Copyright | (c) Artem Chirkin |
---|---|
License | BSD3 |
Maintainer | chirkin@arch.ethz.ch |
Safe Haskell | None |
Language | Haskell2010 |
Re-export most of Data.Semigroup with a few changes and new definitions.
The main initiative behind this module is to provide more strict
alternatives to widely used semigroups.
For example, Option
has lazy (<>)
implementation,
which causes memory leaks in large foldMaps.
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
- foldMap' :: (Foldable t, Monoid m) => (a -> m) -> t a -> m
- 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
- class Semigroup a => Monoid a where
- 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
- newtype Option a = Option {}
- option :: b -> (a -> b) -> Option a -> b
- fromOption :: a -> Option a -> a
- toOption :: a -> Option 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)
- data MinMax a = MinMax a a
- minMax :: a -> MinMax a
- mmDiff :: Num a => MinMax a -> a
- mmAvg :: Fractional a => MinMax a -> a
Documentation
The class of semigroups (types with an associative binary operation).
Instances should satisfy the associativity law:
Since: base-4.9.0.0
(<>) :: a -> a -> a infixr 6 #
An associative operation.
Reduce a non-empty list with <>
The default definition should be sufficient, but this can be overridden for efficiency.
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 O(1) by
picking stimes =
or stimesIdempotent
stimes =
respectively.stimesIdempotentMonoid
Instances
Semigroup Ordering | Since: base-4.9.0.0 |
Semigroup () | Since: base-4.9.0.0 |
Semigroup All | Since: base-4.9.0.0 |
Semigroup Any | Since: base-4.9.0.0 |
Semigroup [a] | Since: base-4.9.0.0 |
Semigroup a => Semigroup (Maybe a) | Since: base-4.9.0.0 |
Semigroup a => Semigroup (IO a) | Since: base-4.10.0.0 |
Ord a => Semigroup (Min a) | Since: base-4.9.0.0 |
Ord a => Semigroup (Max a) | Since: base-4.9.0.0 |
Semigroup (First a) | Since: base-4.9.0.0 |
Semigroup (Last a) | Since: base-4.9.0.0 |
Monoid m => Semigroup (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup (<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m # stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m # | |
Semigroup a => Semigroup (Option a) | Since: base-4.9.0.0 |
Semigroup a => Semigroup (Identity a) | |
Semigroup (First a) | Since: base-4.9.0.0 |
Semigroup (Last a) | Since: base-4.9.0.0 |
Semigroup a => Semigroup (Dual a) | Since: base-4.9.0.0 |
Semigroup (Endo a) | Since: base-4.9.0.0 |
Num a => Semigroup (Sum a) | Since: base-4.9.0.0 |
Num a => Semigroup (Product a) | Since: base-4.9.0.0 |
Semigroup a => Semigroup (Down a) | Since: base-4.11.0.0 |
Semigroup (NonEmpty a) | Since: base-4.9.0.0 |
Semigroup a => Semigroup (Id a) | |
All Semigroup xs => Semigroup (Tuple xs) | |
Semigroup a => Semigroup (Id a) | |
All Semigroup xs => Semigroup (Tuple xs) | |
Ord a => Semigroup (MinMax a) # | |
Semigroup a => Semigroup (Option a) # | |
Semigroup b => Semigroup (a -> b) | Since: base-4.9.0.0 |
Semigroup (Either a b) | Since: base-4.9.0.0 |
(Semigroup a, Semigroup b) => Semigroup (a, b) | Since: base-4.9.0.0 |
Semigroup (Proxy s) | Since: base-4.9.0.0 |
Semigroup a => Semigroup (ST s a) | Since: base-4.11.0.0 |
(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) | Since: base-4.9.0.0 |
Semigroup a => Semigroup (Const a b) | |
Alternative f => Semigroup (Alt f a) | Since: base-4.9.0.0 |
(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) | Since: base-4.9.0.0 |
(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) | Since: base-4.9.0.0 |
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 #
foldMap' :: (Foldable t, Monoid m) => (a -> m) -> t a -> m Source #
Map each element of the structure to a monoid, and combine the results.
This function differs from Data.Foldable.foldMap
in that uses foldl'
instead of foldr
inside.
This makes this function suitable for Monoids with strict mappend
operation.
For example,
foldMap' Sum $ take 1000000000 ([1..] :: [Int])
runs in constant memory, whereas normal foldMap
would cause a memory leak there.
