Data.Semigroup.Compat

base-compat-batteries-0.12.2: base-compat with extra batteries

Safe Haskell | Safe-Inferred
Language | Haskell2010

Data.Semigroup.Compat

Contents

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

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 #

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 #

An associative operation.

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

sconcat :: NonEmpty a -> a #

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 #

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 | 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 #
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 #
Semigroup Void | Since: base-4.9.0.0
Instance details Defined in Data.Void Methods (<>) :: Void -> Void -> Void # sconcat :: NonEmpty Void -> Void # stimes :: Integral b => b -> Void -> Void #
Semigroup Ordering | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Ordering -> Ordering -> Ordering # sconcat :: NonEmpty Ordering -> Ordering # stimes :: Integral b => b -> Ordering -> Ordering #
Semigroup () | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: () -> () -> () # sconcat :: NonEmpty () -> () # stimes :: Integral b => b -> () -> () #
Bits a => Semigroup (And a) | Since: base-4.16
Instance details Defined in Data.Bits Methods (<>) :: And a -> And a -> And a # sconcat :: NonEmpty (And a) -> And a # stimes :: Integral b => b -> And a -> And a #
FiniteBits a => Semigroup (Iff a) | 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 # sconcat :: NonEmpty (Iff a) -> Iff a # stimes :: Integral b => b -> Iff a -> Iff a #
Bits a => Semigroup (Ior a) | Since: base-4.16
Instance details Defined in Data.Bits Methods (<>) :: Ior a -> Ior a -> Ior a # sconcat :: NonEmpty (Ior a) -> Ior a # stimes :: Integral b => b -> Ior a -> Ior a #
Bits a => Semigroup (Xor a) | Since: base-4.16
Instance details Defined in Data.Bits Methods (<>) :: Xor a -> Xor a -> Xor a # sconcat :: NonEmpty (Xor a) -> Xor a # stimes :: Integral b => b -> Xor a -> Xor a #
Semigroup (Comparison a) | `(`<>`)` 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 # sconcat :: NonEmpty (Comparison a) -> Comparison a # stimes :: Integral b => b -> Comparison a -> Comparison a #
Semigroup (Equivalence a) | `(`<>`)` 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 # sconcat :: NonEmpty (Equivalence a) -> Equivalence a # stimes :: Integral b => b -> Equivalence a -> Equivalence a #
Semigroup (Predicate a) | `(`<>`)` 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 # sconcat :: NonEmpty (Predicate a) -> Predicate a # stimes :: Integral b => b -> Predicate a -> Predicate 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 #
Semigroup (First a) | Since: base-4.9.0.0
Instance details Defined in Data.Monoid Methods (<>) :: First a -> First a -> First a # sconcat :: NonEmpty (First a) -> First a # stimes :: Integral b => b -> First a -> First a #
Semigroup (Last a) | Since: base-4.9.0.0
Instance details Defined in Data.Monoid Methods (<>) :: Last a -> Last a -> Last a # sconcat :: NonEmpty (Last a) -> Last a # stimes :: Integral b => b -> Last a -> Last a #
Semigroup (First a) | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: First a -> First a -> First a # sconcat :: NonEmpty (First a) -> First a # stimes :: Integral b => b -> First a -> First a #
Semigroup (Last a) | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Last a -> Last a -> Last a # sconcat :: NonEmpty (Last a) -> Last a # stimes :: Integral b => b -> Last a -> Last a #
Ord a => Semigroup (Max a) | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Max a -> Max a -> Max a # sconcat :: NonEmpty (Max a) -> Max a # stimes :: Integral b => b -> Max a -> Max a #
Ord a => Semigroup (Min a) | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Min a -> Min a -> Min a # sconcat :: NonEmpty (Min a) -> Min a # stimes :: Integral b => b -> Min a -> Min a #
Monoid m => Semigroup (WrappedMonoid m) | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m # stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m #
Semigroup a => Semigroup (Dual a) | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Dual a -> Dual a -> Dual a # sconcat :: NonEmpty (Dual a) -> Dual a # stimes :: Integral b => b -> Dual a -> Dual a #
