Data.Zero

Semigroups with absorbing element

class Semigroup a => Zero a where

Semigroup with a zero element. It’s important to understand that the standard Semigroup types – i.e. Maybe and so on – are already biased, because they’re Monoids. That’s why you’ll find a few Zero instances.

Should satisfies the following laws:

Annihilation

 a <> zero = zero <> a = zero

Associativity

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

Minimal complete definition

zero

Methods

zero :: a

The zero element.

zconcat :: [a] -> a

Concat all the elements according to (<>) and zero.

zconcat :: [a] -> a

Concat all the elements according to (<>) and zero.

Instances

Zero ()

Defined in Data.Zero

Methods

zero :: ()

zconcat :: [()] -> ()

Zero All

Defined in Data.Zero

Methods

zero :: All

zconcat :: [All] -> All

Zero Any

Defined in Data.Zero

Methods

zero :: Any

zconcat :: [Any] -> Any

Num a => Zero (Product a)

Defined in Data.Zero

Methods

zero :: Product a

zconcat :: [Product a] -> Product a

Semigroup a => Zero (Success a)

Defined in Data.Zero

Methods

zero :: Success a

zconcat :: [Success a] -> Success a

Num wrappers

newtype Product a

Monoid under multiplication.

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

Constructors

Product

Fields

• getProduct :: a

Instances

Monad Product

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

(>>=) :: Product a -> (a -> Product b) -> Product b

(>>) :: Product a -> Product b -> Product b

return :: a -> Product a

fail :: String -> Product a

Functor Product

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

fmap :: (a -> b) -> Product a -> Product b

(<$) :: a -> Product b -> Product a

MonadFix Product

Since: base-4.8.0.0

Defined in Control.Monad.Fix

Methods

mfix :: (a -> Product a) -> Product a

Applicative Product

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Product a

(<*>) :: Product (a -> b) -> Product a -> Product b

liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c

(*>) :: Product a -> Product b -> Product b

(<*) :: Product a -> Product b -> Product a

Foldable Product

Since: base-4.8.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => Product m -> m

foldMap :: Monoid m => (a -> m) -> Product a -> m

foldr :: (a -> b -> b) -> b -> Product a -> b

foldr' :: (a -> b -> b) -> b -> Product a -> b

foldl :: (b -> a -> b) -> b -> Product a -> b

foldl' :: (b -> a -> b) -> b -> Product a -> b

foldr1 :: (a -> a -> a) -> Product a -> a

foldl1 :: (a -> a -> a) -> Product a -> a

toList :: Product a -> [a]

null :: Product a -> Bool

length :: Product a -> Int

elem :: Eq a => a -> Product a -> Bool

maximum :: Ord a => Product a -> a

minimum :: Ord a => Product a -> a

sum :: Num a => Product a -> a

product :: Num a => Product a -> a

Traversable Product

Since: base-4.8.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b)

sequenceA :: Applicative f => Product (f a) -> f (Product a)

mapM :: Monad m => (a -> m b) -> Product a -> m (Product b)

sequence :: Monad m => Product (m a) -> m (Product a)

Bounded a => Bounded (Product a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

minBound :: Product a

maxBound :: Product a

Eq a => Eq (Product a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

(==) :: Product a -> Product a -> Bool

(/=) :: Product a -> Product a -> Bool

Num a => Num (Product a)

Since: base-4.7.0.0

Defined in Data.Semigroup.Internal

Methods

(+) :: Product a -> Product a -> Product a

(-) :: Product a -> Product a -> Product a

(*) :: Product a -> Product a -> Product a

negate :: Product a -> Product a

abs :: Product a -> Product a

signum :: Product a -> Product a

fromInteger :: Integer -> Product a

Ord a => Ord (Product a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

compare :: Product a -> Product a -> Ordering

(<) :: Product a -> Product a -> Bool

(<=) :: Product a -> Product a -> Bool

(>) :: Product a -> Product a -> Bool

(>=) :: Product a -> Product a -> Bool

max :: Product a -> Product a -> Product a

min :: Product a -> Product a -> Product a

Read a => Read (Product a)

Since: base-2.1

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

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Product a -> ShowS

show :: Product a -> String

showList :: [Product a] -> ShowS

Generic (Product a)

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Product a) :: Type -> Type

Methods

from :: Product a -> Rep (Product a) x

to :: Rep (Product a) x -> Product a

Num a => Semigroup (Product a)

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

(<>) :: Product a -> Product a -> Product a

sconcat :: NonEmpty (Product a) -> Product a

stimes :: Integral b => b -> Product a -> Product a

Num a => Monoid (Product a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Product a

mappend :: Product a -> Product a -> Product a

mconcat :: [Product a] -> Product a

Num a => Zero (Product a)

Defined in Data.Zero

Methods

zero :: Product a

zconcat :: [Product a] -> Product a

Generic1 Product

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Product :: k -> Type

Methods

from1 :: Product a -> Rep1 Product a

to1 :: Rep1 Product a -> Product a

type Rep (Product a)

Since: base-4.7.0.0

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

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))

