Lens.Family

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.

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 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 -> 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.

• Adapters have type (Functor f, Functor g) => (g a -> f a) -> g s -> f s and Adapters families have type (Functor f, Functor g) => (g (a i) -> f (a j)) -> g (s i) -> f (s j).
• Grids have type (Applicative f, Functor g) => (g a -> f a) -> g s -> f s and Grids families have type (Applicative f, Functor g) => (g (a i) -> f (a j)) -> g (s i) -> f (s j).
• Prisms have type (Applicative f, Traversable g) => (g a -> f a) -> g s -> f s and Prisms families have type (Applicative f, Traversable g) => (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:

• http://www.twanvl.nl/blog/haskell/cps-functional-references
• http://r6.ca/blog/20120623T104901Z.html
• http://comonad.com/reader/2012/mirrored-lenses/
• http://conal.net/blog/posts/semantic-editor-combinators
• https://r6research.livejournal.com/28050.html

Documentation

to :: Phantom f => (s -> a) -> LensLike f s t a b

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

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

(^.) :: 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

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

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

(^..) :: 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

(^?) :: 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]

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

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

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

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

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

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

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

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

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

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

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

Modify all referenced fields.

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

Set all referenced fields to the given value.

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

Set all referenced fields to the given value.

review :: GrateLike (Constant ()) s t a b -> b -> t

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

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

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

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

reset :: Resetter s t a b -> b -> s -> t

Set all referenced fields to the given value.

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

A flipped version of ($).

Pseudo-imperatives

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

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

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

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

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

(||~) :: ASetter s t Bool Bool -> Bool -> s -> t infixr 4

(<>~) :: Monoid a => ASetter s t a a -> a -> s -> t infixr 4

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

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

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

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

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

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

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

type GrateLike' g 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

Instances

Functor (PCont i j)

Defined in Lens.Family

Methods

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

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

data First a

Instances

Monoid (First a)

Defined in Lens.Family

Methods

mempty :: First a

mappend :: First a -> First a -> First a

mconcat :: [First a] -> First a

Semigroup (First a)

Defined in Lens.Family

Methods

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

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

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

data Last a

Instances

Monoid (Last a)

Defined in Lens.Family

Methods

mempty :: Last a

mappend :: Last a -> Last a -> Last a

mconcat :: [Last a] -> Last a

Semigroup (Last a)

Defined in Lens.Family

Methods

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

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

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

class Functor f => Phantom f

Minimal complete definition

coerce

Instances

Phantom (Const a :: Type -> Type)

Defined in Lens.Family.Phantom

Methods

coerce :: Const a a0 -> Const a b

Phantom f => Phantom (AlongsideLeft f a)

Defined in Lens.Family.Stock

Methods

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

Phantom f => Phantom (AlongsideRight f a)

Defined in Lens.Family.Stock

Methods

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

Phantom g => Phantom (FromG e g)

Defined in Lens.Family.Stock

Methods

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

Phantom f => Phantom (Backwards f)

Defined in Lens.Family.Phantom

Methods

coerce :: Backwards f a -> Backwards f b

Phantom (Constant a :: Type -> Type)

Defined in Lens.Family.Phantom

Methods

coerce :: Constant a a0 -> Constant a b

Phantom g => Phantom (FromF i j g)

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)

Defined in Lens.Family.Phantom

Methods

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

Re-exports

data Constant a (b :: k)

Constant functor.

Instances

Generic1 (Constant a :: k -> Type)

Defined in Data.Functor.Constant

Associated Types

type Rep1 (Constant a) :: k -> Type

Methods

from1 :: forall (a0 :: k0). Constant a a0 -> Rep1 (Constant a) a0

to1 :: forall (a0 :: k0). Rep1 (Constant a) a0 -> Constant a a0

Bifoldable (Constant :: Type -> Type -> Type)

Defined in Data.Functor.Constant

Methods

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

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

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

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

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

Defined in Data.Functor.Constant

Methods

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

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

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

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

Defined in Data.Functor.Constant

Methods

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

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

Defined in Data.Functor.Constant

Methods

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

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

Defined in Data.Functor.Constant

Methods

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

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

Defined in Data.Functor.Constant

Methods

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

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

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

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

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

Defined in Data.Functor.Constant

Methods

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

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

Foldable (Constant a :: Type -> Type)

