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

Inf p a represents the type a extended with a new "infinite" value, which is treated as either positive or negative infinity depending on the type index p. This type exists mostly for its Ord, Semigroup, and Monoid instances.

Constructors

Infinity

Finite a

Instances

Bounded a => Bounded (NegInf a)

Methods

minBound :: NegInf a

maxBound :: NegInf a

Bounded a => Bounded (PosInf a)

Methods

minBound :: PosInf a

maxBound :: PosInf a

Monad (Inf p)

Methods

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

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

return :: a -> Inf p a

fail :: String -> Inf p a

Functor (Inf p)

Methods

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

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

Applicative (Inf p)

Methods

pure :: a -> Inf p a

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

liftA2 :: (a -> b -> c) -> Inf p a -> Inf p b -> Inf p c

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

(<*) :: Inf p 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 a, Data p) => 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)

Negative infinity is less than any finite value.

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)

Positive infinity is greater than any finite value.

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)

An ordered type extended with negative infinity is a semigroup under max.

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)

An ordered type extended with positive infinity is a semigroup under min.

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)

An ordered type extended with negative infinity is a monoid under max, with negative infinity as the identity element.

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)

An ordered type extended with positive infinity is a monoid under min, with positive infinity as the identity element.

Methods

mempty :: Inf Pos a

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

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

data Pos

Type index indicating positive infinity.

Instances

Bounded a => Bounded (PosInf a)

Methods

minBound :: PosInf a

maxBound :: PosInf a

Ord a => Ord (Inf Pos a)

Positive infinity is greater than any finite value.

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)

An ordered type extended with positive infinity is a semigroup under min.

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)

An ordered type extended with positive infinity is a monoid under min, with positive infinity as the identity element.

Methods

mempty :: Inf Pos a

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

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

data Neg

Type index indicating negative infinity.

Instances

Bounded a => Bounded (NegInf a)

Methods

minBound :: NegInf a

maxBound :: NegInf a

Ord a => Ord (Inf Neg a)

Negative infinity is less than any finite value.

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)

An ordered type extended with negative infinity is a semigroup under max.

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)

An ordered type extended with negative infinity is a monoid under max, with negative infinity as the identity element.

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

The type a extended with positive infinity.

type NegInf a = Inf Neg a

The type a extended with negative infinity.

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

Find the minimum of a list of values. Returns positive infinity iff the list is empty.

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

Find the maximum of a list of values. Returns negative infinity iff the list is empty.

Type-restricted constructors

posInfty :: PosInf a

Positive infinity.

negInfty :: NegInf a

Negative infinity.

posFinite :: a -> PosInf a

Embed a finite value into the space of such values extended with positive infinity.

negFinite :: a -> NegInf a

Embed a finite value into the space of such values extended with negative infinity.