| 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.Divisibility
Description
Synopsis
- newtype Divisibility a = Divisibility {
- getDivisibility :: a
Documentation
newtype Divisibility a Source #
A divisibility lattice. , join = lcm.meet = gcd
Constructors
| Divisibility | |
Fields
| |
Instances
| Applicative Divisibility Source # | |||||
Defined in Algebra.Lattice.Divisibility Methods pure :: a -> Divisibility a (<*>) :: Divisibility (a -> b) -> Divisibility a -> Divisibility b liftA2 :: (a -> b -> c) -> Divisibility a -> Divisibility b -> Divisibility c (*>) :: Divisibility a -> Divisibility b -> Divisibility b (<*) :: Divisibility a -> Divisibility b -> Divisibility a | |||||
| Functor Divisibility Source # | |||||
Defined in Algebra.Lattice.Divisibility Methods fmap :: (a -> b) -> Divisibility a -> Divisibility b (<$) :: a -> Divisibility b -> Divisibility a | |||||
| Monad Divisibility Source # | |||||
Defined in Algebra.Lattice.Divisibility Methods (>>=) :: Divisibility a -> (a -> Divisibility b) -> Divisibility b (>>) :: Divisibility a -> Divisibility b -> Divisibility b return :: a -> Divisibility a | |||||
| Foldable Divisibility Source # | |||||
Defined in Algebra.Lattice.Divisibility Methods fold :: Monoid m => Divisibility m -> m foldMap :: Monoid m => (a -> m) -> Divisibility a -> m foldMap' :: Monoid m => (a -> m) -> Divisibility a -> m foldr :: (a -> b -> b) -> b -> Divisibility a -> b foldr' :: (a -> b -> b) -> b -> Divisibility a -> b foldl :: (b -> a -> b) -> b -> Divisibility a -> b foldl' :: (b -> a -> b) -> b -> Divisibility a -> b foldr1 :: (a -> a -> a) -> Divisibility a -> a foldl1 :: (a -> a -> a) -> Divisibility a -> a toList :: Divisibility a -> [a] null :: Divisibility a -> Bool length :: Divisibility a -> Int elem :: Eq a => a -> Divisibility a -> Bool maximum :: Ord a => Divisibility a -> a minimum :: Ord a => Divisibility a -> a sum :: Num a => Divisibility a -> a product :: Num a => Divisibility a -> a | |||||
| Traversable Divisibility Source # | |||||
Defined in Algebra.Lattice.Divisibility Methods traverse :: Applicative f => (a -> f b) -> Divisibility a -> f (Divisibility b) sequenceA :: Applicative f => Divisibility (f a) -> f (Divisibility a) mapM :: Monad m => (a -> m b) -> Divisibility a -> m (Divisibility b) sequence :: Monad m => Divisibility (m a) -> m (Divisibility a) | |||||
| Generic1 Divisibility Source # | |||||
Defined in Algebra.Lattice.Divisibility Associated Types
| |||||
| (Arbitrary a, Num a, Ord a) => Arbitrary (Divisibility a) Source # | |||||
Defined in Algebra.Lattice.Divisibility | |||||
| CoArbitrary a => CoArbitrary (Divisibility a) Source # | |||||
Defined in Algebra.Lattice.Divisibility Methods coarbitrary :: Divisibility a -> Gen b -> Gen b | |||||
| Function a => Function (Divisibility a) Source # | |||||
Defined in Algebra.Lattice.Divisibility Methods function :: (Divisibility a -> b) -> Divisibility a :-> b | |||||
| NFData a => NFData (Divisibility a) Source # | |||||
Defined in Algebra.Lattice.Divisibility Methods rnf :: Divisibility a -> () | |||||
| Data a => Data (Divisibility a) Source # | |||||
Defined in Algebra.Lattice.Divisibility Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Divisibility a -> c (Divisibility a) gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Divisibility a) toConstr :: Divisibility a -> Constr dataTypeOf :: Divisibility a -> DataType dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Divisibility a)) dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Divisibility a)) gmapT :: (forall b. Data b => b -> b) -> Divisibility a -> Divisibility a gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Divisibility a -> r gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Divisibility a -> r gmapQ :: (forall d. Data d => d -> u) -> Divisibility a -> [u] gmapQi :: Int -> (forall d. Data d => d -> u) -> Divisibility a -> u gmapM :: Monad m => (forall d. Data d => d -> m d) -> Divisibility a -> m (Divisibility a) gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Divisibility a -> m (Divisibility a) gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Divisibility a -> m (Divisibility a) | |||||
