Copyright	(C) 2010-2015 Maximilian Bolingbroke 2015-2019 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

newtype Op a = Op {
- getOp :: a
}

Documentation

newtype Op a Source #

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

Constructors

Op
Fields getOp :: a

Instances

Instances details

Monad Op Source #
Instance details Defined in Algebra.Lattice.Op Methods (>>=) :: Op a -> (a -> Op b) -> Op b Source # (>>) :: Op a -> Op b -> Op b Source # return :: a -> Op a Source #
Functor Op Source #
Instance details Defined in Algebra.Lattice.Op Methods fmap :: (a -> b) -> Op a -> Op b Source # (<$) :: a -> Op b -> Op a Source #
Applicative Op Source #
Instance details Defined in Algebra.Lattice.Op Methods pure :: a -> Op a Source # (<>) :: Op (a -> b) -> Op a -> Op b Source # liftA2 :: (a -> b -> c) -> Op a -> Op b -> Op c Source # (>) :: Op a -> Op b -> Op b Source # (<*) :: Op a -> Op b -> Op a Source #
Foldable Op Source #
Instance details Defined in Algebra.Lattice.Op Methods fold :: Monoid m => Op m -> m Source # foldMap :: Monoid m => (a -> m) -> Op a -> m Source # foldMap' :: Monoid m => (a -> m) -> Op a -> m Source # foldr :: (a -> b -> b) -> b -> Op a -> b Source # foldr' :: (a -> b -> b) -> b -> Op a -> b Source # foldl :: (b -> a -> b) -> b -> Op a -> b Source # foldl' :: (b -> a -> b) -> b -> Op a -> b Source # foldr1 :: (a -> a -> a) -> Op a -> a Source # foldl1 :: (a -> a -> a) -> Op a -> a Source # toList :: Op a -> [a] Source # null :: Op a -> Bool Source # length :: Op a -> Int Source # elem :: Eq a => a -> Op a -> Bool Source # maximum :: Ord a => Op a -> a Source # minimum :: Ord a => Op a -> a Source # sum :: Num a => Op a -> a Source # product :: Num a => Op a -> a Source #
Traversable Op Source #
Instance details Defined in Algebra.Lattice.Op Methods traverse :: Applicative f => (a -> f b) -> Op a -> f ( Op b) Source # sequenceA :: Applicative f => Op (f a) -> f ( Op a) Source # mapM :: Monad m => (a -> m b) -> Op a -> m ( Op b) Source # sequence :: Monad m => Op (m a) -> m ( Op a) Source #
Eq a => Eq ( Op a) Source #
Instance details Defined in Algebra.Lattice.Op Methods (==) :: Op a -> Op a -> Bool Source # (/=) :: Op a -> Op a -> Bool Source #
Data a => Data ( Op a) Source #
Instance details Defined in Algebra.Lattice.Op Methods gfoldl :: ( forall d b. Data d => c (d -> b) -> d -> c b) -> ( forall g. g -> c g) -> Op a -> c ( Op a) Source # gunfold :: ( forall b r. Data b => c (b -> r) -> c r) -> ( forall r. r -> c r) -> Constr -> c ( Op a) Source # toConstr :: Op a -> Constr Source # dataTypeOf :: Op a -> DataType Source # dataCast1 :: Typeable t => ( forall d. Data d => c (t d)) -> Maybe (c ( Op a)) Source # dataCast2 :: Typeable t => ( forall d e. ( Data d, Data e) => c (t d e)) -> Maybe (c ( Op a)) Source # gmapT :: ( forall b. Data b => b -> b) -> Op a -> Op a Source # gmapQl :: (r -> r' -> r) -> r -> ( forall d. Data d => d -> r') -> Op a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> ( forall d. Data d => d -> r') -> Op a -> r Source # gmapQ :: ( forall d. Data d => d -> u) -> Op a -> [u] Source # gmapQi :: Int -> ( forall d. Data d => d -> u) -> Op a -> u Source # gmapM :: Monad m => ( forall d. Data d => d -> m d) -> Op a -> m ( Op a) Source # gmapMp :: MonadPlus m => ( forall d. Data d => d -> m d) -> Op a -> m ( Op a) Source # gmapMo :: MonadPlus m => ( forall d. Data d => d -> m d) -> Op a -> m ( Op a) Source #
Ord a => Ord ( Op a) Source #
