Safe Haskell	None
Language	Haskell2010

Coda.Algebra.Zero

Synopsis

Documentation

class Semigroup a => SemigroupWithZero a where Source #

zero <> a = zero = a <> zero

Minimal complete definition

zero

Methods

zero :: a Source #

Instances

SemigroupWithZero All Source #
Methods zero :: All Source #
SemigroupWithZero Any Source #
Methods zero :: Any Source #
SemigroupWithZero Prefix Source #
Methods zero :: Prefix Source #
(Ord a, Bounded a) => SemigroupWithZero (Min a) Source #
Methods zero :: Min a Source #
(Ord a, Bounded a) => SemigroupWithZero (Max a) Source #
Methods zero :: Max a Source #
SemigroupWithZero a => SemigroupWithZero (Dual a) Source #
Methods zero :: Dual a Source #
Num a => SemigroupWithZero (Product a) Source #
Methods zero :: Product a Source #
Semigroup a => SemigroupWithZero (WithZero a) Source #
Methods zero :: WithZero a Source #
Composable a => SemigroupWithZero (Partial a) Source #
Methods zero :: Partial a Source #

newtype WithZero a Source #

Constructors

WithZero
Fields runWithZero :: Maybe a

Bundled Patterns

pattern Zero :: WithZero a
pattern NonZero :: a -> WithZero a

Instances

Monad WithZero Source #
Methods (>>=) :: WithZero a -> (a -> WithZero b) -> WithZero b # (>>) :: WithZero a -> WithZero b -> WithZero b # return :: a -> WithZero a # fail :: String -> WithZero a #
Functor WithZero Source #
Methods fmap :: (a -> b) -> WithZero a -> WithZero b # (<$) :: a -> WithZero b -> WithZero a #
Applicative WithZero Source #
Methods pure :: a -> WithZero a # (<>) :: WithZero (a -> b) -> WithZero a -> WithZero b # liftA2 :: (a -> b -> c) -> WithZero a -> WithZero b -> WithZero c # (>) :: WithZero a -> WithZero b -> WithZero b # (<*) :: WithZero a -> WithZero b -> WithZero a #
Foldable WithZero Source #
Methods fold :: Monoid m => WithZero m -> m # foldMap :: Monoid m => (a -> m) -> WithZero a -> m # foldr :: (a -> b -> b) -> b -> WithZero a -> b # foldr' :: (a -> b -> b) -> b -> WithZero a -> b # foldl :: (b -> a -> b) -> b -> WithZero a -> b # foldl' :: (b -> a -> b) -> b -> WithZero a -> b # foldr1 :: (a -> a -> a) -> WithZero a -> a # foldl1 :: (a -> a -> a) -> WithZero a -> a # toList :: WithZero a -> [a] # null :: WithZero a -> Bool # length :: WithZero a -> Int # elem :: Eq a => a -> WithZero a -> Bool # maximum :: Ord a => WithZero a -> a # minimum :: Ord a => WithZero a -> a # sum :: Num a => WithZero a -> a # product :: Num a => WithZero a -> a #
Traversable WithZero Source #
Methods traverse :: Applicative f => (a -> f b) -> WithZero a -> f (WithZero b) # sequenceA :: Applicative f => WithZero (f a) -> f (WithZero a) # mapM :: Monad m => (a -> m b) -> WithZero a -> m (WithZero b) # sequence :: Monad m => WithZero (m a) -> m (WithZero a) #
Alternative WithZero Source #
Methods empty :: WithZero a # (<\|>) :: WithZero a -> WithZero a -> WithZero a # some :: WithZero a -> WithZero [a] # many :: WithZero a -> WithZero [a] #
MonadPlus WithZero Source #
Methods mzero :: WithZero a # mplus :: WithZero a -> WithZero a -> WithZero a #
MonadZip WithZero Source #
Methods mzip :: WithZero a -> WithZero b -> WithZero (a, b) # mzipWith :: (a -> b -> c) -> WithZero a -> WithZero b -> WithZero c # munzip :: WithZero (a, b) -> (WithZero a, WithZero b) #
Eq a => Eq (WithZero a) Source #
Methods (==) :: WithZero a -> WithZero a -> Bool # (/=) :: WithZero a -> WithZero a -> Bool #
Data a => Data (WithZero a) Source #
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> WithZero a -> c (WithZero a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (WithZero a) # toConstr :: WithZero a -> Constr # dataTypeOf :: WithZero a -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (WithZero a)) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (WithZero a)) # gmapT :: (forall b. Data b => b -> b) -> WithZero a -> WithZero a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> WithZero a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> WithZero a -> r # gmapQ :: (forall d. Data d => d -> u) -> WithZero a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> WithZero a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> WithZero a -> m (WithZero a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> WithZero a -> m (WithZero a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> WithZero a -> m (WithZero a) #
Ord a => Ord (WithZero a) Source #
Methods compare :: WithZero a -> WithZero a -> Ordering # (<) :: WithZero a -> WithZero a -> Bool # (<=) :: WithZero a -> WithZero a -> Bool # (>) :: WithZero a -> WithZero a -> Bool # (>=) :: WithZero a -> WithZero a -> Bool # max :: WithZero a -> WithZero a -> WithZero a # min :: WithZero a -> WithZero a -> WithZero a #
Read a => Read (WithZero a) Source #
Methods readsPrec :: Int -> ReadS (WithZero a) # readList :: ReadS [WithZero a] # readPrec :: ReadPrec (WithZero a) # readListPrec :: ReadPrec [WithZero a] #
Show a => Show (WithZero a) Source #
Methods showsPrec :: Int -> WithZero a -> ShowS # show :: WithZero a -> String # showList :: [WithZero a] -> ShowS #
IsString a => IsString (WithZero a) Source #
Methods fromString :: String -> WithZero a #
Generic (WithZero a) Source #
Associated Types type Rep (WithZero a) :: * -> * # Methods from :: WithZero a -> Rep (WithZero a) x # to :: Rep (WithZero a) x -> WithZero a #
Semigroup a => Semigroup (WithZero a) Source #
Methods (<>) :: WithZero a -> WithZero a -> WithZero a # sconcat :: NonEmpty (WithZero a) -> WithZero a # stimes :: Integral b => b -> WithZero a -> WithZero a #
Monoid a => Monoid (WithZero a) Source #
Methods mempty :: WithZero a # mappend :: WithZero a -> WithZero a -> WithZero a # mconcat :: [WithZero a] -> WithZero a #
Semigroup a => SemigroupWithZero (WithZero a) Source #
Methods zero :: WithZero a Source #
Generic1 * WithZero Source #
Associated Types type Rep1 WithZero (f :: WithZero -> ) :: k -> # Methods from1 :: f a -> Rep1 WithZero f a # to1 :: Rep1 WithZero f a -> f a #
type Rep (WithZero a) Source #
type Rep (WithZero a) = D1 * (MetaData "WithZero" "Coda.Algebra.Zero" "coda-0.0.1-Lrfl9CggVgIC7W2mVql1dH" True) (C1 * (MetaCons "WithZero" PrefixI True) (S1 * (MetaSel (Just Symbol "runWithZero") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (Maybe a))))
type Rep1 * WithZero Source #
type Rep1 * WithZero = D1 * (MetaData "WithZero" "Coda.Algebra.Zero" "coda-0.0.1-Lrfl9CggVgIC7W2mVql1dH" True) (C1 * (MetaCons "WithZero" PrefixI True) (S1 * (MetaSel (Just Symbol "runWithZero") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 * Maybe)))