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

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 () #
Methods zero :: () # zconcat :: [()] -> () #
Zero All #
Methods zero :: All # zconcat :: [All] -> All #
Zero Any #
Methods zero :: Any # zconcat :: [Any] -> Any #
Num a => Zero (Product a) #
Methods zero :: Product a # zconcat :: [Product a] -> Product a #
Semigroup a => Zero (Success a) #
Methods zero :: Success a # zconcat :: [Success a] -> Success a #

Num wrappers

newtype Product a :: * -> * #

Monoid under multiplication.

Constructors

Product
Fields getProduct :: a

Instances

Monad Product	Since: 4.8.0.0
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: 4.8.0.0
Methods fmap :: (a -> b) -> Product a -> Product b # (<$) :: a -> Product b -> Product a #
MonadFix Product	Since: 4.8.0.0
Methods mfix :: (a -> Product a) -> Product a #
Applicative Product	Since: 4.8.0.0
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: 4.8.0.0
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: 4.8.0.0
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)
Methods minBound :: Product a # maxBound :: Product a #
Eq a => Eq (Product a)
Methods (==) :: Product a -> Product a -> Bool # (/=) :: Product a -> Product a -> Bool #
Num a => Num (Product a)
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)
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)
Methods readsPrec :: Int -> ReadS (Product a) # readList :: ReadS [Product a] # readPrec :: ReadPrec (Product a) # readListPrec :: ReadPrec [Product a] #
Show a => Show (Product a)
Methods showsPrec :: Int -> Product a -> ShowS # show :: Product a -> String # showList :: [Product a] -> ShowS #
Generic (Product a)
Associated Types type Rep (Product a) :: * -> * # Methods from :: Product a -> Rep (Product a) x # to :: Rep (Product a) x -> Product a #
Num a => Semigroup (Product a)	Since: 4.9.0.0
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: 2.1
Methods mempty :: Product a # mappend :: Product a -> Product a -> Product a # mconcat :: [Product a] -> Product a #
Num a => Zero (Product a) #
Methods zero :: Product a # zconcat :: [Product a] -> Product a #
Generic1 * Product
Associated Types type Rep1 Product (f :: Product -> ) :: k -> # Methods from1 :: f a -> Rep1 Product f a # to1 :: Rep1 Product f a -> f a #
type Rep (Product a)
type Rep (Product a) = D1 * (MetaData "Product" "Data.Monoid" "base" True) (C1 * (MetaCons "Product" PrefixI True) (S1 * (MetaSel (Just Symbol "getProduct") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))
type Rep1 * Product
type Rep1 * Product = D1 * (MetaData "Product" "Data.Monoid" "base" True) (C1 * (MetaCons "Product" PrefixI True) (S1 * (MetaSel (Just Symbol "getProduct") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

Boolean wrappers

newtype Any :: * #

Boolean monoid under disjunction (||).

Constructors

Any
Fields getAny :: Bool

Instances

Bounded Any
Methods minBound :: Any # maxBound :: Any #
Eq Any
Methods (==) :: Any -> Any -> Bool # (/=) :: Any -> Any -> Bool #
Ord Any
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
Methods readsPrec :: Int -> ReadS Any # readList :: ReadS [Any] # readPrec :: ReadPrec Any # readListPrec :: ReadPrec [Any] #
Show Any
Methods showsPrec :: Int -> Any -> ShowS # show :: Any -> String # showList :: [Any] -> ShowS #
Generic Any
Associated Types type Rep Any :: * -> * # Methods from :: Any -> Rep Any x # to :: Rep Any x -> Any #
Semigroup Any	Since: 4.9.0.0
Methods (<>) :: Any -> Any -> Any # sconcat :: NonEmpty Any -> Any # stimes :: Integral b => b -> Any -> Any #
Monoid Any	Since: 2.1
Methods mempty :: Any # mappend :: Any -> Any -> Any # mconcat :: [Any] -> Any #
Zero Any #
Methods zero :: Any # zconcat :: [Any] -> Any #
type Rep Any
type Rep Any = D1 * (MetaData "Any" "Data.Monoid" "base" True) (C1 * (MetaCons "Any" PrefixI True) (S1 * (MetaSel (Just Symbol "getAny") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * Bool)))

newtype All :: * #

Boolean monoid under conjunction (&&).

Constructors

All
Fields getAll :: Bool

Instances

Bounded All
Methods minBound :: All # maxBound :: All #
Eq All
Methods (==) :: All -> All -> Bool # (/=) :: All -> All -> Bool #
Ord All
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
Methods readsPrec :: Int -> ReadS All # readList :: ReadS [All] # readPrec :: ReadPrec All # readListPrec :: ReadPrec [All] #
Show All
Methods showsPrec :: Int -> All -> ShowS # show :: All -> String # showList :: [All] -> ShowS #
Generic All
Associated Types type Rep All :: * -> * # Methods from :: All -> Rep All x # to :: Rep All x -> All #
Semigroup All	Since: 4.9.0.0
Methods (<>) :: All -> All -> All # sconcat :: NonEmpty All -> All # stimes :: Integral b => b -> All -> All #
Monoid All	Since: 2.1
Methods mempty :: All # mappend :: All -> All -> All # mconcat :: [All] -> All #
Zero All #
Methods zero :: All # zconcat :: [All] -> All #
type Rep All
type Rep All = D1 * (MetaData "All" "Data.Monoid" "base" True) (C1 * (MetaCons "All" PrefixI True) (S1 * (MetaSel (Just Symbol "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 #
Methods (>>=) :: Success a -> (a -> Success b) -> Success b # (>>) :: Success a -> Success b -> Success b # return :: a -> Success a # fail :: String -> Success a #
Functor Success #
Methods fmap :: (a -> b) -> Success a -> Success b # (<$) :: a -> Success b -> Success a #
MonadFix Success #
Methods mfix :: (a -> Success a) -> Success a #
Applicative Success #
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 #
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 #
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) #
Methods (==) :: Success a -> Success a -> Bool # (/=) :: Success a -> Success a -> Bool #
Ord a => Ord (Success a) #
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) #
Methods readsPrec :: Int -> ReadS (Success a) # readList :: ReadS [Success a] # readPrec :: ReadPrec (Success a) # readListPrec :: ReadPrec [Success a] #
Show a => Show (Success a) #
Methods showsPrec :: Int -> Success a -> ShowS # show :: Success a -> String # showList :: [Success a] -> ShowS #
Semigroup a => Semigroup (Success a) #
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) #
Methods zero :: Success a # zconcat :: [Success a] -> Success a #

success :: a -> Success a #

A successful value.

failure :: Success a #

A failure.