Safe Haskell	Safe
Language	Haskell98

Lens.Family

Contents

Lenses
Traversals
Grates
Adapters, Grids, and Prisms
Building and Finding Optics
Documentation
Pseudo-imperatives
Types
Re-exports

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 ()) 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 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
data First a
data Last a
class Functor f => Phantom f
data Constant a (b :: k) :: forall k. Type -> k -> Type
data Identity a
type Prod = Product
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 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.

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:

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 ASetter' s a = LensLike' Identity s a Source #

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

type AResetter' s a = GrateLike' Identity s a Source #

data PCont i j a Source #

Instances

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

Instances

Semigroup (First a) Source #
Instance details 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 #
Monoid (First a) Source #
Instance details Defined in Lens.Family Methods mempty :: First a # mappend :: First a -> First a -> First a # mconcat :: [First a] -> First a #

data Last a Source #

Instances

Semigroup (Last a) Source #
Instance details 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 #
Monoid (Last a) Source #
Instance details Defined in Lens.Family Methods mempty :: Last a # mappend :: Last a -> Last a -> Last a # mconcat :: [Last a] -> Last a #

class Functor f => Phantom f Source #

Minimal complete definition

coerce

Instances

Phantom (Const a :: Type -> Type) Source #
Instance details Defined in Lens.Family.Phantom Methods coerce :: Const a a0 -> Const a b
Phantom (Constant a :: Type -> Type) Source #
Instance details Defined in Lens.Family.Phantom Methods coerce :: Constant a a0 -> Constant a b
Phantom f => Phantom (Backwards f) Source #
Instance details Defined in Lens.Family.Phantom Methods coerce :: Backwards f a -> Backwards f 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 (AlongsideRight f a) Source #
Instance details Defined in Lens.Family.Stock Methods coerce :: AlongsideRight f a a0 -> AlongsideRight f 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 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) :: forall k. Type -> k -> Type #

Constant functor.

Instances

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) #
Bifoldable (Constant :: Type -> Type -> Type)
Instance details 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)
Instance details 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 #
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 #
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 #
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) # 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)
Instance details 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 #
Functor (Constant a :: Type -> Type)
Instance details Defined in Data.Functor.Constant Methods fmap :: (a0 -> b) -> Constant a a0 -> Constant a b # (<$) :: a0 -> Constant a b -> Constant a a0 #
Monoid a => Applicative (Constant a :: Type -> Type)
Instance details Defined in Data.Functor.Constant Methods pure :: a0 -> Constant a a0 # (<>) :: Constant a (a0 -> b) -> Constant a a0 -> Constant a b # liftA2 :: (a0 -> b -> c) -> Constant a a0 -> Constant a b -> Constant a c # (>) :: Constant a a0 -> Constant a b -> Constant a b # (<*) :: Constant a a0 -> Constant a b -> Constant a a0 #
Foldable (Constant a :: Type -> Type)
Instance details Defined in Data.Functor.Constant Methods fold :: Monoid m => Constant a m -> m # foldMap :: Monoid m => (a0 -> m) -> Constant a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Constant a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Constant a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Constant a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Constant a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Constant a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Constant a a0 -> a0 # toList :: Constant a a0 -> [a0] # null :: Constant a a0 -> Bool # length :: Constant a a0 -> Int # elem :: Eq a0 => a0 -> Constant a a0 -> Bool # maximum :: Ord a0 => Constant a a0 -> a0 # minimum :: Ord a0 => Constant a a0 -> a0 # sum :: Num a0 => Constant a a0 -> a0 # product :: Num a0 => Constant a a0 -> a0 #
Traversable (Constant a :: Type -> Type)
Instance details Defined in Data.Functor.Constant Methods traverse :: Applicative f => (a0 -> f b) -> Constant a a0 -> f (Constant a b) # sequenceA :: Applicative f => Constant a (f a0) -> f (Constant a a0) # mapM :: Monad m => (a0 -> m b) -> Constant a a0 -> m (Constant a b) # sequence :: Monad m => Constant a (m a0) -> m (Constant a a0) #
Contravariant (Constant a :: Type -> Type)
Instance details Defined in Data.Functor.Constant Methods contramap :: (a0 -> b) -> Constant a b -> Constant a a0 # (>$) :: b -> Constant a b -> Constant a a0 #
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 #
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 #
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) # 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)
Instance details 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 #
Phantom (Constant a :: Type -> Type) Source #
Instance details Defined in Lens.Family.Phantom Methods coerce :: Constant a a0 -> Constant a b
Eq a => Eq (Constant a b)
Instance details 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)
Instance details 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 #
Read a => Read (Constant a b)
Instance details 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)
Instance details Defined in Data.Functor.Constant Methods showsPrec :: Int -> Constant a b -> ShowS # show :: Constant a b -> String # showList :: [Constant a b] -> ShowS #
Semigroup a => Semigroup (Constant a b)
Instance details 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 #
Monoid a => Monoid (Constant a b)
Instance details 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 #