Semigroups
Instances
Monad Min | Since: base-4.9.0.0 |
Functor Min | Since: base-4.9.0.0 |
MonadFix Min | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
Applicative Min | Since: base-4.9.0.0 |
Foldable Min | Since: base-4.9.0.0 |
Defined in Data.Semigroup fold :: Monoid m => Min m -> 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 # elem :: Eq a => a -> Min a -> Bool # maximum :: Ord a => Min a -> a # | |
Traversable Min | Since: base-4.9.0.0 |
Bounded a => Bounded (Min a) | |
Enum a => Enum (Min a) | Since: base-4.9.0.0 |
Eq a => Eq (Min a) | |
Data a => Data (Min a) | |
Defined in Data.Semigroup 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) # 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 :: (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) # | |
Num a => Num (Min a) | Since: base-4.9.0.0 |
Ord a => Ord (Min a) | |
Read a => Read (Min a) | |
Show a => Show (Min a) | |
Generic (Min a) | |
Ord a => Semigroup (Min a) | Since: base-4.9.0.0 |
(Ord a, Bounded a) => Monoid (Min a) | Since: base-4.9.0.0 |
Generic1 Min | |
type Rep (Min a) | |
Defined in Data.Semigroup | |
type Rep1 Min | |
Defined in Data.Semigroup |
Instances
Monad Max | Since: base-4.9.0.0 |
Functor Max | Since: base-4.9.0.0 |
MonadFix Max | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
Applicative Max | Since: base-4.9.0.0 |
Foldable Max | Since: base-4.9.0.0 |
Defined in Data.Semigroup fold :: Monoid m => Max m -> 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 # elem :: Eq a => a -> Max a -> Bool # maximum :: Ord a => Max a -> a # | |
Traversable Max | Since: base-4.9.0.0 |
Bounded a => Bounded (Max a) | |
Enum a => Enum (Max a) | Since: base-4.9.0.0 |
Eq a => Eq (Max a) | |
Data a => Data (Max a) | |
Defined in Data.Semigroup 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) # 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 :: (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) # | |
Num a => Num (Max a) | Since: base-4.9.0.0 |
Ord a => Ord (Max a) | |
Read a => Read (Max a) | |
Show a => Show (Max a) | |
Generic (Max a) | |
Ord a => Semigroup (Max a) | Since: base-4.9.0.0 |
(Ord a, Bounded a) => Monoid (Max a) | Since: base-4.9.0.0 |
Generic1 Max | |
type Rep (Max a) | |
Defined in Data.Semigroup | |
type Rep1 Max | |
Defined in Data.Semigroup |
Use
to get the behavior of
Option
(First
a)First
from Data.Monoid.
Instances
Monad First | Since: base-4.9.0.0 |
Functor First | Since: base-4.9.0.0 |
MonadFix First | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
Applicative First | Since: base-4.9.0.0 |
Foldable First | Since: base-4.9.0.0 |
Defined in Data.Semigroup fold :: Monoid m => First m -> 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 # elem :: Eq a => a -> First a -> Bool # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # | |
Traversable First | Since: base-4.9.0.0 |
Bounded a => Bounded (First a) | |
Enum a => Enum (First a) | Since: base-4.9.0.0 |
Eq a => Eq (First a) | |
Data a => Data (First a) | |
Defined in Data.Semigroup 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 :: (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) # | |
Ord a => Ord (First a) | |
Read a => Read (First a) | |
Show a => Show (First a) | |
Generic (First a) | |
Semigroup (First a) | Since: base-4.9.0.0 |
Generic1 First | |
type Rep (First a) | |
Defined in Data.Semigroup | |
type Rep1 First | |
Defined in Data.Semigroup |
Use
to get the behavior of
Option
(Last
a)Last
from Data.Monoid
Instances
Monad Last | Since: base-4.9.0.0 |
Functor Last | Since: base-4.9.0.0 |
MonadFix Last | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
Applicative Last | Since: base-4.9.0.0 |
Foldable Last | Since: base-4.9.0.0 |
Defined in Data.Semigroup fold :: Monoid m => Last m -> 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 # elem :: Eq a => a -> Last a -> Bool # maximum :: Ord a => Last a -> a # | |
Traversable Last | Since: base-4.9.0.0 |
Bounded a => Bounded (Last a) | |
Enum a => Enum (Last a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
Eq a => Eq (Last a) | |
Data a => Data (Last a) | |
Defined in Data.Semigroup 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 :: (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) # | |
Ord a => Ord (Last a) | |
Read a => Read (Last a) | |
Show a => Show (Last a) | |
Generic (Last a) | |
Semigroup (Last a) | Since: base-4.9.0.0 |
Generic1 Last | |
type Rep (Last a) | |
Defined in Data.Semigroup | |
type Rep1 Last | |
Defined in Data.Semigroup |
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.