| Generic (Divisibility a) Source # | |||||
Defined in Algebra.Lattice.Divisibility Associated Types
Methods from :: Divisibility a -> Rep (Divisibility a) x to :: Rep (Divisibility a) x -> Divisibility a | |||||
| Read a => Read (Divisibility a) Source # | |||||
Defined in Algebra.Lattice.Divisibility Methods readsPrec :: Int -> ReadS (Divisibility a) readList :: ReadS [Divisibility a] readPrec :: ReadPrec (Divisibility a) readListPrec :: ReadPrec [Divisibility a] | |||||
| Show a => Show (Divisibility a) Source # | |||||
Defined in Algebra.Lattice.Divisibility Methods showsPrec :: Int -> Divisibility a -> ShowS show :: Divisibility a -> String showList :: [Divisibility a] -> ShowS | |||||
| Eq a => Eq (Divisibility a) Source # | |||||
Defined in Algebra.Lattice.Divisibility Methods (==) :: Divisibility a -> Divisibility a -> Bool (/=) :: Divisibility a -> Divisibility a -> Bool | |||||
| Ord a => Ord (Divisibility a) Source # | |||||
Defined in Algebra.Lattice.Divisibility Methods compare :: Divisibility a -> Divisibility a -> Ordering (<) :: Divisibility a -> Divisibility a -> Bool (<=) :: Divisibility a -> Divisibility a -> Bool (>) :: Divisibility a -> Divisibility a -> Bool (>=) :: Divisibility a -> Divisibility a -> Bool max :: Divisibility a -> Divisibility a -> Divisibility a min :: Divisibility a -> Divisibility a -> Divisibility a | |||||
| Hashable a => Hashable (Divisibility a) Source # | |||||
Defined in Algebra.Lattice.Divisibility | |||||
| Integral a => BoundedJoinSemiLattice (Divisibility a) Source # | |||||
Defined in Algebra.Lattice.Divisibility Methods bottom :: Divisibility a Source # | |||||
| Integral a => Lattice (Divisibility a) Source # | |||||
Defined in Algebra.Lattice.Divisibility Methods (\/) :: Divisibility a -> Divisibility a -> Divisibility a Source # (/\) :: Divisibility a -> Divisibility a -> Divisibility a Source # | |||||
| (Eq a, Integral a) => PartialOrd (Divisibility a) Source # | |||||
Defined in Algebra.Lattice.Divisibility Methods leq :: Divisibility a -> Divisibility a -> Bool Source # comparable :: Divisibility a -> Divisibility a -> Bool Source # | |||||
| Finite a => Finite (Divisibility a) Source # | |||||
Defined in Algebra.Lattice.Divisibility | |||||
| Universe a => Universe (Divisibility a) Source # | |||||
Defined in Algebra.Lattice.Divisibility Methods universe :: [Divisibility a] | |||||
| type Rep1 Divisibility Source # | |||||
Defined in Algebra.Lattice.Divisibility type Rep1 Divisibility = D1 ('MetaData "Divisibility" "Algebra.Lattice.Divisibility" "lattices-2.2.1.1-DOiSBgvrTjdFgPaGHAnlJl" 'True) (C1 ('MetaCons "Divisibility" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDivisibility") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1)) | |||||
| type Rep (Divisibility a) Source # | |||||
Defined in Algebra.Lattice.Divisibility type Rep (Divisibility a) = D1 ('MetaData "Divisibility" "Algebra.Lattice.Divisibility" "lattices-2.2.1.1-DOiSBgvrTjdFgPaGHAnlJl" 'True) (C1 ('MetaCons "Divisibility" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDivisibility") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a))) | |||||