _2 "hello" (1,())
--   (1,"hello")
--

-- --

--   >>> set mapped () [1,2,3,4]
--   [(),(),(),()]
--

-- -- Note: Attempting to set a Fold or Getter will -- fail at compile time with an relatively nice error message. -- --

--   set :: Setter s t a b    -> b -> s -> t
--   set :: Iso s t a b       -> b -> s -> t
--   set :: Lens s t a b      -> b -> s -> t
--   set :: Traversal s t a b -> b -> s -> t
--

set :: () => ASetter s t a b -> b -> s -> t -- | Modify the target of a Lens or all the targets of a -- Setter or Traversal with a function. -- --

--   fmap ≡ over mapped
--   fmapDefault ≡ over traverse
--   sets . over ≡ id
--   over . sets ≡ id
--

-- -- Given any valid Setter l, you can also rely on the -- law: -- --

--   over l f . over l g = over l (f . g)
--

-- -- e.g. -- --

--   >>> over mapped f (over mapped g [a,b,c]) == over mapped (f . g) [a,b,c]
--   True
--

-- -- Another way to view over is to say that it transforms a -- Setter into a "semantic editor combinator". -- --

--   >>> over mapped f (Just a)
--   Just (f a)
--

-- --

--   >>> over mapped (*10) [1,2,3]
--   [10,20,30]
--

-- --

--   >>> over _1 f (a,b)
--   (f a,b)
--

-- --

--   >>> over _1 show (10,20)
--   ("10",20)
--

-- --

--   over :: Setter s t a b -> (a -> b) -> s -> t
--   over :: ASetter s t a b -> (a -> b) -> s -> t
--

over :: () => ASetter s t a b -> a -> b -> s -> t -- | Clone an IndexedSetter. cloneIndexedSetter :: () => AnIndexedSetter i s t a b -> IndexedSetter i s t a b -- | Build an IndexPreservingSetter from any Setter. cloneIndexPreservingSetter :: () => ASetter s t a b -> IndexPreservingSetter s t a b -- | Restore ASetter to a full Setter. cloneSetter :: () => ASetter s t a b -> Setter s t a b -- | Build a Setter, IndexedSetter or -- IndexPreservingSetter depending on your choice of -- Profunctor. -- --

--   sets :: ((a -> b) -> s -> t) -> Setter s t a b
--

sets :: (Profunctor p, Profunctor q, Settable f) => p a b -> q s t -> Optical p q f s t a b -- | Build an index-preserving Setter from a map-like function. -- -- Your supplied function f is required to satisfy: -- --

--   f id ≡ id
--   f g . f h ≡ f (g . h)
--

-- -- Equational reasoning: -- --

--   setting . over ≡ id
--   over . setting ≡ id
--

-- -- Another way to view sets is that it takes a "semantic editor -- combinator" and transforms it into a Setter. -- --

--   setting :: ((a -> b) -> s -> t) -> Setter s t a b
--

setting :: () => a -> b -> s -> t -> IndexPreservingSetter s t a b -- | This Setter can be used to map over the input of a -- Profunctor. -- -- The most common Profunctor to use this with is -- (->). -- --

--   >>> (argument %~ f) g x
--   g (f x)
--

-- --

--   >>> (argument %~ show) length [1,2,3]
--   7
--

-- --

--   >>> (argument %~ f) h x y
--   h (f x) y
--

-- -- Map over the argument of the result of a function -- i.e., its second -- argument: -- --

--   >>> (mapped.argument %~ f) h x y
--   h x (f y)
--

-- --

--   argument :: Setter (b -> r) (a -> r) a b
--

argument :: Profunctor p => Setter p b r p a r a b -- | This Setter can be used to map over all of the inputs to a -- Contravariant. -- --

--   contramap ≡ over contramapped
--

-- --

--   >>> getPredicate (over contramapped (*2) (Predicate even)) 5
--   True
--

-- --

--   >>> getOp (over contramapped (*5) (Op show)) 100
--   "500"
--

-- --

--   >>> Prelude.map ($ 1) $ over (mapped . _Unwrapping' Op . contramapped) (*12) [(*2),(+1),(^3)]
--   [24,13,1728]
--

contramapped :: Contravariant f => Setter f b f a a b -- | This setter can be used to modify all of the values in a -- Monad. -- -- You sometimes have to use this rather than mapped -- due to -- temporary insanity Functor was not a superclass of Monad -- until GHC 7.10. -- --

--   liftM ≡ over lifted
--

-- --

--   >>> over lifted f [a,b,c]
--   [f a,f b,f c]
--

-- --

--   >>> set lifted b (Just a)
--   Just b
--

-- -- If you want an IndexPreservingSetter use setting -- liftM. lifted :: Monad m => Setter m a m b a b -- | This Setter can be used to map over all of the values in a -- Functor. -- --

--   fmap ≡ over mapped
--   fmapDefault ≡ over traverse
--   (<$) ≡ set mapped
--

-- --

--   >>> over mapped f [a,b,c]
--   [f a,f b,f c]
--

-- --

--   >>> over mapped (+1) [1,2,3]
--   [2,3,4]
--

-- --

--   >>> set mapped x [a,b,c]
--   [x,x,x]
--

-- --

--   >>> [[a,b],[c]] & mapped.mapped +~ x
--   [[a + x,b + x],[c + x]]
--

-- --

--   >>> over (mapped._2) length [("hello","world"),("leaders","!!!")]
--   [("hello",5),("leaders",3)]
--