WrapMonoid | |
|
Instances
Re-exported monoids from Data.Monoid
class Semigroup a => Monoid a where #
The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following laws:
x
<>
mempty
= xmempty
<>
x = xx
(<>
(y<>
z) = (x<>
y)<>
zSemigroup
law)mconcat
=foldr
'(<>)'mempty
The method names refer to the monoid of lists under concatenation, but there are many other instances.
Some types can be viewed as a monoid in more than one way,
e.g. both addition and multiplication on numbers.
In such cases we often define newtype
s and make those instances
of Monoid
, e.g. Sum
and Product
.
NOTE: Semigroup
is a superclass of Monoid
since base-4.11.0.0.
Identity of mappend
An associative operation
NOTE: This method is redundant and has the default
implementation
since base-4.11.0.0.mappend
= '(<>)'
Fold a list using the monoid.
For most types, the default definition for mconcat
will be
used, but the function is included in the class definition so
that an optimized version can be provided for specific types.
Instances
Monoid Ordering | Since: base-2.1 |
Monoid () | Since: base-2.1 |
Monoid All | Since: base-2.1 |
Monoid Any | Since: base-2.1 |
Monoid [a] | Since: base-2.1 |
Semigroup a => Monoid (Maybe a) | Lift a semigroup into Since 4.11.0: constraint on inner Since: base-2.1 |
Monoid a => Monoid (IO a) | Since: base-4.9.0.0 |
(Ord a, Bounded a) => Monoid (Min a) | Since: base-4.9.0.0 |
(Ord a, Bounded a) => Monoid (Max a) | Since: base-4.9.0.0 |
Monoid m => Monoid (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup mempty :: WrappedMonoid m # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # mconcat :: [WrappedMonoid m] -> WrappedMonoid m # | |
Semigroup a => Monoid (Option a) | Since: base-4.9.0.0 |
Monoid a => Monoid (Identity a) | |
Monoid (First a) | Since: base-2.1 |
Monoid (Last a) | Since: base-2.1 |
Monoid a => Monoid (Dual a) | Since: base-2.1 |
Monoid (Endo a) | Since: base-2.1 |
Num a => Monoid (Sum a) | Since: base-2.1 |
Num a => Monoid (Product a) | Since: base-2.1 |
Monoid a => Monoid (Down a) | Since: base-4.11.0.0 |
Monoid a => Monoid (Id a) | |
(Semigroup (Tuple xs), RepresentableList xs, All Monoid xs) => Monoid (Tuple xs) | |
Monoid a => Monoid (Id a) | |
(Semigroup (Tuple xs), RepresentableList xs, All Monoid xs) => Monoid (Tuple xs) | |
(Ord a, Bounded a) => Monoid (MinMax a) # | |
Semigroup a => Monoid (Option a) # | |
Monoid b => Monoid (a -> b) | Since: base-2.1 |
(Monoid a, Monoid b) => Monoid (a, b) | Since: base-2.1 |
Monoid (Proxy s) | Since: base-4.7.0.0 |
Monoid a => Monoid (ST s a) | Since: base-4.11.0.0 |
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) | Since: base-2.1 |
Monoid a => Monoid (Const a b) | |
Alternative f => Monoid (Alt f a) | Since: base-4.8.0.0 |
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) | Since: base-2.1 |
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) | Since: base-2.1 |
The dual of a Monoid
, obtained by swapping the arguments of mappend
.
