Data.Semigroup

base-4.16.0.0: Basic libraries

Copyright | (C) 2011-2015 Edward Kmett
License | BSD-style (see the file LICENSE)
Maintainer | libraries@haskell.org
Stability | provisional
Portability | portable
Safe Haskell | Trustworthy
Language | Haskell2010

Data.Semigroup

Contents

- Semigroups
- Re-exported monoids from Data.Monoid
- Difference lists of a semigroup
- ArgMin, ArgMax

Description

A type `a` is a `Semigroup` if it provides an associative function (`<>`) that lets you combine any two values of type `a` into one. Where being associative means that the following must always hold:

    (a <> b) <> c == a <> (b <> c)

#### Examples

Expand

The `Min` `Semigroup` instance for `Int` is defined to always pick the smaller number: >>> Min 1 <> Min 2 <> Min 3 <> Min 4 :: Min Int Min {getMin = 1}

If we need to combine multiple values we can use the `sconcat` function to do so. We need to ensure however that we have at least one value to operate on, since otherwise our result would be undefined. It is for this reason that `sconcat` uses Data.List.NonEmpty.NonEmpty - a list that can never be empty:

    >>> (1 :| [])
    1 :| []               -- equivalent to [1] but guaranteed to be non-empty.

    >>> (1 :| [2, 3, 4])
    1 :| [2,3,4]          -- equivalent to [1,2,3,4] but guaranteed to be non-empty.

Equipped with this guaranteed to be non-empty data structure, we can combine values using `sconcat` and a `Semigroup` of our choosing. We can try the `Min` and `Max` instances of `Int` which pick the smallest, or largest number respectively:

    >>> sconcat (1 :| [2, 3, 4]) :: Min Int
    Min {getMin = 1}
    >>> sconcat (1 :| [2, 3, 4]) :: Max Int
    Max {getMax = 4}

String concatenation is another example of a `Semigroup` instance:

    >>> "foo" <> "bar"
    "foobar"

A `Semigroup` is a generalization of a `Monoid`. Yet unlike the `Semigroup`, the `Monoid` requires the presence of a neutral element (`mempty`) in addition to the associative operator. The requirement for a neutral element prevents many types from being a full Monoid, like Data.List.NonEmpty.NonEmpty.

Note that the use of `(<>)` in this module conflicts with an operator with the same name that is being exported by Data.Monoid. However, this package re-exports (most of) the contents of Data.Monoid, so to use semigroups and monoids in the same package just

    import Data.Semigroup

Since: base-4.9.0.0

Synopsis

- class Semigroup a where
  - (<>) :: a -> a -> a
  - sconcat :: NonEmpty a -> a
  - stimes :: Integral b => b -> a -> a
- stimesMonoid :: (Integral b, Monoid a) => b -> a -> a
- stimesIdempotent :: Integral b => b -> a -> a
- stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a
- mtimesDefault :: (Integral b, Monoid a) => b -> a -> a
- newtype Min a = Min {
  - getMin :: a
  }
- newtype Max a = Max {
  - getMax :: a
  }
- newtype First a = First {
  - getFirst :: a
  }
- newtype Last a = Last {
  - getLast :: a
  }
- newtype WrappedMonoid m = WrapMonoid {
  - unwrapMonoid :: m
  }
- newtype Dual a = Dual {
  - getDual :: a
  }
- newtype Endo a = Endo {
  - appEndo :: a -> a
  }
- newtype All = All {
  - getAll :: Bool
  }
- newtype Any = Any {
  - getAny :: Bool
  }
- newtype Sum a = Sum {
  - getSum :: a
  }
- newtype Product a = Product {
  - getProduct :: a
  }
- diff :: Semigroup m => m -> Endo m
- cycle1 :: Semigroup m => m -> m
- data Arg a b = Arg a b
- type ArgMin a b = Min (Arg a b)
- type ArgMax a b = Max (Arg a b)

# Documentation

class Semigroup a where Source #

The class of semigroups (types with an associative binary operation).

Instances should satisfy the following:

Associativity
  `x `<>` (y `<>` z) = (x `<>` y) `<>` z`

Since: base-4.9.0.0

Minimal complete definition

(<>)

Methods

(<>) :: a -> a -> a infixr 6 Source #

An associative operation.

    >>> [1,2,3] <> [4,5,6]
    [1,2,3,4,5,6]

sconcat :: NonEmpty a -> a Source #

Reduce a non-empty list with `<>`

The default definition should be sufficient, but this can be overridden for efficiency.

    >>> import Data.List.NonEmpty (NonEmpty (..))
    >>> sconcat $ "Hello" :| [" ", "Haskell", "!"]
    "Hello Haskell!"

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

Repeat a value `n` times.

Given that this works on a `Semigroup` it is allowed to fail if you request 0 or fewer repetitions, and the default definition will do so.

By making this a member of the class, idempotent semigroups and monoids can upgrade this to execute in \(\mathcal{O}(1)\) by picking `stimes = `stimesIdempotent`` or `stimes = `stimesIdempotentMonoid`` respectively.

    >>> stimes 4 [1]
    [1,1,1,1]

