Copyright	(C) 2010-2015 Maximilian Bolingbroke, 2015 Oleg Grenrus
License	BSD-3-Clause (see the file LICENSE)
Maintainer	Oleg Grenrus <oleg.grenrus@iki.fi>
Safe Haskell	Safe
Language	Haskell2010

Algebra.Lattice.Ordered

Description

Synopsis

Documentation

newtype Ordered a Source

A total order gives rise to a lattice. Join is max, meet is min.

Constructors

Ordered
Fields getOrdered :: a

Instances

Monad Ordered Source
Methods (>>=) :: Ordered a -> (a -> Ordered b) -> Ordered b (>>) :: Ordered a -> Ordered b -> Ordered b return :: a -> Ordered a fail :: String -> Ordered a
Functor Ordered Source
Methods fmap :: (a -> b) -> Ordered a -> Ordered b (<$) :: a -> Ordered b -> Ordered a
Applicative Ordered Source
Methods pure :: a -> Ordered a (<>) :: Ordered (a -> b) -> Ordered a -> Ordered b (>) :: Ordered a -> Ordered b -> Ordered b (<*) :: Ordered a -> Ordered b -> Ordered a
Foldable Ordered Source
Methods fold :: Monoid m => Ordered m -> m foldMap :: Monoid m => (a -> m) -> Ordered a -> m foldr :: (a -> b -> b) -> b -> Ordered a -> b foldr' :: (a -> b -> b) -> b -> Ordered a -> b foldl :: (b -> a -> b) -> b -> Ordered a -> b foldl' :: (b -> a -> b) -> b -> Ordered a -> b foldr1 :: (a -> a -> a) -> Ordered a -> a foldl1 :: (a -> a -> a) -> Ordered a -> a toList :: Ordered a -> [a] null :: Ordered a -> Bool length :: Ordered a -> Int elem :: Eq a => a -> Ordered a -> Bool maximum :: Ord a => Ordered a -> a minimum :: Ord a => Ordered a -> a sum :: Num a => Ordered a -> a product :: Num a => Ordered a -> a
Traversable Ordered Source
Methods traverse :: Applicative f => (a -> f b) -> Ordered a -> f (Ordered b) sequenceA :: Applicative f => Ordered (f a) -> f (Ordered a) mapM :: Monad m => (a -> m b) -> Ordered a -> m (Ordered b) sequence :: Monad m => Ordered (m a) -> m (Ordered a)
Generic1 Ordered Source
Associated Types type Rep1 (Ordered :: * -> ) :: -> * Methods from1 :: Ordered a -> Rep1 Ordered a to1 :: Rep1 Ordered a -> Ordered a
Eq a => Eq (Ordered a) Source
Methods (==) :: Ordered a -> Ordered a -> Bool (/=) :: Ordered a -> Ordered a -> Bool
Data a => Data (Ordered a) Source
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Ordered a -> c (Ordered a) gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Ordered a) toConstr :: Ordered a -> Constr dataTypeOf :: Ordered a -> DataType dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Ordered a)) dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Ordered a)) gmapT :: (forall b. Data b => b -> b) -> Ordered a -> Ordered a gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Ordered a -> r gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Ordered a -> r gmapQ :: (forall d. Data d => d -> u) -> Ordered a -> [u] gmapQi :: Int -> (forall d. Data d => d -> u) -> Ordered a -> u gmapM :: Monad m => (forall d. Data d => d -> m d) -> Ordered a -> m (Ordered a) gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Ordered a -> m (Ordered a) gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Ordered a -> m (Ordered a)
Ord a => Ord (Ordered a) Source
Methods compare :: Ordered a -> Ordered a -> Ordering (<) :: Ordered a -> Ordered a -> Bool (<=) :: Ordered a -> Ordered a -> Bool (>) :: Ordered a -> Ordered a -> Bool (>=) :: Ordered a -> Ordered a -> Bool max :: Ordered a -> Ordered a -> Ordered a min :: Ordered a -> Ordered a -> Ordered a
Read a => Read (Ordered a) Source
Methods readsPrec :: Int -> ReadS (Ordered a) readList :: ReadS [Ordered a] readPrec :: ReadPrec (Ordered a) readListPrec :: ReadPrec [Ordered a]
Show a => Show (Ordered a) Source
Methods showsPrec :: Int -> Ordered a -> ShowS show :: Ordered a -> String showList :: [Ordered a] -> ShowS
Generic (Ordered a) Source
Associated Types type Rep (Ordered a) :: * -> * Methods from :: Ordered a -> Rep (Ordered a) x to :: Rep (Ordered a) x -> Ordered a
NFData a => NFData (Ordered a) Source
Methods rnf :: Ordered a -> ()
Hashable a => Hashable (Ordered a) Source
Methods hashWithSalt :: Int -> Ordered a -> Int hash :: Ordered a -> Int
Ord a => PartialOrd (Ordered a) Source
Methods leq :: Ordered a -> Ordered a -> Bool Source
(BoundedLattice a, Ord a, Bounded a) => BoundedLattice (Ordered a) Source

(Ord a, Bounded a) => BoundedMeetSemiLattice (Ordered a) Source
Methods top :: Ordered a Source
(Ord a, Bounded a) => BoundedJoinSemiLattice (Ordered a) Source
Methods bottom :: Ordered a Source
(Lattice a, Ord a) => Lattice (Ordered a) Source

Ord a => MeetSemiLattice (Ordered a) Source
Methods (/\) :: Ordered a -> Ordered a -> Ordered a Source meet :: Ordered a -> Ordered a -> Ordered a Source
Ord a => JoinSemiLattice (Ordered a) Source
Methods (\/) :: Ordered a -> Ordered a -> Ordered a Source join :: Ordered a -> Ordered a -> Ordered a Source
type Rep1 Ordered Source
type Rep (Ordered a) Source