Defined in Data.Functor.Constant

Methods

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

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

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

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

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

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

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

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

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

toList :: Constant a a0 -> [a0]

null :: Constant a a0 -> Bool

length :: Constant a a0 -> Int

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

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

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

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

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

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

Defined in Data.Functor.Constant

Methods

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

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

Defined in Data.Functor.Constant

Methods

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

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

Defined in Data.Functor.Constant

Methods

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

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

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

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

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

Defined in Data.Functor.Constant

Methods

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

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

Contravariant (Constant a :: Type -> Type)

Defined in Data.Functor.Constant

Methods

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

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

Traversable (Constant a :: Type -> Type)

Defined in Data.Functor.Constant

Methods

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

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

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

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

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

Defined in Data.Functor.Constant

Methods

pure :: a0 -> Constant a a0

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

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

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

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

Functor (Constant a :: Type -> Type)

Defined in Data.Functor.Constant

Methods

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

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

Phantom (Constant a :: Type -> Type)

Defined in Lens.Family.Phantom

Methods

coerce :: Constant a a0 -> Constant a b

(Typeable b, Typeable k, Data a) => Data (Constant a b)

Defined in Data.Functor.Constant

Methods

gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Constant a b -> c (Constant a b)

gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Constant a b)

toConstr :: Constant a b -> Constr

dataTypeOf :: Constant a b -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Constant a b))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Constant a b))

gmapT :: (forall b0. Data b0 => b0 -> b0) -> Constant a b -> Constant a b

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Constant a b -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Constant a b -> r

gmapQ :: (forall d. Data d => d -> u) -> Constant a b -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Constant a b -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Constant a b -> m (Constant a b)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Constant a b -> m (Constant a b)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Constant a b -> m (Constant a b)

Monoid a => Monoid (Constant a b)

Defined in Data.Functor.Constant

Methods

mempty :: Constant a b

mappend :: Constant a b -> Constant a b -> Constant a b

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

Semigroup a => Semigroup (Constant a b)

Defined in Data.Functor.Constant

Methods

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

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

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

Generic (Constant a b)

Defined in Data.Functor.Constant

Associated Types

type Rep (Constant a b) :: Type -> Type

Methods

from :: Constant a b -> Rep (Constant a b) x

to :: Rep (Constant a b) x -> Constant a b

Read a => Read (Constant a b)

Defined in Data.Functor.Constant

Methods

readsPrec :: Int -> ReadS (Constant a b)

readList :: ReadS [Constant a b]

readPrec :: ReadPrec (Constant a b)

readListPrec :: ReadPrec [Constant a b]

Show a => Show (Constant a b)

Defined in Data.Functor.Constant

Methods

showsPrec :: Int -> Constant a b -> ShowS

show :: Constant a b -> String

showList :: [Constant a b] -> ShowS

Eq a => Eq (Constant a b)

Defined in Data.Functor.Constant

Methods

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

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

Ord a => Ord (Constant a b)

Defined in Data.Functor.Constant

Methods

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

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

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

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

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

max :: Constant a b -> Constant a b -> Constant a b

min :: Constant a b -> Constant a b -> Constant a b

type Rep1 (Constant a :: k -> Type)

Defined in Data.Functor.Constant

type Rep1 (Constant a :: k -> Type) = D1 ('MetaData "Constant" "Data.Functor.Constant" "transformers-0.6.1.0" 'True) (C1 ('MetaCons "Constant" 'PrefixI 'True) (S1 ('MetaSel ('Just "getConstant") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

type Rep (Constant a b)