#### Instances

Instances details

Semigroup All Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: All -> All -> All Source # sconcat :: NonEmpty All -> All Source # stimes :: Integral b => b -> All -> All Source #
Semigroup Any Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Any -> Any -> Any Source # sconcat :: NonEmpty Any -> Any Source # stimes :: Integral b => b -> Any -> Any Source #
Semigroup Void Source # | Since: base-4.9.0.0
Instance details Defined in Data.Void Methods (<>) :: Void -> Void -> Void Source # sconcat :: NonEmpty Void -> Void Source # stimes :: Integral b => b -> Void -> Void Source #
Semigroup Event Source # | Since: base-4.10.0.0
Instance details Defined in GHC.Event.Internal.Types Methods (<>) :: Event -> Event -> Event Source # sconcat :: NonEmpty Event -> Event Source # stimes :: Integral b => b -> Event -> Event Source #
Semigroup Lifetime Source # | Since: base-4.10.0.0
Instance details Defined in GHC.Event.Internal.Types Methods (<>) :: Lifetime -> Lifetime -> Lifetime Source # sconcat :: NonEmpty Lifetime -> Lifetime Source # stimes :: Integral b => b -> Lifetime -> Lifetime Source #
Semigroup Ordering Source # | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Ordering -> Ordering -> Ordering Source # sconcat :: NonEmpty Ordering -> Ordering Source # stimes :: Integral b => b -> Ordering -> Ordering Source #
Semigroup () Source # | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: () -> () -> () Source # sconcat :: NonEmpty () -> () Source # stimes :: Integral b => b -> () -> () Source #
Bits a => Semigroup (And a) Source # | Since: base-4.16
Instance details Defined in Data.Bits Methods (<>) :: And a -> And a -> And a Source # sconcat :: NonEmpty (And a) -> And a Source # stimes :: Integral b => b -> And a -> And a Source #
FiniteBits a => Semigroup (Iff a) Source # | This constraint is arguably too strong. However, as some types (such as `Natural`) have undefined `complement`, this is the only safe choice. Since: base-4.16
Instance details Defined in Data.Bits Methods (<>) :: Iff a -> Iff a -> Iff a Source # sconcat :: NonEmpty (Iff a) -> Iff a Source # stimes :: Integral b => b -> Iff a -> Iff a Source #
Bits a => Semigroup (Ior a) Source # | Since: base-4.16
Instance details Defined in Data.Bits Methods (<>) :: Ior a -> Ior a -> Ior a Source # sconcat :: NonEmpty (Ior a) -> Ior a Source # stimes :: Integral b => b -> Ior a -> Ior a Source #
Bits a => Semigroup (Xor a) Source # | Since: base-4.16
Instance details Defined in Data.Bits Methods (<>) :: Xor a -> Xor a -> Xor a Source # sconcat :: NonEmpty (Xor a) -> Xor a Source # stimes :: Integral b => b -> Xor a -> Xor a Source #
Semigroup (Comparison a) Source # | `(`<>`)` on comparisons combines results with `(`<>`) @Ordering`. Without newtypes this equals ``liftA2` (`liftA2` (`<>`))`.
    (<>) :: Comparison a -> Comparison a -> Comparison a
    Comparison cmp <> Comparison cmp' = Comparison a a' ->
      cmp a a' <> cmp a a'
Instance details Defined in Data.Functor.Contravariant Methods (<>) :: Comparison a -> Comparison a -> Comparison a Source # sconcat :: NonEmpty (Comparison a) -> Comparison a Source # stimes :: Integral b => b -> Comparison a -> Comparison a Source #
Semigroup (Equivalence a) Source # | `(`<>`)` on equivalences uses logical conjunction `(`&&`)` on the results. Without newtypes this equals ``liftA2` (`liftA2` (&&))`.
    (<>) :: Equivalence a -> Equivalence a -> Equivalence a
    Equivalence equiv <> Equivalence equiv' = Equivalence a b ->
      equiv a b && equiv a b
Instance details Defined in Data.Functor.Contravariant Methods (<>) :: Equivalence a -> Equivalence a -> Equivalence a Source # sconcat :: NonEmpty (Equivalence a) -> Equivalence a Source # stimes :: Integral b => b -> Equivalence a -> Equivalence a Source #
Semigroup (Predicate a) Source # | `(`<>`)` on predicates uses logical conjunction `(`&&`)` on the results. Without newtypes this equals ``liftA2` (&&)`.
    (<>) :: Predicate a -> Predicate a -> Predicate a
    Predicate pred <> Predicate pred' = Predicate a ->
      pred a && pred' a
Instance details Defined in Data.Functor.Contravariant Methods (<>) :: Predicate a -> Predicate a -> Predicate a Source # sconcat :: NonEmpty (Predicate a) -> Predicate a Source # stimes :: Integral b => b -> Predicate a -> Predicate a Source #
Semigroup a => Semigroup (Identity a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods (<>) :: Identity a -> Identity a -> Identity a Source # sconcat :: NonEmpty (Identity a) -> Identity a Source # stimes :: Integral b => b -> Identity a -> Identity a Source #
Semigroup (First a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Monoid Methods (<>) :: First a -> First a -> First a Source # sconcat :: NonEmpty (First a) -> First a Source # stimes :: Integral b => b -> First a -> First a Source #
Semigroup (Last a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Monoid Methods (<>) :: Last a -> Last a -> Last a Source # sconcat :: NonEmpty (Last a) -> Last a Source # stimes :: Integral b => b -> Last a -> Last a Source #
Semigroup a => Semigroup (Down a) Source # | Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods (<>) :: Down a -> Down a -> Down a Source # sconcat :: NonEmpty (Down a) -> Down a Source # stimes :: Integral b => b -> Down a -> Down a Source #
Semigroup (First a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: First a -> First a -> First a Source # sconcat :: NonEmpty (First a) -> First a Source # stimes :: Integral b => b -> First a -> First a Source #
Semigroup (Last a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Last a -> Last a -> Last a Source # sconcat :: NonEmpty (Last a) -> Last a Source # stimes :: Integral b => b -> Last a -> Last a Source #
Ord a => Semigroup (Max a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Max a -> Max a -> Max a Source # sconcat :: NonEmpty (Max a) -> Max a Source # stimes :: Integral b => b -> Max a -> Max a Source #
Ord a => Semigroup (Min a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Min a -> Min a -> Min a Source # sconcat :: NonEmpty (Min a) -> Min a Source # stimes :: Integral b => b -> Min a -> Min a Source #
Monoid m => Semigroup (WrappedMonoid m) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source # sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m Source # stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m Source #
Semigroup a => Semigroup (Dual a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Dual a -> Dual a -> Dual a Source # sconcat :: NonEmpty (Dual a) -> Dual a Source # stimes :: Integral b => b -> Dual a -> Dual a Source #
Semigroup (Endo a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Endo a -> Endo a -> Endo a Source # sconcat :: NonEmpty (Endo a) -> Endo a Source # stimes :: Integral b => b -> Endo a -> Endo a Source #
Num a => Semigroup (Product a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Product a -> Product a -> Product a Source # sconcat :: NonEmpty (Product a) -> Product a Source # stimes :: Integral b => b -> Product a -> Product a Source #
Num a => Semigroup (Sum a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Sum a -> Sum a -> Sum a Source # sconcat :: NonEmpty (Sum a) -> Sum a Source # stimes :: Integral b => b -> Sum a -> Sum a Source #
Semigroup p => Semigroup (Par1 p) Source # | Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: Par1 p -> Par1 p -> Par1 p Source # sconcat :: NonEmpty (Par1 p) -> Par1 p Source # stimes :: Integral b => b -> Par1 p -> Par1 p Source #
Semigroup a => Semigroup (IO a) Source # | Since: base-4.10.0.0
Instance details Defined in GHC.Base Methods (<>) :: IO a -> IO a -> IO a Source # sconcat :: NonEmpty (IO a) -> IO a Source # stimes :: Integral b => b -> IO a -> IO a Source #
Semigroup (NonEmpty a) Source # | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a Source # sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a Source # stimes :: Integral b => b -> NonEmpty a -> NonEmpty a Source #
Semigroup a => Semigroup (Maybe a) Source # | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Maybe a -> Maybe a -> Maybe a Source # sconcat :: NonEmpty (Maybe a) -> Maybe a Source # stimes :: Integral b => b -> Maybe a -> Maybe a Source #
Semigroup a => Semigroup (a) Source # | Since: base-4.15
Instance details Defined in GHC.Base Methods (<>) :: (a) -> (a) -> (a) Source # sconcat :: NonEmpty (a) -> (a) Source # stimes :: Integral b => b -> (a) -> (a) Source #
Semigroup [a] Source # | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: [a] -> [a] -> [a] Source # sconcat :: NonEmpty [a] -> [a] Source # stimes :: Integral b => b -> [a] -> [a] Source #
Semigroup (Either a b) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Either Methods (<>) :: Either a b -> Either a b -> Either a b Source # sconcat :: NonEmpty (Either a b) -> Either a b Source # stimes :: Integral b0 => b0 -> Either a b -> Either a b Source #
Semigroup a => Semigroup (Op a b) Source # | `(`<>`) @(Op a b)` without newtypes is `(`<>`) @(b->a)` = `liftA2 (`<>`)`. This lifts the `Semigroup` operation `(`<>`)` over the output of `a`.
    (<>) :: Op a b -> Op a b -> Op a b
    Op f <> Op g = Op a -> f a <> g a
Instance details Defined in Data.Functor.Contravariant Methods (<>) :: Op a b -> Op a b -> Op a b Source # sconcat :: NonEmpty (Op a b) -> Op a b Source # stimes :: Integral b0 => b0 -> Op a b -> Op a b Source #
Semigroup (Proxy s) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Proxy Methods (<>) :: Proxy s -> Proxy s -> Proxy s Source # sconcat :: NonEmpty (Proxy s) -> Proxy s Source # stimes :: Integral b => b -> Proxy s -> Proxy s Source #
Semigroup (U1 p) Source # | Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: U1 p -> U1 p -> U1 p Source # sconcat :: NonEmpty (U1 p) -> U1 p Source # stimes :: Integral b => b -> U1 p -> U1 p Source #
Semigroup (V1 p) Source # | Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: V1 p -> V1 p -> V1 p Source # sconcat :: NonEmpty (V1 p) -> V1 p Source # stimes :: Integral b => b -> V1 p -> V1 p Source #
Semigroup a => Semigroup (ST s a) Source # | Since: base-4.11.0.0
Instance details Defined in GHC.ST Methods (<>) :: ST s a -> ST s a -> ST s a Source # sconcat :: NonEmpty (ST s a) -> ST s a Source # stimes :: Integral b => b -> ST s a -> ST s a Source #
Semigroup b => Semigroup (a -> b) Source # | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a -> b) -> (a -> b) -> a -> b Source # sconcat :: NonEmpty (a -> b) -> a -> b Source # stimes :: Integral b0 => b0 -> (a -> b) -> a -> b Source #
(Semigroup a, Semigroup b) => Semigroup (a, b) Source # | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b) -> (a, b) -> (a, b) Source # sconcat :: NonEmpty (a, b) -> (a, b) Source # stimes :: Integral b0 => b0 -> (a, b) -> (a, b) Source #
Semigroup a => Semigroup (Const a b) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (<>) :: Const a b -> Const a b -> Const a b Source # sconcat :: NonEmpty (Const a b) -> Const a b Source # stimes :: Integral b0 => b0 -> Const a b -> Const a b Source #
(Applicative f, Semigroup a) => Semigroup (Ap f a) Source # | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (<>) :: Ap f a -> Ap f a -> Ap f a Source # sconcat :: NonEmpty (Ap f a) -> Ap f a Source # stimes :: Integral b => b -> Ap f a -> Ap f a Source #
Alternative f => Semigroup (Alt f a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Alt f a -> Alt f a -> Alt f a Source # sconcat :: NonEmpty (Alt f a) -> Alt f a Source # stimes :: Integral b => b -> Alt f a -> Alt f a Source #
Semigroup (f p) => Semigroup (Rec1 f p) Source # | Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: Rec1 f p -> Rec1 f p -> Rec1 f p Source # sconcat :: NonEmpty (Rec1 f p) -> Rec1 f p Source # stimes :: Integral b => b -> Rec1 f p -> Rec1 f p Source #
(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) Source # | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b, c) -> (a, b, c) -> (a, b, c) Source # sconcat :: NonEmpty (a, b, c) -> (a, b, c) Source # stimes :: Integral b0 => b0 -> (a, b, c) -> (a, b, c) Source #
(Semigroup (f a), Semigroup (g a)) => Semigroup (Product f g a) Source # | Since: base-4.16.0.0
Instance details Defined in Data.Functor.Product Methods (<>) :: Product f g a -> Product f g a -> Product f g a Source # sconcat :: NonEmpty (Product f g a) -> Product f g a Source # stimes :: Integral b => b -> Product f g a -> Product f g a Source #
(Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p) Source # | Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p Source # sconcat :: NonEmpty ((f :*: g) p) -> (f :*: g) p Source # stimes :: Integral b => b -> (f :*: g) p -> (f :*: g) p Source #
Semigroup c => Semigroup (K1 i c p) Source # | Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: K1 i c p -> K1 i c p -> K1 i c p Source # sconcat :: NonEmpty (K1 i c p) -> K1 i c p Source # stimes :: Integral b => b -> K1 i c p -> K1 i c p Source #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) Source # | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # sconcat :: NonEmpty (a, b, c, d) -> (a, b, c, d) Source # stimes :: Integral b0 => b0 -> (a, b, c, d) -> (a, b, c, d) Source #
Semigroup (f (g a)) => Semigroup (Compose f g a) Source # | Since: base-4.16.0.0
Instance details Defined in Data.Functor.Compose Methods (<>) :: Compose f g a -> Compose f g a -> Compose f g a Source # sconcat :: NonEmpty (Compose f g a) -> Compose f g a Source # stimes :: Integral b => b -> Compose f g a -> Compose f g a Source #
Semigroup (f (g p)) => Semigroup ((f :.: g) p) Source # | Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p Source # sconcat :: NonEmpty ((f :.: g) p) -> (f :.: g) p Source # stimes :: Integral b => b -> (f :.: g) p -> (f :.: g) p Source #
Semigroup (f p) => Semigroup (M1 i c f p) Source # | Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: M1 i c f p -> M1 i c f p -> M1 i c f p Source # sconcat :: NonEmpty (M1 i c f p) -> M1 i c f p Source # stimes :: Integral b => b -> M1 i c f p -> M1 i c f p Source #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) Source # | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source # sconcat :: NonEmpty (a, b, c, d, e) -> (a, b, c, d, e) Source # stimes :: Integral b0 => b0 -> (a, b, c, d, e) -> (a, b, c, d, e) Source #

