Copyright	(C) Frank Staals
License	see the LICENSE file
Maintainer	Frank Staals
Safe Haskell	None
Language	GHC2021

HGeometry.Unbounded

Description

Add an unbounded/infintity element to a data type. Essentially, Bottom adds $-\infty$ (and is pretty much identical to Maybe), whereas Top adds $\infty$. The UnBounded type adds both.

Synopsis

data Top a where
- pattern ValT :: a -> Top a
- pattern Top :: Top a
topToMaybe :: Top a -> Maybe a
_ValT :: forall a b p f. (Choice p, Applicative f) => p a (f b) -> p (Top a) (f (Top b))
_Top :: forall a p f. (Choice p, Applicative f) => p () (f ()) -> p (Top a) (f (Top a))
_TopMaybe :: forall a p f. (Profunctor p, Functor f) => p (Maybe a) (f (Maybe a)) -> p (Top a) (f (Top a))
data Bottom a where
- pattern Bottom :: Bottom a
- pattern ValB :: a -> Bottom a
bottomToMaybe :: Bottom a -> Maybe a
_ValB :: forall a b p f. (Choice p, Applicative f) => p a (f b) -> p (Bottom a) (f (Bottom b))
_Bottom :: forall a p f. (Choice p, Applicative f) => p () (f ()) -> p (Bottom a) (f (Bottom a))
_BottomMaybe :: forall a p f. (Profunctor p, Functor f) => p (Maybe a) (f (Maybe a)) -> p (Bottom a) (f (Bottom a))
data UnBounded a
- = MinInfinity
- | Val {
  - _unUnBounded :: a
  }
- | MaxInfinity
_Val :: forall a b p f. (Choice p, Applicative f) => p a (f b) -> p (UnBounded a) (f (UnBounded b))
unBoundedToMaybe :: UnBounded a -> Maybe a

Documentation

data Top a where Source #

Top a represents the type a, together with a Top element, i.e. an element that is greater than any other element. We can think of `Top a` being defined as:

>>> data Top a = ValT a | Top

Bundled Patterns

pattern ValT :: a -> Top a
pattern Top :: Top a

Instances

Instances details

Eq1 Top Source #
Instance details Defined in HGeometry.Unbounded Methods liftEq :: (a -> b -> Bool) -> Top a -> Top b -> Bool #
Ord1 Top Source #
Instance details Defined in HGeometry.Unbounded Methods liftCompare :: (a -> b -> Ordering) -> Top a -> Top b -> Ordering #
Applicative Top Source #
Instance details Defined in HGeometry.Unbounded Methods pure :: a -> Top a # (<>) :: Top (a -> b) -> Top a -> Top b # liftA2 :: (a -> b -> c) -> Top a -> Top b -> Top c # (>) :: Top a -> Top b -> Top b # (<*) :: Top a -> Top b -> Top a #
Functor Top Source #
Instance details Defined in HGeometry.Unbounded Methods fmap :: (a -> b) -> Top a -> Top b # (<$) :: a -> Top b -> Top a #
Monad Top Source #
Instance details Defined in HGeometry.Unbounded Methods (>>=) :: Top a -> (a -> Top b) -> Top b # (>>) :: Top a -> Top b -> Top b # return :: a -> Top a #
Foldable Top Source #
Instance details Defined in HGeometry.Unbounded Methods fold :: Monoid m => Top m -> m # foldMap :: Monoid m => (a -> m) -> Top a -> m # foldMap' :: Monoid m => (a -> m) -> Top a -> m # foldr :: (a -> b -> b) -> b -> Top a -> b # foldr' :: (a -> b -> b) -> b -> Top a -> b # foldl :: (b -> a -> b) -> b -> Top a -> b # foldl' :: (b -> a -> b) -> b -> Top a -> b # foldr1 :: (a -> a -> a) -> Top a -> a # foldl1 :: (a -> a -> a) -> Top a -> a # toList :: Top a -> [a] # null :: Top a -> Bool # length :: Top a -> Int # elem :: Eq a => a -> Top a -> Bool # maximum :: Ord a => Top a -> a # minimum :: Ord a => Top a -> a # sum :: Num a => Top a -> a # product :: Num a => Top a -> a #
Traversable Top Source #
Instance details Defined in HGeometry.Unbounded Methods traverse :: Applicative f => (a -> f b) -> Top a -> f (Top b) # sequenceA :: Applicative f => Top (f a) -> f (Top a) # mapM :: Monad m => (a -> m b) -> Top a -> m (Top b) # sequence :: Monad m => Top (m a) -> m (Top a) #
Semigroup a => Monoid (Top a) Source #
Instance details Defined in HGeometry.Unbounded Methods mempty :: Top a # mappend :: Top a -> Top a -> Top a # mconcat :: [Top a] -> Top a #
Semigroup a => Semigroup (Top a) Source #
Instance details Defined in HGeometry.Unbounded Methods (<>) :: Top a -> Top a -> Top a # sconcat :: NonEmpty (Top a) -> Top a # stimes :: Integral b => b -> Top a -> Top a #
Show a => Show (Top a) Source #
Instance details Defined in HGeometry.Unbounded Methods showsPrec :: Int -> Top a -> ShowS # show :: Top a -> String # showList :: [Top a] -> ShowS #
Eq a => Eq (Top a) Source #
Instance details Defined in HGeometry.Unbounded Methods (==) :: Top a -> Top a -> Bool # (/=) :: Top a -> Top a -> Bool #
Ord a => Ord (Top a) Source #
Instance details Defined in HGeometry.Unbounded Methods compare :: Top a -> Top a -> Ordering # (<) :: Top a -> Top a -> Bool # (<=) :: Top a -> Top a -> Bool # (>) :: Top a -> Top a -> Bool # (>=) :: Top a -> Top a -> Bool # max :: Top a -> Top a -> Top a # min :: Top a -> Top a -> Top a #