-- --

--   mapped :: Functor f => Setter (f a) (f b) a b
--

-- -- If you want an IndexPreservingSetter use setting -- fmap. mapped :: Functor f => Setter f a f b a b -- | Running a Setter instantiates it to a concrete type. -- -- When consuming a setter directly to perform a mapping, you can use -- this type, but most user code will not need to use this type. type ASetter s t a b = a -> Identity b -> s -> Identity t -- | This is a useful alias for use when consuming a Setter'. -- -- Most user code will never have to use this type. -- --

--   type ASetter' = Simple ASetter
--

type ASetter' s a = ASetter s s a a -- | Running an IndexedSetter instantiates it to a concrete type. -- -- When consuming a setter directly to perform a mapping, you can use -- this type, but most user code will not need to use this type. type AnIndexedSetter i s t a b = Indexed i a Identity b -> s -> Identity t -- |

--   type AnIndexedSetter' i = Simple (AnIndexedSetter i)
--

type AnIndexedSetter' i s a = AnIndexedSetter i s s a a -- | This is a convenient alias when defining highly polymorphic code that -- takes both ASetter and AnIndexedSetter as appropriate. -- If a function takes this it is expecting one of those two things based -- on context. type Setting (p :: * -> * -> *) s t a b = p a Identity b -> s -> Identity t -- | This is a convenient alias when defining highly polymorphic code that -- takes both ASetter' and AnIndexedSetter' as appropriate. -- If a function takes this it is expecting one of those two things based -- on context. type Setting' (p :: * -> * -> *) s a = Setting p s s a a -- | A Lens is actually a lens family as described in -- http://comonad.com/reader/2012/mirrored-lenses/. -- -- With great power comes great responsibility and a Lens is -- subject to the three common sense Lens laws: -- -- 1) You get back what you put in: -- --

--   view l (set l v s)  ≡ v
--

-- -- 2) Putting back what you got doesn't change anything: -- --

--   set l (view l s) s  ≡ s
--

-- -- 3) Setting twice is the same as setting once: -- --

--   set l v' (set l v s) ≡ set l v' s
--

-- -- These laws are strong enough that the 4 type parameters of a -- Lens cannot vary fully independently. For more on how they -- interact, read the "Why is it a Lens Family?" section of -- http://comonad.com/reader/2012/mirrored-lenses/. -- -- There are some emergent properties of these laws: -- -- 1) set l s must be injective for every s This -- is a consequence of law #1 -- -- 2) set l must be surjective, because of law #2, which -- indicates that it is possible to obtain any v from some -- s such that set s v = s -- -- 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: -- --

--   set l v (set l v s) ≡ set l v s
--

-- -- Every Lens can be used directly as a Setter or -- Traversal. -- -- You can also use a Lens for Getting as if it were a -- Fold or Getter. -- -- Since every Lens is a valid Traversal, the -- Traversal laws are required of any Lens you create: -- --

--   l pure ≡ pure
--   fmap (l f) . l g ≡ getCompose . l (Compose . fmap f . g)
--

-- --

--   type Lens s t a b = forall f. Functor f => LensLike f s t a b
--

type Lens s t a b = forall (f :: * -> *). Functor f => a -> f b -> s -> f t -- |

--   type Lens' = Simple Lens
--

type Lens' s a = Lens s s a a -- | Every IndexedLens is a valid Lens and a valid -- IndexedTraversal. type IndexedLens i s t a b = forall (f :: * -> *) (p :: * -> * -> *). (Indexable i p, Functor f) => p a f b -> s -> f t -- |

--   type IndexedLens' i = Simple (IndexedLens i)
--

type IndexedLens' i s a = IndexedLens i s s a a -- | An IndexPreservingLens leaves any index it is composed with -- alone. type IndexPreservingLens s t a b = forall (p :: * -> * -> *) (f :: * -> *). (Conjoined p, Functor f) => p a f b -> p s f t -- |

--   type IndexPreservingLens' = Simple IndexPreservingLens
--

type IndexPreservingLens' s a = IndexPreservingLens s s a a -- | A Traversal can be used directly as a Setter or a -- Fold (but not as a Lens) and provides the ability to -- both read and update multiple fields, subject to some relatively weak -- Traversal laws. -- -- These have also been known as multilenses, but they have the signature -- and spirit of -- --

--   traverse :: Traversable f => Traversal (f a) (f b) a b
--

-- -- and the more evocative name suggests their application. -- -- Most of the time the Traversal you will want to use is just -- traverse, but you can also pass any Lens or Iso -- as a Traversal, and composition of a Traversal (or -- Lens or Iso) with a Traversal (or Lens or -- Iso) using (.) forms a valid Traversal. -- -- The laws for a Traversal t follow from the laws for -- Traversable as stated in "The Essence of the Iterator Pattern". -- --

--   t pure ≡ pure
--   fmap (t f) . t g ≡ getCompose . t (Compose . fmap f . g)
--

-- -- One consequence of this requirement is that a Traversal needs -- to leave the same number of elements as a candidate for subsequent -- Traversal that it started with. Another testament to the -- strength of these laws is that the caveat expressed in section 5.5 of -- the "Essence of the Iterator Pattern" about exotic Traversable -- instances that traverse the same entry multiple times was -- actually already ruled out by the second law in that same paper! type Traversal s t a b = forall (f :: * -> *). Applicative f => a -> f b -> s -> f t -- |