stimesMonoid :: (Integral b, Monoid a) => b -> a -> a Source #

This is a valid definition of `stimes` for a `Monoid`.

Unlike the default definition of `stimes`, it is defined for 0 and so it should be preferred where possible.

stimesIdempotent :: Integral b => b -> a -> a Source #

This is a valid definition of `stimes` for an idempotent `Semigroup`.

When `x <> x = x`, this definition should be preferred, because it works in \(\mathcal{O}(1)\) rather than \(\mathcal{O}(\log n)\).

stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a Source #

This is a valid definition of `stimes` for an idempotent `Monoid`.

When `mappend x x = x`, this definition should be preferred, because it works in \(\mathcal{O}(1)\) rather than \(\mathcal{O}(\log n)\)

mtimesDefault :: (Integral b, Monoid a) => b -> a -> a Source #

Repeat a value `n` times.

    mtimesDefault n a = a <> a <> ... <> a  -- using <> (n-1) times

Implemented using `stimes` and `mempty`.

This is a suitable definition for an `mtimes` member of `Monoid`.

# Semigroups

newtype Min a Source #

Constructors

Min |
Fields getMin :: a

#### Instances

Instances details

MonadFix Min Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mfix :: (a -> Min a) -> Min a Source #
Foldable Min Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Min m -> m Source # foldMap :: Monoid m => (a -> m) -> Min a -> m Source # foldMap' :: Monoid m => (a -> m) -> Min a -> m Source # foldr :: (a -> b -> b) -> b -> Min a -> b Source # foldr' :: (a -> b -> b) -> b -> Min a -> b Source # foldl :: (b -> a -> b) -> b -> Min a -> b Source # foldl' :: (b -> a -> b) -> b -> Min a -> b Source # foldr1 :: (a -> a -> a) -> Min a -> a Source # foldl1 :: (a -> a -> a) -> Min a -> a Source # toList :: Min a -> [a] Source # null :: Min a -> Bool Source # length :: Min a -> Int Source # elem :: Eq a => a -> Min a -> Bool Source # maximum :: Ord a => Min a -> a Source # minimum :: Ord a => Min a -> a Source # sum :: Num a => Min a -> a Source # product :: Num a => Min a -> a Source #
Traversable Min Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Min a -> f (Min b) Source # sequenceA :: Applicative f => Min (f a) -> f (Min a) Source # mapM :: Monad m => (a -> m b) -> Min a -> m (Min b) Source # sequence :: Monad m => Min (m a) -> m (Min a) Source #
Applicative Min Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Min a Source # (<*>) :: Min (a -> b) -> Min a -> Min b Source # liftA2 :: (a -> b -> c) -> Min a -> Min b -> Min c Source # (*>) :: Min a -> Min b -> Min b Source # (<*) :: Min a -> Min b -> Min a Source #
Functor Min Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Min a -> Min b Source # (<$) :: a -> Min b -> Min a Source #
Monad Min Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Min a -> (a -> Min b) -> Min b Source # (>>) :: Min a -> Min b -> Min b Source # return :: a -> Min a Source #
Data a => Data (Min a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Min a -> c (Min a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Min a) Source # toConstr :: Min a -> Constr Source # dataTypeOf :: Min a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Min a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Min a)) Source # gmapT :: (forall b. Data b => b -> b) -> Min a -> Min a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Min a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Min a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) Source #
(Ord a, Bounded a) => Monoid (Min a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Min a Source # mappend :: Min a -> Min a -> Min a Source # mconcat :: [Min a] -> Min a Source #
Ord a => Semigroup (Min a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Min a -> Min a -> Min a Source # sconcat :: NonEmpty (Min a) -> Min a Source # stimes :: Integral b => b -> Min a -> Min a Source #
Bounded a => Bounded (Min a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods minBound :: Min a Source # maxBound :: Min a Source #
Enum a => Enum (Min a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods succ :: Min a -> Min a Source # pred :: Min a -> Min a Source # toEnum :: Int -> Min a Source # fromEnum :: Min a -> Int Source # enumFrom :: Min a -> [Min a] Source # enumFromThen :: Min a -> Min a -> [Min a] Source # enumFromTo :: Min a -> Min a -> [Min a] Source # enumFromThenTo :: Min a -> Min a -> Min a -> [Min a] Source #
Generic (Min a) Source # |
Instance details Defined in Data.Semigroup Associated Types type Rep (Min a) :: Type -> Type Source # Methods from :: Min a -> Rep (Min a) x Source # to :: Rep (Min a) x -> Min a Source #
Num a => Num (Min a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (+) :: Min a -> Min a -> Min a Source # (-) :: Min a -> Min a -> Min a Source # (*) :: Min a -> Min a -> Min a Source # negate :: Min a -> Min a Source # abs :: Min a -> Min a Source # signum :: Min a -> Min a Source # fromInteger :: Integer -> Min a Source #
Read a => Read (Min a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (Min a) Source # readList :: ReadS [Min a] Source # readPrec :: ReadPrec (Min a) Source # readListPrec :: ReadPrec [Min a] Source #
Show a => Show (Min a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> Min a -> ShowS Source # show :: Min a -> String Source # showList :: [Min a] -> ShowS Source #
Eq a => Eq (Min a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: Min a -> Min a -> Bool Source # (/=) :: Min a -> Min a -> Bool Source #
Ord a => Ord (Min a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: Min a -> Min a -> Ordering Source # (<) :: Min a -> Min a -> Bool Source # (<=) :: Min a -> Min a -> Bool Source # (>) :: Min a -> Min a -> Bool Source # (>=) :: Min a -> Min a -> Bool Source # max :: Min a -> Min a -> Min a Source # min :: Min a -> Min a -> Min a Source #
Generic1 Min Source # |
Instance details Defined in Data.Semigroup Associated Types type Rep1 Min :: k -> Type Source # Methods from1 :: forall (a :: k). Min a -> Rep1 Min a Source # to1 :: forall (a :: k). Rep1 Min a -> Min a Source #
type Rep (Min a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep (Min a) = D1 ('MetaData "Min" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "Min" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMin") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Rep1 Min Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep1 Min = D1 ('MetaData "Min" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "Min" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMin") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

