| Safe Haskell | Safe-Inferred |
|---|---|
| Language | Haskell2010 |
Lens.Family
Description
This is the main module for end-users of lens-families-core. If you are not building your own optics such as lenses, traversals, grates, etc., but just using optics made by others, this is the only module you need.
Synopsis
- to :: Phantom f => (s -> a) -> LensLike f s t a b
- view :: FoldLike a s t a b -> s -> a
- (^.) :: s -> FoldLike a s t a b -> a
- folding :: (Foldable g, Phantom f, Applicative f) => (s -> g a) -> LensLike f s t a b
- views :: FoldLike r s t a b -> (a -> r) -> s -> r
- (^..) :: s -> FoldLike [a] s t a b -> [a]
- (^?) :: s -> FoldLike (First a) s t a b -> Maybe a
- toListOf :: FoldLike [a] s t a b -> s -> [a]
- allOf :: FoldLike All s t a b -> (a -> Bool) -> s -> Bool
- anyOf :: FoldLike Any s t a b -> (a -> Bool) -> s -> Bool
- firstOf :: FoldLike (First a) s t a b -> s -> Maybe a
- lastOf :: FoldLike (Last a) s t a b -> s -> Maybe a
- sumOf :: Num a => FoldLike (Sum a) s t a b -> s -> a
- productOf :: Num a => FoldLike (Product a) s t a b -> s -> a
- lengthOf :: Num r => FoldLike (Sum r) s t a b -> s -> r
- nullOf :: FoldLike All s t a b -> s -> Bool
- matching :: LensLike (Either a) s t a b -> s -> Either t a
- over :: ASetter s t a b -> (a -> b) -> s -> t
- (%~) :: ASetter s t a b -> (a -> b) -> s -> t
- set :: ASetter s t a b -> b -> s -> t
- (.~) :: ASetter s t a b -> b -> s -> t
- review :: GrateLike (Constant () :: Type -> Type) s t a b -> b -> t
- zipWithOf :: GrateLike (Prod Identity Identity) s t a b -> (a -> a -> b) -> s -> s -> t
- degrating :: AGrate s t a b -> ((s -> a) -> b) -> t
- under :: AResetter s t a b -> (a -> b) -> s -> t
- reset :: AResetter s t a b -> b -> s -> t
- (&) :: s -> (s -> t) -> t
- (+~) :: Num a => ASetter s t a a -> a -> s -> t
- (*~) :: Num a => ASetter s t a a -> a -> s -> t
- (-~) :: Num a => ASetter s t a a -> a -> s -> t
- (//~) :: Fractional a => ASetter s t a a -> a -> s -> t
- (&&~) :: ASetter s t Bool Bool -> Bool -> s -> t
- (||~) :: ASetter s t Bool Bool -> Bool -> s -> t
- (<>~) :: Monoid a => ASetter s t a a -> a -> s -> t
- type AdapterLike (f :: Type -> Type) (g :: Type -> Type) s t a b = (g a -> f b) -> g s -> f t
- type AdapterLike' (f :: Type -> Type) (g :: Type -> Type) s a = (g a -> f a) -> g s -> f s
- type LensLike (f :: Type -> Type) s t a b = (a -> f b) -> s -> f t
- type LensLike' (f :: Type -> Type) s a = (a -> f a) -> s -> f s
- type FoldLike r s t a b = LensLike (Constant r :: Type -> Type) s t a b
- type FoldLike' r s a = LensLike' (Constant r :: Type -> Type) s a
- type GrateLike (g :: Type -> Type) s t a b = (g a -> b) -> g s -> t
- type GrateLike' (g :: Type -> Type) s a = (g a -> a) -> g s -> s
- type AGrate s t a b = GrateLike (PCont b a) s t a b
- type AGrate' s a = GrateLike' (PCont a a) s a
- type ASetter s t a b = LensLike Identity s t a b
- type ASetter' s a = LensLike' Identity s a
- type AResetter s t a b = GrateLike Identity s t a b
- type AResetter' s a = GrateLike' Identity s a
- data PCont i j a
- data First a
- data Last a
- class Functor f => Phantom (f :: Type -> Type)
- data Constant a (b :: k)
- data Identity a
- type Prod = Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type
- data All
- data Any
- data Sum a
- data Product a
Lenses
This module provides ^. for accessing fields and .~ and %~ for setting and modifying fields.