--   type Traversal' = Simple Traversal
--

type Traversal' s a = Traversal s s a a type Traversal1 s t a b = forall (f :: * -> *). Apply f => a -> f b -> s -> f t type Traversal1' s a = Traversal1 s s a a -- | Every IndexedTraversal is a valid Traversal or -- IndexedFold. -- -- The Indexed constraint is used to allow an -- IndexedTraversal to be used directly as a Traversal. -- -- The Traversal laws are still required to hold. -- -- In addition, the index i should satisfy the requirement that -- it stays unchanged even when modifying the value a, otherwise -- traversals like indices break the Traversal laws. type IndexedTraversal i s t a b = forall (p :: * -> * -> *) (f :: * -> *). (Indexable i p, Applicative f) => p a f b -> s -> f t -- |

--   type IndexedTraversal' i = Simple (IndexedTraversal i)
--

type IndexedTraversal' i s a = IndexedTraversal i s s a a type IndexedTraversal1 i s t a b = forall (p :: * -> * -> *) (f :: * -> *). (Indexable i p, Apply f) => p a f b -> s -> f t type IndexedTraversal1' i s a = IndexedTraversal1 i s s a a -- | An IndexPreservingLens leaves any index it is composed with -- alone. type IndexPreservingTraversal s t a b = forall (p :: * -> * -> *) (f :: * -> *). (Conjoined p, Applicative f) => p a f b -> p s f t -- |

--   type IndexPreservingTraversal' = Simple IndexPreservingTraversal
--

type IndexPreservingTraversal' s a = IndexPreservingTraversal s s a a type IndexPreservingTraversal1 s t a b = forall (p :: * -> * -> *) (f :: * -> *). (Conjoined p, Apply f) => p a f b -> p s f t type IndexPreservingTraversal1' s a = IndexPreservingTraversal1 s s a a -- | The only LensLike law that can apply to a Setter -- l is that -- --

--   set l y (set l x a) ≡ set l y a
--

-- -- You can't view a Setter in general, so the other two -- laws are irrelevant. -- -- However, two Functor laws apply to a Setter: -- --

--   over l id ≡ id
--   over l f . over l g ≡ over l (f . g)
--

-- -- These can be stated more directly: -- --

--   l pure ≡ pure
--   l f . untainted . l g ≡ l (f . untainted . g)
--

-- -- You can compose a Setter with a Lens or a -- Traversal using (.) from the Prelude and the -- result is always only a Setter and nothing more. -- --

--   >>> over traverse f [a,b,c,d]
--   [f a,f b,f c,f d]
--

-- --

--   >>> over _1 f (a,b)
--   (f a,b)
--

-- --

--   >>> over (traverse._1) f [(a,b),(c,d)]
--   [(f a,b),(f c,d)]
--

-- --

--   >>> over both f (a,b)
--   (f a,f b)
--

-- --

--   >>> over (traverse.both) f [(a,b),(c,d)]
--   [(f a,f b),(f c,f d)]
--

type Setter s t a b = forall (f :: * -> *). Settable f => a -> f b -> s -> f t -- | A Setter' is just a Setter that doesn't change the -- types. -- -- These are particularly common when talking about monomorphic -- containers. e.g. -- --

--   sets Data.Text.map :: Setter' Text Char
--

-- --

--   type Setter' = Simple Setter
--

type Setter' s a = Setter s s a a -- | Every IndexedSetter is a valid Setter. -- -- The Setter laws are still required to hold. type IndexedSetter i s t a b = forall (f :: * -> *) (p :: * -> * -> *). (Indexable i p, Settable f) => p a f b -> s -> f t -- |

--   type IndexedSetter' i = Simple (IndexedSetter i)
--

type IndexedSetter' i s a = IndexedSetter i s s a a -- | An IndexPreservingSetter can be composed with a -- IndexedSetter, IndexedTraversal or IndexedLens -- and leaves the index intact, yielding an IndexedSetter. type IndexPreservingSetter s t a b = forall (p :: * -> * -> *) (f :: * -> *). (Conjoined p, Settable f) => p a f b -> p s f t -- |

--   type IndexedPreservingSetter' i = Simple IndexedPreservingSetter
--

type IndexPreservingSetter' s a = IndexPreservingSetter s s a a -- | Isomorphism families can be composed with another Lens using -- (.) and id. -- -- Since every Iso is both a valid Lens and a valid -- Prism, the laws for those types imply the following laws for an -- Iso f: -- --

--   f . from f ≡ id
--   from f . f ≡ id
--

-- -- Note: Composition with an Iso is index- and measure- -- preserving. type Iso s t a b = forall (p :: * -> * -> *) (f :: * -> *). (Profunctor p, Functor f) => p a f b -> p s f t -- |

--   type Iso' = Simple Iso
--

type Iso' s a = Iso s s a a -- | This is a limited form of a Prism that can only be used for -- re operations. -- -- Like with a Getter, there are no laws to state for a -- Review. -- -- You can generate a Review by using unto. You can also -- use any Prism or Iso directly as a Review. type Review t b = forall (p :: * -> * -> *) (f :: * -> *). (Choice p, Bifunctor p, Settable f) => Optic' p f t b -- | If you see this in a signature for a function, the function is -- expecting a Review (in practice, this usually means a -- Prism). type AReview t b = Optic' (Tagged :: * -> * -> *) Identity t b -- | A Prism l is a Traversal that can also be -- turned around with re to obtain a Getter in the opposite -- direction. -- -- There are two laws that a Prism should satisfy: -- -- First, if I re or review a value with a Prism and -- then preview or use (^?), I will get it back: -- --

--   preview l (review l b) ≡ Just b
--

-- -- 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: -- -- If preview l s ≡ Just a then -- review l a ≡ s -- -- These two laws imply that the Traversal laws hold for every -- Prism and that we traverse at most 1 element: -- --

