lattices-1.7.1.1: Fine-grained library for constructing and manipulating lattices

Copyright (C) 2010-2015 Maximilian Bolingbroke 2015 Oleg Grenrus BSD-3-Clause (see the file LICENSE) Oleg Grenrus Safe 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 FieldsgetOrdered :: a
Instances
 Source # Instance detailsDefined in Algebra.Lattice.Ordered Methods(>>=) :: Ordered a -> (a -> Ordered b) -> Ordered b #(>>) :: Ordered a -> Ordered b -> Ordered b #return :: a -> Ordered a #fail :: String -> Ordered a # Source # Instance detailsDefined in Algebra.Lattice.Ordered Methodsfmap :: (a -> b) -> Ordered a -> Ordered b #(<\$) :: a -> Ordered b -> Ordered a # Source # Instance detailsDefined in Algebra.Lattice.Ordered Methodspure :: a -> Ordered a #(<*>) :: Ordered (a -> b) -> Ordered a -> Ordered b #liftA2 :: (a -> b -> c) -> Ordered a -> Ordered b -> Ordered c #(*>) :: Ordered a -> Ordered b -> Ordered b #(<*) :: Ordered a -> Ordered b -> Ordered a # Source # Instance detailsDefined in Algebra.Lattice.Ordered Methodsfold :: 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 # Source # Instance detailsDefined in Algebra.Lattice.Ordered Methodstraverse :: 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) # Eq a => Eq (Ordered a) Source # Instance detailsDefined in Algebra.Lattice.Ordered Methods(==) :: Ordered a -> Ordered a -> Bool #(/=) :: Ordered a -> Ordered a -> Bool # Data a => Data (Ordered a) Source # Instance detailsDefined in Algebra.Lattice.Ordered Methodsgfoldl :: (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 #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 # Instance detailsDefined in Algebra.Lattice.Ordered Methodscompare :: 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 # Instance detailsDefined in Algebra.Lattice.Ordered MethodsreadsPrec :: Int -> ReadS (Ordered a) # Show a => Show (Ordered a) Source # Instance detailsDefined in Algebra.Lattice.Ordered MethodsshowsPrec :: Int -> Ordered a -> ShowS #show :: Ordered a -> String #showList :: [Ordered a] -> ShowS # Source # Instance detailsDefined in Algebra.Lattice.Ordered Associated Typestype Rep (Ordered a) :: * -> * # Methodsfrom :: Ordered a -> Rep (Ordered a) x #to :: Rep (Ordered a) x -> Ordered a # NFData a => NFData (Ordered a) Source # Instance detailsDefined in Algebra.Lattice.Ordered Methodsrnf :: Ordered a -> () # Hashable a => Hashable (Ordered a) Source # Instance detailsDefined in Algebra.Lattice.Ordered MethodshashWithSalt :: Int -> Ordered a -> Int #hash :: Ordered a -> Int # Ord a => PartialOrd (Ordered a) Source # Instance detailsDefined in Algebra.Lattice.Ordered Methodsleq :: Ordered a -> Ordered a -> Bool Source #comparable :: Ordered a -> Ordered a -> Bool Source # (Ord a, Bounded a) => BoundedLattice (Ordered a) Source # Instance detailsDefined in Algebra.Lattice.Ordered (Ord a, Bounded a) => BoundedMeetSemiLattice (Ordered a) Source # Instance detailsDefined in Algebra.Lattice.Ordered Methods (Ord a, Bounded a) => BoundedJoinSemiLattice (Ordered a) Source # Instance detailsDefined in Algebra.Lattice.Ordered Methods Ord a => Lattice (Ordered a) Source # Instance detailsDefined in Algebra.Lattice.Ordered Ord a => MeetSemiLattice (Ordered a) Source # Instance detailsDefined in Algebra.Lattice.Ordered Methods(/\) :: Ordered a -> Ordered a -> Ordered a Source #meet :: Ordered a -> Ordered a -> Ordered a Source # Ord a => JoinSemiLattice (Ordered a) Source # Instance detailsDefined in Algebra.Lattice.Ordered Methods(\/) :: Ordered a -> Ordered a -> Ordered a Source #join :: Ordered a -> Ordered a -> Ordered a Source # Source # Instance detailsDefined in Algebra.Lattice.Ordered Associated Typestype Rep1 Ordered :: k -> * # Methodsfrom1 :: Ordered a -> Rep1 Ordered a #to1 :: Rep1 Ordered a -> Ordered a # type Rep (Ordered a) Source # Instance detailsDefined in Algebra.Lattice.Ordered type Rep (Ordered a) = D1 (MetaData "Ordered" "Algebra.Lattice.Ordered" "lattices-1.7.1.1-KHhCTNp0Jlu7lPrYOy5eaF" True) (C1 (MetaCons "Ordered" PrefixI True) (S1 (MetaSel (Just "getOrdered") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a))) type Rep1 Ordered Source # Instance detailsDefined in Algebra.Lattice.Ordered type Rep1 Ordered = D1 (MetaData "Ordered" "Algebra.Lattice.Ordered" "lattices-1.7.1.1-KHhCTNp0Jlu7lPrYOy5eaF" True) (C1 (MetaCons "Ordered" PrefixI True) (S1 (MetaSel (Just "getOrdered") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))