| 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.Ordered
Description
Synopsis
- newtype Ordered a = Ordered {
- getOrdered :: a
Documentation
A total order gives rise to a lattice. Join is
max, meet is min.
Constructors
| Ordered | |
Fields
| |
Instances
| Applicative Ordered Source # | |||||
| Functor Ordered Source # | |||||
| Monad Ordered Source # | |||||
| Foldable Ordered Source # | |||||
Defined in Algebra.Lattice.Ordered Methods fold :: Monoid m => Ordered m -> m foldMap :: Monoid m => (a -> m) -> Ordered a -> 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 elem :: Eq a => a -> Ordered a -> Bool maximum :: Ord a => Ordered a -> a minimum :: Ord a => Ordered a -> a | |||||
| Traversable Ordered Source # | |||||
| Generic1 Ordered Source # | |||||
Defined in Algebra.Lattice.Ordered Associated Types
| |||||
| Arbitrary a => Arbitrary (Ordered a) Source # | |||||
| CoArbitrary a => CoArbitrary (Ordered a) Source # | |||||
Defined in Algebra.Lattice.Ordered Methods coarbitrary :: Ordered a -> Gen b -> Gen b | |||||
| Function a => Function (Ordered a) Source # | |||||
Defined in Algebra.Lattice.Ordered | |||||
| NFData a => NFData (Ordered a) Source # | |||||
Defined in Algebra.Lattice.Ordered | |||||
| Data a => Data (Ordered a) Source # | |||||
Defined in Algebra.Lattice.Ordered 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 :: forall r r'. (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) | |||||
| Generic (Ordered a) Source # | |||||
Defined in Algebra.Lattice.Ordered Associated Types
| |||||
| Read a => Read (Ordered a) Source # | |||||
Defined in Algebra.Lattice.Ordered | |||||
| Show a => Show (Ordered a) Source # | |||||
| Eq a => Eq (Ordered a) Source # | |||||
| Ord a => Ord (Ordered a) Source # | |||||
Defined in Algebra.Lattice.Ordered | |||||
| Hashable a => Hashable (Ordered a) Source # | |||||
Defined in Algebra.Lattice.Ordered | |||||
| (Ord a, Bounded a) => Heyting (Ordered a) Source # | This is interesting logic, as it satisfies both de Morgan laws; but isn't Boolean: i.e. law of exluded middle doesn't hold. Negation "smashes" value into | ||||
| (Ord a, Bounded a) => BoundedJoinSemiLattice (Ordered a) Source # | |||||
Defined in Algebra.Lattice.Ordered | |||||
| (Ord a, Bounded a) => BoundedMeetSemiLattice (Ordered a) Source # | |||||
Defined in Algebra.Lattice.Ordered | |||||
| Ord a => Lattice (Ordered a) Source # | |||||
| Ord a => PartialOrd (Ordered a) Source # | |||||
| Finite a => Finite (Ordered a) Source # | |||||
Defined in Algebra.Lattice.Ordered | |||||
| Universe a => Universe (Ordered a) Source # | |||||
Defined in Algebra.Lattice.Ordered | |||||
| type Rep1 Ordered Source # | |||||
Defined in Algebra.Lattice.Ordered type Rep1 Ordered = D1 ('MetaData "Ordered" "Algebra.Lattice.Ordered" "lattices-2.2.1.1-DOiSBgvrTjdFgPaGHAnlJl" 'True) (C1 ('MetaCons "Ordered" 'PrefixI 'True) (S1 ('MetaSel ('Just "getOrdered") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1)) | |||||
| type Rep (Ordered a) Source # | |||||
Defined in Algebra.Lattice.Ordered type Rep (Ordered a) = D1 ('MetaData "Ordered" "Algebra.Lattice.Ordered" "lattices-2.2.1.1-DOiSBgvrTjdFgPaGHAnlJl" 'True) (C1 ('MetaCons "Ordered" 'PrefixI 'True) (S1 ('MetaSel ('Just "getOrdered") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a))) | |||||