--   lengthOf l x <= 1
--

-- -- It may help to think of this as a Iso that can be partial in -- one direction. -- -- Every Prism is a valid Traversal. -- -- Every Iso is a valid Prism. -- -- For example, you might have a Prism' Integer -- Natural allows you to always go from a Natural to -- an Integer, and provide you with tools to check if an -- Integer is a Natural and/or to edit one if it is. -- --

--   nat :: Prism' Integer Natural
--   nat = prism toInteger $ \ i ->
--      if i < 0
--      then Left i
--      else Right (fromInteger i)
--

-- -- Now we can ask if an Integer is a Natural. -- --

--   >>> 5^?nat
--   Just 5
--

-- --

--   >>> (-5)^?nat
--   Nothing
--

-- -- We can update the ones that are: -- --

--   >>> (-3,4) & both.nat *~ 2
--   (-3,8)
--

-- -- And we can then convert from a Natural to an Integer. -- --

--   >>> 5 ^. re nat -- :: Natural
--   5
--

-- -- Similarly we can use a Prism to traverse the -- Left half of an Either: -- --

--   >>> Left "hello" & _Left %~ length
--   Left 5
--

-- -- or to construct an Either: -- --

--   >>> 5^.re _Left
--   Left 5
--

-- -- such that if you query it with the Prism, you will get your -- original input back. -- --

--   >>> 5^.re _Left ^? _Left
--   Just 5
--

-- -- Another interesting way to think of a Prism is as the -- categorical dual of a Lens -- a co-Lens, so to speak. -- This is what permits the construction of outside. -- -- Note: Composition with a Prism is index-preserving. type Prism s t a b = forall (p :: * -> * -> *) (f :: * -> *). (Choice p, Applicative f) => p a f b -> p s f t -- | A Simple Prism. type Prism' s a = Prism s s a a -- | A witness that (a ~ s, b ~ t). -- -- Note: Composition with an Equality is index-preserving. type Equality (s :: k1) (t :: k2) (a :: k1) (b :: k2) = forall k3 (p :: k1 -> k3 -> Type) (f :: k2 -> k3). () => p a f b -> p s f t -- | A Simple Equality. type Equality' (s :: k2) (a :: k2) = Equality s s a a -- | Composable asTypeOf. Useful for constraining excess -- polymorphism, foo . (id :: As Int) . bar. type As (a :: k2) = Equality' a a -- | A Getter describes how to retrieve a single value in a way that -- can be composed with other LensLike constructions. -- -- Unlike a Lens a Getter is read-only. Since a -- Getter cannot be used to write back there are no Lens -- laws that can be applied to it. In fact, it is isomorphic to an -- arbitrary function from (s -> a). -- -- Moreover, a Getter can be used directly as a Fold, since -- it just ignores the Applicative. type Getter s a = forall (f :: * -> *). (Contravariant f, Functor f) => a -> f a -> s -> f s -- | Every IndexedGetter is a valid IndexedFold and can be -- used for Getting like a Getter. type IndexedGetter i s a = forall (p :: * -> * -> *) (f :: * -> *). (Indexable i p, Contravariant f, Functor f) => p a f a -> s -> f s -- | An IndexPreservingGetter can be used as a Getter, but -- when composed with an IndexedTraversal, IndexedFold, or -- IndexedLens yields an IndexedFold, IndexedFold or -- IndexedGetter respectively. type IndexPreservingGetter s a = forall (p :: * -> * -> *) (f :: * -> *). (Conjoined p, Contravariant f, Functor f) => p a f a -> p s f s -- | A Fold describes how to retrieve multiple values in a way that -- can be composed with other LensLike constructions. -- -- A Fold s a provides a structure with operations very -- similar to those of the Foldable typeclass, see -- foldMapOf and the other Fold combinators. -- -- By convention, if there exists a foo method that expects a -- Foldable (f a), then there should be a fooOf -- method that takes a Fold s a and a value of type -- s. -- -- A Getter is a legal Fold that just ignores the supplied -- Monoid. -- -- Unlike a Traversal a Fold is read-only. Since a -- Fold cannot be used to write back there are no Lens laws -- that apply. type Fold s a = forall (f :: * -> *). (Contravariant f, Applicative f) => a -> f a -> s -> f s -- | Every IndexedFold is a valid Fold and can be used for -- Getting. type IndexedFold i s a = forall (p :: * -> * -> *) (f :: * -> *). (Indexable i p, Contravariant f, Applicative f) => p a f a -> s -> f s -- | An IndexPreservingFold can be used as a Fold, but when -- composed with an IndexedTraversal, IndexedFold, or -- IndexedLens yields an IndexedFold respectively. type IndexPreservingFold s a = forall (p :: * -> * -> *) (f :: * -> *). (Conjoined p, Contravariant f, Applicative f) => p a f a -> p s f s -- | A relevant Fold (aka Fold1) has one or more targets. type Fold1 s a = forall (f :: * -> *). (Contravariant f, Apply f) => a -> f a -> s -> f s type IndexedFold1 i s a = forall (p :: * -> * -> *) (f :: * -> *). (Indexable i p, Contravariant f, Apply f) => p a f a -> s -> f s type IndexPreservingFold1 s a = forall (p :: * -> * -> *) (f :: * -> *). (Conjoined p, Contravariant f, Apply f) => p a f a -> p s f s -- | A Simple Lens, Simple Traversal, ... can -- be used instead of a Lens,Traversal, ... whenever the -- type variables don't change upon setting a value. -- --

--   _imagPart :: Simple Lens (Complex a) a
--   traversed :: Simple (IndexedTraversal Int) [a] a
--