Defined in Data.Functor.Constant

type Rep (Constant a b) = D1 ('MetaData "Constant" "Data.Functor.Constant" "transformers-0.6.1.0" 'True) (C1 ('MetaCons "Constant" 'PrefixI 'True) (S1 ('MetaSel ('Just "getConstant") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

data Identity a

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

Since: base-4.8.0.0

Instances

MonadFix Identity

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

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

Foldable Identity

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

fold :: Monoid m => Identity m -> m

foldMap :: Monoid m => (a -> m) -> Identity a -> m

foldMap' :: Monoid m => (a -> m) -> Identity a -> m

foldr :: (a -> b -> b) -> b -> Identity a -> b

foldr' :: (a -> b -> b) -> b -> Identity a -> b

foldl :: (b -> a -> b) -> b -> Identity a -> b

foldl' :: (b -> a -> b) -> b -> Identity a -> b

foldr1 :: (a -> a -> a) -> Identity a -> a

foldl1 :: (a -> a -> a) -> Identity a -> a

toList :: Identity a -> [a]

null :: Identity a -> Bool

length :: Identity a -> Int

elem :: Eq a => a -> Identity a -> Bool

maximum :: Ord a => Identity a -> a

minimum :: Ord a => Identity a -> a

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

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

Eq1 Identity

Since: base-4.9.0.0

Defined in Data.Functor.Classes

Methods

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

Ord1 Identity

Since: base-4.9.0.0

Defined in Data.Functor.Classes

Methods

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

Read1 Identity

Since: base-4.9.0.0

Defined in Data.Functor.Classes

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Identity a)

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Identity a]

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Identity a)

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Identity a]

Show1 Identity

Since: base-4.9.0.0

Defined in Data.Functor.Classes

Methods

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

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

Traversable Identity

Since: base-4.9.0.0

Defined in Data.Traversable

Methods

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

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

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

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

Applicative Identity

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

pure :: a -> Identity a

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

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

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

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

Functor Identity

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

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

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

Monad Identity

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

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

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

return :: a -> Identity a

NFData1 Identity

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

liftRnf :: (a -> ()) -> Identity a -> ()

Identical Identity

Defined in Lens.Family.Identical

Methods

extract :: Identity a -> a

Generic1 Identity

Defined in Data.Functor.Identity

Associated Types

type Rep1 Identity :: k -> Type

Methods

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

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

Storable a => Storable (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

sizeOf :: Identity a -> Int

alignment :: Identity a -> Int

peekElemOff :: Ptr (Identity a) -> Int -> IO (Identity a)

pokeElemOff :: Ptr (Identity a) -> Int -> Identity a -> IO ()

peekByteOff :: Ptr b -> Int -> IO (Identity a)

pokeByteOff :: Ptr b -> Int -> Identity a -> IO ()

peek :: Ptr (Identity a) -> IO (Identity a)

poke :: Ptr (Identity a) -> Identity a -> IO ()

Monoid a => Monoid (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

mempty :: Identity a

mappend :: Identity a -> Identity a -> Identity a

mconcat :: [Identity a] -> Identity a

Semigroup a => Semigroup (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

(<>) :: Identity a -> Identity a -> Identity a

sconcat :: NonEmpty (Identity a) -> Identity a

stimes :: Integral b => b -> Identity a -> Identity a

Bits a => Bits (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

(.&.) :: Identity a -> Identity a -> Identity a

(.|.) :: Identity a -> Identity a -> Identity a

xor :: Identity a -> Identity a -> Identity a

complement :: Identity a -> Identity a

shift :: Identity a -> Int -> Identity a

rotate :: Identity a -> Int -> Identity a

zeroBits :: Identity a

bit :: Int -> Identity a

setBit :: Identity a -> Int -> Identity a

clearBit :: Identity a -> Int -> Identity a

complementBit :: Identity a -> Int -> Identity a

testBit :: Identity a -> Int -> Bool

bitSizeMaybe :: Identity a -> Maybe Int

bitSize :: Identity a -> Int

isSigned :: Identity a -> Bool

shiftL :: Identity a -> Int -> Identity a

unsafeShiftL :: Identity a -> Int -> Identity a

shiftR :: Identity a -> Int -> Identity a

unsafeShiftR :: Identity a -> Int -> Identity a

rotateL :: Identity a -> Int -> Identity a

rotateR :: Identity a -> Int -> Identity a

popCount :: Identity a -> Int

FiniteBits a => FiniteBits (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

finiteBitSize :: Identity a -> Int

countLeadingZeros :: Identity a -> Int

countTrailingZeros :: Identity a -> Int

Bounded a => Bounded (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

minBound :: Identity a

maxBound :: Identity a

Enum a => Enum (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

succ :: Identity a -> Identity a

pred :: Identity a -> Identity a

toEnum :: Int -> Identity a

fromEnum :: Identity a -> Int

enumFrom :: Identity a -> [Identity a]

enumFromThen :: Identity a -> Identity a -> [Identity a]

enumFromTo :: Identity a -> Identity a -> [Identity a]

enumFromThenTo :: Identity a -> Identity a -> Identity a -> [Identity a]