Lenses are composed with . from the Prelude and id is the identity lens.
Lens composition in this library enjoys the following identities.
x^.l1.l2 === x^.l1^.l2
l1.l2 %~ f === l1 %~ l2 %~ f
The identity lens behaves as follows.
x^.id === x
id %~ f === f
The & operator, allows for a convenient way to sequence record updating:
record & l1 .~ value1 & l2 .~ value2
Lenses are implemented in van Laarhoven style.
Lenses have type Functor f => (a -> f a) -> s -> f sFunctor f => (a i -> f (a j)) -> s i -> f (s j)
Keep in mind that lenses and lens families can be used directly for functorial updates.
For example, _2 id gives you strength.
_2 id :: Functor f => (a, f b) -> f (a, b)
Here is an example of code that uses the Maybe functor to preserves sharing during update when possible.
-- | 'sharedUpdate' returns the *identical* object if the update doesn't change anything.
-- This is useful for preserving sharing.
sharedUpdate :: Eq a => LensLike' Maybe s a -> (a -> a) -> s -> s
sharedUpdate l f s = fromMaybe s (l f' s)
where
f' a | b == a = Nothing
| otherwise = Just b
where
b = f aTraversals
^. can be used with traversals to access monoidal fields.
The result will be a mconcat of all the fields referenced.
The various fooOf functions can be used to access different monoidal summaries of some kinds of values.
^? can be used to access the first value of a traversal.
Nothing is returned when the traversal has no references.
^.. can be used with a traversals and will return a list of all fields referenced.
When .~ is used with a traversal, all referenced fields will be set to the same value, and when %~ is used with a traversal, all referenced fields will be modified with the same function.
A variant of ^? call matching returns Either a Right value which is the first value of the traversal, or a Left value which is a "proof" that the traversal has no elements.
The "proof" consists of the original input structure, but in the case of polymorphic families, the type parameter is replaced with a fresh type variable, thus proving that the type parameter was unused.
Like all optics, traversals can be composed with ., and because every lens is automatically a traversal, lenses and traversals can be composed with . yielding a traversal.
Traversals are implemented in van Laarhoven style.
Traversals have type Applicative f => (a -> f a) -> s -> f sApplicative f => (a i -> f (a j)) -> s i -> f (s j)
Grates
zipWithOf can be used with grates to zip two structure together provided a binary operation.
under can be used to modify each value in a structure according to a function. This works analogous to how over works for lenses and traversals.
review can be used with grates to construct a constant grate from a single value. This is like a 0-ary zipWith function.
degrating can be used to build higher arity zipWithOf functions:
zipWith3Of :: AGrate s t a b -> (a -> a -> a -> b) -> s -> s -> s -> t zipWith3Of l f s1 s2 s3 = degrating l (\k -> f (k s1) (k s2) (k s3))
Like all optics, grates can be composed with ., and id is the identity grate.
Grates are implemented in van Laarhoven style.
Grates have type Functor g => (g a -> a) -> g s -> sFunctor g => (g (a i) -> a j) -> g (s i) -> s j
Keep in mind that grates and grate families can be used directly for functorial zipping. For example,
both sum :: Num a => [(a, a)] -> (a, a)
will take a list of pairs return the sum of the first components and the sum of the second components. For another example,
cod id :: Functor f => f (r -> a) -> r -> f a
will turn a functor full of functions into a function returning a functor full of results.
Adapters, Grids, and Prisms
The Adapter, Prism, and Grid optics are all AdapterLike optics and typically not used directly, but either converted to a LensLike optic using under, or into a GrateLike optic using over.
See under and over for details about which conversions are possible.
These optics are implemented in van Laarhoven style.
- Adapters have type
(and Adapters families have typeFunctorf,Functorg) => (g a -> f a) -> g s -> f s(.Functorf,Functorg) => (g (a i) -> f (a j)) -> g (s i) -> f (s j) - Grids have type
(and Grids families have typeApplicativef,Functorg) => (g a -> f a) -> g s -> f s(.Applicativef,Functorg) => (g (a i) -> f (a j)) -> g (s i) -> f (s j) - Prisms have type
(and Prisms families have typeApplicativef,Traversableg) => (g a -> f a) -> g s -> f s(.Applicativef,Traversableg) => (g (a i) -> f (a j)) -> g (s i) -> f (s j)
Keep in mind that these optics and their families can sometimes be used directly, without using over and under. Sometimes you can take advantage of the fact that
LensLike f (g s) t (g a) b == AdapterLike f g s t a b == GrateLike g s (f t) a (f b)
For example, if you have a grid for your structure to another type that has an Arbitray instance, such as grid from a custom word type to Bool, e.g. myWordBitVector :: (Applicative f, Functor g) => AdapterLike' f g MyWord Bool, you can use the grid to create an Arbitrary instance for your structure by directly applying review:
instance Arbitrary MyWord where arbitrary = review myWordBitVector arbitrary
Building and Finding Optics
To build your own optics, see Lens.Family.Unchecked.