-- -- Note: To use this alias in your own code with LensLike -- f or Setter, you may have to turn on -- LiberalTypeSynonyms. -- -- This is commonly abbreviated as a "prime" marker, e.g. -- Lens' = Simple Lens. type Simple (f :: k -> k -> k1 -> k1 -> k2) (s :: k) (a :: k1) = f s s a a -- | A valid Optic l should satisfy the laws: -- --

--   l pure ≡ pure
--   l (Procompose f g) = Procompose (l f) (l g)
--

-- -- This gives rise to the laws for Equality, Iso, -- Prism, Lens, Traversal, Traversal1, -- Setter, Fold, Fold1, and Getter as well -- along with their index-preserving variants. -- --

--   type LensLike f s t a b = Optic (->) f s t a b
--

type Optic (p :: k1 -> k -> *) (f :: k2 -> k) (s :: k1) (t :: k2) (a :: k1) (b :: k2) = p a f b -> p s f t -- |

--   type Optic' p f s a = Simple (Optic p f) s a
--

type Optic' (p :: k1 -> k -> *) (f :: k1 -> k) (s :: k1) (a :: k1) = Optic p f s s a a -- |

--   type LensLike f s t a b = Optical (->) (->) f s t a b
--

-- --

--   type Over p f s t a b = Optical p (->) f s t a b
--

-- --

--   type Optic p f s t a b = Optical p p f s t a b
--

type Optical (p :: k2 -> k -> *) (q :: k1 -> k -> *) (f :: k3 -> k) (s :: k1) (t :: k3) (a :: k2) (b :: k3) = p a f b -> q s f t -- |

--   type Optical' p q f s a = Simple (Optical p q f) s a
--

type Optical' (p :: k1 -> k -> *) (q :: k1 -> k -> *) (f :: k1 -> k) (s :: k1) (a :: k1) = Optical p q f s s a a -- | Many combinators that accept a Lens can also accept a -- Traversal in limited situations. -- -- They do so by specializing the type of Functor that they -- require of the caller. -- -- If a function accepts a LensLike f s t a b for some -- Functor f, then they may be passed a Lens. -- -- Further, if f is an Applicative, they may also be -- passed a Traversal. type LensLike (f :: k -> *) s (t :: k) a (b :: k) = a -> f b -> s -> f t -- |

--   type LensLike' f = Simple (LensLike f)
--

type LensLike' (f :: * -> *) s a = LensLike f s s a a -- | Convenient alias for constructing indexed lenses and their ilk. type IndexedLensLike i (f :: k -> *) s (t :: k) a (b :: k) = forall (p :: * -> * -> *). Indexable i p => p a f b -> s -> f t -- | Convenient alias for constructing simple indexed lenses and their ilk. type IndexedLensLike' i (f :: * -> *) s a = IndexedLensLike i f s s a a -- | This is a convenient alias for use when you need to consume either -- indexed or non-indexed lens-likes based on context. type Over (p :: k -> * -> *) (f :: k1 -> *) s (t :: k1) (a :: k) (b :: k1) = p a f b -> s -> f t -- | This is a convenient alias for use when you need to consume either -- indexed or non-indexed lens-likes based on context. -- --

--   type Over' p f = Simple (Over p f)
--

type Over' (p :: * -> * -> *) (f :: * -> *) s a = Over p f s s a a -- | Anything Settable must be isomorphic to the Identity -- Functor. class (Applicative f, Distributive f, Traversable f) => Settable (f :: * -> *) -- | This is a profunctor used internally to implement Review -- -- It plays a role similar to that of Accessor or Const -- do for Control.Lens.Getter retagged :: (Profunctor p, Bifunctor p) => p a b -> p s b -- | This class is provided mostly for backwards compatibility with lens -- 3.8, but it can also shorten type signatures. class (Profunctor p, Bifunctor p) => Reviewable (p :: * -> * -> *) -- | This provides a way to peek at the internal structure of a -- Traversal or IndexedTraversal data Magma i t b a -- | This data type represents a path-compressed copy of one level of a -- source data structure. We can safely use path-compression because we -- know the depth of the tree. -- -- Path compression is performed by viewing a Level as a PATRICIA -- trie of the paths into the structure to leaves at a given depth, -- similar in many ways to a IntMap, but unlike a regular PATRICIA -- trie we do not need to store the mask bits merely the depth of the -- fork. -- -- One invariant of this structure is that underneath a Two node -- you will not find any Zero nodes, so Zero can only occur -- at the root. data Level i a -- | This class provides a generalized notion of list reversal extended to -- other containers. class Reversing t reversing :: Reversing t => t -> t -- | This is used to characterize a Traversal. -- -- a.k.a. indexed Cartesian store comonad, indexed Kleene store comonad, -- or an indexed FunList. -- -- http://twanvl.nl/blog/haskell/non-regular1 -- -- A Bazaar is like a Traversal that has already been -- applied to some structure. -- -- Where a Context a b t holds an a and a -- function from b to t, a Bazaar a b t -- holds N as and a function from N -- bs to t, (where N might be infinite). -- -- Mnemonically, a Bazaar holds many stores and you can easily add -- more. -- -- This is a final encoding of Bazaar. newtype Bazaar (p :: * -> * -> *) a b t Bazaar :: forall (f :: * -> *). Applicative f => p a f b -> f t -> Bazaar a b t [runBazaar] :: Bazaar a b t -> forall (f :: * -> *). Applicative f => p a f b -> f t -- | This alias is helpful when it comes to reducing repetition in type -- signatures. -- --