newtype Max a Source #

Constructors

Max |
Fields getMax :: a

#### Instances

Instances details

MonadFix Max Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mfix :: (a -> Max a) -> Max a Source #
Foldable Max Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Max m -> m Source # foldMap :: Monoid m => (a -> m) -> Max a -> m Source # foldMap' :: Monoid m => (a -> m) -> Max a -> m Source # foldr :: (a -> b -> b) -> b -> Max a -> b Source # foldr' :: (a -> b -> b) -> b -> Max a -> b Source # foldl :: (b -> a -> b) -> b -> Max a -> b Source # foldl' :: (b -> a -> b) -> b -> Max a -> b Source # foldr1 :: (a -> a -> a) -> Max a -> a Source # foldl1 :: (a -> a -> a) -> Max a -> a Source # toList :: Max a -> [a] Source # null :: Max a -> Bool Source # length :: Max a -> Int Source # elem :: Eq a => a -> Max a -> Bool Source # maximum :: Ord a => Max a -> a Source # minimum :: Ord a => Max a -> a Source # sum :: Num a => Max a -> a Source # product :: Num a => Max a -> a Source #
Traversable Max Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Max a -> f (Max b) Source # sequenceA :: Applicative f => Max (f a) -> f (Max a) Source # mapM :: Monad m => (a -> m b) -> Max a -> m (Max b) Source # sequence :: Monad m => Max (m a) -> m (Max a) Source #
Applicative Max Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Max a Source # (<*>) :: Max (a -> b) -> Max a -> Max b Source # liftA2 :: (a -> b -> c) -> Max a -> Max b -> Max c Source # (*>) :: Max a -> Max b -> Max b Source # (<*) :: Max a -> Max b -> Max a Source #
Functor Max Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Max a -> Max b Source # (<$) :: a -> Max b -> Max a Source #
Monad Max Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Max a -> (a -> Max b) -> Max b Source # (>>) :: Max a -> Max b -> Max b Source # return :: a -> Max a Source #
Data a => Data (Max a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Max a -> c (Max a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Max a) Source # toConstr :: Max a -> Constr Source # dataTypeOf :: Max a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Max a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Max a)) Source # gmapT :: (forall b. Data b => b -> b) -> Max a -> Max a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Max a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Max a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) Source #
(Ord a, Bounded a) => Monoid (Max a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Max a Source # mappend :: Max a -> Max a -> Max a Source # mconcat :: [Max a] -> Max a Source #
Ord a => Semigroup (Max a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Max a -> Max a -> Max a Source # sconcat :: NonEmpty (Max a) -> Max a Source # stimes :: Integral b => b -> Max a -> Max a Source #
Bounded a => Bounded (Max a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods minBound :: Max a Source # maxBound :: Max a Source #
Enum a => Enum (Max a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods succ :: Max a -> Max a Source # pred :: Max a -> Max a Source # toEnum :: Int -> Max a Source # fromEnum :: Max a -> Int Source # enumFrom :: Max a -> [Max a] Source # enumFromThen :: Max a -> Max a -> [Max a] Source # enumFromTo :: Max a -> Max a -> [Max a] Source # enumFromThenTo :: Max a -> Max a -> Max a -> [Max a] Source #
Generic (Max a) Source # |
Instance details Defined in Data.Semigroup Associated Types type Rep (Max a) :: Type -> Type Source # Methods from :: Max a -> Rep (Max a) x Source # to :: Rep (Max a) x -> Max a Source #
Num a => Num (Max a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (+) :: Max a -> Max a -> Max a Source # (-) :: Max a -> Max a -> Max a Source # (*) :: Max a -> Max a -> Max a Source # negate :: Max a -> Max a Source # abs :: Max a -> Max a Source # signum :: Max a -> Max a Source # fromInteger :: Integer -> Max a Source #
Read a => Read (Max a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (Max a) Source # readList :: ReadS [Max a] Source # readPrec :: ReadPrec (Max a) Source # readListPrec :: ReadPrec [Max a] Source #
Show a => Show (Max a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> Max a -> ShowS Source # show :: Max a -> String Source # showList :: [Max a] -> ShowS Source #
Eq a => Eq (Max a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: Max a -> Max a -> Bool Source # (/=) :: Max a -> Max a -> Bool Source #
Ord a => Ord (Max a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: Max a -> Max a -> Ordering Source # (<) :: Max a -> Max a -> Bool Source # (<=) :: Max a -> Max a -> Bool Source # (>) :: Max a -> Max a -> Bool Source # (>=) :: Max a -> Max a -> Bool Source # max :: Max a -> Max a -> Max a Source # min :: Max a -> Max a -> Max a Source #
Generic1 Max Source # |
Instance details Defined in Data.Semigroup Associated Types type Rep1 Max :: k -> Type Source # Methods from1 :: forall (a :: k). Max a -> Rep1 Max a Source # to1 :: forall (a :: k). Rep1 Max a -> Max a Source #
type Rep (Max a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep (Max a) = D1 ('MetaData "Max" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "Max" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMax") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Rep1 Max Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep1 Max = D1 ('MetaData "Max" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "Max" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMax") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

newtype First a Source #

Constructors

First |
Fields getFirst :: a

#### Instances

Instances details

MonadFix First Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mfix :: (a -> First a) -> First a Source #
Foldable First Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => First m -> m Source # foldMap :: Monoid m => (a -> m) -> First a -> m Source # foldMap' :: Monoid m => (a -> m) -> First a -> m Source # foldr :: (a -> b -> b) -> b -> First a -> b Source # foldr' :: (a -> b -> b) -> b -> First a -> b Source # foldl :: (b -> a -> b) -> b -> First a -> b Source # foldl' :: (b -> a -> b) -> b -> First a -> b Source # foldr1 :: (a -> a -> a) -> First a -> a Source # foldl1 :: (a -> a -> a) -> First a -> a Source # toList :: First a -> [a] Source # null :: First a -> Bool Source # length :: First a -> Int Source # elem :: Eq a => a -> First a -> Bool Source # maximum :: Ord a => First a -> a Source # minimum :: Ord a => First a -> a Source # sum :: Num a => First a -> a Source # product :: Num a => First a -> a Source #
Traversable First Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> First a -> f (First b) Source # sequenceA :: Applicative f => First (f a) -> f (First a) Source # mapM :: Monad m => (a -> m b) -> First a -> m (First b) Source # sequence :: Monad m => First (m a) -> m (First a) Source #
Applicative First Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> First a Source # (<*>) :: First (a -> b) -> First a -> First b Source # liftA2 :: (a -> b -> c) -> First a -> First b -> First c Source # (*>) :: First a -> First b -> First b Source # (<*) :: First a -> First b -> First a Source #
Functor First Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> First a -> First b Source # (<$) :: a -> First b -> First a Source #
Monad First Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: First a -> (a -> First b) -> First b Source # (>>) :: First a -> First b -> First b Source # return :: a -> First a Source #
Data a => Data (First a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> First a -> c (First a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (First a) Source # toConstr :: First a -> Constr Source # dataTypeOf :: First a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (First a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (First a)) Source # gmapT :: (forall b. Data b => b -> b) -> First a -> First a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> First a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> First a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> First a -> m (First a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) Source #
Semigroup (First a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: First a -> First a -> First a Source # sconcat :: NonEmpty (First a) -> First a Source # stimes :: Integral b => b -> First a -> First a Source #
Bounded a => Bounded (First a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods minBound :: First a Source # maxBound :: First a Source #
Enum a => Enum (First a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods succ :: First a -> First a Source # pred :: First a -> First a Source # toEnum :: Int -> First a Source # fromEnum :: First a -> Int Source # enumFrom :: First a -> [First a] Source # enumFromThen :: First a -> First a -> [First a] Source # enumFromTo :: First a -> First a -> [First a] Source # enumFromThenTo :: First a -> First a -> First a -> [First a] Source #
Generic (First a) Source # |
Instance details Defined in Data.Semigroup Associated Types type Rep (First a) :: Type -> Type Source # Methods from :: First a -> Rep (First a) x Source # to :: Rep (First a) x -> First a Source #
Read a => Read (First a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (First a) Source # readList :: ReadS [First a] Source # readPrec :: ReadPrec (First a) Source # readListPrec :: ReadPrec [First a] Source #
Show a => Show (First a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> First a -> ShowS Source # show :: First a -> String Source # showList :: [First a] -> ShowS Source #
Eq a => Eq (First a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: First a -> First a -> Bool Source # (/=) :: First a -> First a -> Bool Source #
Ord a => Ord (First a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: First a -> First a -> Ordering Source # (<) :: First a -> First a -> Bool Source # (<=) :: First a -> First a -> Bool Source # (>) :: First a -> First a -> Bool Source # (>=) :: First a -> First a -> Bool Source # max :: First a -> First a -> First a Source # min :: First a -> First a -> First a Source #
Generic1 First Source # |
Instance details Defined in Data.Semigroup Associated Types type Rep1 First :: k -> Type Source # Methods from1 :: forall (a :: k). First a -> Rep1 First a Source # to1 :: forall (a :: k). Rep1 First a -> First a Source #
type Rep (First a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep (First a) = D1 ('MetaData "First" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "First" 'PrefixI 'True) (S1 ('MetaSel ('Just "getFirst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Rep1 First Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep1 First = D1 ('MetaData "First" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "First" 'PrefixI 'True) (S1 ('MetaSel ('Just "getFirst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