For stock optics, see Lens.Family.Stock.
References:
Documentation
to :: Phantom f => (s -> a) -> LensLike f s t a b Source #
to :: (s -> a) -> Getter s t a b
to promotes a projection function to a read-only lens called a getter.
To demote a lens to a projection function, use the section (^.l) or view l.
>>>(3 :+ 4, "example")^._1.to(abs)5.0 :+ 0.0
view :: FoldLike a s t a b -> s -> a Source #
view :: Getter s t a b -> s -> a
Demote a lens or getter to a projection function.
view :: Monoid a => Fold s t a b -> s -> a
Returns the monoidal summary of a traversal or a fold.
(^.) :: s -> FoldLike a s t a b -> a infixl 8 Source #
(^.) :: s -> Getter s t a b -> a
Access the value referenced by a getter or lens.
(^.) :: Monoid a => s -> Fold s t a b -> a
Access the monoidal summary referenced by a traversal or a fold.
folding :: (Foldable g, Phantom f, Applicative f) => (s -> g a) -> LensLike f s t a b Source #
folding :: (s -> [a]) -> Fold s t a b
folding promotes a "toList" function to a read-only traversal called a fold.
To demote a traversal or fold to a "toList" function use the section (^..l) or toListOf l.
views :: FoldLike r s t a b -> (a -> r) -> s -> r Source #
views :: Monoid r => Fold s t a b -> (a -> r) -> s -> r
Given a fold or traversal, return the foldMap of all the values using the given function.
views :: Getter s t a b -> (a -> r) -> s -> r
views is not particularly useful for getters or lenses, but given a getter or lens, it returns the referenced value passed through the given function.
views l f s = f (view l s)
(^..) :: s -> FoldLike [a] s t a b -> [a] infixl 8 Source #
(^..) :: s -> Fold s t a b -> [a]
Returns a list of all of the referenced values in order.
toListOf :: FoldLike [a] s t a b -> s -> [a] Source #
toListOf :: Fold s t a b -> s -> [a]
Returns a list of all of the referenced values in order.
allOf :: FoldLike All s t a b -> (a -> Bool) -> s -> Bool Source #
allOf :: Fold s t a b -> (a -> Bool) -> s -> Bool
Returns true if all of the referenced values satisfy the given predicate.
anyOf :: FoldLike Any s t a b -> (a -> Bool) -> s -> Bool Source #
anyOf :: Fold s t a b -> (a -> Bool) -> s -> Bool
Returns true if any of the referenced values satisfy the given predicate.
sumOf :: Num a => FoldLike (Sum a) s t a b -> s -> a Source #
sumOf :: Num a => Fold s t a b -> s -> a
Returns the sum of all the referenced values.
productOf :: Num a => FoldLike (Product a) s t a b -> s -> a Source #
productOf :: Num a => Fold s t a b -> s -> a
Returns the product of all the referenced values.
lengthOf :: Num r => FoldLike (Sum r) s t a b -> s -> r Source #
lengthOf :: Num r => Fold s t a b -> s -> r
Counts the number of references in a traversal or fold for the input.
nullOf :: FoldLike All s t a b -> s -> Bool Source #
nullOf :: Fold s t a b -> s -> Bool
Returns true if the number of references in the input is zero.
matching :: LensLike (Either a) s t a b -> s -> Either t a Source #
matching :: Traversal s t a b -> s -> Either t a
Returns Right of the first referenced value.
Returns Left the original value when there are no referenced values.
In case there are no referenced values, the result might have a fresh type parameter, thereby proving the original value had no referenced values.
over :: ASetter s t a b -> (a -> b) -> s -> t Source #
over :: Setter s t a b -> (a -> b) -> s -> t
Demote a setter to a semantic editor combinator.
over :: Prism s t a b -> Reviwer s t a b over :: Grid s t a b -> Grate s t a b over :: Adapter s t a b -> Grate s t a b
Covert an AdapterLike optic into a GrateLike optic.