--   type Bazaar' p a t = Bazaar p a a t
--

type Bazaar' (p :: * -> * -> *) a = Bazaar p a a -- | This is used to characterize a Traversal. -- -- a.k.a. indexed Cartesian store comonad, indexed Kleene store comonad, -- or an indexed FunList. -- -- http://twanvl.nl/blog/haskell/non-regular1 -- -- A Bazaar1 is like a Traversal that has already been -- applied to some structure. -- -- Where a Context a b t holds an a and a -- function from b to t, a Bazaar1 a b -- t holds N as and a function from N -- bs to t, (where N might be infinite). -- -- Mnemonically, a Bazaar1 holds many stores and you can easily -- add more. -- -- This is a final encoding of Bazaar1. newtype Bazaar1 (p :: * -> * -> *) a b t Bazaar1 :: forall (f :: * -> *). Apply f => p a f b -> f t -> Bazaar1 a b t [runBazaar1] :: Bazaar1 a b t -> forall (f :: * -> *). Apply f => p a f b -> f t -- | This alias is helpful when it comes to reducing repetition in type -- signatures. -- --

--   type Bazaar1' p a t = Bazaar1 p a a t
--

type Bazaar1' (p :: * -> * -> *) a = Bazaar1 p a a -- | The indexed store can be used to characterize a Lens and is -- used by cloneLens. -- -- Context a b t is isomorphic to newtype -- Context a b t = Context { runContext :: forall f. -- Functor f => (a -> f b) -> f t }, and to -- exists s. (s, Lens s t a b). -- -- A Context is like a Lens that has already been applied -- to a some structure. data Context a b t Context :: b -> t -> a -> Context a b t -- |

--   type Context' a s = Context a a s
--

type Context' a = Context a a -- | When composed with an IndexedFold or -- IndexedTraversal this yields an (Indexed) -- Fold of the indices. asIndex :: (Indexable i p, Contravariant f, Functor f) => p i f i -> Indexed i s f s -- | Fold a container with indices returning both the indices and the -- values. -- -- The result is only valid to compose in a Traversal, if you -- don't edit the index as edits to the index have no effect. -- --

--   >>> [10, 20, 30] ^.. ifolded . withIndex
--   [(0,10),(1,20),(2,30)]
--

-- --

--   >>> [10, 20, 30] ^.. ifolded . withIndex . alongside negated (re _Show)
--   [(0,"10"),(-1,"20"),(-2,"30")]
--

withIndex :: (Indexable i p, Functor f) => p (i, s) f (j, t) -> Indexed i s f t -- | Transform a Traversal into an IndexedTraversal or a -- Fold into an IndexedFold, etc. -- -- This combinator is like indexing except that it handles large -- traversals and folds gracefully. -- --

--   indexing64 :: Traversal s t a b -> IndexedTraversal Int64 s t a b
--   indexing64 :: Prism s t a b     -> IndexedTraversal Int64 s t a b
--   indexing64 :: Lens s t a b      -> IndexedLens Int64 s t a b
--   indexing64 :: Iso s t a b       -> IndexedLens Int64 s t a b
--   indexing64 :: Fold s a          -> IndexedFold Int64 s a
--   indexing64 :: Getter s a        -> IndexedGetter Int64 s a
--

-- --

--   indexing64 :: Indexable Int64 p => LensLike (Indexing64 f) s t a b -> Over p f s t a b
--

indexing64 :: Indexable Int64 p => a -> Indexing64 f b -> s -> Indexing64 f t -> p a f b -> s -> f t -- | Transform a Traversal into an IndexedTraversal or a -- Fold into an IndexedFold, etc. -- --

--   indexing :: Traversal s t a b -> IndexedTraversal Int s t a b
--   indexing :: Prism s t a b     -> IndexedTraversal Int s t a b
--   indexing :: Lens s t a b      -> IndexedLens Int  s t a b
--   indexing :: Iso s t a b       -> IndexedLens Int s t a b
--   indexing :: Fold s a          -> IndexedFold Int s a
--   indexing :: Getter s a        -> IndexedGetter Int s a
--

-- --

--   indexing :: Indexable Int p => LensLike (Indexing f) s t a b -> Over p f s t a b
--

indexing :: Indexable Int p => a -> Indexing f b -> s -> Indexing f t -> p a f b -> s -> f t -- | This is a Profunctor that is both Corepresentable by -- f and Representable by g such that f -- is left adjoint to g. From this you can derive a lot of -- structure due to the preservation of limits and colimits. class (Choice p, Corepresentable p, Comonad Corep p, Traversable Corep p, Strong p, Representable p, Monad Rep p, MonadFix Rep p, Distributive Rep p, Costrong p, ArrowLoop p, ArrowApply p, ArrowChoice p, Closed p) => Conjoined (p :: * -> * -> *) -- | Conjoined is strong enough to let us distribute every -- Conjoined Profunctor over every Haskell Functor. -- This is effectively a generalization of fmap. distrib :: (Conjoined p, Functor f) => p a b -> p f a f b -- | This permits us to make a decision at an outermost point about whether -- or not we use an index. -- -- Ideally any use of this function should be done in such a way so that -- you compute the same answer, but this cannot be enforced at the type -- level. conjoined :: Conjoined p => p ~ ((->) :: * -> * -> *) -> q a -> b r -> q p a b r -> q p a b r -- | This class permits overloading of function application for things that -- also admit a notion of a key or index. class Conjoined p => Indexable i (p :: * -> * -> *) -- | Build a function from an indexed function. indexed :: Indexable i p => p a b -> i -> a -> b -- | A function with access to a index. This constructor may be useful when -- you need to store an Indexable in a container to avoid -- ImpredicativeTypes. -- --