Floating a => Floating (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

pi :: Identity a

exp :: Identity a -> Identity a

log :: Identity a -> Identity a

sqrt :: Identity a -> Identity a

(**) :: Identity a -> Identity a -> Identity a

logBase :: Identity a -> Identity a -> Identity a

sin :: Identity a -> Identity a

cos :: Identity a -> Identity a

tan :: Identity a -> Identity a

asin :: Identity a -> Identity a

acos :: Identity a -> Identity a

atan :: Identity a -> Identity a

sinh :: Identity a -> Identity a

cosh :: Identity a -> Identity a

tanh :: Identity a -> Identity a

asinh :: Identity a -> Identity a

acosh :: Identity a -> Identity a

atanh :: Identity a -> Identity a

log1p :: Identity a -> Identity a

expm1 :: Identity a -> Identity a

log1pexp :: Identity a -> Identity a

log1mexp :: Identity a -> Identity a

RealFloat a => RealFloat (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

floatRadix :: Identity a -> Integer

floatDigits :: Identity a -> Int

floatRange :: Identity a -> (Int, Int)

decodeFloat :: Identity a -> (Integer, Int)

encodeFloat :: Integer -> Int -> Identity a

exponent :: Identity a -> Int

significand :: Identity a -> Identity a

scaleFloat :: Int -> Identity a -> Identity a

isNaN :: Identity a -> Bool

isInfinite :: Identity a -> Bool

isDenormalized :: Identity a -> Bool

isNegativeZero :: Identity a -> Bool

isIEEE :: Identity a -> Bool

atan2 :: Identity a -> Identity a -> Identity a

Generic (Identity a)

Defined in Data.Functor.Identity

Associated Types

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

Methods

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

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

Ix a => Ix (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

range :: (Identity a, Identity a) -> [Identity a]

index :: (Identity a, Identity a) -> Identity a -> Int

unsafeIndex :: (Identity a, Identity a) -> Identity a -> Int

inRange :: (Identity a, Identity a) -> Identity a -> Bool

rangeSize :: (Identity a, Identity a) -> Int

unsafeRangeSize :: (Identity a, Identity a) -> Int

Num a => Num (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

(+) :: Identity a -> Identity a -> Identity a

(-) :: Identity a -> Identity a -> Identity a

(*) :: Identity a -> Identity a -> Identity a

negate :: Identity a -> Identity a

abs :: Identity a -> Identity a

signum :: Identity a -> Identity a

fromInteger :: Integer -> Identity a

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

Defined in Data.Functor.Identity

Methods

readsPrec :: Int -> ReadS (Identity a)

readList :: ReadS [Identity a]

readPrec :: ReadPrec (Identity a)

readListPrec :: ReadPrec [Identity a]

Fractional a => Fractional (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

(/) :: Identity a -> Identity a -> Identity a

recip :: Identity a -> Identity a

fromRational :: Rational -> Identity a

Integral a => Integral (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

quot :: Identity a -> Identity a -> Identity a

rem :: Identity a -> Identity a -> Identity a

div :: Identity a -> Identity a -> Identity a

mod :: Identity a -> Identity a -> Identity a

quotRem :: Identity a -> Identity a -> (Identity a, Identity a)

divMod :: Identity a -> Identity a -> (Identity a, Identity a)

toInteger :: Identity a -> Integer

Real a => Real (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

toRational :: Identity a -> Rational

RealFrac a => RealFrac (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

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

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

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

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

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

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

Defined in Data.Functor.Identity

Methods

showsPrec :: Int -> Identity a -> ShowS

show :: Identity a -> String

showList :: [Identity a] -> ShowS

NFData a => NFData (Identity a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Identity a -> ()