topToMaybe :: Top a -> Maybe a Source #

Top a values are isomorphing to Maybe a values.

_ValT :: forall a b p f. (Choice p, Applicative f) => p a (f b) -> p (Top a) (f (Top b)) Source #

ValT prism. Can be used to access the non-bottom element if it exists:

>>> ValT True & _ValT %~ not
ValT False

>>> Top & _ValT %~ not
Top

_Top :: forall a p f. (Choice p, Applicative f) => p () (f ()) -> p (Top a) (f (Top a)) Source #

Top prism.

_TopMaybe :: forall a p f. (Profunctor p, Functor f) => p (Maybe a) (f (Maybe a)) -> p (Top a) (f (Top a)) Source #

Iso between a Top a and a Maybe a, interpreting a Top as a Nothing and vice versa. Note that this reverses the ordering of the elements.

>>> ValT 5 ^. _TopMaybe
Just 5
>>> Just 5 ^.re _TopMaybe
ValT 5
>>> Top ^. _TopMaybe
Nothing
>>> Nothing ^.re _TopMaybe
Top

data Bottom a where Source #

`Bottom a` represents the type a, together with a Bottom element, i.e. an element that is smaller than any other element. We can think of `Bottom a` being defined as:

>>> data Bottom a = Bottom | ValB a

Bundled Patterns

pattern Bottom :: Bottom a
pattern ValB :: a -> Bottom a

Instances

Instances details

Eq1 Bottom Source #
Instance details Defined in HGeometry.Unbounded Methods liftEq :: (a -> b -> Bool) -> Bottom a -> Bottom b -> Bool #
Ord1 Bottom Source #
Instance details Defined in HGeometry.Unbounded Methods liftCompare :: (a -> b -> Ordering) -> Bottom a -> Bottom b -> Ordering #
Applicative Bottom Source #
Instance details Defined in HGeometry.Unbounded Methods pure :: a -> Bottom a # (<>) :: Bottom (a -> b) -> Bottom a -> Bottom b # liftA2 :: (a -> b -> c) -> Bottom a -> Bottom b -> Bottom c # (>) :: Bottom a -> Bottom b -> Bottom b # (<*) :: Bottom a -> Bottom b -> Bottom a #
Functor Bottom Source #
Instance details Defined in HGeometry.Unbounded Methods fmap :: (a -> b) -> Bottom a -> Bottom b # (<$) :: a -> Bottom b -> Bottom a #
Monad Bottom Source #
Instance details Defined in HGeometry.Unbounded Methods (>>=) :: Bottom a -> (a -> Bottom b) -> Bottom b # (>>) :: Bottom a -> Bottom b -> Bottom b # return :: a -> Bottom a #
Foldable Bottom Source #
Instance details Defined in HGeometry.Unbounded Methods fold :: Monoid m => Bottom m -> m # foldMap :: Monoid m => (a -> m) -> Bottom a -> m # foldMap' :: Monoid m => (a -> m) -> Bottom a -> m # foldr :: (a -> b -> b) -> b -> Bottom a -> b # foldr' :: (a -> b -> b) -> b -> Bottom a -> b # foldl :: (b -> a -> b) -> b -> Bottom a -> b # foldl' :: (b -> a -> b) -> b -> Bottom a -> b # foldr1 :: (a -> a -> a) -> Bottom a -> a # foldl1 :: (a -> a -> a) -> Bottom a -> a # toList :: Bottom a -> [a] # null :: Bottom a -> Bool # length :: Bottom a -> Int # elem :: Eq a => a -> Bottom a -> Bool # maximum :: Ord a => Bottom a -> a # minimum :: Ord a => Bottom a -> a # sum :: Num a => Bottom a -> a # product :: Num a => Bottom a -> a #
