lens-family-core-2.1.2: Haskell 2022 Lens Families
Safe HaskellSafe-Inferred
LanguageHaskell2010

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

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 s and lens families have type Functor 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 a

Traversals

^. 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 s and traversal families have type Applicative 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 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 -> s and grate families have type Functor 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.

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

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.

(^?) :: s -> FoldLike (First a) s t a b -> Maybe a infixl 8 Source #

(^?) :: s -> Fold s t a b -> Maybe a

Returns Just the first referenced value. Returns Nothing if there are no referenced values.

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.

firstOf :: FoldLike (First a) s t a b -> s -> Maybe a Source #

firstOf :: Fold s t a b -> s -> Maybe a

Returns Just the first referenced value. Returns Nothing if there are no referenced values. See ^? for an infix version of firstOf

lastOf :: FoldLike (Last a) s t a b -> s -> Maybe a Source #

lastOf :: Fold s t a b -> s -> Maybe a

Returns Just the last referenced value. Returns Nothing if there are no referenced values.

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 -> (a -> b) -> s -> t infixr 4 Source #

Modify all referenced fields.

set :: ASetter s t a b -> b -> s -> t Source #

Set all referenced fields to the given value.

(.~) :: ASetter s t a b -> b -> s -> t infixr 4 Source #

Set all referenced fields to the given value.

review :: GrateLike (Constant ()) 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.

(&) :: s -> (s -> t) -> t infixl 1 Source #

A flipped version of ($).

Pseudo-imperatives

(+~) :: Num a => ASetter s t a a -> a -> s -> t infixr 4 Source #

(*~) :: Num a => ASetter s t a a -> a -> s -> t infixr 4 Source #

(-~) :: Num a => ASetter s t a a -> a -> s -> t infixr 4 Source #

(//~) :: Fractional a => ASetter s t a a -> a -> s -> t infixr 4 Source #

(&&~) :: ASetter s t Bool Bool -> Bool -> s -> t infixr 4 Source #

(||~) :: ASetter s t Bool Bool -> Bool -> 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 g s t a b = (g a -> f b) -> g s -> f t Source #