Semigroup (Endo a) | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Endo a -> Endo a -> Endo a # sconcat :: NonEmpty (Endo a) -> Endo a # stimes :: Integral b => b -> Endo a -> Endo 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 => 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 #
Semigroup a => Semigroup (IO a) | Since: base-4.10.0.0
Instance details Defined in GHC.Base Methods (<>) :: IO a -> IO a -> IO a # sconcat :: NonEmpty (IO a) -> IO a # stimes :: Integral b => b -> IO a -> IO a #
Semigroup (NonEmpty a) | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a # sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a # stimes :: Integral b => b -> NonEmpty a -> NonEmpty a #
Semigroup a => Semigroup (Maybe a) | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Maybe a -> Maybe a -> Maybe a # sconcat :: NonEmpty (Maybe a) -> Maybe a # stimes :: Integral b => b -> Maybe a -> Maybe a #
Semigroup a => Semigroup (a) | Since: base-4.15
Instance details Defined in GHC.Base Methods (<>) :: (a) -> (a) -> (a) # sconcat :: NonEmpty (a) -> (a) # stimes :: Integral b => b -> (a) -> (a) #
Semigroup [a] | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: [a] -> [a] -> [a] # sconcat :: NonEmpty [a] -> [a] # stimes :: Integral b => b -> [a] -> [a] #
Semigroup (Either a b) | Since: base-4.9.0.0
Instance details Defined in Data.Either Methods (<>) :: Either a b -> Either a b -> Either a b # sconcat :: NonEmpty (Either a b) -> Either a b # stimes :: Integral b0 => b0 -> Either a b -> Either a b #
Semigroup a => Semigroup (Op a b) | `(`<>`) @(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 # sconcat :: NonEmpty (Op a b) -> Op a b # stimes :: Integral b0 => b0 -> Op a b -> Op a b #
Semigroup (Proxy s) | Since: base-4.9.0.0
Instance details Defined in Data.Proxy Methods (<>) :: Proxy s -> Proxy s -> Proxy s # sconcat :: NonEmpty (Proxy s) -> Proxy s # stimes :: Integral b => b -> Proxy s -> Proxy s #
Semigroup b => Semigroup (a -> b) | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a -> b) -> (a -> b) -> a -> b # sconcat :: NonEmpty (a -> b) -> a -> b # stimes :: Integral b0 => b0 -> (a -> b) -> a -> b #
(Semigroup a, Semigroup b) => Semigroup (a, b) | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b) -> (a, b) -> (a, b) # sconcat :: NonEmpty (a, b) -> (a, b) # stimes :: Integral b0 => b0 -> (a, b) -> (a, b) #
Semigroup a => Semigroup (Const a b) | Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (<>) :: Const a b -> Const a b -> Const a b # sconcat :: NonEmpty (Const a b) -> Const a b # stimes :: Integral b0 => b0 -> Const a b -> Const a b #
(Applicative f, Semigroup a) => Semigroup (Ap f a) | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (<>) :: Ap f a -> Ap f a -> Ap f a # sconcat :: NonEmpty (Ap f a) -> Ap f a # stimes :: Integral b => b -> Ap f a -> Ap f a #
Alternative f => Semigroup (Alt f a) | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Alt f a -> Alt f a -> Alt f a # sconcat :: NonEmpty (Alt f a) -> Alt f a # stimes :: Integral b => b -> Alt f a -> Alt f a #
(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b, c) -> (a, b, c) -> (a, b, c) # sconcat :: NonEmpty (a, b, c) -> (a, b, c) # stimes :: Integral b0 => b0 -> (a, b, c) -> (a, b, c) #
(Semigroup (f a), Semigroup (g a)) => Semigroup (Product f g a) | 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 # sconcat :: NonEmpty (Product f g a) -> Product f g a # stimes :: Integral b => b -> Product f g a -> Product f g a #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) | 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) # sconcat :: NonEmpty (a, b, c, d) -> (a, b, c, d) # stimes :: Integral b0 => b0 -> (a, b, c, d) -> (a, b, c, d) #
Semigroup (f (g a)) => Semigroup (Compose f g a) | 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 # sconcat :: NonEmpty (Compose f g a) -> Compose f g a # stimes :: Integral b => b -> Compose f g a -> Compose f g a #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) | 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) # sconcat :: NonEmpty (a, b, c, d, e) -> (a, b, c, d, e) # stimes :: Integral b0 => b0 -> (a, b, c, d, e) -> (a, b, c, d, e) #