data Identity a #

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

Since: base-4.8.0.0

Instances

Monad Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods (>>=) :: Identity a -> (a -> Identity b) -> Identity b # (>>) :: Identity a -> Identity b -> Identity b # return :: a -> Identity a # fail :: String -> Identity a #
Functor Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods fmap :: (a -> b) -> Identity a -> Identity b # (<$) :: a -> Identity b -> Identity a #
MonadFix Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods mfix :: (a -> Identity a) -> Identity a #
Applicative Identity	Since: base-4.8.0.0
Instance details 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 #
Foldable Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods fold :: Monoid m => Identity m -> 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 #
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) # 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) #
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 #
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 #
Read1 Identity	Since: base-4.9.0.0
Instance details 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
Instance details 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 #
Identical Identity Source #
Instance details Defined in Lens.Family.Identical Methods extract :: Identity a -> a
Bounded a => Bounded (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods minBound :: Identity a # maxBound :: Identity a #
Enum a => Enum (Identity a)	Since: base-4.9.0.0
Instance details 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] #
Eq a => Eq (Identity a)	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods (==) :: Identity a -> Identity a -> Bool # (/=) :: Identity a -> Identity a -> Bool #
Floating a => Floating (Identity a)	Since: base-4.9.0.0
Instance details 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 #
Fractional a => Fractional (Identity a)	Since: base-4.9.0.0
Instance details 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
Instance details 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 #
Num a => Num (Identity a)	Since: base-4.9.0.0
Instance details 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 #
Ord a => Ord (Identity a)	Since: base-4.8.0.0
Instance details 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 #
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 Methods readsPrec :: Int -> ReadS (Identity a) # readList :: ReadS [Identity a] # readPrec :: ReadPrec (Identity a) # readListPrec :: ReadPrec [Identity a] #
Real a => Real (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods toRational :: Identity a -> Rational #
RealFloat a => RealFloat (Identity a)	Since: base-4.9.0.0
Instance details 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 #
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) # 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
Instance details Defined in Data.Functor.Identity Methods showsPrec :: Int -> Identity a -> ShowS # show :: Identity a -> String # showList :: [Identity a] -> ShowS #
Ix a => Ix (Identity a)	Since: base-4.9.0.0
Instance details 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
Generic (Identity a)
Instance details 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 #
Semigroup a => Semigroup (Identity a)	Since: base-4.9.0.0
Instance details 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 #
Monoid a => Monoid (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods mempty :: Identity a # mappend :: Identity a -> Identity a -> Identity a # mconcat :: [Identity a] -> Identity a #
Storable a => Storable (Identity a)	Since: base-4.9.0.0
Instance details 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 () #
Bits a => Bits (Identity a)	Since: base-4.9.0.0
Instance details 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
Instance details Defined in Data.Functor.Identity Methods finiteBitSize :: Identity a -> Int # countLeadingZeros :: Identity a -> Int # countTrailingZeros :: Identity a -> Int #
Generic1 Identity
Instance details Defined in Data.Functor.Identity Associated Types type Rep1 Identity :: k -> Type # Methods from1 :: Identity a -> Rep1 Identity a # to1 :: Rep1 Identity a -> Identity a #
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))