newtype Last a Source #

Constructors

Last |
Fields getLast :: a

#### Instances

Instances details

MonadFix Last Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mfix :: (a -> Last a) -> Last a Source #
Foldable Last Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Last m -> m Source # foldMap :: Monoid m => (a -> m) -> Last a -> m Source # foldMap' :: Monoid m => (a -> m) -> Last a -> m Source # foldr :: (a -> b -> b) -> b -> Last a -> b Source # foldr' :: (a -> b -> b) -> b -> Last a -> b Source # foldl :: (b -> a -> b) -> b -> Last a -> b Source # foldl' :: (b -> a -> b) -> b -> Last a -> b Source # foldr1 :: (a -> a -> a) -> Last a -> a Source # foldl1 :: (a -> a -> a) -> Last a -> a Source # toList :: Last a -> [a] Source # null :: Last a -> Bool Source # length :: Last a -> Int Source # elem :: Eq a => a -> Last a -> Bool Source # maximum :: Ord a => Last a -> a Source # minimum :: Ord a => Last a -> a Source # sum :: Num a => Last a -> a Source # product :: Num a => Last a -> a Source #
Traversable Last Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) Source # sequenceA :: Applicative f => Last (f a) -> f (Last a) Source # mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) Source # sequence :: Monad m => Last (m a) -> m (Last a) Source #
Applicative Last Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Last a Source # (<*>) :: Last (a -> b) -> Last a -> Last b Source # liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c Source # (*>) :: Last a -> Last b -> Last b Source # (<*) :: Last a -> Last b -> Last a Source #
Functor Last Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Last a -> Last b Source # (<$) :: a -> Last b -> Last a Source #
Monad Last Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Last a -> (a -> Last b) -> Last b Source # (>>) :: Last a -> Last b -> Last b Source # return :: a -> Last a Source #
Data a => Data (Last a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Last a -> c (Last a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Last a) Source # toConstr :: Last a -> Constr Source # dataTypeOf :: Last a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Last a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Last a)) Source # gmapT :: (forall b. Data b => b -> b) -> Last a -> Last a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Last a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Last a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) Source #
Semigroup (Last a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Last a -> Last a -> Last a Source # sconcat :: NonEmpty (Last a) -> Last a Source # stimes :: Integral b => b -> Last a -> Last a Source #
Bounded a => Bounded (Last a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods minBound :: Last a Source # maxBound :: Last a Source #
Enum a => Enum (Last a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods succ :: Last a -> Last a Source # pred :: Last a -> Last a Source # toEnum :: Int -> Last a Source # fromEnum :: Last a -> Int Source # enumFrom :: Last a -> [Last a] Source # enumFromThen :: Last a -> Last a -> [Last a] Source # enumFromTo :: Last a -> Last a -> [Last a] Source # enumFromThenTo :: Last a -> Last a -> Last a -> [Last a] Source #
Generic (Last a) Source # |
Instance details Defined in Data.Semigroup Associated Types type Rep (Last a) :: Type -> Type Source # Methods from :: Last a -> Rep (Last a) x Source # to :: Rep (Last a) x -> Last a Source #
Read a => Read (Last a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (Last a) Source # readList :: ReadS [Last a] Source # readPrec :: ReadPrec (Last a) Source # readListPrec :: ReadPrec [Last a] Source #
Show a => Show (Last a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> Last a -> ShowS Source # show :: Last a -> String Source # showList :: [Last a] -> ShowS Source #
Eq a => Eq (Last a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: Last a -> Last a -> Bool Source # (/=) :: Last a -> Last a -> Bool Source #
Ord a => Ord (Last a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: Last a -> Last a -> Ordering Source # (<) :: Last a -> Last a -> Bool Source # (<=) :: Last a -> Last a -> Bool Source # (>) :: Last a -> Last a -> Bool Source # (>=) :: Last a -> Last a -> Bool Source # max :: Last a -> Last a -> Last a Source # min :: Last a -> Last a -> Last a Source #
Generic1 Last Source # |
Instance details Defined in Data.Semigroup Associated Types type Rep1 Last :: k -> Type Source # Methods from1 :: forall (a :: k). Last a -> Rep1 Last a Source # to1 :: forall (a :: k). Rep1 Last a -> Last a Source #
type Rep (Last a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep (Last a) = D1 ('MetaData "Last" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "Last" 'PrefixI 'True) (S1 ('MetaSel ('Just "getLast") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Rep1 Last Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep1 Last = D1 ('MetaData "Last" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "Last" 'PrefixI 'True) (S1 ('MetaSel ('Just "getLast") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

newtype WrappedMonoid m Source #

Provide a Semigroup for an arbitrary Monoid.

NOTE: This is not needed anymore since `Semigroup` became a superclass of `Monoid` in base-4.11 and this newtype be deprecated at some point in the future.

Constructors

WrapMonoid |
Fields unwrapMonoid :: m

#### Instances

Instances details

Data m => Data (WrappedMonoid m) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> WrappedMonoid m -> c (WrappedMonoid m) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (WrappedMonoid m) Source # toConstr :: WrappedMonoid m -> Constr Source # dataTypeOf :: WrappedMonoid m -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (WrappedMonoid m)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (WrappedMonoid m)) Source # gmapT :: (forall b. Data b => b -> b) -> WrappedMonoid m -> WrappedMonoid m Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonoid m -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonoid m -> r Source # gmapQ :: (forall d. Data d => d -> u) -> WrappedMonoid m -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> WrappedMonoid m -> u Source # gmapM :: Monad m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) Source # gmapMp :: MonadPlus m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) Source # gmapMo :: MonadPlus m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) Source #
Monoid m => Monoid (WrappedMonoid m) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: WrappedMonoid m Source # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source # mconcat :: [WrappedMonoid m] -> WrappedMonoid m Source #
Monoid m => Semigroup (WrappedMonoid m) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source # sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m Source # stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m Source #
Bounded m => Bounded (WrappedMonoid m) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods minBound :: WrappedMonoid m Source # maxBound :: WrappedMonoid m Source #
Enum a => Enum (WrappedMonoid a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods succ :: WrappedMonoid a -> WrappedMonoid a Source # pred :: WrappedMonoid a -> WrappedMonoid a Source # toEnum :: Int -> WrappedMonoid a Source # fromEnum :: WrappedMonoid a -> Int Source # enumFrom :: WrappedMonoid a -> [WrappedMonoid a] Source # enumFromThen :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] Source # enumFromTo :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] Source # enumFromThenTo :: WrappedMonoid a -> WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] Source #
Generic (WrappedMonoid m) Source # |
Instance details Defined in Data.Semigroup Associated Types type Rep (WrappedMonoid m) :: Type -> Type Source # Methods from :: WrappedMonoid m -> Rep (WrappedMonoid m) x Source # to :: Rep (WrappedMonoid m) x -> WrappedMonoid m Source #
Read m => Read (WrappedMonoid m) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (WrappedMonoid m) Source # readList :: ReadS [WrappedMonoid m] Source # readPrec :: ReadPrec (WrappedMonoid m) Source # readListPrec :: ReadPrec [WrappedMonoid m] Source #
Show m => Show (WrappedMonoid m) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> WrappedMonoid m -> ShowS Source # show :: WrappedMonoid m -> String Source # showList :: [WrappedMonoid m] -> ShowS Source #
Eq m => Eq (WrappedMonoid m) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # (/=) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source #
Ord m => Ord (WrappedMonoid m) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: WrappedMonoid m -> WrappedMonoid m -> Ordering Source # (<) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # (<=) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # (>) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # (>=) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # max :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source # min :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source #
Generic1 WrappedMonoid Source # |
Instance details Defined in Data.Semigroup Associated Types type Rep1 WrappedMonoid :: k -> Type Source # Methods from1 :: forall (a :: k). WrappedMonoid a -> Rep1 WrappedMonoid a Source # to1 :: forall (a :: k). Rep1 WrappedMonoid a -> WrappedMonoid a Source #
type Rep (WrappedMonoid m) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep (WrappedMonoid m) = D1 ('MetaData "WrappedMonoid" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "WrapMonoid" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapMonoid") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 m)))
type Rep1 WrappedMonoid Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep1 WrappedMonoid = D1 ('MetaData "WrappedMonoid" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "WrapMonoid" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapMonoid") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

# Re-exported monoids from Data.Monoid

newtype Dual a Source #

The dual of a `Monoid`, obtained by swapping the arguments of `mappend`.