Instance details Defined in Algebra.Lattice.Op Methods compare :: Op a -> Op a -> Ordering Source # (<) :: Op a -> Op a -> Bool Source # (<=) :: Op a -> Op a -> Bool Source # (>) :: Op a -> Op a -> Bool Source # (>=) :: Op a -> Op a -> Bool Source # max :: Op a -> Op a -> Op a Source # min :: Op a -> Op a -> Op a Source #
Read a => Read ( Op a) Source #
Instance details Defined in Algebra.Lattice.Op Methods readsPrec :: Int -> ReadS ( Op a) Source # readList :: ReadS [ Op a] Source # readPrec :: ReadPrec ( Op a) Source # readListPrec :: ReadPrec [ Op a] Source #
Show a => Show ( Op a) Source #
Instance details Defined in Algebra.Lattice.Op Methods showsPrec :: Int -> Op a -> ShowS Source # show :: Op a -> String Source # showList :: [ Op a] -> ShowS Source #
Generic ( Op a) Source #
Instance details Defined in Algebra.Lattice.Op Associated Types type Rep ( Op a) :: Type -> Type Source # Methods from :: Op a -> Rep ( Op a) x Source # to :: Rep ( Op a) x -> Op a Source #
Function a => Function ( Op a) Source #
Instance details Defined in Algebra.Lattice.Op Methods function :: ( Op a -> b) -> Op a :-> b Source #
Arbitrary a => Arbitrary ( Op a) Source #
Instance details Defined in Algebra.Lattice.Op Methods arbitrary :: Gen ( Op a) Source # shrink :: Op a -> [ Op a] Source #
CoArbitrary a => CoArbitrary ( Op a) Source #
Instance details Defined in Algebra.Lattice.Op Methods coarbitrary :: Op a -> Gen b -> Gen b Source #
NFData a => NFData ( Op a) Source #
Instance details Defined in Algebra.Lattice.Op Methods rnf :: Op a -> () Source #
Hashable a => Hashable ( Op a) Source #
Instance details Defined in Algebra.Lattice.Op Methods hashWithSalt :: Int -> Op a -> Int Source # hash :: Op a -> Int Source #
Universe a => Universe ( Op a) Source #
Instance details Defined in Algebra.Lattice.Op Methods universe :: [ Op a] Source #
Finite a => Finite ( Op a) Source #
Instance details Defined in Algebra.Lattice.Op Methods universeF :: [ Op a] Source # cardinality :: Tagged ( Op a) Natural Source #
PartialOrd a => PartialOrd ( Op a) Source #
Instance details Defined in Algebra.Lattice.Op Methods leq :: Op a -> Op a -> Bool Source # comparable :: Op a -> Op a -> Bool Source #
BoundedJoinSemiLattice a => BoundedMeetSemiLattice ( Op a) Source #
Instance details Defined in Algebra.Lattice.Op Methods top :: Op a Source #
BoundedMeetSemiLattice a => BoundedJoinSemiLattice ( Op a) Source #
Instance details Defined in Algebra.Lattice.Op Methods bottom :: Op a Source #
Lattice a => Lattice ( Op a) Source #
Instance details Defined in Algebra.Lattice.Op Methods (\/) :: Op a -> Op a -> Op a Source # (/\) :: Op a -> Op a -> Op a Source #
Generic1 Op Source #
Instance details Defined in Algebra.Lattice.Op Associated Types type Rep1 Op :: k -> Type Source # Methods from1 :: forall (a :: k). Op a -> Rep1 Op a Source # to1 :: forall (a :: k). Rep1 Op a -> Op a Source #
type Rep ( Op a) Source #
Instance details Defined in Algebra.Lattice.Op type Rep ( Op a) = D1 (' MetaData "Op" "Algebra.Lattice.Op" "lattices-2.1-Aj77JapAM1ZIiO74F5gL5i" ' True ) ( C1 (' MetaCons "Op" ' PrefixI ' True ) ( S1 (' MetaSel (' Just "getOp") ' NoSourceUnpackedness ' NoSourceStrictness ' DecidedLazy ) ( Rec0 a)))
type Rep1 Op Source #
Instance details Defined in Algebra.Lattice.Op type Rep1 Op = D1 (' MetaData "Op" "Algebra.Lattice.Op" "lattices-2.1-Aj77JapAM1ZIiO74F5gL5i" ' True ) ( C1 (' MetaCons "Op" ' PrefixI ' True ) ( S1 (' MetaSel (' Just "getOp") ' NoSourceUnpackedness ' NoSourceStrictness ' DecidedLazy ) Par1 ))