>>>
getDual (mappend (Dual "Hello") (Dual "World"))
"WorldHello"
Instances
Monad Dual | Since: base-4.8.0.0 |
Functor Dual | Since: base-4.8.0.0 |
MonadFix Dual | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix | |
Applicative Dual | Since: base-4.8.0.0 |
Foldable Dual | Since: base-4.8.0.0 |
Defined in Data.Foldable fold :: Monoid m => Dual m -> 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 # elem :: Eq a => a -> Dual a -> Bool # maximum :: Ord a => Dual a -> a # | |
Traversable Dual | Since: base-4.8.0.0 |
Bounded a => Bounded (Dual a) | |
Eq a => Eq (Dual a) | |
Data a => Data (Dual a) | Since: base-4.8.0.0 |
Defined in Data.Data gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Dual a -> c (Dual a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Dual a) # toConstr :: Dual a -> Constr # dataTypeOf :: Dual a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Dual a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Dual a)) # gmapT :: (forall b. Data b => b -> b) -> Dual a -> Dual a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r # gmapQ :: (forall d. Data d => d -> u) -> Dual a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Dual a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) # | |
Ord a => Ord (Dual a) | |
Read a => Read (Dual a) | |
Show a => Show (Dual a) | |
Generic (Dual a) | |
Semigroup a => Semigroup (Dual a) | Since: base-4.9.0.0 |
Monoid a => Monoid (Dual a) | Since: base-2.1 |
Generic1 Dual | |
type Rep (Dual a) | |
Defined in Data.Semigroup.Internal | |
type Rep1 Dual | |
Defined in Data.Semigroup.Internal |
The monoid of endomorphisms under composition.
>>>
let computation = Endo ("Hello, " ++) <> Endo (++ "!")
>>>
appEndo computation "Haskell"
"Hello, Haskell!"
Boolean monoid under conjunction (&&
).
>>>
getAll (All True <> mempty <> All False)
False
>>>
getAll (mconcat (map (\x -> All (even x)) [2,4,6,7,8]))
False
Instances
Bounded All | |
Eq All | |
Data All | Since: base-4.8.0.0 |
Defined in Data.Data gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> All -> c All # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c All # dataTypeOf :: All -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c All) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c All) # gmapT :: (forall b. Data b => b -> b) -> All -> All # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> All -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> All -> r # gmapQ :: (forall d. Data d => d -> u) -> All -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> All -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> All -> m All # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All # | |
Ord All | |
Read All | |
Show All | |
Generic All | |
Semigroup All | Since: base-4.9.0.0 |
Monoid All | Since: base-2.1 |
type Rep All | |
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
Bounded Any | |
Eq Any | |
Data Any | Since: base-4.8.0.0 |
Defined in Data.Data gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Any -> c Any # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Any # dataTypeOf :: Any -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Any) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Any) # gmapT :: (forall b. Data b => b -> b) -> Any -> Any # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r # gmapQ :: (forall d. Data d => d -> u) -> Any -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Any -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Any -> m Any # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any # | |
Ord Any | |
Read Any | |
Show Any | |
Generic Any | |
Semigroup Any | Since: base-4.9.0.0 |
Monoid Any | Since: base-2.1 |
type Rep Any | |
Defined in Data.Semigroup.Internal |
Monoid under addition.
>>>
getSum (Sum 1 <> Sum 2 <> mempty)
3
Instances
Monad Sum | Since: base-4.8.0.0 |
Functor Sum | Since: base-4.8.0.0 |
MonadFix Sum | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix | |
Applicative Sum | Since: base-4.8.0.0 |
Foldable Sum | Since: base-4.8.0.0 |
Defined in Data.Foldable fold :: Monoid m => Sum m -> m # foldMap :: Monoid m => (a -> m) -> Sum a -> m # foldr :: (a -> b -> b) -> b -> Sum a -> b # foldr' :: (a -> b -> b) -> b -> Sum a -> b # foldl :: (b -> a -> b) -> b -> Sum a -> b # foldl' :: (b -> a -> b) -> b -> Sum a -> b # foldr1 :: (a -> a -> a) -> Sum a -> a # foldl1 :: (a -> a -> a) -> Sum a -> a # elem :: Eq a => a -> Sum a -> Bool # maximum :: Ord a => Sum a -> a # | |
Traversable Sum | Since: base-4.8.0.0 |
Bounded a => Bounded (Sum a) | |
Eq a => Eq (Sum a) | |
Data a => Data (Sum a) | Since: base-4.8.0.0 |
Defined in Data.Data gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Sum a -> c (Sum a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Sum a) # dataTypeOf :: Sum a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Sum a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Sum a)) # gmapT :: (forall b. Data b => b -> b) -> Sum a -> Sum a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r # gmapQ :: (forall d. Data d => d -> u) -> Sum a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Sum a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) # | |
Num a => Num (Sum a) | |
Ord a => Ord (Sum a) | |
Read a => Read (Sum a) | |
Show a => Show (Sum a) | |
Generic (Sum a) | |
Num a => Semigroup (Sum a) | Since: base-4.9.0.0 |
Num a => Monoid (Sum a) | Since: base-2.1 |
Generic1 Sum | |
type Rep (Sum a) | |
Defined in Data.Semigroup.Internal | |
type Rep1 Sum | |
Defined in Data.Semigroup.Internal |
Monoid under multiplication.