    >>> getDual (mappend (Dual "Hello") (Dual "World"))
    "WorldHello"

Constructors

Dual |
Fields getDual :: a

#### Instances

Instances details

MonadFix Dual Source # | Since: base-4.8.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> Dual a) -> Dual a Source #
MonadZip Dual Source # | Since: base-4.8.0.0
Instance details Defined in Control.Monad.Zip Methods mzip :: Dual a -> Dual b -> Dual (a, b) Source # mzipWith :: (a -> b -> c) -> Dual a -> Dual b -> Dual c Source # munzip :: Dual (a, b) -> (Dual a, Dual b) Source #
Foldable Dual Source # | Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Dual m -> m Source # foldMap :: Monoid m => (a -> m) -> Dual a -> m Source # foldMap' :: Monoid m => (a -> m) -> Dual a -> m Source # foldr :: (a -> b -> b) -> b -> Dual a -> b Source # foldr' :: (a -> b -> b) -> b -> Dual a -> b Source # foldl :: (b -> a -> b) -> b -> Dual a -> b Source # foldl' :: (b -> a -> b) -> b -> Dual a -> b Source # foldr1 :: (a -> a -> a) -> Dual a -> a Source # foldl1 :: (a -> a -> a) -> Dual a -> a Source # toList :: Dual a -> [a] Source # null :: Dual a -> Bool Source # length :: Dual a -> Int Source # elem :: Eq a => a -> Dual a -> Bool Source # maximum :: Ord a => Dual a -> a Source # minimum :: Ord a => Dual a -> a Source # sum :: Num a => Dual a -> a Source # product :: Num a => Dual a -> a Source #
Traversable Dual Source # | Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b) Source # sequenceA :: Applicative f => Dual (f a) -> f (Dual a) Source # mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b) Source # sequence :: Monad m => Dual (m a) -> m (Dual a) Source #
Applicative Dual Source # | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Dual a Source # (<*>) :: Dual (a -> b) -> Dual a -> Dual b Source # liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c Source # (*>) :: Dual a -> Dual b -> Dual b Source # (<*) :: Dual a -> Dual b -> Dual a Source #
Functor Dual Source # | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Dual a -> Dual b Source # (<$) :: a -> Dual b -> Dual a Source #
Monad Dual Source # | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Dual a -> (a -> Dual b) -> Dual b Source # (>>) :: Dual a -> Dual b -> Dual b Source # return :: a -> Dual a Source #
Data a => Data (Dual a) Source # | Since: base-4.8.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Dual a -> c (Dual a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Dual a) Source # toConstr :: Dual a -> Constr Source # dataTypeOf :: Dual a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Dual a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Dual a)) Source # gmapT :: (forall b. Data b => b -> b) -> Dual a -> Dual a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Dual a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Dual a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) Source #
Monoid a => Monoid (Dual a) Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Dual a Source # mappend :: Dual a -> Dual a -> Dual a Source # mconcat :: [Dual a] -> Dual a Source #
Semigroup a => Semigroup (Dual a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Dual a -> Dual a -> Dual a Source # sconcat :: NonEmpty (Dual a) -> Dual a Source # stimes :: Integral b => b -> Dual a -> Dual a Source #
Bounded a => Bounded (Dual a) Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Dual a Source # maxBound :: Dual a Source #
Generic (Dual a) Source # |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Dual a) :: Type -> Type Source # Methods from :: Dual a -> Rep (Dual a) x Source # to :: Rep (Dual a) x -> Dual a Source #
Read a => Read (Dual a) Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Dual a) Source # readList :: ReadS [Dual a] Source # readPrec :: ReadPrec (Dual a) Source # readListPrec :: ReadPrec [Dual a] Source #
Show a => Show (Dual a) Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Dual a -> ShowS Source # show :: Dual a -> String Source # showList :: [Dual a] -> ShowS Source #
Eq a => Eq (Dual a) Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Dual a -> Dual a -> Bool Source # (/=) :: Dual a -> Dual a -> Bool Source #
Ord a => Ord (Dual a) Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Dual a -> Dual a -> Ordering Source # (<) :: Dual a -> Dual a -> Bool Source # (<=) :: Dual a -> Dual a -> Bool Source # (>) :: Dual a -> Dual a -> Bool Source # (>=) :: Dual a -> Dual a -> Bool Source # max :: Dual a -> Dual a -> Dual a Source # min :: Dual a -> Dual a -> Dual a Source #
Generic1 Dual Source # |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 Dual :: k -> Type Source # Methods from1 :: forall (a :: k). Dual a -> Rep1 Dual a Source # to1 :: forall (a :: k). Rep1 Dual a -> Dual a Source #
type Rep (Dual a) Source # | Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep (Dual a) = D1 ('MetaData "Dual" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Dual" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDual") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Rep1 Dual Source # | Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep1 Dual = D1 ('MetaData "Dual" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Dual" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDual") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

newtype Endo a Source #

The monoid of endomorphisms under composition.

    >>> let computation = Endo ("Hello, " ++) <> Endo (++ "!")
    >>> appEndo computation "Haskell"
    "Hello, Haskell!"

Constructors

Endo |
Fields appEndo :: a -> a

#### Instances

Instances details

Monoid (Endo a) Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Endo a Source # mappend :: Endo a -> Endo a -> Endo a Source # mconcat :: [Endo a] -> Endo a Source #
Semigroup (Endo a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Endo a -> Endo a -> Endo a Source # sconcat :: NonEmpty (Endo a) -> Endo a Source # stimes :: Integral b => b -> Endo a -> Endo a Source #
Generic (Endo a) Source # |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Endo a) :: Type -> Type Source # Methods from :: Endo a -> Rep (Endo a) x Source # to :: Rep (Endo a) x -> Endo a Source #
type Rep (Endo a) Source # | Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep (Endo a) = D1 ('MetaData "Endo" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Endo" 'PrefixI 'True) (S1 ('MetaSel ('Just "appEndo") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (a -> a))))

newtype All Source #

Boolean monoid under conjunction (`&&`).

    >>> getAll (All True <> mempty <> All False)
    False

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

Constructors

All |
Fields getAll :: Bool

#### Instances

Instances details

Data All Source # | Since: base-4.8.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> All -> c All Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c All Source # toConstr :: All -> Constr Source # dataTypeOf :: All -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c All) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c All) Source # gmapT :: (forall b. Data b => b -> b) -> All -> All Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> All -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> All -> r Source # gmapQ :: (forall d. Data d => d -> u) -> All -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> All -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> All -> m All Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All Source #
Monoid All Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: All Source # mappend :: All -> All -> All Source # mconcat :: [All] -> All Source #
Semigroup All Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: All -> All -> All Source # sconcat :: NonEmpty All -> All Source # stimes :: Integral b => b -> All -> All Source #
Bounded All Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: All Source # maxBound :: All Source #
Generic All Source # |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep All :: Type -> Type Source # Methods from :: All -> Rep All x Source # to :: Rep All x -> All Source #
Read All Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS All Source # readList :: ReadS [All] Source # readPrec :: ReadPrec All Source # readListPrec :: ReadPrec [All] Source #
Show All Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> All -> ShowS Source # show :: All -> String Source # showList :: [All] -> ShowS Source #
Eq All Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: All -> All -> Bool Source # (/=) :: All -> All -> Bool Source #
Ord All Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: All -> All -> Ordering Source # (<) :: All -> All -> Bool Source # (<=) :: All -> All -> Bool Source # (>) :: All -> All -> Bool Source # (>=) :: All -> All -> Bool Source # max :: All -> All -> All Source # min :: All -> All -> All Source #
type Rep All Source # | 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)))

newtype Any Source #

Boolean monoid under disjunction (`||`).