Traversable Bottom Source #
Instance details Defined in HGeometry.Unbounded Methods traverse :: Applicative f => (a -> f b) -> Bottom a -> f (Bottom b) # sequenceA :: Applicative f => Bottom (f a) -> f (Bottom a) # mapM :: Monad m => (a -> m b) -> Bottom a -> m (Bottom b) # sequence :: Monad m => Bottom (m a) -> m (Bottom a) #
Semigroup a => Monoid (Bottom a) Source #
Instance details Defined in HGeometry.Unbounded Methods mempty :: Bottom a # mappend :: Bottom a -> Bottom a -> Bottom a # mconcat :: [Bottom a] -> Bottom a #
Semigroup a => Semigroup (Bottom a) Source #
Instance details Defined in HGeometry.Unbounded Methods (<>) :: Bottom a -> Bottom a -> Bottom a # sconcat :: NonEmpty (Bottom a) -> Bottom a # stimes :: Integral b => b -> Bottom a -> Bottom a #
Show a => Show (Bottom a) Source #
Instance details Defined in HGeometry.Unbounded Methods showsPrec :: Int -> Bottom a -> ShowS # show :: Bottom a -> String # showList :: [Bottom a] -> ShowS #
Eq a => Eq (Bottom a) Source #
Instance details Defined in HGeometry.Unbounded Methods (==) :: Bottom a -> Bottom a -> Bool # (/=) :: Bottom a -> Bottom a -> Bool #
Ord a => Ord (Bottom a) Source #
Instance details Defined in HGeometry.Unbounded Methods compare :: Bottom a -> Bottom a -> Ordering # (<) :: Bottom a -> Bottom a -> Bool # (<=) :: Bottom a -> Bottom a -> Bool # (>) :: Bottom a -> Bottom a -> Bool # (>=) :: Bottom a -> Bottom a -> Bool # max :: Bottom a -> Bottom a -> Bottom a # min :: Bottom a -> Bottom a -> Bottom a #

bottomToMaybe :: Bottom a -> Maybe a Source #

`Bottom a` values are isomorphing to `Maybe a` values.

_ValB :: forall a b p f. (Choice p, Applicative f) => p a (f b) -> p (Bottom a) (f (Bottom b)) Source #

ValB prism. Can be used to access the non-bottom element if it exists:

>>> ValB True & _ValB %~ not
ValB False

>>> Bottom & _ValB %~ not
Bottom

_Bottom :: forall a p f. (Choice p, Applicative f) => p () (f ()) -> p (Bottom a) (f (Bottom a)) Source #

Bottom prism.

_BottomMaybe :: forall a p f. (Profunctor p, Functor f) => p (Maybe a) (f (Maybe a)) -> p (Bottom a) (f (Bottom a)) Source #

Iso between a 'Bottom a' and a 'Maybe a', interpreting a Bottom as a Nothing and vice versa.

>>> ValB 5 ^. _BottomMaybe
Just 5
>>> Just 5 ^.re _BottomMaybe
ValB 5
>>> Bottom ^. _BottomMaybe
Nothing
>>> Nothing ^.re _BottomMaybe
Bottom

data UnBounded a Source #

`UnBounded a` represents the type a, together with an element MaxInfinity larger than any other element, and an element MinInfinity, smaller than any other element.

