Data.Monoid.Inf

Make semigroups under min or max into monoids by adjoining an element corresponding to infinity (positive or negative, respectively). These types are similar to Option (Min a) and Option (Max a) respectively, except that the Ord instance matches the Monoid instance.

Documentation

data Inf p a

Constructors

Infinity

Finite a

Instances

Functor (Inf p)

Methods

fmap :: (a -> b) -> Inf p a -> Inf p b

(<$) :: a -> Inf p b -> Inf p a

Foldable (Inf p)

Methods

fold :: Monoid m => Inf p m -> m

foldMap :: Monoid m => (a -> m) -> Inf p a -> m

foldr :: (a -> b -> b) -> b -> Inf p a -> b

foldr' :: (a -> b -> b) -> b -> Inf p a -> b

foldl :: (b -> a -> b) -> b -> Inf p a -> b

foldl' :: (b -> a -> b) -> b -> Inf p a -> b

foldr1 :: (a -> a -> a) -> Inf p a -> a

foldl1 :: (a -> a -> a) -> Inf p a -> a

toList :: Inf p a -> [a]

null :: Inf p a -> Bool

length :: Inf p a -> Int

elem :: Eq a => a -> Inf p a -> Bool

maximum :: Ord a => Inf p a -> a

minimum :: Ord a => Inf p a -> a

sum :: Num a => Inf p a -> a

product :: Num a => Inf p a -> a

Traversable (Inf p)

Methods

traverse :: Applicative f => (a -> f b) -> Inf p a -> f (Inf p b)

sequenceA :: Applicative f => Inf p (f a) -> f (Inf p a)

mapM :: Monad m => (a -> m b) -> Inf p a -> m (Inf p b)

sequence :: Monad m => Inf p (m a) -> m (Inf p a)

Eq a => Eq (Inf p a)

Methods

(==) :: Inf p a -> Inf p a -> Bool

(/=) :: Inf p a -> Inf p a -> Bool

(Data p, Data a) => Data (Inf p a)

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Inf p a -> c (Inf p a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Inf p a)

toConstr :: Inf p a -> Constr

dataTypeOf :: Inf p a -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Inf p a))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Inf p a))

gmapT :: (forall b. Data b => b -> b) -> Inf p a -> Inf p a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Inf p a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Inf p a -> r

gmapQ :: (forall d. Data d => d -> u) -> Inf p a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Inf p a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Inf p a -> m (Inf p a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Inf p a -> m (Inf p a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Inf p a -> m (Inf p a)

Ord a => Ord (Inf Neg a)

Methods

compare :: Inf Neg a -> Inf Neg a -> Ordering

(<) :: Inf Neg a -> Inf Neg a -> Bool

(<=) :: Inf Neg a -> Inf Neg a -> Bool

(>) :: Inf Neg a -> Inf Neg a -> Bool

(>=) :: Inf Neg a -> Inf Neg a -> Bool

max :: Inf Neg a -> Inf Neg a -> Inf Neg a

min :: Inf Neg a -> Inf Neg a -> Inf Neg a

Ord a => Ord (Inf Pos a)

Methods

compare :: Inf Pos a -> Inf Pos a -> Ordering

(<) :: Inf Pos a -> Inf Pos a -> Bool

(<=) :: Inf Pos a -> Inf Pos a -> Bool

(>) :: Inf Pos a -> Inf Pos a -> Bool

(>=) :: Inf Pos a -> Inf Pos a -> Bool

max :: Inf Pos a -> Inf Pos a -> Inf Pos a

min :: Inf Pos a -> Inf Pos a -> Inf Pos a

Read a => Read (Inf p a)

Methods

readsPrec :: Int -> ReadS (Inf p a)

readList :: ReadS [Inf p a]

readPrec :: ReadPrec (Inf p a)

readListPrec :: ReadPrec [Inf p a]

Show a => Show (Inf p a)

Methods

showsPrec :: Int -> Inf p a -> ShowS

show :: Inf p a -> String

showList :: [Inf p a] -> ShowS

Ord a => Semigroup (Inf Neg a)

Methods

(<>) :: Inf Neg a -> Inf Neg a -> Inf Neg a

sconcat :: NonEmpty (Inf Neg a) -> Inf Neg a

stimes :: Integral b => b -> Inf Neg a -> Inf Neg a

Ord a => Semigroup (Inf Pos a)

Methods

(<>) :: Inf Pos a -> Inf Pos a -> Inf Pos a

sconcat :: NonEmpty (Inf Pos a) -> Inf Pos a

stimes :: Integral b => b -> Inf Pos a -> Inf Pos a

Ord a => Monoid (Inf Neg a)

Methods

mempty :: Inf Neg a

mappend :: Inf Neg a -> Inf Neg a -> Inf Neg a

mconcat :: [Inf Neg a] -> Inf Neg a

Ord a => Monoid (Inf Pos a)

Methods

mempty :: Inf Pos a

mappend :: Inf Pos a -> Inf Pos a -> Inf Pos a

mconcat :: [Inf Pos a] -> Inf Pos a

data Pos

Instances

Ord a => Ord (Inf Pos a)

Methods

compare :: Inf Pos a -> Inf Pos a -> Ordering

(<) :: Inf Pos a -> Inf Pos a -> Bool

(<=) :: Inf Pos a -> Inf Pos a -> Bool

(>) :: Inf Pos a -> Inf Pos a -> Bool

(>=) :: Inf Pos a -> Inf Pos a -> Bool

max :: Inf Pos a -> Inf Pos a -> Inf Pos a

min :: Inf Pos a -> Inf Pos a -> Inf Pos a

Ord a => Semigroup (Inf Pos a)

Methods

(<>) :: Inf Pos a -> Inf Pos a -> Inf Pos a

sconcat :: NonEmpty (Inf Pos a) -> Inf Pos a

stimes :: Integral b => b -> Inf Pos a -> Inf Pos a

Ord a => Monoid (Inf Pos a)

Methods

mempty :: Inf Pos a

mappend :: Inf Pos a -> Inf Pos a -> Inf Pos a

mconcat :: [Inf Pos a] -> Inf Pos a

data Neg

Instances

Ord a => Ord (Inf Neg a)

Methods

compare :: Inf Neg a -> Inf Neg a -> Ordering

(<) :: Inf Neg a -> Inf Neg a -> Bool

(<=) :: Inf Neg a -> Inf Neg a -> Bool

(>) :: Inf Neg a -> Inf Neg a -> Bool

(>=) :: Inf Neg a -> Inf Neg a -> Bool

max :: Inf Neg a -> Inf Neg a -> Inf Neg a

min :: Inf Neg a -> Inf Neg a -> Inf Neg a

Ord a => Semigroup (Inf Neg a)

Methods

(<>) :: Inf Neg a -> Inf Neg a -> Inf Neg a

sconcat :: NonEmpty (Inf Neg a) -> Inf Neg a

stimes :: Integral b => b -> Inf Neg a -> Inf Neg a

Ord a => Monoid (Inf Neg a)

Methods

mempty :: Inf Neg a

mappend :: Inf Neg a -> Inf Neg a -> Inf Neg a

mconcat :: [Inf Neg a] -> Inf Neg a

type PosInf a = Inf Pos a

type NegInf a = Inf Neg a

minimum :: Ord a => [a] -> PosInf a

maximum :: Ord a => [a] -> NegInf a

Type-restricted constructors

posInfty :: PosInf a

negInfty :: NegInf a

posFinite :: a -> PosInf a

negFinite :: a -> NegInf a