(.~) :: ASetter s t a b -> b -> s -> t infixr 4 Source #
Set all referenced fields to the given value.
review :: GrateLike (Constant () :: Type -> Type) s t a b -> b -> t Source #
review :: Grate s t a b -> b -> t review :: Reviewer s t a b -> b -> t
zipWithOf :: GrateLike (Prod Identity Identity) s t a b -> (a -> a -> b) -> s -> s -> t Source #
zipWithOf :: Grate s t a b -> (a -> a -> b) -> s -> s -> t
Returns a binary instance of a grate.
zipWithOf l f x y = degrating l (k -> f (k x) (k y))
degrating :: AGrate s t a b -> ((s -> a) -> b) -> t Source #
degrating :: Grate s t a b -> ((s -> a) -> b) -> t
Demote a grate to its normal, higher-order function, form.
degrating . grate = id grate . degrating = id
under :: AResetter s t a b -> (a -> b) -> s -> t Source #
under :: Resetter s t a b -> (a -> b) -> s -> t
Demote a resetter to a semantic editor combinator.
under :: Prism s t a b -> Traversal s t a b under :: Grid s t a b -> Traversal s t a b under :: Adapter s t a b -> Lens s t a b
Covert an AdapterLike optic into a LensLike optic.
Note: this function is unrelated to the lens package's under function.
reset :: AResetter s t a b -> b -> s -> t Source #
reset :: Resetter s t a b -> b -> s -> t
Set all referenced fields to the given value.
Pseudo-imperatives
(//~) :: Fractional a => ASetter s t a a -> a -> s -> t infixr 4 Source #
(<>~) :: Monoid a => ASetter s t a a -> a -> s -> t infixr 4 Source #
Monoidally append a value to all referenced fields.
Types
type AdapterLike (f :: Type -> Type) (g :: Type -> Type) s t a b = (g a -> f b) -> g s -> f t Source #
type GrateLike' (g :: Type -> Type) s a = (g a -> a) -> g s -> s Source #
type AGrate' s a = GrateLike' (PCont a a) s a Source #
type AResetter' s a = GrateLike' Identity s a Source #
class Functor f => Phantom (f :: Type -> Type) Source #
Minimal complete definition
coerce
Instances
| Phantom (Const a :: Type -> Type) Source # | |
Defined in Lens.Family.Phantom | |
| Phantom f => Phantom (AlongsideLeft f a) Source # | |
Defined in Lens.Family.Stock Methods coerce :: AlongsideLeft f a a0 -> AlongsideLeft f a b | |
| Phantom f => Phantom (AlongsideRight f a) Source # | |
Defined in Lens.Family.Stock Methods coerce :: AlongsideRight f a a0 -> AlongsideRight f a b | |
| Phantom g => Phantom (FromG e g) Source # | |
Defined in Lens.Family.Stock | |
| Phantom f => Phantom (Backwards f) Source # | |
Defined in Lens.Family.Phantom | |
| Phantom (Constant a :: Type -> Type) Source # | |
Defined in Lens.Family.Phantom | |
| Phantom g => Phantom (FromF i j g) Source # | |
Defined in Lens.Family.Stock | |
| (Phantom f, Functor g) => Phantom (Compose f g) Source # | |
Defined in Lens.Family.Phantom | |
Re-exports
data Constant a (b :: k) Source #
Constant functor.