    >>> getAny (Any True <> mempty <> Any False)
    True

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

Constructors

Any |
Fields getAny :: Bool

#### Instances

Instances details

Data Any Source # | Since: base-4.8.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Any -> c Any Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Any Source # toConstr :: Any -> Constr Source # dataTypeOf :: Any -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Any) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Any) Source # gmapT :: (forall b. Data b => b -> b) -> Any -> Any Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Any -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Any -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Any -> m Any Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any Source #
Monoid Any Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Any Source # mappend :: Any -> Any -> Any Source # mconcat :: [Any] -> Any Source #
Semigroup Any Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Any -> Any -> Any Source # sconcat :: NonEmpty Any -> Any Source # stimes :: Integral b => b -> Any -> Any Source #
Bounded Any Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Any Source # maxBound :: Any Source #
Generic Any Source # |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep Any :: Type -> Type Source # Methods from :: Any -> Rep Any x Source # to :: Rep Any x -> Any Source #
Read Any Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS Any Source # readList :: ReadS [Any] Source # readPrec :: ReadPrec Any Source # readListPrec :: ReadPrec [Any] Source #
Show Any Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Any -> ShowS Source # show :: Any -> String Source # showList :: [Any] -> ShowS Source #
Eq Any Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Any -> Any -> Bool Source # (/=) :: Any -> Any -> Bool Source #
Ord Any Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Any -> Any -> Ordering Source # (<) :: Any -> Any -> Bool Source # (<=) :: Any -> Any -> Bool Source # (>) :: Any -> Any -> Bool Source # (>=) :: Any -> Any -> Bool Source # max :: Any -> Any -> Any Source # min :: Any -> Any -> Any Source #
type Rep Any Source # | 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)))

newtype Sum a Source #

Monoid under addition.

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

Constructors

Sum |
Fields getSum :: a

#### Instances

Instances details

MonadFix Sum Source # | Since: base-4.8.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> Sum a) -> Sum a Source #
MonadZip Sum Source # | Since: base-4.8.0.0
Instance details Defined in Control.Monad.Zip Methods mzip :: Sum a -> Sum b -> Sum (a, b) Source # mzipWith :: (a -> b -> c) -> Sum a -> Sum b -> Sum c Source # munzip :: Sum (a, b) -> (Sum a, Sum b) Source #
Foldable Sum Source # | Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Sum m -> m Source # foldMap :: Monoid m => (a -> m) -> Sum a -> m Source # foldMap' :: Monoid m => (a -> m) -> Sum a -> m Source # foldr :: (a -> b -> b) -> b -> Sum a -> b Source # foldr' :: (a -> b -> b) -> b -> Sum a -> b Source # foldl :: (b -> a -> b) -> b -> Sum a -> b Source # foldl' :: (b -> a -> b) -> b -> Sum a -> b Source # foldr1 :: (a -> a -> a) -> Sum a -> a Source # foldl1 :: (a -> a -> a) -> Sum a -> a Source # toList :: Sum a -> [a] Source # null :: Sum a -> Bool Source # length :: Sum a -> Int Source # elem :: Eq a => a -> Sum a -> Bool Source # maximum :: Ord a => Sum a -> a Source # minimum :: Ord a => Sum a -> a Source # sum :: Num a => Sum a -> a Source # product :: Num a => Sum a -> a Source #
Traversable Sum Source # | Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b) Source # sequenceA :: Applicative f => Sum (f a) -> f (Sum a) Source # mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b) Source # sequence :: Monad m => Sum (m a) -> m (Sum a) Source #
Applicative Sum Source # | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Sum a Source # (<*>) :: Sum (a -> b) -> Sum a -> Sum b Source # liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c Source # (*>) :: Sum a -> Sum b -> Sum b Source # (<*) :: Sum a -> Sum b -> Sum a Source #
Functor Sum Source # | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Sum a -> Sum b Source # (<$) :: a -> Sum b -> Sum a Source #
Monad Sum Source # | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Sum a -> (a -> Sum b) -> Sum b Source # (>>) :: Sum a -> Sum b -> Sum b Source # return :: a -> Sum a Source #
Data a => Data (Sum a) Source # | Since: base-4.8.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Sum a -> c (Sum a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Sum a) Source # toConstr :: Sum a -> Constr Source # dataTypeOf :: Sum a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Sum a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Sum a)) Source # gmapT :: (forall b. Data b => b -> b) -> Sum a -> Sum a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Sum a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Sum a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) Source #
Num a => Monoid (Sum a) Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Sum a Source # mappend :: Sum a -> Sum a -> Sum a Source # mconcat :: [Sum a] -> Sum a Source #
Num a => Semigroup (Sum a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Sum a -> Sum a -> Sum a Source # sconcat :: NonEmpty (Sum a) -> Sum a Source # stimes :: Integral b => b -> Sum a -> Sum a Source #
Bounded a => Bounded (Sum a) Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Sum a Source # maxBound :: Sum a Source #
Generic (Sum a) Source # |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Sum a) :: Type -> Type Source # Methods from :: Sum a -> Rep (Sum a) x Source # to :: Rep (Sum a) x -> Sum a Source #
Num a => Num (Sum a) Source # | Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Methods (+) :: Sum a -> Sum a -> Sum a Source # (-) :: Sum a -> Sum a -> Sum a Source # (*) :: Sum a -> Sum a -> Sum a Source # negate :: Sum a -> Sum a Source # abs :: Sum a -> Sum a Source # signum :: Sum a -> Sum a Source # fromInteger :: Integer -> Sum a Source #
Read a => Read (Sum a) Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Sum a) Source # readList :: ReadS [Sum a] Source # readPrec :: ReadPrec (Sum a) Source # readListPrec :: ReadPrec [Sum a] Source #
Show a => Show (Sum a) Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Sum a -> ShowS Source # show :: Sum a -> String Source # showList :: [Sum a] -> ShowS Source #
Eq a => Eq (Sum a) Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Sum a -> Sum a -> Bool Source # (/=) :: Sum a -> Sum a -> Bool Source #
Ord a => Ord (Sum a) Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Sum a -> Sum a -> Ordering Source # (<) :: Sum a -> Sum a -> Bool Source # (<=) :: Sum a -> Sum a -> Bool Source # (>) :: Sum a -> Sum a -> Bool Source # (>=) :: Sum a -> Sum a -> Bool Source # max :: Sum a -> Sum a -> Sum a Source # min :: Sum a -> Sum a -> Sum a Source #
Generic1 Sum Source # |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 Sum :: k -> Type Source # Methods from1 :: forall (a :: k). Sum a -> Rep1 Sum a Source # to1 :: forall (a :: k). Rep1 Sum a -> Sum a Source #
type Rep (Sum a) Source # | 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 Source # | 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))

newtype Product a Source #

Monoid under multiplication.

