Copyright	(C) 2015 Dimitri Sabadie
License	BSD3
Maintainer	Dimitri Sabadie <dimitri.sabadie@gmail.com>
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell2010

Data.Zero

Contents

Semigroups with absorbing element
Num wrappers
Boolean wrappers
Maybe wrappers

Description

Synopsis

class Semigroup a => Zero a where
- zero :: a
- zconcat :: [a] -> a
newtype Product a = Product {
- getProduct :: a
}
newtype Any = Any {
- getAny :: Bool
}
newtype All = All {
- getAll :: Bool
}
newtype Success a = Success {
- getSuccess :: Maybe a
}
success :: a -> Success a
failure :: Success a

Semigroups with absorbing element

class Semigroup a => Zero a where Source #

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 Source #

The zero element.

zconcat :: [a] -> a Source #

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

zconcat :: [a] -> a Source #

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

Instances

Zero () Source #
Instance details Defined in Data.Zero Methods zero :: () Source # zconcat :: [()] -> () Source #
Zero All Source #
Instance details Defined in Data.Zero Methods zero :: All Source # zconcat :: [All] -> All Source #
Zero Any Source #
Instance details Defined in Data.Zero Methods zero :: Any Source # zconcat :: [Any] -> Any Source #
Num a => Zero (Product a) Source #
Instance details Defined in Data.Zero Methods zero :: Product a Source # zconcat :: [Product a] -> Product a Source #
Semigroup a => Zero (Success a) Source #
Instance details Defined in Data.Zero Methods zero :: Success a Source # zconcat :: [Success a] -> Success a Source #

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
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 # fail :: String -> 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 #
MonadFix Product	Since: base-4.8.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> Product a) -> 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 #
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 # 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) #
Bounded a => Bounded (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Product a # maxBound :: Product a #
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 #
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 #
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 #
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 #
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 => 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 => 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 => Zero (Product a) Source #
Instance details Defined in Data.Zero Methods zero :: Product a Source # zconcat :: [Product a] -> Product a Source #
Generic1 Product
Instance details 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
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))

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
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Any # maxBound :: Any #
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 #
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 #
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 #
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 #
Monoid Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Any # mappend :: Any -> Any -> Any # mconcat :: [Any] -> Any #
Zero Any Source #
Instance details Defined in Data.Zero Methods zero :: Any Source # zconcat :: [Any] -> Any Source #
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 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
Instance details Defined in Data.Semigroup.Internal Methods minBound :: All # maxBound :: All #
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 #
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 #
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 #
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 #
Monoid All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: All # mappend :: All -> All -> All # mconcat :: [All] -> All #
Zero All Source #
Instance details Defined in Data.Zero Methods zero :: All Source # zconcat :: [All] -> All Source #
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)))

Maybe wrappers

newtype Success a Source #

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 Source #
Instance details 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 Source #
Instance details Defined in Data.Zero Methods fmap :: (a -> b) -> Success a -> Success b # (<$) :: a -> Success b -> Success a #
MonadFix Success Source #
Instance details Defined in Data.Zero Methods mfix :: (a -> Success a) -> Success a #
Applicative Success Source #
Instance details 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 Source #
Instance details 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 Source #
Instance details 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) Source #
Instance details Defined in Data.Zero Methods (==) :: Success a -> Success a -> Bool # (/=) :: Success a -> Success a -> Bool #
Ord a => Ord (Success a) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details Defined in Data.Zero Methods showsPrec :: Int -> Success a -> ShowS # show :: Success a -> String # showList :: [Success a] -> ShowS #
Semigroup a => Semigroup (Success a) Source #
Instance details 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) Source #
Instance details Defined in Data.Zero Methods zero :: Success a Source # zconcat :: [Success a] -> Success a Source #

success :: a -> Success a Source #

A successful value.

failure :: Success a Source #

A failure.