Instances
Identity functor and monad. (a non-strict monad)
Examples
>>>fmap (+1) (Identity 0)Identity 1
>>>Identity [1, 2, 3] <> Identity [4, 5, 6]Identity [1,2,3,4,5,6]
>>> do
x <- Identity 10
y <- Identity (x + 5)
pure (x + y)
Identity 25
Since: base-4.8.0.0
Instances
| MonadZip Identity | Since: base-4.8.0.0 | ||||
| Foldable1 Identity | Since: base-4.18.0.0 | ||||
Defined in Data.Foldable1 Methods fold1 :: Semigroup m => Identity m -> m Source # foldMap1 :: Semigroup m => (a -> m) -> Identity a -> m Source # foldMap1' :: Semigroup m => (a -> m) -> Identity a -> m Source # toNonEmpty :: Identity a -> NonEmpty a Source # maximum :: Ord a => Identity a -> a Source # minimum :: Ord a => Identity a -> a Source # head :: Identity a -> a Source # last :: Identity a -> a Source # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Identity a -> b Source # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Identity a -> b Source # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Identity a -> b Source # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Identity a -> b Source # | |||||
| Eq1 Identity | Since: base-4.9.0.0 | ||||
| Ord1 Identity | Since: base-4.9.0.0 | ||||
Defined in Data.Functor.Classes | |||||
| Read1 Identity | Since: base-4.9.0.0 | ||||
Defined in Data.Functor.Classes Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Identity a) Source # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Identity a] Source # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Identity a) Source # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Identity a] Source # | |||||
| Show1 Identity | Since: base-4.9.0.0 | ||||
| NFData1 Identity | Since: deepseq-1.4.3.0 | ||||
Defined in Control.DeepSeq | |||||
| Applicative Identity | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Functor.Identity | |||||
| Functor Identity | Since: base-4.8.0.0 | ||||
| Monad Identity | Since: base-4.8.0.0 | ||||
| MonadFix Identity | Since: base-4.8.0.0 | ||||
| Foldable Identity | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Functor.Identity Methods fold :: Monoid m => Identity m -> m Source # foldMap :: Monoid m => (a -> m) -> Identity a -> m Source # foldMap' :: Monoid m => (a -> m) -> Identity a -> m Source # foldr :: (a -> b -> b) -> b -> Identity a -> b Source # foldr' :: (a -> b -> b) -> b -> Identity a -> b Source # foldl :: (b -> a -> b) -> b -> Identity a -> b Source # foldl' :: (b -> a -> b) -> b -> Identity a -> b Source # foldr1 :: (a -> a -> a) -> Identity a -> a Source # foldl1 :: (a -> a -> a) -> Identity a -> a Source # toList :: Identity a -> [a] Source # null :: Identity a -> Bool Source # length :: Identity a -> Int Source # elem :: Eq a => a -> Identity a -> Bool Source # maximum :: Ord a => Identity a -> a Source # minimum :: Ord a => Identity a -> a Source # | |||||
| Traversable Identity | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Traversable | |||||
| Identical Identity Source # | |||||
Defined in Lens.Family.Identical | |||||
| Generic1 Identity | |||||
Defined in GHC.Internal.Data.Functor.Identity Associated Types
| |||||
| NFData a => NFData (Identity a) | Since: deepseq-1.4.0.0 | ||||
Defined in Control.DeepSeq | |||||
| Monoid a => Monoid (Identity a) | Since: base-4.9.0.0 | ||||
| Semigroup a => Semigroup (Identity a) | Since: base-4.9.0.0 | ||||
| Bits a => Bits (Identity a) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Functor.Identity Methods (.&.) :: Identity a -> Identity a -> Identity a Source # (.|.) :: Identity a -> Identity a -> Identity a Source # xor :: Identity a -> Identity a -> Identity a Source # complement :: Identity a -> Identity a Source # shift :: Identity a -> Int -> Identity a Source # rotate :: Identity a -> Int -> Identity a Source # zeroBits :: Identity a Source # bit :: Int -> Identity a Source # setBit :: Identity a -> Int -> Identity a Source # clearBit :: Identity a -> Int -> Identity a Source # complementBit :: Identity a -> Int -> Identity a Source # testBit :: Identity a -> Int -> Bool Source # bitSizeMaybe :: Identity a -> Maybe Int Source # bitSize :: Identity a -> Int Source # isSigned :: Identity a -> Bool Source # shiftL :: Identity a -> Int -> Identity a Source # unsafeShiftL :: Identity a -> Int -> Identity a Source # shiftR :: Identity a -> Int -> Identity a Source # unsafeShiftR :: Identity a -> Int -> Identity a Source # rotateL :: Identity a -> Int -> Identity a Source # | |||||
| FiniteBits a => FiniteBits (Identity a) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Functor.Identity Methods finiteBitSize :: Identity a -> Int Source # countLeadingZeros :: Identity a -> Int Source # countTrailingZeros :: Identity a -> Int Source # | |||||
| Bounded a => Bounded (Identity a) | Since: base-4.9.0.0 | ||||
