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.Op

Description

Synopsis

Documentation

newtype Op a Source #

The opposite lattice of a given lattice. That is, switch meets and joins.

Constructors

Op
Fields getOp :: a

Instances

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

BoundedJoinSemiLattice a => BoundedMeetSemiLattice (Op a) Source #
Methods top :: Op a Source #
BoundedMeetSemiLattice a => BoundedJoinSemiLattice (Op a) Source #
Methods bottom :: Op a Source #
Lattice a => Lattice (Op a) Source #

JoinSemiLattice a => MeetSemiLattice (Op a) Source #
Methods (/\) :: Op a -> Op a -> Op a Source # meet :: Op a -> Op a -> Op a Source #
MeetSemiLattice a => JoinSemiLattice (Op a) Source #
Methods (\/) :: Op a -> Op a -> Op a Source # join :: Op a -> Op a -> Op a Source #
type Rep1 Op Source #
type Rep1 Op = D1 (MetaData "Op" "Algebra.Lattice.Op" "lattices-1.7-LVxdjRPvAj7FxWDUYmNHEJ" True) (C1 (MetaCons "Op" PrefixI True) (S1 (MetaSel (Just Symbol "getOp") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))
type Rep (Op a) Source #
type Rep (Op a) = D1 (MetaData "Op" "Algebra.Lattice.Op" "lattices-1.7-LVxdjRPvAj7FxWDUYmNHEJ" True) (C1 (MetaCons "Op" PrefixI True) (S1 (MetaSel (Just Symbol "getOp") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))