Eq a => Eq (Identity a)

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

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

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

Ord a => Ord (Identity a)

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

compare :: Identity a -> Identity a -> Ordering

(<) :: Identity a -> Identity a -> Bool

(<=) :: Identity a -> Identity a -> Bool

(>) :: Identity a -> Identity a -> Bool

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

max :: Identity a -> Identity a -> Identity a

min :: Identity a -> Identity a -> Identity a

type Rep1 Identity

Since: base-4.8.0.0

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))

type Rep (Identity a)

Since: base-4.8.0.0

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 Prod = Product

data All

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

Monoid All

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: All

mappend :: All -> All -> All

mconcat :: [All] -> All

Semigroup All

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

(<>) :: All -> All -> All

sconcat :: NonEmpty All -> All

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

Bounded All

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

minBound :: All

maxBound :: All

Generic All

Defined in Data.Semigroup.Internal

Associated Types

type Rep All :: Type -> Type

Methods

from :: All -> Rep All x

to :: Rep All x -> All

Read All

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS All

readList :: ReadS [All]

readPrec :: ReadPrec All

readListPrec :: ReadPrec [All]

Show All

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> All -> ShowS

show :: All -> String

showList :: [All] -> ShowS

NFData All

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: All -> ()

Eq All

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

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

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

Ord All

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

compare :: All -> All -> Ordering

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

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

(>) :: All -> All -> Bool

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

max :: All -> All -> All

min :: All -> All -> All

type Rep All

Since: base-4.7.0.0

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

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

Monoid Any

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Any

mappend :: Any -> Any -> Any

mconcat :: [Any] -> Any

Semigroup Any

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

(<>) :: Any -> Any -> Any

sconcat :: NonEmpty Any -> Any

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

Bounded Any

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

minBound :: Any

maxBound :: Any

Generic Any

Defined in Data.Semigroup.Internal

Associated Types

type Rep Any :: Type -> Type

Methods

from :: Any -> Rep Any x

to :: Rep Any x -> Any

Read Any

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS Any

readList :: ReadS [Any]

readPrec :: ReadPrec Any

readListPrec :: ReadPrec [Any]

Show Any

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Any -> ShowS

show :: Any -> String

showList :: [Any] -> ShowS

NFData Any

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Any -> ()

Eq Any

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

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

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

Ord Any

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

compare :: Any -> Any -> Ordering

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

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

(>) :: Any -> Any -> Bool

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

max :: Any -> Any -> Any

min :: Any -> Any -> Any

type Rep Any

Since: base-4.7.0.0

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

Monoid under addition.

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

Instances

Foldable Sum

Since: base-4.8.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => Sum m -> m

foldMap :: Monoid m => (a -> m) -> Sum a -> m

foldMap' :: Monoid m => (a -> m) -> Sum a -> m

foldr :: (a -> b -> b) -> b -> Sum a -> b

foldr' :: (a -> b -> b) -> b -> Sum a -> b

foldl :: (b -> a -> b) -> b -> Sum a -> b

foldl' :: (b -> a -> b) -> b -> Sum a -> b

foldr1 :: (a -> a -> a) -> Sum a -> a

foldl1 :: (a -> a -> a) -> Sum a -> a

toList :: Sum a -> [a]

null :: Sum a -> Bool

length :: Sum a -> Int

elem :: Eq a => a -> Sum a -> Bool

maximum :: Ord a => Sum a -> a

minimum :: Ord a => Sum a -> a

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

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

Traversable Sum

Since: base-4.8.0.0

Defined in Data.Traversable

Methods

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

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

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

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

Applicative Sum

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Sum a

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

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

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

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

Functor Sum

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

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

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

Monad Sum

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

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

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

return :: a -> Sum a

NFData1 Sum

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

liftRnf :: (a -> ()) -> Sum a -> ()

Generic1 Sum

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Sum :: k -> Type

Methods

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

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

Num a => Monoid (Sum a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Sum a

mappend :: Sum a -> Sum a -> Sum a

mconcat :: [Sum a] -> Sum a

Num a => Semigroup (Sum a)

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

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

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

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

Bounded a => Bounded (Sum a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

minBound :: Sum a

maxBound :: Sum a

Generic (Sum a)