| Enum a => Enum (Identity a) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Functor.Identity Methods succ :: Identity a -> Identity a Source # pred :: Identity a -> Identity a Source # toEnum :: Int -> Identity a Source # fromEnum :: Identity a -> Int Source # enumFrom :: Identity a -> [Identity a] Source # enumFromThen :: Identity a -> Identity a -> [Identity a] Source # enumFromTo :: Identity a -> Identity a -> [Identity a] Source # enumFromThenTo :: Identity a -> Identity a -> Identity a -> [Identity a] Source # | |||||
| Floating a => Floating (Identity a) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Functor.Identity Methods exp :: Identity a -> Identity a Source # log :: Identity a -> Identity a Source # sqrt :: Identity a -> Identity a Source # (**) :: Identity a -> Identity a -> Identity a Source # logBase :: Identity a -> Identity a -> Identity a Source # sin :: Identity a -> Identity a Source # cos :: Identity a -> Identity a Source # tan :: Identity a -> Identity a Source # asin :: Identity a -> Identity a Source # acos :: Identity a -> Identity a Source # atan :: Identity a -> Identity a Source # sinh :: Identity a -> Identity a Source # cosh :: Identity a -> Identity a Source # tanh :: Identity a -> Identity a Source # asinh :: Identity a -> Identity a Source # acosh :: Identity a -> Identity a Source # atanh :: Identity a -> Identity a Source # log1p :: Identity a -> Identity a Source # expm1 :: Identity a -> Identity a Source # | |||||
| RealFloat a => RealFloat (Identity a) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Functor.Identity Methods floatRadix :: Identity a -> Integer Source # floatDigits :: Identity a -> Int Source # floatRange :: Identity a -> (Int, Int) Source # decodeFloat :: Identity a -> (Integer, Int) Source # encodeFloat :: Integer -> Int -> Identity a Source # exponent :: Identity a -> Int Source # significand :: Identity a -> Identity a Source # scaleFloat :: Int -> Identity a -> Identity a Source # isNaN :: Identity a -> Bool Source # isInfinite :: Identity a -> Bool Source # isDenormalized :: Identity a -> Bool Source # isNegativeZero :: Identity a -> Bool Source # | |||||
| Storable a => Storable (Identity a) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Functor.Identity Methods sizeOf :: Identity a -> Int Source # alignment :: Identity a -> Int Source # peekElemOff :: Ptr (Identity a) -> Int -> IO (Identity a) Source # pokeElemOff :: Ptr (Identity a) -> Int -> Identity a -> IO () Source # peekByteOff :: Ptr b -> Int -> IO (Identity a) Source # pokeByteOff :: Ptr b -> Int -> Identity a -> IO () Source # | |||||
| Generic (Identity a) | |||||
Defined in GHC.Internal.Data.Functor.Identity Associated Types
| |||||
| Ix a => Ix (Identity a) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Functor.Identity Methods range :: (Identity a, Identity a) -> [Identity a] Source # index :: (Identity a, Identity a) -> Identity a -> Int Source # unsafeIndex :: (Identity a, Identity a) -> Identity a -> Int Source # inRange :: (Identity a, Identity a) -> Identity a -> Bool Source # | |||||
| Num a => Num (Identity a) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Functor.Identity Methods (+) :: Identity a -> Identity a -> Identity a Source # (-) :: Identity a -> Identity a -> Identity a Source # (*) :: Identity a -> Identity a -> Identity a Source # negate :: Identity a -> Identity a Source # abs :: Identity a -> Identity a Source # signum :: Identity a -> Identity a Source # fromInteger :: Integer -> Identity a Source # | |||||
| Read a => Read (Identity a) | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 | ||||
| Fractional a => Fractional (Identity a) | Since: base-4.9.0.0 | ||||
| Integral a => Integral (Identity a) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Functor.Identity Methods quot :: Identity a -> Identity a -> Identity a Source # rem :: Identity a -> Identity a -> Identity a Source # div :: Identity a -> Identity a -> Identity a Source # mod :: Identity a -> Identity a -> Identity a Source # quotRem :: Identity a -> Identity a -> (Identity a, Identity a) Source # divMod :: Identity a -> Identity a -> (Identity a, Identity a) Source # | |||||
| Real a => Real (Identity a) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Functor.Identity Methods toRational :: Identity a -> Rational Source # | |||||
| RealFrac a => RealFrac (Identity a) | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Functor.Identity | |||||
| Show a => Show (Identity a) | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 | ||||
| Eq a => Eq (Identity a) | Since: base-4.8.0.0 | ||||
| Ord a => Ord (Identity a) | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Functor.Identity Methods compare :: Identity a -> Identity a -> Ordering Source # (<) :: Identity a -> Identity a -> Bool Source # (<=) :: Identity a -> Identity a -> Bool Source # (>) :: Identity a -> Identity a -> Bool Source # (>=) :: Identity a -> Identity a -> Bool Source # | |||||
| type Rep1 Identity | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Functor.Identity | |||||
| type Rep (Identity a) | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Functor.Identity | |||||
Boolean monoid under conjunction (&&).