Constructors

MinInfinity
Val
Fields _unUnBounded :: a
MaxInfinity

Instances

Instances details

Functor UnBounded Source #
Instance details Defined in HGeometry.Unbounded Methods fmap :: (a -> b) -> UnBounded a -> UnBounded b # (<$) :: a -> UnBounded b -> UnBounded a #
Foldable UnBounded Source #
Instance details Defined in HGeometry.Unbounded Methods fold :: Monoid m => UnBounded m -> m # foldMap :: Monoid m => (a -> m) -> UnBounded a -> m # foldMap' :: Monoid m => (a -> m) -> UnBounded a -> m # foldr :: (a -> b -> b) -> b -> UnBounded a -> b # foldr' :: (a -> b -> b) -> b -> UnBounded a -> b # foldl :: (b -> a -> b) -> b -> UnBounded a -> b # foldl' :: (b -> a -> b) -> b -> UnBounded a -> b # foldr1 :: (a -> a -> a) -> UnBounded a -> a # foldl1 :: (a -> a -> a) -> UnBounded a -> a # toList :: UnBounded a -> [a] # null :: UnBounded a -> Bool # length :: UnBounded a -> Int # elem :: Eq a => a -> UnBounded a -> Bool # maximum :: Ord a => UnBounded a -> a # minimum :: Ord a => UnBounded a -> a # sum :: Num a => UnBounded a -> a # product :: Num a => UnBounded a -> a #
Traversable UnBounded Source #
Instance details Defined in HGeometry.Unbounded Methods traverse :: Applicative f => (a -> f b) -> UnBounded a -> f (UnBounded b) # sequenceA :: Applicative f => UnBounded (f a) -> f (UnBounded a) # mapM :: Monad m => (a -> m b) -> UnBounded a -> m (UnBounded b) # sequence :: Monad m => UnBounded (m a) -> m (UnBounded a) #
Num a => Num (UnBounded a) Source #
Instance details Defined in HGeometry.Unbounded Methods (+) :: UnBounded a -> UnBounded a -> UnBounded a # (-) :: UnBounded a -> UnBounded a -> UnBounded a # (*) :: UnBounded a -> UnBounded a -> UnBounded a # negate :: UnBounded a -> UnBounded a # abs :: UnBounded a -> UnBounded a # signum :: UnBounded a -> UnBounded a # fromInteger :: Integer -> UnBounded a #
Fractional a => Fractional (UnBounded a) Source #
Instance details Defined in HGeometry.Unbounded Methods (/) :: UnBounded a -> UnBounded a -> UnBounded a # recip :: UnBounded a -> UnBounded a # fromRational :: Rational -> UnBounded a #
Show a => Show (UnBounded a) Source #
Instance details Defined in HGeometry.Unbounded Methods showsPrec :: Int -> UnBounded a -> ShowS # show :: UnBounded a -> String # showList :: [UnBounded a] -> ShowS #
Eq a => Eq (UnBounded a) Source #
Instance details Defined in HGeometry.Unbounded Methods (==) :: UnBounded a -> UnBounded a -> Bool # (/=) :: UnBounded a -> UnBounded a -> Bool #
Ord a => Ord (UnBounded a) Source #
Instance details Defined in HGeometry.Unbounded Methods compare :: UnBounded a -> UnBounded a -> Ordering # (<) :: UnBounded a -> UnBounded a -> Bool # (<=) :: UnBounded a -> UnBounded a -> Bool # (>) :: UnBounded a -> UnBounded a -> Bool # (>=) :: UnBounded a -> UnBounded a -> Bool # max :: UnBounded a -> UnBounded a -> UnBounded a # min :: UnBounded a -> UnBounded a -> UnBounded a #

_Val :: forall a b p f. (Choice p, Applicative f) => p a (f b) -> p (UnBounded a) (f (UnBounded b)) Source #

Prism to access unbounded value if it exists.

>>> Val True ^? _Val
Just True

>>> MinInfinity ^? _Val :: Maybe Bool
Nothing

>>> Val True & _Val %~ not
Val False

>>> MaxInfinity & _Val %~ not
MaxInfinity

unBoundedToMaybe :: UnBounded a -> Maybe a Source #

Test if an Unbounded is actually bounded.

>>> unBoundedToMaybe (Val 5)
Just 5
>>> unBoundedToMaybe MinInfinity
Nothing
>>> unBoundedToMaybe MaxInfinity
Nothing