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

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 #

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 #

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 #

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 #

Constructors

Min |
Fields getMin :: a

#### Instances

Instances details

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

Constructors

Max |
Fields getMax :: a

#### Instances

Instances details

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

Constructors

First |
Fields getFirst :: a

#### Instances

Instances details

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

Constructors

Last |
Fields getLast :: a

#### Instances

Instances details

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

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

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

Foldable Dual | Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Dual m -> m # foldMap :: Monoid m => (a -> m) -> Dual a -> m # foldMap' :: Monoid m => (a -> m) -> Dual a -> m # foldr :: (a -> b -> b) -> b -> Dual a -> b # foldr' :: (a -> b -> b) -> b -> Dual a -> b # foldl :: (b -> a -> b) -> b -> Dual a -> b # foldl' :: (b -> a -> b) -> b -> Dual a -> b # foldr1 :: (a -> a -> a) -> Dual a -> a # foldl1 :: (a -> a -> a) -> Dual a -> a # toList :: Dual a -> [a] # null :: Dual a -> Bool # length :: Dual a -> Int # elem :: Eq a => a -> Dual a -> Bool # maximum :: Ord a => Dual a -> a # minimum :: Ord a => Dual a -> a # sum :: Num a => Dual a -> a # product :: Num a => Dual a -> a #
Traversable Dual | Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b) # sequenceA :: Applicative f => Dual (f a) -> f (Dual a) # mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b) # sequence :: Monad m => Dual (m a) -> m (Dual a) #
Applicative Dual | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Dual a # (<*>) :: Dual (a -> b) -> Dual a -> Dual b # liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c # (*>) :: Dual a -> Dual b -> Dual b # (<*) :: Dual a -> Dual b -> Dual a #
Functor Dual | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Dual a -> Dual b # (<$) :: a -> Dual b -> Dual a #
Monad Dual | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Dual a -> (a -> Dual b) -> Dual b # (>>) :: Dual a -> Dual b -> Dual b # return :: a -> Dual a #
Monoid a => Monoid (Dual a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Dual a # mappend :: Dual a -> Dual a -> Dual a # mconcat :: [Dual a] -> Dual a #
Semigroup a => Semigroup (Dual a) | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Dual a -> Dual a -> Dual a # sconcat :: NonEmpty (Dual a) -> Dual a # stimes :: Integral b => b -> Dual a -> Dual a #
Bounded a => Bounded (Dual a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Dual a # maxBound :: Dual a #
Generic (Dual a) |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Dual a) :: Type -> Type # Methods from :: Dual a -> Rep (Dual a) x # to :: Rep (Dual a) x -> Dual a #
Read a => Read (Dual a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Dual a) # readList :: ReadS [Dual a] # readPrec :: ReadPrec (Dual a) # readListPrec :: ReadPrec [Dual a] #
Show a => Show (Dual a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Dual a -> ShowS # show :: Dual a -> String # showList :: [Dual a] -> ShowS #
Eq a => Eq (Dual a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Dual a -> Dual a -> Bool # (/=) :: Dual a -> Dual a -> Bool #
Ord a => Ord (Dual a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Dual a -> Dual a -> Ordering # (<) :: Dual a -> Dual a -> Bool # (<=) :: Dual a -> Dual a -> Bool # (>) :: Dual a -> Dual a -> Bool # (>=) :: Dual a -> Dual a -> Bool # max :: Dual a -> Dual a -> Dual a # min :: Dual a -> Dual a -> Dual a #
Generic1 Dual |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 Dual :: k -> Type # Methods from1 :: forall (a :: k). Dual a -> Rep1 Dual a # to1 :: forall (a :: k). Rep1 Dual a -> Dual a #
type Rep (Dual a) | 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 | 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 #

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) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Endo a # mappend :: Endo a -> Endo a -> Endo a # mconcat :: [Endo a] -> Endo a #
Semigroup (Endo a) | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Endo a -> Endo a -> Endo a # sconcat :: NonEmpty (Endo a) -> Endo a # stimes :: Integral b => b -> Endo a -> Endo a #
Generic (Endo a) |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Endo a) :: Type -> Type # Methods from :: Endo a -> Rep (Endo a) x # to :: Rep (Endo a) x -> Endo a #
type Rep (Endo a) | 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 #

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

Monoid All | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: All # mappend :: All -> All -> All # mconcat :: [All] -> 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 #
Bounded All | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: All # maxBound :: All #
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 #
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 #
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 #
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)))

newtype 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

Constructors

Any |
Fields getAny :: Bool

#### Instances

Instances details

Monoid Any | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Any # mappend :: Any -> Any -> Any # mconcat :: [Any] -> 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 #
Bounded Any | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Any # maxBound :: Any #
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 #
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 #
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 #
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)))

newtype Sum a #

Monoid under addition.

