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 # comparable :: Ordered a -> Ordered a -> Bool Source #
(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 #
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 Rep1 Ordered = D1 (MetaData "Ordered" "Algebra.Lattice.Ordered" "lattices-1.7-LVxdjRPvAj7FxWDUYmNHEJ" True) (C1 (MetaCons "Ordered" PrefixI True) (S1 (MetaSel (Just Symbol "getOrdered") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))
type Rep (Ordered a) Source #
type Rep (Ordered a) = D1 (MetaData "Ordered" "Algebra.Lattice.Ordered" "lattices-1.7-LVxdjRPvAj7FxWDUYmNHEJ" True) (C1 (MetaCons "Ordered" PrefixI True) (S1 (MetaSel (Just Symbol "getOrdered") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))