type AdapterLike' f g s a = (g a -> f a) -> g s -> f s Source #

type LensLike f s t a b = (a -> f b) -> s -> f t Source #

type LensLike' f s a = (a -> f a) -> s -> f s Source #

type FoldLike r s t a b = LensLike (Constant r) s t a b Source #

type FoldLike' r s a = LensLike' (Constant r) s a Source #

type GrateLike g s t a b = (g a -> b) -> g s -> t Source #

type GrateLike' g s a = (g a -> a) -> g s -> s Source #

type AGrate s t a b = GrateLike (PCont b a) s t a b Source #

type AGrate' s a = GrateLike' (PCont a a) s a Source #

type ASetter s t a b = LensLike Identity s t a b Source #

type AResetter s t a b = GrateLike Identity s t a b Source #

data PCont i j a Source #

Instances

Instances details
Functor (PCont i j) Source # 
Instance details

Defined in Lens.Family

Methods

fmap :: (a -> b) -> PCont i j a -> PCont i j b Source #

(<$) :: a -> PCont i j b -> PCont i j a Source #

data First a Source #

Instances

Instances details
Monoid (First a) Source # 
Instance details

Defined in Lens.Family

Methods

mempty :: First a Source #

mappend :: First a -> First a -> First a Source #

mconcat :: [First a] -> First a Source #

Semigroup (First a) Source # 
Instance details

Defined in Lens.Family

Methods

(<>) :: First a -> First a -> First a Source #

sconcat :: NonEmpty (First a) -> First a Source #

stimes :: Integral b => b -> First a -> First a Source #

data Last a Source #

Instances

Instances details
Monoid (Last a) Source # 
Instance details

Defined in Lens.Family

Methods

mempty :: Last a Source #

mappend :: Last a -> Last a -> Last a Source #

mconcat :: [Last a] -> Last a Source #

Semigroup (Last a) Source # 
Instance details

Defined in Lens.Family

Methods

(<>) :: Last a -> Last a -> Last a Source #

sconcat :: NonEmpty (Last a) -> Last a Source #

stimes :: Integral b => b -> Last a -> Last a Source #

class Functor f => Phantom f Source #

Minimal complete definition

coerce

Instances

Instances details
Phantom (Const a :: Type -> Type) Source # 
Instance details

Defined in Lens.Family.Phantom

Methods

coerce :: Const a a0 -> Const a b

Phantom f => Phantom (AlongsideLeft f a) Source # 
Instance details

Defined in Lens.Family.Stock

Methods

coerce :: AlongsideLeft f a a0 -> AlongsideLeft f a b

Phantom f => Phantom (AlongsideRight f a) Source # 
Instance details

Defined in Lens.Family.Stock

Methods

coerce :: AlongsideRight f a a0 -> AlongsideRight f a b

Phantom g => Phantom (FromG e g) Source # 
Instance details

Defined in Lens.Family.Stock

Methods

coerce :: FromG e g a -> FromG e g b

Phantom f => Phantom (Backwards f) Source # 
Instance details

Defined in Lens.Family.Phantom

Methods

coerce :: Backwards f a -> Backwards f b

Phantom (Constant a :: Type -> Type) Source # 
Instance details

Defined in Lens.Family.Phantom

Methods

coerce :: Constant a a0 -> Constant a b

Phantom g => Phantom (FromF i j g) Source # 
Instance details

Defined in Lens.Family.Stock

Methods

coerce :: FromF i j g a -> FromF i j g b

(Phantom f, Functor g) => Phantom (Compose f g) Source # 
Instance details

Defined in Lens.Family.Phantom

Methods

coerce :: Compose f g a -> Compose f g b

Re-exports

data Constant a (b :: k) Source #

Constant functor.

Instances

Instances details
Bifoldable (Constant :: Type -> Type -> Type) 
Instance details

Defined in Data.Functor.Constant

Methods

bifold :: Monoid m => Constant m m -> m Source #

bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Constant a b -> m Source #

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Constant a b -> c Source #

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Constant a b -> c Source #

Bifunctor (Constant :: Type -> Type -> Type) 
Instance details

Defined in Data.Functor.Constant

Methods

bimap :: (a -> b) -> (c -> d) -> Constant a c -> Constant b d Source #

first :: (a -> b) -> Constant a c -> Constant b c Source #

second :: (b -> c) -> Constant a b -> Constant a c Source #

Bitraversable (Constant :: Type -> Type -> Type) 
Instance details

Defined in Data.Functor.Constant

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Constant a b -> f (Constant c d) Source #

Eq2 (Constant :: Type -> Type -> Type) 
Instance details

Defined in Data.Functor.Constant

Methods

liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Constant a c -> Constant b d -> Bool Source #

Ord2 (Constant :: Type -> Type -> Type) 
Instance details

Defined in Data.Functor.Constant

Methods

liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Constant a c -> Constant b d -> Ordering Source #

Read2 (Constant :: Type -> Type -> Type) 
Instance details

Defined in Data.Functor.Constant

Methods

liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (Constant a b) Source #

liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [Constant a b] Source #

liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (Constant a b) Source #

liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [Constant a b] Source #

Show2 (Constant :: Type -> Type -> Type) 
Instance details

Defined in Data.Functor.Constant

Methods

liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> Constant a b -> ShowS Source #

liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [Constant a b] -> ShowS Source #