--   index :: Indexed i a b -> i -> a -> b
--

newtype Indexed i a b Indexed :: i -> a -> b -> Indexed i a b [runIndexed] :: Indexed i a b -> i -> a -> b -- | Used internally by traverseOf_ and the like. -- -- The argument a of the result should not be used! data Traversed a (f :: * -> *) -- | Used internally by mapM_ and the like. -- -- The argument a of the result should not be used! -- -- See 4.16 Changelog entry for the explanation of "why not Apply f -- =>"? data Sequenced a (m :: * -> *) -- | Used for preview. data Leftmost a -- | Used for lastOf. data Rightmost a class (Foldable1 t, Traversable t) => Traversable1 (t :: * -> *) traverse1 :: (Traversable1 t, Apply f) => a -> f b -> t a -> f t b -- | Fold a value using its Foldable instance using explicitly -- provided Monoid operations. This is like fold where -- the Monoid instance can be manually specified. -- --

--   foldBy mappend mempty ≡ fold
--

-- --

--   >>> foldBy (++) [] ["hello","world"]
--   "helloworld"
--

foldBy :: Foldable t => a -> a -> a -> a -> t a -> a -- | Fold a value using its Foldable instance using explicitly -- provided Monoid operations. This is like foldMap where -- the Monoid instance can be manually specified. -- --

--   foldMapBy mappend mempty ≡ foldMap
--

-- --

--   >>> foldMapBy (+) 0 length ["hello","world"]
--   10
--

foldMapBy :: Foldable t => r -> r -> r -> r -> a -> r -> t a -> r -- | Traverse a container using its Traversable instance using -- explicitly provided Applicative operations. This is like -- traverse where the Applicative instance can be manually -- specified. traverseBy :: Traversable t => forall x. () => x -> f x -> forall x y. () => f x -> y -> f x -> f y -> a -> f b -> t a -> f t b -- | Sequence a container using its Traversable instance using -- explicitly provided Applicative operations. This is like -- sequence where the Applicative instance can be manually -- specified. sequenceBy :: Traversable t => forall x. () => x -> f x -> forall x y. () => f x -> y -> f x -> f y -> t f a -> f t a -- | The generalization of Costar of Functor that is strong -- with respect to Either. -- -- Note: This is also a notion of strength, except with regards to -- another monoidal structure that we can choose to equip Hask with: the -- cocartesian coproduct. class Profunctor p => Choice (p :: * -> * -> *) -- | Laws: -- --

--   left' ≡ dimap swapE swapE . right' where
--     swapE :: Either a b -> Either b a
--     swapE = either Right Left
--   rmap Left ≡ lmap Left . left'
--   lmap (right f) . left' ≡ rmap (right f) . left'
--   left' . left' ≡ dimap assocE unassocE . left' where
--     assocE :: Either (Either a b) c -> Either a (Either b c)
--     assocE (Left (Left a)) = Left a
--     assocE (Left (Right b)) = Right (Left b)
--     assocE (Right c) = Right (Right c)
--     unassocE :: Either a (Either b c) -> Either (Either a b) c
--     unassocE (Left a) = Left (Left a)
--     unassocE (Right (Left b) = Left (Right b)
--     unassocE (Right (Right c)) = Right c)
--

left' :: Choice p => p a b -> p Either a c Either b c -- | Laws: -- --

--   right' ≡ dimap swapE swapE . left' where
--     swapE :: Either a b -> Either b a
--     swapE = either Right Left
--   rmap Right ≡ lmap Right . right'
--   lmap (left f) . right' ≡ rmap (left f) . right'
--   right' . right' ≡ dimap unassocE assocE . right' where
--     assocE :: Either (Either a b) c -> Either a (Either b c)
--     assocE (Left (Left a)) = Left a
--     assocE (Left (Right b)) = Right (Left b)
--     assocE (Right c) = Right (Right c)
--     unassocE :: Either a (Either b c) -> Either (Either a b) c
--     unassocE (Left a) = Left (Left a)
--     unassocE (Right (Left b) = Left (Right b)
--     unassocE (Right (Right c)) = Right c)
--

right' :: Choice p => p a b -> p Either c a Either c b data Document Document :: Prologue -> Element -> [Miscellaneous] -> Document [documentPrologue] :: Document -> Prologue [documentRoot] :: Document -> Element [documentEpilogue] :: Document -> [Miscellaneous] data Node NodeElement :: Element -> Node NodeInstruction :: Instruction -> Node NodeContent :: Text -> Node NodeComment :: Text -> Node data Element Element :: Name -> Map Name Text -> [Node] -> Element [elementName] :: Element -> Name [elementAttributes] :: Element -> Map Name Text [elementNodes] :: Element -> [Node] -- | A fully qualified name. -- -- Prefixes are not semantically important; they are included only to -- simplify pass-through parsing. When comparing names with Eq or -- Ord methods, prefixes are ignored. -- -- The IsString instance supports Clark notation; see -- http://www.jclark.com/xml/xmlns.htm and -- http://infohost.nmt.edu/tcc/help/pubs/pylxml/etree-QName.html. -- Use the OverloadedStrings language extension for very simple -- Name construction: -- --

--   myname :: Name
--   myname = "{http://example.com/ns/my-namespace}my-name"
--

data Name Name :: Text -> Maybe Text -> Maybe Text -> Name [nameLocalName] :: Name -> Text [nameNamespace] :: Name -> Maybe Text [namePrefix] :: Name -> Maybe Text data Instruction Instruction :: Text -> Text -> Instruction [instructionTarget] :: Instruction -> Text [instructionData] :: Instruction -> Text -- | Combine two Traversals just like XPath's slash. Identical to -- (...). -- --