>>>
getProduct (Product 3 <> Product 4 <> mempty)
12
Product | |
|
Instances
Monad Product | Since: base-4.8.0.0 |
Functor Product | Since: base-4.8.0.0 |
MonadFix Product | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix | |
Applicative Product | Since: base-4.8.0.0 |
Foldable Product | Since: base-4.8.0.0 |
Defined in Data.Foldable fold :: Monoid m => Product m -> m # foldMap :: Monoid m => (a -> m) -> Product a -> m # foldr :: (a -> b -> b) -> b -> Product a -> b # foldr' :: (a -> b -> b) -> b -> Product a -> b # foldl :: (b -> a -> b) -> b -> Product a -> b # foldl' :: (b -> a -> b) -> b -> Product a -> b # foldr1 :: (a -> a -> a) -> Product a -> a # foldl1 :: (a -> a -> a) -> Product a -> a # elem :: Eq a => a -> Product a -> Bool # maximum :: Ord a => Product a -> a # minimum :: Ord a => Product a -> a # | |
Traversable Product | Since: base-4.8.0.0 |
Bounded a => Bounded (Product a) | |
Eq a => Eq (Product a) | |
Data a => Data (Product a) | Since: base-4.8.0.0 |
Defined in Data.Data gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Product a -> c (Product a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Product a) # toConstr :: Product a -> Constr # dataTypeOf :: Product a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Product a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Product a)) # gmapT :: (forall b. Data b => b -> b) -> Product a -> Product a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r # gmapQ :: (forall d. Data d => d -> u) -> Product a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Product a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) # | |
Num a => Num (Product a) | |
Defined in Data.Semigroup.Internal | |
Ord a => Ord (Product a) | |
Defined in Data.Semigroup.Internal | |
Read a => Read (Product a) | |
Show a => Show (Product a) | |
Generic (Product a) | |
Num a => Semigroup (Product a) | Since: base-4.9.0.0 |
Num a => Monoid (Product a) | Since: base-2.1 |
Generic1 Product | |
type Rep (Product a) | |
Defined in Data.Semigroup.Internal | |
type Rep1 Product | |
Defined in Data.Semigroup.Internal |
A better monoid for Maybe
Option
is effectively Maybe
with a better instance of
Monoid
, built off of an underlying Semigroup
instead of an
underlying Monoid
.
This version of Option
data type is more strict than the one from
Data.Semigroup.
Instances
Monad Option Source # | |
Functor Option Source # | |
MonadFix Option Source # | |
Defined in Numeric.Semigroup | |
Applicative Option Source # | |
Foldable Option Source # | |
Defined in Numeric.Semigroup fold :: Monoid m => Option m -> m # foldMap :: Monoid m => (a -> m) -> Option a -> m # foldr :: (a -> b -> b) -> b -> Option a -> b # foldr' :: (a -> b -> b) -> b -> Option a -> b # foldl :: (b -> a -> b) -> b -> Option a -> b # foldl' :: (b -> a -> b) -> b -> Option a -> b # foldr1 :: (a -> a -> a) -> Option a -> a # foldl1 :: (a -> a -> a) -> Option a -> a # elem :: Eq a => a -> Option a -> Bool # maximum :: Ord a => Option a -> a # minimum :: Ord a => Option a -> a # | |
Traversable Option Source # | |
Alternative Option Source # | |
Eq a => Eq (Option a) Source # | |
Data a => Data (Option a) Source # | |
Defined in Numeric.Semigroup gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Option a -> c (Option a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Option a) # toConstr :: Option a -> Constr # dataTypeOf :: Option a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Option a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Option a)) # gmapT :: (forall b. Data b => b -> b) -> Option a -> Option a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Option a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Option a -> r # gmapQ :: (forall d. Data d => d -> u) -> Option a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Option a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Option a -> m (Option a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Option a -> m (Option a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Option a -> m (Option a) # | |
Ord a => Ord (Option a) Source # | |
Defined in Numeric.Semigroup | |
Read a => Read (Option a) Source # | |
Show a => Show (Option a) Source # | |
Generic (Option a) Source # | |
Semigroup a => Semigroup (Option a) Source # | |
Semigroup a => Monoid (Option a) Source # | |
Generic1 Option Source # | |
type Rep (Option a) Source # | |
Defined in Numeric.Semigroup | |
type Rep1 Option Source # | |
Defined in Numeric.Semigroup |
fromOption :: a -> Option a -> a Source #
Get value from Option
with default value.