All x <> All y = All (x && y)
Examples
>>>All True <> mempty <> All False)All {getAll = False}
>>>mconcat (map (\x -> All (even x)) [2,4,6,7,8])All {getAll = False}
>>>All True <> memptyAll {getAll = True}
Instances
| NFData All | Since: deepseq-1.4.0.0 | ||||
Defined in Control.DeepSeq | |||||
| Monoid All | Since: base-2.1 | ||||
| Semigroup All | Since: base-4.9.0.0 | ||||
| Bounded All | Since: base-2.1 | ||||
| Generic All | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Read All | Since: base-2.1 | ||||
| Show All | Since: base-2.1 | ||||
| Eq All | Since: base-2.1 | ||||
| Ord All | Since: base-2.1 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep All | Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
Boolean monoid under disjunction (||).
Any x <> Any y = Any (x || y)
Examples
>>>Any True <> mempty <> Any FalseAny {getAny = True}
>>>mconcat (map (\x -> Any (even x)) [2,4,6,7,8])Any {getAny = True}
>>>Any False <> memptyAny {getAny = False}
Instances
| NFData Any | Since: deepseq-1.4.0.0 | ||||
Defined in Control.DeepSeq | |||||
| Monoid Any | Since: base-2.1 | ||||
| Semigroup Any | Since: base-4.9.0.0 | ||||
| Bounded Any | Since: base-2.1 | ||||
| Generic Any | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Read Any | Since: base-2.1 | ||||
| Show Any | Since: base-2.1 | ||||
| Eq Any | Since: base-2.1 | ||||
| Ord Any | Since: base-2.1 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep Any | Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
Monoid under addition.
Sum a <> Sum b = Sum (a + b)
Examples
>>>Sum 1 <> Sum 2 <> memptySum {getSum = 3}
>>>mconcat [ Sum n | n <- [3 .. 9]]Sum {getSum = 42}
Instances
| MonadZip Sum | Since: base-4.8.0.0 | ||||
| Foldable1 Sum | Since: base-4.18.0.0 | ||||
Defined in Data.Foldable1 Methods fold1 :: Semigroup m => Sum m -> m Source # foldMap1 :: Semigroup m => (a -> m) -> Sum a -> m Source # foldMap1' :: Semigroup m => (a -> m) -> Sum a -> m Source # toNonEmpty :: Sum a -> NonEmpty a Source # maximum :: Ord a => Sum a -> a Source # minimum :: Ord a => Sum a -> a Source # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Sum a -> b Source # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Sum a -> b Source # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Sum a -> b Source # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Sum a -> b Source # | |||||
| NFData1 Sum | Since: deepseq-1.4.3.0 | ||||
Defined in Control.DeepSeq | |||||
| Applicative Sum | Since: base-4.8.0.0 | ||||
| Functor Sum | Since: base-4.8.0.0 | ||||
| Monad Sum | Since: base-4.8.0.0 | ||||
| Foldable Sum | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Sum m -> m Source # foldMap :: Monoid m => (a -> m) -> Sum a -> m Source # foldMap' :: Monoid m => (a -> m) -> Sum a -> m Source # foldr :: (a -> b -> b) -> b -> Sum a -> b Source # foldr' :: (a -> b -> b) -> b -> Sum a -> b Source # foldl :: (b -> a -> b) -> b -> Sum a -> b Source # foldl' :: (b -> a -> b) -> b -> Sum a -> b Source # foldr1 :: (a -> a -> a) -> Sum a -> a Source # foldl1 :: (a -> a -> a) -> Sum a -> a Source # toList :: Sum a -> [a] Source # null :: Sum a -> Bool Source # length :: Sum a -> Int Source # elem :: Eq a => a -> Sum a -> Bool Source # maximum :: Ord a => Sum a -> a Source # minimum :: Ord a => Sum a -> a Source # | |||||
| Traversable Sum | Since: base-4.8.0.0 | ||||
| Generic1 Sum | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| NFData a => NFData (Sum a) | Since: deepseq-1.4.0.0 | ||||
Defined in Control.DeepSeq | |||||
| Num a => Monoid (Sum a) | Since: base-2.1 | ||||
| Num a => Semigroup (Sum a) | Since: base-4.9.0.0 | ||||
| Bounded a => Bounded (Sum a) | Since: base-2.1 | ||||
| Generic (Sum a) | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Num a => Num (Sum a) | Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| Read a => Read (Sum a) | Since: base-2.1 | ||||
| Show a => Show (Sum a) | Since: base-2.1 | ||||
| Eq a => Eq (Sum a) | Since: base-2.1 | ||||
| Ord a => Ord (Sum a) | Since: base-2.1 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep1 Sum | Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep (Sum a) | Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
Monoid under multiplication.