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

Constructors

Sum |
Fields getSum :: a

#### Instances

Instances details

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 # 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) #
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 #
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 #
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 #
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 #
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 #
Bounded a => Bounded (Sum a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Sum a # maxBound :: Sum a #
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 => 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 #
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 #
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 #
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 #
Generic1 Sum |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 Sum :: k -> Type # Methods from1 :: forall (a :: k). Sum a -> Rep1 Sum a # to1 :: forall (a :: k). Rep1 Sum a -> Sum a #
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))

newtype Product a #

Monoid under multiplication.

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

Constructors

Product |
Fields getProduct :: a

#### Instances

Instances details

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 # 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) #
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 #
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 #
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 #
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 #
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 #
Bounded a => Bounded (Product a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Product a # maxBound :: Product a #
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 => 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 #
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 #
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 #
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 #
Generic1 Product |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 Product :: k -> Type # Methods from1 :: forall (a :: k). Product a -> Rep1 Product a # to1 :: forall (a :: k). Rep1 Product a -> Product a #
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))

# Difference lists of a semigroup

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

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 #

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

# ArgMin, ArgMax

data Arg a b #

`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 | Since: base-4.10.0.0
Instance details Defined in Data.Semigroup Methods bifold :: Monoid m => Arg m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Arg a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Arg a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Arg a b -> c #
Bifunctor Arg | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods bimap :: (a -> b) -> (c -> d) -> Arg a c -> Arg b d # first :: (a -> b) -> Arg a c -> Arg b c # second :: (b -> c) -> Arg a b -> Arg a c #
Bitraversable Arg | 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) #
Foldable (Arg a) | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Arg a m -> m # foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Arg a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 # toList :: Arg a a0 -> [a0] # null :: Arg a a0 -> Bool # length :: Arg a a0 -> Int # elem :: Eq a0 => a0 -> Arg a a0 -> Bool # maximum :: Ord a0 => Arg a a0 -> a0 # minimum :: Ord a0 => Arg a a0 -> a0 # sum :: Num a0 => Arg a a0 -> a0 # product :: Num a0 => Arg a a0 -> a0 #
Traversable (Arg a) | 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) # sequenceA :: Applicative f => Arg a (f a0) -> f (Arg a a0) # mapM :: Monad m => (a0 -> m b) -> Arg a a0 -> m (Arg a b) # sequence :: Monad m => Arg a (m a0) -> m (Arg a a0) #
Functor (Arg a) | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a0 -> b) -> Arg a a0 -> Arg a b # (<$) :: a0 -> Arg a b -> Arg a a0 #
Generic1 (Arg a :: Type -> Type) |
Instance details Defined in Data.Semigroup Associated Types type Rep1 (Arg a) :: k -> Type # Methods from1 :: forall (a0 :: k). Arg a a0 -> Rep1 (Arg a) a0 # to1 :: forall (a0 :: k). Rep1 (Arg a) a0 -> Arg a a0 #
(Data a, Data b) => Data (Arg a b) | 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) # gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Arg a b) # toConstr :: Arg a b -> Constr # dataTypeOf :: Arg a b -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Arg a b)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Arg a b)) # gmapT :: (forall b0. Data b0 => b0 -> b0) -> Arg a b -> Arg a b # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r # gmapQ :: (forall d. Data d => d -> u) -> Arg a b -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Arg a b -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) #
Generic (Arg a b) |
Instance details Defined in Data.Semigroup Associated Types type Rep (Arg a b) :: Type -> Type # Methods from :: Arg a b -> Rep (Arg a b) x # to :: Rep (Arg a b) x -> Arg a b #
(Read a, Read b) => Read (Arg a b) | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (Arg a b) # readList :: ReadS [Arg a b] # readPrec :: ReadPrec (Arg a b) # readListPrec :: ReadPrec [Arg a b] #
(Show a, Show b) => Show (Arg a b) | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> Arg a b -> ShowS # show :: Arg a b -> String # showList :: [Arg a b] -> ShowS #
Eq a => Eq (Arg a b) | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: Arg a b -> Arg a b -> Bool # (/=) :: Arg a b -> Arg a b -> Bool #
Ord a => Ord (Arg a b) | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: Arg a b -> Arg a b -> Ordering # (<) :: Arg a b -> Arg a b -> Bool # (<=) :: Arg a b -> Arg a b -> Bool # (>) :: Arg a b -> Arg a b -> Bool # (>=) :: Arg a b -> Arg a b -> Bool # max :: Arg a b -> Arg a b -> Arg a b # min :: Arg a b -> Arg a b -> Arg a b #
type Rep1 (Arg a :: Type -> Type) | 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) | 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) #

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

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

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