Foldable (Constant a :: Type -> Type) 
Instance details

Defined in Data.Functor.Constant

Methods

fold :: Monoid m => Constant a m -> m Source #

foldMap :: Monoid m => (a0 -> m) -> Constant a a0 -> m Source #

foldMap' :: Monoid m => (a0 -> m) -> Constant a a0 -> m Source #

foldr :: (a0 -> b -> b) -> b -> Constant a a0 -> b Source #

foldr' :: (a0 -> b -> b) -> b -> Constant a a0 -> b Source #

foldl :: (b -> a0 -> b) -> b -> Constant a a0 -> b Source #

foldl' :: (b -> a0 -> b) -> b -> Constant a a0 -> b Source #

foldr1 :: (a0 -> a0 -> a0) -> Constant a a0 -> a0 Source #

foldl1 :: (a0 -> a0 -> a0) -> Constant a a0 -> a0 Source #

toList :: Constant a a0 -> [a0] Source #

null :: Constant a a0 -> Bool Source #

length :: Constant a a0 -> Int Source #

elem :: Eq a0 => a0 -> Constant a a0 -> Bool Source #

maximum :: Ord a0 => Constant a a0 -> a0 Source #

minimum :: Ord a0 => Constant a a0 -> a0 Source #

sum :: Num a0 => Constant a a0 -> a0 Source #

product :: Num a0 => Constant a a0 -> a0 Source #

Eq a => Eq1 (Constant a :: Type -> Type) 
Instance details

Defined in Data.Functor.Constant

Methods

liftEq :: (a0 -> b -> Bool) -> Constant a a0 -> Constant a b -> Bool Source #

Ord a => Ord1 (Constant a :: Type -> Type) 
Instance details

Defined in Data.Functor.Constant

Methods

liftCompare :: (a0 -> b -> Ordering) -> Constant a a0 -> Constant a b -> Ordering Source #

Read a => Read1 (Constant a :: Type -> Type) 
Instance details

Defined in Data.Functor.Constant

Methods

liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (Constant a a0) Source #

liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [Constant a a0] Source #

liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (Constant a a0) Source #

liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [Constant a a0] Source #

Show a => Show1 (Constant a :: Type -> Type) 
Instance details

Defined in Data.Functor.Constant

Methods

liftShowsPrec :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> Int -> Constant a a0 -> ShowS Source #

liftShowList :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> [Constant a a0] -> ShowS Source #

Contravariant (Constant a :: Type -> Type) 
Instance details

Defined in Data.Functor.Constant

Methods

contramap :: (a' -> a0) -> Constant a a0 -> Constant a a' Source #

(>$) :: b -> Constant a b -> Constant a a0 Source #

Traversable (Constant a :: Type -> Type) 
Instance details

Defined in Data.Functor.Constant

Methods

traverse :: Applicative f => (a0 -> f b) -> Constant a a0 -> f (Constant a b) Source #

sequenceA :: Applicative f => Constant a (f a0) -> f (Constant a a0) Source #

mapM :: Monad m => (a0 -> m b) -> Constant a a0 -> m (Constant a b) Source #

sequence :: Monad m => Constant a (m a0) -> m (Constant a a0) Source #

Monoid a => Applicative (Constant a :: Type -> Type) 
Instance details

Defined in Data.Functor.Constant

Methods

pure :: a0 -> Constant a a0 Source #

(<*>) :: Constant a (a0 -> b) -> Constant a a0 -> Constant a b Source #

liftA2 :: (a0 -> b -> c) -> Constant a a0 -> Constant a b -> Constant a c Source #

(*>) :: Constant a a0 -> Constant a b -> Constant a b Source #

(<*) :: Constant a a0 -> Constant a b -> Constant a a0 Source #

Functor (Constant a :: Type -> Type) 
Instance details

Defined in Data.Functor.Constant

Methods

fmap :: (a0 -> b) -> Constant a a0 -> Constant a b Source #

(<$) :: a0 -> Constant a b -> Constant a a0 Source #

Phantom (Constant a :: Type -> Type) Source # 
Instance details

Defined in Lens.Family.Phantom

Methods

coerce :: Constant a a0 -> Constant a b

Monoid a => Monoid (Constant a b) 
Instance details

Defined in Data.Functor.Constant

Methods

mempty :: Constant a b Source #

mappend :: Constant a b -> Constant a b -> Constant a b Source #

mconcat :: [Constant a b] -> Constant a b Source #

Semigroup a => Semigroup (Constant a b) 
Instance details

Defined in Data.Functor.Constant

Methods

(<>) :: Constant a b -> Constant a b -> Constant a b Source #

sconcat :: NonEmpty (Constant a b) -> Constant a b Source #

stimes :: Integral b0 => b0 -> Constant a b -> Constant a b Source #

Read a => Read (Constant a b) 
Instance details

Defined in Data.Functor.Constant

Show a => Show (Constant a b) 
Instance details

Defined in Data.Functor.Constant

Eq a => Eq (Constant a b) 
Instance details

Defined in Data.Functor.Constant

Methods

(==) :: Constant a b -> Constant a b -> Bool Source #

(/=) :: Constant a b -> Constant a b -> Bool Source #

Ord a => Ord (Constant a b) 
Instance details

Defined in Data.Functor.Constant

Methods

compare :: Constant a b -> Constant a b -> Ordering Source #

(<) :: Constant a b -> Constant a b -> Bool Source #

(<=) :: Constant a b -> Constant a b -> Bool Source #

(>) :: Constant a b -> Constant a b -> Bool Source #

(>=) :: Constant a b -> Constant a b -> Bool Source #

max :: Constant a b -> Constant a b -> Constant a b Source #

min :: Constant a b -> Constant a b -> Constant a b Source #

data Identity a Source #

Identity functor and monad. (a non-strict monad)