Eagerly evaluates the value before returning!
toOption :: a -> Option a Source #
Wrap a value into Option
container.
Eagerly evaluates the value before wrapping!
Difference lists of a semigroup
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.
Arg a b |
Instances
Bitraversable Arg | Since: base-4.10.0.0 |
Defined in Data.Semigroup bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Arg a b -> f (Arg c d) # | |
Bifoldable Arg | Since: base-4.10.0.0 |
Bifunctor Arg | Since: base-4.9.0.0 |
Functor (Arg a) | Since: base-4.9.0.0 |
Foldable (Arg a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup fold :: Monoid m => Arg a m -> 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 # elem :: Eq a0 => a0 -> Arg a a0 -> Bool # maximum :: Ord a0 => Arg a a0 -> a0 # minimum :: Ord a0 => Arg a a0 -> a0 # | |
Traversable (Arg a) | Since: base-4.9.0.0 |
Generic1 (Arg a :: * -> *) | |
Eq a => Eq (Arg a b) | Since: base-4.9.0.0 |
(Data a, Data b) => Data (Arg a b) | |
Defined in Data.Semigroup 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 :: (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) # | |
Ord a => Ord (Arg a b) | Since: base-4.9.0.0 |
(Read a, Read b) => Read (Arg a b) | |
(Show a, Show b) => Show (Arg a b) | |
Generic (Arg a b) | |
type Rep1 (Arg a :: * -> *) | |
Defined in Data.Semigroup type Rep1 (Arg a :: * -> *) = 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) | |
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))) |
Evaluate minimum and maximum at the same time. Arithmetics and semigroup operations are eager, functorial operations are lazy.
This data type is especially useful for calculating bounds
of foldable containers with numeric data using foldMap minMax
.
MinMax a a |
Instances
Monad MinMax Source # | |
Functor MinMax Source # | |
MonadFix MinMax Source # | |
Defined in Numeric.Semigroup | |
Applicative MinMax Source # | |
Bounded a => Bounded (MinMax a) Source # | |
Eq a => Eq (MinMax a) Source # | |
Data a => Data (MinMax a) Source # | |
Defined in Numeric.Semigroup gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> MinMax a -> c (MinMax a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (MinMax a) # toConstr :: MinMax a -> Constr # dataTypeOf :: MinMax a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (MinMax a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (MinMax a)) # gmapT :: (forall b. Data b => b -> b) -> MinMax a -> MinMax a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> MinMax a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> MinMax a -> r # gmapQ :: (forall d. Data d => d -> u) -> MinMax a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> MinMax a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> MinMax a -> m (MinMax a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> MinMax a -> m (MinMax a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> MinMax a -> m (MinMax a) # | |
(Num a, Ord a) => Num (MinMax a) Source # | |
Ord a => Ord (MinMax a) Source # | MinMax checks whether bounds overlap.
|
Defined in Numeric.Semigroup | |
Read a => Read (MinMax a) Source # | |
Show a => Show (MinMax a) Source # | |
Generic (MinMax a) Source # | |
Ord a => Semigroup (MinMax a) Source # | |
(Ord a, Bounded a) => Monoid (MinMax a) Source # | |
Generic1 MinMax Source # | |
type Rep (MinMax a) Source # | |
Defined in Numeric.Semigroup type Rep (MinMax a) = D1 (MetaData "MinMax" "Numeric.Semigroup" "easytensor-1.0.0.1-7r03XVgmuRc4WESVMvBjNe" False) (C1 (MetaCons "MinMax" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a))) | |
type Rep1 MinMax Source # | |
Defined in Numeric.Semigroup type Rep1 MinMax = D1 (MetaData "MinMax" "Numeric.Semigroup" "easytensor-1.0.0.1-7r03XVgmuRc4WESVMvBjNe" False) (C1 (MetaCons "MinMax" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1 :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1)) |
mmAvg :: Fractional a => MinMax a -> a Source #