Boolean wrappers

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

Bounded Any

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

minBound :: Any

maxBound :: Any

Eq Any

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

(==) :: Any -> Any -> Bool

(/=) :: Any -> Any -> Bool

Ord Any

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

compare :: Any -> Any -> Ordering

(<) :: Any -> Any -> Bool

(<=) :: Any -> Any -> Bool

(>) :: Any -> Any -> Bool

(>=) :: Any -> Any -> Bool

max :: Any -> Any -> Any

min :: Any -> Any -> Any

Read Any

Since: base-2.1

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

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Any -> ShowS

show :: Any -> String

showList :: [Any] -> ShowS

Generic Any

Defined in Data.Semigroup.Internal

Associated Types

type Rep Any :: Type -> Type

Methods

from :: Any -> Rep Any x

to :: Rep Any x -> Any

Semigroup Any

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

(<>) :: Any -> Any -> Any

sconcat :: NonEmpty Any -> Any

stimes :: Integral b => b -> Any -> Any

Monoid Any

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Any

mappend :: Any -> Any -> Any

mconcat :: [Any] -> Any

Zero Any

Defined in Data.Zero

Methods

zero :: Any

zconcat :: [Any] -> Any

type Rep Any

Since: base-4.7.0.0

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 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

Bounded All

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

minBound :: All

maxBound :: All

Eq All

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

(==) :: All -> All -> Bool

(/=) :: All -> All -> Bool

Ord All

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

compare :: All -> All -> Ordering

(<) :: All -> All -> Bool

(<=) :: All -> All -> Bool

(>) :: All -> All -> Bool

(>=) :: All -> All -> Bool

max :: All -> All -> All

min :: All -> All -> All

Read All

Since: base-2.1

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

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> All -> ShowS

show :: All -> String

showList :: [All] -> ShowS

Generic All

Defined in Data.Semigroup.Internal

Associated Types

type Rep All :: Type -> Type

Methods

from :: All -> Rep All x

to :: Rep All x -> All

Semigroup All

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

(<>) :: All -> All -> All

sconcat :: NonEmpty All -> All

stimes :: Integral b => b -> All -> All

Monoid All

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: All

mappend :: All -> All -> All

mconcat :: [All] -> All

Zero All

Defined in Data.Zero

Methods

zero :: All

zconcat :: [All] -> All

type Rep All

Since: base-4.7.0.0

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)))

Maybe wrappers

newtype Success a

Zero for Maybe.

Called Success because of the absorbing law:

  Success (Just a) <> Success Nothing = Nothing

Constructors

Success

Fields

• getSuccess :: Maybe a

Instances

Monad Success

Defined in Data.Zero

Methods

(>>=) :: Success a -> (a -> Success b) -> Success b

(>>) :: Success a -> Success b -> Success b

return :: a -> Success a

fail :: String -> Success a

Functor Success

Defined in Data.Zero

Methods

fmap :: (a -> b) -> Success a -> Success b

(<$) :: a -> Success b -> Success a

MonadFix Success

Defined in Data.Zero

Methods

mfix :: (a -> Success a) -> Success a

Applicative Success

Defined in Data.Zero

Methods

pure :: a -> Success a

(<*>) :: Success (a -> b) -> Success a -> Success b

liftA2 :: (a -> b -> c) -> Success a -> Success b -> Success c

(*>) :: Success a -> Success b -> Success b

(<*) :: Success a -> Success b -> Success a

Foldable Success

Defined in Data.Zero

Methods

fold :: Monoid m => Success m -> m

foldMap :: Monoid m => (a -> m) -> Success a -> m

foldr :: (a -> b -> b) -> b -> Success a -> b

foldr' :: (a -> b -> b) -> b -> Success a -> b

foldl :: (b -> a -> b) -> b -> Success a -> b

foldl' :: (b -> a -> b) -> b -> Success a -> b

foldr1 :: (a -> a -> a) -> Success a -> a

foldl1 :: (a -> a -> a) -> Success a -> a

toList :: Success a -> [a]

null :: Success a -> Bool

length :: Success a -> Int

elem :: Eq a => a -> Success a -> Bool

maximum :: Ord a => Success a -> a

minimum :: Ord a => Success a -> a

sum :: Num a => Success a -> a

product :: Num a => Success a -> a

Traversable Success

Defined in Data.Zero

Methods

traverse :: Applicative f => (a -> f b) -> Success a -> f (Success b)

sequenceA :: Applicative f => Success (f a) -> f (Success a)

mapM :: Monad m => (a -> m b) -> Success a -> m (Success b)

sequence :: Monad m => Success (m a) -> m (Success a)

Eq a => Eq (Success a)

Defined in Data.Zero

Methods

(==) :: Success a -> Success a -> Bool

(/=) :: Success a -> Success a -> Bool

Ord a => Ord (Success a)

Defined in Data.Zero

Methods

compare :: Success a -> Success a -> Ordering

(<) :: Success a -> Success a -> Bool

(<=) :: Success a -> Success a -> Bool

(>) :: Success a -> Success a -> Bool

(>=) :: Success a -> Success a -> Bool

max :: Success a -> Success a -> Success a

min :: Success a -> Success a -> Success a

Read a => Read (Success a)

Defined in Data.Zero

Methods

readsPrec :: Int -> ReadS (Success a)

readList :: ReadS [Success a]

readPrec :: ReadPrec (Success a)

readListPrec :: ReadPrec [Success a]

Show a => Show (Success a)

Defined in Data.Zero

Methods

showsPrec :: Int -> Success a -> ShowS

show :: Success a -> String

showList :: [Success a] -> ShowS

Semigroup a => Semigroup (Success a)

Defined in Data.Zero

Methods

(<>) :: Success a -> Success a -> Success a

sconcat :: NonEmpty (Success a) -> Success a

stimes :: Integral b => b -> Success a -> Success a

Semigroup a => Zero (Success a)

Defined in Data.Zero

Methods

zero :: Success a

zconcat :: [Success a] -> Success a

success :: a -> Success a

A successful value.

failure :: Success a

A failure.