Since: base-4.8.0.0

Instances

Instances details
MonadFix Identity

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Methods

mfix :: (a -> Identity a) -> Identity a Source #

Foldable Identity

Since: base-4.8.0.0

Instance details

Defined in 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 #

sum :: Num a => Identity a -> a Source #

product :: Num a => Identity a -> a Source #

Eq1 Identity

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftEq :: (a -> b -> Bool) -> Identity a -> Identity b -> Bool Source #

Ord1 Identity

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftCompare :: (a -> b -> Ordering) -> Identity a -> Identity b -> Ordering Source #

Read1 Identity

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Show1 Identity

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Identity a -> ShowS Source #

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Identity a] -> ShowS Source #

Traversable Identity

Since: base-4.9.0.0

Instance details

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Identity a -> f (Identity b) Source #

sequenceA :: Applicative f => Identity (f a) -> f (Identity a) Source #

mapM :: Monad m => (a -> m b) -> Identity a -> m (Identity b) Source #

sequence :: Monad m => Identity (m a) -> m (Identity a) Source #

Applicative Identity

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Methods

pure :: a -> Identity a Source #

(<*>) :: Identity (a -> b) -> Identity a -> Identity b Source #

liftA2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c Source #

(*>) :: Identity a -> Identity b -> Identity b Source #

(<*) :: Identity a -> Identity b -> Identity a Source #

Functor Identity

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Methods

fmap :: (a -> b) -> Identity a -> Identity b Source #

(<$) :: a -> Identity b -> Identity a Source #

Monad Identity

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Methods

(>>=) :: Identity a -> (a -> Identity b) -> Identity b Source #

(>>) :: Identity a -> Identity b -> Identity b Source #

return :: a -> Identity a Source #

Identical Identity Source # 
Instance details

Defined in Lens.Family.Identical

Methods

extract :: Identity a -> a

Bits a => Bits (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

FiniteBits a => FiniteBits (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Storable a => Storable (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Monoid a => Monoid (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Semigroup a => Semigroup (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Bounded a => Bounded (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Enum a => Enum (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Floating a => Floating (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

RealFloat a => RealFloat (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Generic (Identity a) 
Instance details

Defined in Data.Functor.Identity

Associated Types

type Rep (Identity a) :: Type -> Type Source #

Methods

from :: Identity a -> Rep (Identity a) x Source #

to :: Rep (Identity a) x -> Identity a Source #

Ix a => Ix (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Num a => Num (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Read a => Read (Identity a)

This instance would be equivalent to the derived instances of the Identity newtype if the runIdentity field were removed

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Fractional a => Fractional (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Integral a => Integral (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Real a => Real (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

RealFrac a => RealFrac (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Methods

properFraction :: Integral b => Identity a -> (b, Identity a) Source #

truncate :: Integral b => Identity a -> b Source #

round :: Integral b => Identity a -> b Source #

ceiling :: Integral b => Identity a -> b Source #

floor :: Integral b => Identity a -> b Source #

Show a => Show (Identity a)

This instance would be equivalent to the derived instances of the Identity newtype if the runIdentity field were removed

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Eq a => Eq (Identity a)

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Methods

(==) :: Identity a -> Identity a -> Bool Source #

(/=) :: Identity a -> Identity a -> Bool Source #

Ord a => Ord (Identity a)

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Generic1 Identity 
Instance details

Defined in Data.Functor.Identity

Associated Types

type Rep1 Identity :: k -> Type Source #

Methods

from1 :: forall (a :: k). Identity a -> Rep1 Identity a Source #

to1 :: forall (a :: k). Rep1 Identity a -> Identity a Source #

type Rep (Identity a)

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

type Rep (Identity a) = D1 ('MetaData "Identity" "Data.Functor.Identity" "base" 'True) (C1 ('MetaCons "Identity" 'PrefixI 'True) (S1 ('MetaSel ('Just "runIdentity") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Rep1 Identity

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

type Rep1 Identity = D1 ('MetaData "Identity" "Data.Functor.Identity" "base" 'True) (C1 ('MetaCons "Identity" 'PrefixI 'True) (S1 ('MetaSel ('Just "runIdentity") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

data All Source #

Boolean monoid under conjunction (&&).