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

Constructors

Product |
Fields getProduct :: a

#### Instances

Instances details

MonadFix Product Source # | Since: base-4.8.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> Product a) -> Product a Source #
MonadZip Product Source # | Since: base-4.8.0.0
Instance details Defined in Control.Monad.Zip Methods mzip :: Product a -> Product b -> Product (a, b) Source # mzipWith :: (a -> b -> c) -> Product a -> Product b -> Product c Source # munzip :: Product (a, b) -> (Product a, Product b) Source #
Foldable Product Source # | Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Product m -> m Source # foldMap :: Monoid m => (a -> m) -> Product a -> m Source # foldMap' :: Monoid m => (a -> m) -> Product a -> m Source # foldr :: (a -> b -> b) -> b -> Product a -> b Source # foldr' :: (a -> b -> b) -> b -> Product a -> b Source # foldl :: (b -> a -> b) -> b -> Product a -> b Source # foldl' :: (b -> a -> b) -> b -> Product a -> b Source # foldr1 :: (a -> a -> a) -> Product a -> a Source # foldl1 :: (a -> a -> a) -> Product a -> a Source # toList :: Product a -> [a] Source # null :: Product a -> Bool Source # length :: Product a -> Int Source # elem :: Eq a => a -> Product a -> Bool Source # maximum :: Ord a => Product a -> a Source # minimum :: Ord a => Product a -> a Source # sum :: Num a => Product a -> a Source # product :: Num a => Product a -> a Source #
Traversable Product Source # | Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b) Source # sequenceA :: Applicative f => Product (f a) -> f (Product a) Source # mapM :: Monad m => (a -> m b) -> Product a -> m (Product b) Source # sequence :: Monad m => Product (m a) -> m (Product a) Source #
Applicative Product Source # | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Product a Source # (<*>) :: Product (a -> b) -> Product a -> Product b Source # liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c Source # (*>) :: Product a -> Product b -> Product b Source # (<*) :: Product a -> Product b -> Product a Source #
Functor Product Source # | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Product a -> Product b Source # (<$) :: a -> Product b -> Product a Source #
Monad Product Source # | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Product a -> (a -> Product b) -> Product b Source # (>>) :: Product a -> Product b -> Product b Source # return :: a -> Product a Source #
Data a => Data (Product a) Source # | Since: base-4.8.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Product a -> c (Product a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Product a) Source # toConstr :: Product a -> Constr Source # dataTypeOf :: Product a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Product a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Product a)) Source # gmapT :: (forall b. Data b => b -> b) -> Product a -> Product a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Product a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Product a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) Source #
Num a => Monoid (Product a) Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Product a Source # mappend :: Product a -> Product a -> Product a Source # mconcat :: [Product a] -> Product a Source #
Num a => Semigroup (Product a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Product a -> Product a -> Product a Source # sconcat :: NonEmpty (Product a) -> Product a Source # stimes :: Integral b => b -> Product a -> Product a Source #
Bounded a => Bounded (Product a) Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Product a Source # maxBound :: Product a Source #
Generic (Product a) Source # |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Product a) :: Type -> Type Source # Methods from :: Product a -> Rep (Product a) x Source # to :: Rep (Product a) x -> Product a Source #
Num a => Num (Product a) Source # | Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Methods (+) :: Product a -> Product a -> Product a Source # (-) :: Product a -> Product a -> Product a Source # (*) :: Product a -> Product a -> Product a Source # negate :: Product a -> Product a Source # abs :: Product a -> Product a Source # signum :: Product a -> Product a Source # fromInteger :: Integer -> Product a Source #
Read a => Read (Product a) Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Product a) Source # readList :: ReadS [Product a] Source # readPrec :: ReadPrec (Product a) Source # readListPrec :: ReadPrec [Product a] Source #
Show a => Show (Product a) Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Product a -> ShowS Source # show :: Product a -> String Source # showList :: [Product a] -> ShowS Source #
Eq a => Eq (Product a) Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Product a -> Product a -> Bool Source # (/=) :: Product a -> Product a -> Bool Source #
Ord a => Ord (Product a) Source # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Product a -> Product a -> Ordering Source # (<) :: Product a -> Product a -> Bool Source # (<=) :: Product a -> Product a -> Bool Source # (>) :: Product a -> Product a -> Bool Source # (>=) :: Product a -> Product a -> Bool Source # max :: Product a -> Product a -> Product a Source # min :: Product a -> Product a -> Product a Source #
Generic1 Product Source # |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 Product :: k -> Type Source # Methods from1 :: forall (a :: k). Product a -> Rep1 Product a Source # to1 :: forall (a :: k). Rep1 Product a -> Product a Source #
type Rep (Product a) Source # | 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 Source # | 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))

# Difference lists of a semigroup

diff :: Semigroup m => m -> Endo m Source #

This lets you use a difference list of a `Semigroup` as a `Monoid`.

### Example:

Expand

    >>> let hello = diff "Hello, "
    >>> appEndo hello "World!"
    "Hello, World!"
    >>> appEndo (hello <> mempty) "World!"
    "Hello, World!"
    >>> appEndo (mempty <> hello) "World!"
    "Hello, World!"
    >>> let world = diff "World"
    >>> let excl = diff "!"
    >>> appEndo (hello <> (world <> excl)) mempty
    "Hello, World!"
    >>> appEndo ((hello <> world) <> excl) mempty
    "Hello, World!"

cycle1 :: Semigroup m => m -> m Source #

A generalization of `cycle` to an arbitrary `Semigroup`. May fail to terminate for some values in some semigroups.

# ArgMin, ArgMax

data Arg a b Source #

`Arg` isn't itself a `Semigroup` in its own right, but it can be placed inside `Min` and `Max` to compute an arg min or arg max.

    >>> minimum [ Arg (x * x) x | x <- [-10 .. 10] ]
    Arg 0 0

Constructors

Arg |
Fields a The argument used for comparisons in `Eq` and `Ord`. b The "value" exposed via the `Functor`, `Foldable` etc. instances.

#### Instances

Instances details

Bifoldable Arg Source # | Since: base-4.10.0.0
Instance details Defined in Data.Semigroup Methods bifold :: Monoid m => Arg m m -> m Source # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Arg a b -> m Source # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Arg a b -> c Source # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Arg a b -> c Source #
Bifunctor Arg Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods bimap :: (a -> b) -> (c -> d) -> Arg a c -> Arg b d Source # first :: (a -> b) -> Arg a c -> Arg b c Source # second :: (b -> c) -> Arg a b -> Arg a c Source #
Bitraversable Arg Source # | Since: base-4.10.0.0
Instance details Defined in Data.Semigroup Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Arg a b -> f (Arg c d) Source #
Foldable (Arg a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Arg a m -> m Source # foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m Source # foldMap' :: Monoid m => (a0 -> m) -> Arg a a0 -> m Source # foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b Source # foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b Source # foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b Source # foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b Source # foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 Source # toList :: Arg a a0 -> [a0] Source # null :: Arg a a0 -> Bool Source # length :: Arg a a0 -> Int Source # elem :: Eq a0 => a0 -> Arg a a0 -> Bool Source # maximum :: Ord a0 => Arg a a0 -> a0 Source # minimum :: Ord a0 => Arg a a0 -> a0 Source # sum :: Num a0 => Arg a a0 -> a0 Source # product :: Num a0 => Arg a a0 -> a0 Source #
Traversable (Arg a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a0 -> f b) -> Arg a a0 -> f (Arg a b) Source # sequenceA :: Applicative f => Arg a (f a0) -> f (Arg a a0) Source # mapM :: Monad m => (a0 -> m b) -> Arg a a0 -> m (Arg a b) Source # sequence :: Monad m => Arg a (m a0) -> m (Arg a a0) Source #
Functor (Arg a) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a0 -> b) -> Arg a a0 -> Arg a b Source # (<$) :: a0 -> Arg a b -> Arg a a0 Source #
Generic1 (Arg a :: Type -> Type) Source # |
Instance details Defined in Data.Semigroup Associated Types type Rep1 (Arg a) :: k -> Type Source # Methods from1 :: forall (a0 :: k). Arg a a0 -> Rep1 (Arg a) a0 Source # to1 :: forall (a0 :: k). Rep1 (Arg a) a0 -> Arg a a0 Source #
(Data a, Data b) => Data (Arg a b) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Arg a b -> c (Arg a b) Source # gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Arg a b) Source # toConstr :: Arg a b -> Constr Source # dataTypeOf :: Arg a b -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Arg a b)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Arg a b)) Source # gmapT :: (forall b0. Data b0 => b0 -> b0) -> Arg a b -> Arg a b Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Arg a b -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Arg a b -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) Source #
Generic (Arg a b) Source # |
Instance details Defined in Data.Semigroup Associated Types type Rep (Arg a b) :: Type -> Type Source # Methods from :: Arg a b -> Rep (Arg a b) x Source # to :: Rep (Arg a b) x -> Arg a b Source #
(Read a, Read b) => Read (Arg a b) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (Arg a b) Source # readList :: ReadS [Arg a b] Source # readPrec :: ReadPrec (Arg a b) Source # readListPrec :: ReadPrec [Arg a b] Source #
(Show a, Show b) => Show (Arg a b) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> Arg a b -> ShowS Source # show :: Arg a b -> String Source # showList :: [Arg a b] -> ShowS Source #
Eq a => Eq (Arg a b) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: Arg a b -> Arg a b -> Bool Source # (/=) :: Arg a b -> Arg a b -> Bool Source #
Ord a => Ord (Arg a b) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: Arg a b -> Arg a b -> Ordering Source # (<) :: Arg a b -> Arg a b -> Bool Source # (<=) :: Arg a b -> Arg a b -> Bool Source # (>) :: Arg a b -> Arg a b -> Bool Source # (>=) :: Arg a b -> Arg a b -> Bool Source # max :: Arg a b -> Arg a b -> Arg a b Source # min :: Arg a b -> Arg a b -> Arg a b Source #
type Rep1 (Arg a :: Type -> Type) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep1 (Arg a :: Type -> Type) = D1 ('MetaData "Arg" "Data.Semigroup" "base" 'False) (C1 ('MetaCons "Arg" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
type Rep (Arg a b) Source # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep (Arg a b) = D1 ('MetaData "Arg" "Data.Semigroup" "base" 'False) (C1 ('MetaCons "Arg" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 b)))

type ArgMin a b = Min (Arg a b) Source #

    >>> Min (Arg 0 ()) <> Min (Arg 1 ())
    Min {getMin = Arg 0 ()}

type ArgMax a b = Max (Arg a b) Source #

    >>> Max (Arg 0 ()) <> Max (Arg 1 ())
    Max {getMax = Arg 1 ()}