--   l ./ m ≡ l . plate . m
--

(./) :: (Applicative f, Plated c) => LensLike f s t c c -> Over p f c c a b -> Over p f s t a b infixr 9 ./ -- | Traverse all comments of the element. comment :: Traversal' Element Text -- | Traverse all contents of the element. text :: Traversal' Element Text attributeIs :: Name -> Text -> Traversal' Element Element attributeSatisfies :: Name -> Text -> Bool -> Traversal' Element Element -- | Traverse elements which has the specified name. el :: Name -> Traversal' Element Element -- | Old name for named ell :: Text -> Traversal' Element Element -- | Traverse elements which has the specified *local* name -- (case-insensitive). named :: CI Text -> Traversal' Element Element -- | Traverse itself with its all children. Rewriting subnodes of each -- children will break a traversal law. entire :: Traversal' Element Element attribute :: Name -> Lens' Element Maybe Text attr :: Name -> Traversal' Element Text nodes :: Lens' Element [Node] attrs :: Lens' Element Map Name Text localName :: Lens' Element Text name :: Lens' Element Name _Content :: Prism' Node Text _Element :: Prism' Node Element _namePrefix :: Lens' Name Maybe Text _nameNamespace :: Lens' Name Maybe Text _nameLocalName :: Lens' Name Text _instructionData :: Lens' Instruction Text _instructionTarget :: Lens' Instruction Text doctype :: Lens' Prologue Maybe Doctype epilogue :: Lens' Document [Miscellaneous] -- | The root element of the document. root :: Lens' Document Element prologue :: Lens' Document Prologue class AsInstruction t _Instruction :: AsInstruction t => Prism' t Instruction class AsComment t _Comment :: AsComment t => Prism' t Text module Data.Microformats2.Parser.HtmlUtil data HtmlContentMode Unsafe :: HtmlContentMode Escape :: HtmlContentMode Sanitize :: HtmlContentMode getInnerHtml :: Maybe URI -> Element -> Maybe Text getInnerHtmlSanitized :: Maybe URI -> Element -> Maybe Text getInnerTextRaw :: Element -> Maybe Text getInnerTextWithImgs :: Element -> Maybe Text getProcessedInnerHtml :: HtmlContentMode -> Maybe URI -> Element -> Maybe Text deduplicateElements :: [Element] -> [Element] unescapeHtml :: Text -> Text instance GHC.Classes.Eq Data.Microformats2.Parser.HtmlUtil.HtmlContentMode instance GHC.Show.Show Data.Microformats2.Parser.HtmlUtil.HtmlContentMode module Data.Microformats2.Parser.Property unwrapName :: (Name, α) -> (Text, α) classes :: Element -> [Text] isPClass :: Text -> Bool isUClass :: Text -> Bool isEClass :: Text -> Bool isDtClass :: Text -> Bool isPropertyClass :: Text -> Bool isMf2Class :: Text -> Bool isProperty :: Element -> Bool propertyElements :: Traversal' Element Element hasOneClass :: [String] -> Traversal' Element Element hasClass :: String -> Traversal' Element Element getOnlyChildren :: Element -> [Element] getOnlyChild :: Name -> Element -> Maybe Element getOnlyOfType :: Name -> Element -> Maybe Element els :: [Name] -> Traversal' Element Element getAbbrTitle :: Element -> Maybe Text getDataInputValue :: Element -> Maybe Text getImgSrc :: Element -> Maybe Text getObjectData :: Element -> Maybe Text getImgAreaAlt :: Element -> Maybe Text getAAreaHref :: Element -> Maybe Text getImgAudioVideoSourceSrc :: Element -> Maybe Text getTimeInsDelDatetime :: Element -> Maybe Text getOnlyChildImgAreaAlt :: Element -> Maybe Text getOnlyChildAbbrTitle :: Element -> Maybe Text getOnlyOfTypeImgSrc :: Element -> Maybe Text getOnlyOfTypeObjectData :: Element -> Maybe Text getOnlyOfTypeAAreaHref :: Element -> Maybe Text extractValue :: Element -> Maybe Text extractValueTitle :: Element -> Maybe Text extractValueClassPattern :: [Element -> Maybe Text] -> Element -> Maybe [Text] extractValueClassPatternConcat :: [Element -> Maybe Text] -> Element -> Maybe Text extractValueClassPatternDate :: [Element -> Maybe Text] -> Element -> Maybe Text extractP :: Element -> Maybe Text extractU :: Element -> Maybe (Text, Bool) extractDt :: Element -> Maybe Text implyProperty :: String -> Element -> Maybe Text module Data.Microformats2.Parser data Mf2ParserSettings Mf2ParserSettings :: HtmlContentMode -> Maybe URI -> Mf2ParserSettings [htmlMode] :: Mf2ParserSettings -> HtmlContentMode [baseUri] :: Mf2ParserSettings -> Maybe URI data HtmlContentMode Unsafe :: HtmlContentMode Escape :: HtmlContentMode Sanitize :: HtmlContentMode -- | Parses Microformats 2 from an HTML Element into a JSON Value. parseMf2 :: Mf2ParserSettings -> Element -> Value extractProperty :: Mf2ParserSettings -> Text -> Element -> Value documentRoot :: Document -> Element parseLBS :: ByteString -> Document sinkDoc :: MonadThrow m => ConduitT ByteString o m Document instance GHC.Classes.Eq Data.Microformats2.Parser.Mf2ParserSettings instance GHC.Show.Show Data.Microformats2.Parser.Mf2ParserSettings instance Data.Default.Class.Default Data.Microformats2.Parser.Mf2ParserSettings