| 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
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 IntMin {getMin = 1}>>>sconcat (1 :| [2, 3, 4]) :: Max IntMax {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
- 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 {}
- newtype Any = Any {}
- 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:
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 = or stimesIdempotent stimes =
respectively.stimesIdempotentMonoid
>>>stimes 4 [1][1,1,1,1]
Instances
Instances details
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
( on comparisons combines results with <> )(. Without newtypes this equals <> )
@OrderingliftA2 (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 #
( 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 #
( 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.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 #
Instance details
Defined in GHC.Generics
Methods
(<>) :: Generically a -> Generically a -> Generically a Source #
sconcat :: NonEmpty (Generically a) -> Generically a Source #
stimes :: Integral b => b -> Generically a -> Generically a Source #
( without newtypes is <> ) @(Op a b)( =
<> ) @(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
Since: base-4.9.0.0
stimesMonoid :: (Integral b, Monoid a) => b -> a -> a Source #
stimesIdempotent :: Integral b => b -> a -> a Source #
stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a Source #
mtimesDefault :: (Integral b, Monoid a) => b -> a -> a Source #
Repeat a value n times.
mtimesDefault n a = a <> a <> ... <> a -- using <> (n-1) times
In many cases, `stimes 0 a` for a Monoid will produce mempty .
However, there are situations when it cannot do so. In particular,
the following situation is fairly common:
data T a = ... class Constraint1 a class Constraint1 a => Constraint2 a
instance Constraint1 a => Semigroup (T a)
instance Constraint2 a => Monoid (T a)
@
Since Constraint1 is insufficient to implement mempty ,
stimes for T a cannot do so.
When working with such a type, or when working polymorphically with
Semigroup instances, mtimesDefault should be used when the
multiplier might be zero. It is implemented using stimes when
the multiplier is nonzero and mempty when it is zero.
Semigroups
Instances
Instances details
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 #
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 #
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 #
Instance details
Defined in Data.Semigroup
Instance details
Defined in Data.Semigroup
Instance details
Defined in Data.Semigroup
Instance details
Defined in Data.Semigroup
Instances
Instances details
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 #
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 #
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 #
Instance details
Defined in Data.Semigroup
Instance details
Defined in Data.Semigroup
Instance details
Defined in Data.Semigroup
Instance details
Defined in Data.Semigroup
Instances
Instances details
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 #
Instance details
Defined in Data.Semigroup
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 #
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 #
Instance details
Defined in Data.Semigroup
Instance details
Defined in Data.Semigroup
Instance details
Defined in Data.Semigroup
Instances
Instances details
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 #
Instance details
Defined in Data.Semigroup
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 #
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 #
Instance details
Defined in Data.Semigroup
Instance details
Defined in Data.Semigroup
Instance details
Defined in Data.Semigroup
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.
Instances
Instances details
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 #
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 #
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 #
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 #
Instance details
Defined in Data.Semigroup
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 #
Instance details
Defined in Data.Semigroup
Methods
from :: WrappedMonoid m -> Rep (WrappedMonoid m) x Source #
to :: Rep (WrappedMonoid m) x -> WrappedMonoid m Source #
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 #
Instance details
Defined in Data.Semigroup
Instance details
Defined in Data.Semigroup
Methods
(==) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source #
(/=) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source #
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 #
Instance details
Defined in Data.Semigroup
Instance details
Defined in Data.Semigroup
Re-exported monoids from Data.Monoid
The dual of a Monoid , obtained by swapping the arguments of mappend .
>>>getDual (mappend (Dual "Hello") (Dual "World"))"WorldHello"
Instances
Instances details
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 #
Instance details
Defined in Data.Traversable
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 #
Instance details
Defined in Data.Semigroup.Internal
Instance details
Defined in Data.Semigroup.Internal
Instance details
Defined in Data.Semigroup.Internal
The monoid of endomorphisms under composition.
>>>let computation = Endo ("Hello, " ++) <> Endo (++ "!")>>>appEndo computation "Haskell""Hello, Haskell!"
Instances
Boolean monoid under conjunction (&& ).
>>>getAll (All True <> mempty <> All False)False
>>>getAll (mconcat (map (\x -> All (even x)) [2,4,6,7,8]))False
Instances
Instances details
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 #
Instance details
Defined in Data.Semigroup.Internal
Instance details
Defined in Data.Semigroup.Internal
Boolean monoid under disjunction (|| ).
>>>getAny (Any True <> mempty <> Any False)True
>>>getAny (mconcat (map (\x -> Any (even x)) [2,4,6,7,8]))True
Instances
Instances details
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 #
Instance details
Defined in Data.Semigroup.Internal
Instance details
Defined in Data.Semigroup.Internal
Monoid under addition.
>>>getSum (Sum 1 <> Sum 2 <> mempty)3
Instances
Instances details
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 #
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 #
Instance details
Defined in Data.Semigroup.Internal
Instance details
Defined in Data.Semigroup.Internal
Instance details
Defined in Data.Semigroup.Internal
Instance details
Defined in Data.Semigroup.Internal
Monoid under multiplication.
>>>getProduct (Product 3 <> Product 4 <> mempty)12
Instances
Instances details
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 #
Instance details
Defined in Data.Traversable
Instance details
Defined in Data.Semigroup.Internal
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 #
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 #
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 #
Instance details
Defined in Data.Semigroup.Internal
Instance details
Defined in Data.Semigroup.Internal
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!"
ArgMin, ArgMax
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
Instances
Instances details
Instance details
Defined in Data.Semigroup
Instance details
Defined in Data.Semigroup
Methods
bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Arg a b -> f (Arg c d) Source #
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 #
Instance details
Defined in Data.Semigroup
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 #
Instance details
Defined in Data.Semigroup
Instance details
Defined in Data.Semigroup
Instance details
Defined in Data.Semigroup