>>> getAll (All True <> mempty <> All False)
False
>>> getAll (mconcat (map (\x -> All (even x)) [2,4,6,7,8]))
False

Instances

Instances details
Monoid All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Semigroup All

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(<>) :: All -> All -> All Source #

sconcat :: NonEmpty All -> All Source #

stimes :: Integral b => b -> All -> All Source #

Bounded All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Generic All 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep All :: Type -> Type Source #

Methods

from :: All -> Rep All x Source #

to :: Rep All x -> All Source #

Read All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Show All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Eq All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

(==) :: All -> All -> Bool Source #

(/=) :: All -> All -> Bool Source #

Ord All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

compare :: All -> All -> Ordering Source #

(<) :: All -> All -> Bool Source #

(<=) :: All -> All -> Bool Source #

(>) :: All -> All -> Bool Source #

(>=) :: All -> All -> Bool Source #

max :: All -> All -> All Source #

min :: All -> All -> All Source #

type Rep All

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

type Rep All = D1 ('MetaData "All" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "All" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAll") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Bool)))

data Any Source #

Boolean monoid under disjunction (||).

>>> getAny (Any True <> mempty <> Any False)
True
>>> getAny (mconcat (map (\x -> Any (even x)) [2,4,6,7,8]))
True

Instances

Instances details
Monoid Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Semigroup Any

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(<>) :: Any -> Any -> Any Source #

sconcat :: NonEmpty Any -> Any Source #

stimes :: Integral b => b -> Any -> Any Source #

Bounded Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Generic Any 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep Any :: Type -> Type Source #

Methods

from :: Any -> Rep Any x Source #

to :: Rep Any x -> Any Source #

Read Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Show Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Eq Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

(==) :: Any -> Any -> Bool Source #

(/=) :: Any -> Any -> Bool Source #

Ord Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

compare :: Any -> Any -> Ordering Source #

(<) :: Any -> Any -> Bool Source #

(<=) :: Any -> Any -> Bool Source #

(>) :: Any -> Any -> Bool Source #

(>=) :: Any -> Any -> Bool Source #

max :: Any -> Any -> Any Source #

min :: Any -> Any -> Any Source #

type Rep Any

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

type Rep Any = D1 ('MetaData "Any" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Any" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAny") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Bool)))

data Sum a Source #

Monoid under addition.

>>> getSum (Sum 1 <> Sum 2 <> mempty)
3

Instances

Instances details
Foldable Sum

Since: base-4.8.0.0

Instance details

Defined in 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 #

sum :: Num a => Sum a -> a Source #

product :: Num a => Sum a -> a Source #

Traversable Sum

Since: base-4.8.0.0

Instance details

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b) Source #

sequenceA :: Applicative f => Sum (f a) -> f (Sum a) Source #

mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b) Source #

sequence :: Monad m => Sum (m a) -> m (Sum a) Source #

Applicative Sum

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Sum a Source #

(<*>) :: Sum (a -> b) -> Sum a -> Sum b Source #

liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c Source #

(*>) :: Sum a -> Sum b -> Sum b Source #

(<*) :: Sum a -> Sum b -> Sum a Source #

Functor Sum

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

fmap :: (a -> b) -> Sum a -> Sum b Source #

(<$) :: a -> Sum b -> Sum a Source #

Monad Sum

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(>>=) :: Sum a -> (a -> Sum b) -> Sum b Source #

(>>) :: Sum a -> Sum b -> Sum b Source #

return :: a -> Sum a Source #

Num a => Monoid (Sum a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Sum a Source #

mappend :: Sum a -> Sum a -> Sum a Source #

mconcat :: [Sum a] -> Sum a Source #

Num a => Semigroup (Sum a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(<>) :: Sum a -> Sum a -> Sum a Source #

sconcat :: NonEmpty (Sum a) -> Sum a Source #

stimes :: Integral b => b -> Sum a -> Sum a Source #

Bounded a => Bounded (Sum a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Generic (Sum a) 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Sum a) :: Type -> Type Source #

Methods

from :: Sum a -> Rep (Sum a) x Source #

to :: Rep (Sum a) x -> Sum a Source #

Num a => Num (Sum a)

