Copyright	(c) 2012-2015 diagrams-core team (see LICENSE)
License	BSD-style (see LICENSE)
Maintainer	diagrams-discuss@googlegroups.com
Safe Haskell	Safe-Inferred
Language	Haskell2010

Data.Monoid.Inf

Contents

Type-restricted constructors

Description

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

Synopsis

data Inf p a
- = Infinity
- | Finite a
data Pos
data Neg
type PosInf a = Inf Pos a
type NegInf a = Inf Neg a
minimum :: Ord a => [a] -> PosInf a
maximum :: Ord a => [a] -> NegInf a
posInfty :: PosInf a
negInfty :: NegInf a
posFinite :: a -> PosInf a
negFinite :: a -> NegInf a

Documentation

data Inf p a Source #

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

Instances details

Applicative (Inf p) Source #
Instance details Defined in Data.Monoid.Inf 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
Functor (Inf p) Source #
Instance details Defined in Data.Monoid.Inf Methods fmap :: (a -> b) -> Inf p a -> Inf p b # (<$) :: a -> Inf p b -> Inf p a #
Monad (Inf p) Source #
Instance details Defined in Data.Monoid.Inf 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 #
Foldable (Inf p) Source #
Instance details Defined in Data.Monoid.Inf Methods fold :: Monoid m => Inf p m -> m foldMap :: Monoid m => (a -> m) -> Inf p a -> 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) Source #
Instance details Defined in Data.Monoid.Inf 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)
Bounded a => Bounded (NegInf a) Source #
Instance details Defined in Data.Monoid.Inf Methods minBound :: NegInf a maxBound :: NegInf a
Bounded a => Bounded (PosInf a) Source #
Instance details Defined in Data.Monoid.Inf Methods minBound :: PosInf a maxBound :: PosInf a
Ord a => Monoid (Inf Neg a) Source #	An ordered type extended with negative infinity is a monoid under `max`, with negative infinity as the identity element.
Instance details Defined in Data.Monoid.Inf 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) Source #	An ordered type extended with positive infinity is a monoid under `min`, with positive infinity as the identity element.
Instance details Defined in Data.Monoid.Inf Methods mempty :: Inf Pos a mappend :: Inf Pos a -> Inf Pos a -> Inf Pos a mconcat :: [Inf Pos a] -> Inf Pos a
Ord a => Semigroup (Inf Neg a) Source #	An ordered type extended with negative infinity is a semigroup under `max`.
Instance details Defined in Data.Monoid.Inf 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) Source #	An ordered type extended with positive infinity is a semigroup under `min`.
Instance details Defined in Data.Monoid.Inf 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
(Data p, Data a) => Data (Inf p a) Source #
Instance details Defined in Data.Monoid.Inf 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 :: forall r r'. (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)
Read a => Read (Inf p a) Source #
Instance details Defined in Data.Monoid.Inf 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) Source #
Instance details Defined in Data.Monoid.Inf Methods showsPrec :: Int -> Inf p a -> ShowS show :: Inf p a -> String showList :: [Inf p a] -> ShowS
Eq a => Eq (Inf p a) Source #
Instance details Defined in Data.Monoid.Inf Methods (==) :: Inf p a -> Inf p a -> Bool (/=) :: Inf p a -> Inf p a -> Bool
Ord a => Ord (Inf Neg a) Source #	Negative infinity is less than any finite value.
Instance details Defined in Data.Monoid.Inf 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) Source #	Positive infinity is greater than any finite value.
Instance details Defined in Data.Monoid.Inf 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

data Pos Source #

Type index indicating positive infinity.

Instances

Instances details

Bounded a => Bounded (PosInf a) Source #
Instance details Defined in Data.Monoid.Inf Methods minBound :: PosInf a maxBound :: PosInf a
Ord a => Monoid (Inf Pos a) Source #	An ordered type extended with positive infinity is a monoid under `min`, with positive infinity as the identity element.
Instance details Defined in Data.Monoid.Inf Methods mempty :: Inf Pos a mappend :: Inf Pos a -> Inf Pos a -> Inf Pos a mconcat :: [Inf Pos a] -> Inf Pos a
Ord a => Semigroup (Inf Pos a) Source #	An ordered type extended with positive infinity is a semigroup under `min`.
Instance details Defined in Data.Monoid.Inf 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 => Ord (Inf Pos a) Source #	Positive infinity is greater than any finite value.
Instance details Defined in Data.Monoid.Inf 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

data Neg Source #

Type index indicating negative infinity.

Instances

Instances details

Bounded a => Bounded (NegInf a) Source #
Instance details Defined in Data.Monoid.Inf Methods minBound :: NegInf a maxBound :: NegInf a
Ord a => Monoid (Inf Neg a) Source #	An ordered type extended with negative infinity is a monoid under `max`, with negative infinity as the identity element.
Instance details Defined in Data.Monoid.Inf Methods mempty :: Inf Neg a mappend :: Inf Neg a -> Inf Neg a -> Inf Neg a mconcat :: [Inf Neg a] -> Inf Neg a
Ord a => Semigroup (Inf Neg a) Source #	An ordered type extended with negative infinity is a semigroup under `max`.
Instance details Defined in Data.Monoid.Inf 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 => Ord (Inf Neg a) Source #	Negative infinity is less than any finite value.
Instance details Defined in Data.Monoid.Inf 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

type PosInf a = Inf Pos a Source #

The type a extended with positive infinity.

type NegInf a = Inf Neg a Source #

The type a extended with negative infinity.

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

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

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

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

Type-restricted constructors

posInfty :: PosInf a Source #

Positive infinity.

negInfty :: NegInf a Source #

Negative infinity.

posFinite :: a -> PosInf a Source #

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

negFinite :: a -> NegInf a Source #

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