Defined in Data.Semigroup.Internal

Associated Types

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

Methods

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

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

Num a => Num (Sum a)

Since: base-4.7.0.0

Defined in Data.Semigroup.Internal

Methods

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

(-) :: Sum a -> Sum a -> Sum a

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

negate :: Sum a -> Sum a

abs :: Sum a -> Sum a

signum :: Sum a -> Sum a

fromInteger :: Integer -> Sum a

Read a => Read (Sum a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS (Sum a)

readList :: ReadS [Sum a]

readPrec :: ReadPrec (Sum a)

readListPrec :: ReadPrec [Sum a]

Show a => Show (Sum a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Sum a -> ShowS

show :: Sum a -> String

showList :: [Sum a] -> ShowS

NFData a => NFData (Sum a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Sum a -> ()

Eq a => Eq (Sum a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

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

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

Ord a => Ord (Sum a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

compare :: Sum a -> Sum a -> Ordering

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

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

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

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

max :: Sum a -> Sum a -> Sum a

min :: Sum a -> Sum a -> Sum a

type Rep1 Sum

Since: base-4.7.0.0

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))

type Rep (Sum a)

Since: base-4.7.0.0

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)))

data Product a

Monoid under multiplication.

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

Instances

Foldable Product

Since: base-4.8.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => Product m -> m

foldMap :: Monoid m => (a -> m) -> Product a -> m

foldMap' :: Monoid m => (a -> m) -> Product a -> m

foldr :: (a -> b -> b) -> b -> Product a -> b

foldr' :: (a -> b -> b) -> b -> Product a -> b

foldl :: (b -> a -> b) -> b -> Product a -> b

foldl' :: (b -> a -> b) -> b -> Product a -> b

foldr1 :: (a -> a -> a) -> Product a -> a

foldl1 :: (a -> a -> a) -> Product a -> a

toList :: Product a -> [a]

null :: Product a -> Bool

length :: Product a -> Int

elem :: Eq a => a -> Product a -> Bool

maximum :: Ord a => Product a -> a

minimum :: Ord a => Product a -> a

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

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

Traversable Product

Since: base-4.8.0.0

Defined in Data.Traversable

Methods

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

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

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

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

Applicative Product

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Product a

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

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

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

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

Functor Product

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

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

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

Monad Product

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

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

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

return :: a -> Product a

NFData1 Product

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

liftRnf :: (a -> ()) -> Product a -> ()

Generic1 Product

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Product :: k -> Type

Methods

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

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

Num a => Monoid (Product a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Product a

mappend :: Product a -> Product a -> Product a

mconcat :: [Product a] -> Product a

Num a => Semigroup (Product a)

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

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

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

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

Bounded a => Bounded (Product a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

minBound :: Product a

maxBound :: Product a

Generic (Product a)

Defined in Data.Semigroup.Internal

Associated Types

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

Methods

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

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

Num a => Num (Product a)

Since: base-4.7.0.0

Defined in Data.Semigroup.Internal

Methods

(+) :: Product a -> Product a -> Product a

(-) :: Product a -> Product a -> Product a

(*) :: Product a -> Product a -> Product a

negate :: Product a -> Product a

abs :: Product a -> Product a

signum :: Product a -> Product a

fromInteger :: Integer -> Product a

Read a => Read (Product a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS (Product a)

readList :: ReadS [Product a]

readPrec :: ReadPrec (Product a)

readListPrec :: ReadPrec [Product a]

Show a => Show (Product a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Product a -> ShowS

show :: Product a -> String

showList :: [Product a] -> ShowS

NFData a => NFData (Product a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Product a -> ()

Eq a => Eq (Product a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

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

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

Ord a => Ord (Product a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

compare :: Product a -> Product a -> Ordering

(<) :: Product a -> Product a -> Bool

(<=) :: Product a -> Product a -> Bool

(>) :: Product a -> Product a -> Bool

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

max :: Product a -> Product a -> Product a

min :: Product a -> Product a -> Product a

type Rep1 Product

Since: base-4.7.0.0

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))

type Rep (Product a)

Since: base-4.7.0.0

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)))