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
(BoundedLattice a, Ord a, Bounded 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, Ord 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 Rep (Op a) Source