monoid-extras-0.4.2: Various extra monoid-related definitions and utilities

Copyright(c) 2012-2015 diagrams-core team (see LICENSE)
LicenseBSD-style (see LICENSE)
Maintainerdiagrams-discuss@googlegroups.com
Safe HaskellSafe
LanguageHaskell2010

Data.Monoid.Inf

Contents

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 Option (Min a) and Option (Max a) respectively, except that the Ord instance matches the Monoid instance.

Synopsis

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 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) # 

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

posFinite :: a -> PosInf a #

negFinite :: a -> NegInf a #