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(+) :: Sum a -> Sum a -> Sum a Source #

(-) :: Sum a -> Sum a -> Sum a Source #

(*) :: Sum a -> Sum a -> Sum a Source #

negate :: Sum a -> Sum a Source #

abs :: Sum a -> Sum a Source #

signum :: Sum a -> Sum a Source #

fromInteger :: Integer -> Sum a Source #

Read a => Read (Sum a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Show a => Show (Sum a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Sum a -> ShowS Source #

show :: Sum a -> String Source #

showList :: [Sum a] -> ShowS Source #

Eq a => Eq (Sum a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

(==) :: Sum a -> Sum a -> Bool Source #

(/=) :: Sum a -> Sum a -> Bool Source #

Ord a => Ord (Sum a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

compare :: Sum a -> Sum a -> Ordering Source #

(<) :: Sum a -> Sum a -> Bool Source #

(<=) :: Sum a -> Sum a -> Bool Source #

(>) :: Sum a -> Sum a -> Bool Source #

(>=) :: Sum a -> Sum a -> Bool Source #

max :: Sum a -> Sum a -> Sum a Source #

min :: Sum a -> Sum a -> Sum a Source #

Generic1 Sum 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Sum :: k -> Type Source #

Methods

from1 :: forall (a :: k). Sum a -> Rep1 Sum a Source #

to1 :: forall (a :: k). Rep1 Sum a -> Sum a Source #

type Rep (Sum a)

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

type Rep (Sum a) = D1 ('MetaData "Sum" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Sum" 'PrefixI 'True) (S1 ('MetaSel ('Just "getSum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Rep1 Sum

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

type Rep1 Sum = D1 ('MetaData "Sum" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Sum" 'PrefixI 'True) (S1 ('MetaSel ('Just "getSum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

data Product a Source #

Monoid under multiplication.

>>> getProduct (Product 3 <> Product 4 <> mempty)
12

Instances

Instances details
Foldable Product

Since: base-4.8.0.0

Instance details

Defined in 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 #

sum :: Num a => Product a -> a Source #

product :: Num a => Product a -> a Source #

Traversable Product

Since: base-4.8.0.0

Instance details

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b) Source #

sequenceA :: Applicative f => Product (f a) -> f (Product a) Source #

mapM :: Monad m => (a -> m b) -> Product a -> m (Product b) Source #

sequence :: Monad m => Product (m a) -> m (Product a) Source #

Applicative Product

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Product a Source #

(<*>) :: Product (a -> b) -> Product a -> Product b Source #

liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c Source #

(*>) :: Product a -> Product b -> Product b Source #

(<*) :: Product a -> Product b -> Product a Source #

Functor Product

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

fmap :: (a -> b) -> Product a -> Product b Source #

(<$) :: a -> Product b -> Product a Source #

Monad Product

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(>>=) :: Product a -> (a -> Product b) -> Product b Source #

(>>) :: Product a -> Product b -> Product b Source #

return :: a -> Product a Source #

Num a => Monoid (Product a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Num a => Semigroup (Product a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(<>) :: Product a -> Product a -> Product a Source #

sconcat :: NonEmpty (Product a) -> Product a Source #

stimes :: Integral b => b -> Product a -> Product a Source #

Bounded a => Bounded (Product a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Generic (Product a) 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Product a) :: Type -> Type Source #

Methods

from :: Product a -> Rep (Product a) x Source #

to :: Rep (Product a) x -> Product a Source #

Num a => Num (Product a)

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

Read a => Read (Product a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Show a => Show (Product a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Eq a => Eq (Product a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

(==) :: Product a -> Product a -> Bool Source #

(/=) :: Product a -> Product a -> Bool Source #

Ord a => Ord (Product a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Generic1 Product 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Product :: k -> Type Source #

Methods

from1 :: forall (a :: k). Product a -> Rep1 Product a Source #

to1 :: forall (a :: k). Rep1 Product a -> Product a Source #

type Rep (Product a)

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

type Rep (Product a) = D1 ('MetaData "Product" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Product" 'PrefixI 'True) (S1 ('MetaSel ('Just "getProduct") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Rep1 Product

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

type Rep1 Product = D1 ('MetaData "Product" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Product" 'PrefixI 'True) (S1 ('MetaSel ('Just "getProduct") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))