type Prod = Product Source #

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

Bounded All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: All # maxBound :: All #
Eq All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: All -> All -> Bool # (/=) :: All -> All -> Bool #
Ord All	Since: base-2.1
Instance details 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 #
Read All	Since: base-2.1
Instance details 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
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> All -> ShowS # show :: All -> String # showList :: [All] -> ShowS #
Generic All
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep All :: Type -> Type # Methods from :: All -> Rep All x # to :: Rep All x -> All #
Semigroup All	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: All -> All -> All # sconcat :: NonEmpty All -> All # stimes :: Integral b => b -> All -> All #
Monoid All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: All # mappend :: All -> All -> All # mconcat :: [All] -> All #
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 #

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

Bounded Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Any # maxBound :: Any #
Eq Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Any -> Any -> Bool # (/=) :: Any -> Any -> Bool #
Ord Any	Since: base-2.1
Instance details 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 #
Read Any	Since: base-2.1
Instance details 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
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Any -> ShowS # show :: Any -> String # showList :: [Any] -> ShowS #
Generic Any
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep Any :: Type -> Type # Methods from :: Any -> Rep Any x # to :: Rep Any x -> Any #
Semigroup Any	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Any -> Any -> Any # sconcat :: NonEmpty Any -> Any # stimes :: Integral b => b -> Any -> Any #
Monoid Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Any # mappend :: Any -> Any -> Any # mconcat :: [Any] -> Any #
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 #

Monoid under addition.

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

Instances

Monad Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Sum a -> (a -> Sum b) -> Sum b # (>>) :: Sum a -> Sum b -> Sum b # return :: a -> Sum a # fail :: String -> Sum a #
Functor Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Sum a -> Sum b # (<$) :: a -> Sum b -> Sum a #
Applicative Sum	Since: base-4.8.0.0
Instance details 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 #
Foldable Sum	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Sum m -> 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
Instance details 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) #
Bounded a => Bounded (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Sum a # maxBound :: Sum a #
Eq a => Eq (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Sum a -> Sum a -> Bool # (/=) :: Sum a -> Sum a -> Bool #
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 # (-) :: 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 #
Ord a => Ord (Sum a)	Since: base-2.1
Instance details 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 #
Read a => Read (Sum a)	Since: base-2.1
Instance details 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
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Sum a -> ShowS # show :: Sum a -> String # showList :: [Sum a] -> ShowS #
Generic (Sum a)
Instance details 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 => Semigroup (Sum a)	Since: base-4.9.0.0
Instance details 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 #
Num a => Monoid (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Sum a # mappend :: Sum a -> Sum a -> Sum a # mconcat :: [Sum a] -> Sum a #
Generic1 Sum
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 Sum :: k -> Type # Methods from1 :: Sum a -> Rep1 Sum a # to1 :: Rep1 Sum a -> Sum a #
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 #

Monoid under multiplication.

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

Instances

Monad Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Product a -> (a -> Product b) -> Product b # (>>) :: Product a -> Product b -> Product b # return :: a -> Product a # fail :: String -> Product a #
Functor Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Product a -> Product b # (<$) :: a -> Product b -> Product a #
Applicative Product	Since: base-4.8.0.0
Instance details 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 #
Foldable Product	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Product m -> 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
Instance details 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) #
Bounded a => Bounded (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Product a # maxBound :: Product a #
Eq a => Eq (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Product a -> Product a -> Bool # (/=) :: Product a -> Product a -> Bool #
Num a => Num (Product a)	Since: base-4.7.0.0
Instance details 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 #
Ord a => Ord (Product a)	Since: base-2.1
Instance details 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 #
Read a => Read (Product a)	Since: base-2.1
Instance details 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
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Product a -> ShowS # show :: Product a -> String # showList :: [Product a] -> ShowS #
Generic (Product a)
Instance details 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 => Semigroup (Product a)	Since: base-4.9.0.0
Instance details 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 #
Num a => Monoid (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Product a # mappend :: Product a -> Product a -> Product a # mconcat :: [Product a] -> Product a #
Generic1 Product
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 Product :: k -> Type # Methods from1 :: Product a -> Rep1 Product a # to1 :: Rep1 Product a -> Product a #
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))