Product x <> Product y == Product (x * y)
Examples
>>>Product 3 <> Product 4 <> memptyProduct {getProduct = 12}
>>>mconcat [ Product n | n <- [2 .. 10]]Product {getProduct = 3628800}
Instances
| MonadZip Product | Since: base-4.8.0.0 | ||||
| Foldable1 Product | Since: base-4.18.0.0 | ||||
Defined in Data.Foldable1 Methods fold1 :: Semigroup m => Product m -> m Source # foldMap1 :: Semigroup m => (a -> m) -> Product a -> m Source # foldMap1' :: Semigroup m => (a -> m) -> Product a -> m Source # toNonEmpty :: Product a -> NonEmpty a Source # maximum :: Ord a => Product a -> a Source # minimum :: Ord a => Product a -> a Source # head :: Product a -> a Source # last :: Product a -> a Source # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Product a -> b Source # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Product a -> b Source # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Product a -> b Source # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Product a -> b Source # | |||||
| NFData1 Product | Since: deepseq-1.4.3.0 | ||||
Defined in Control.DeepSeq | |||||
| Applicative Product | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| Functor Product | Since: base-4.8.0.0 | ||||
| Monad Product | Since: base-4.8.0.0 | ||||
| Foldable Product | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Product m -> m Source # foldMap :: Monoid m => (a -> m) -> Product a -> m Source # foldMap' :: Monoid m => (a -> m) -> Product a -> m Source # foldr :: (a -> b -> b) -> b -> Product a -> b Source # foldr' :: (a -> b -> b) -> b -> Product a -> b Source # foldl :: (b -> a -> b) -> b -> Product a -> b Source # foldl' :: (b -> a -> b) -> b -> Product a -> b Source # foldr1 :: (a -> a -> a) -> Product a -> a Source # foldl1 :: (a -> a -> a) -> Product a -> a Source # toList :: Product a -> [a] Source # null :: Product a -> Bool Source # length :: Product a -> Int Source # elem :: Eq a => a -> Product a -> Bool Source # maximum :: Ord a => Product a -> a Source # minimum :: Ord a => Product a -> a Source # | |||||
| Traversable Product | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Traversable | |||||
| Generic1 Product | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| NFData a => NFData (Product a) | Since: deepseq-1.4.0.0 | ||||
Defined in Control.DeepSeq | |||||
| Num a => Monoid (Product a) | Since: base-2.1 | ||||
| Num a => Semigroup (Product a) | Since: base-4.9.0.0 | ||||
| Bounded a => Bounded (Product a) | Since: base-2.1 | ||||
| Generic (Product a) | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Num a => Num (Product a) | Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal Methods (+) :: Product a -> Product a -> Product a Source # (-) :: Product a -> Product a -> Product a Source # (*) :: Product a -> Product a -> Product a Source # negate :: Product a -> Product a Source # abs :: Product a -> Product a Source # signum :: Product a -> Product a Source # fromInteger :: Integer -> Product a Source # | |||||
| Read a => Read (Product a) | Since: base-2.1 | ||||
| Show a => Show (Product a) | Since: base-2.1 | ||||
| Eq a => Eq (Product a) | Since: base-2.1 | ||||
| Ord a => Ord (Product a) | Since: base-2.1 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep1 Product | Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep (Product a) | Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||