Algebra.Lattice.Divisibility

Documentation

newtype Divisibility a

A divisibility lattice. join = lcm, meet = gcd.

Constructors

Divisibility

Fields

• getDivisibility :: a

Instances

Foldable Divisibility

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

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)

Applicative Divisibility

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

Defined in Algebra.Lattice.Divisibility

Methods

fmap :: (a -> b) -> Divisibility a -> Divisibility b

(<$) :: a -> Divisibility b -> Divisibility a

Monad Divisibility

Defined in Algebra.Lattice.Divisibility

Methods

(>>=) :: Divisibility a -> (a -> Divisibility b) -> Divisibility b

(>>) :: Divisibility a -> Divisibility b -> Divisibility b

return :: a -> Divisibility a

Generic1 Divisibility

Defined in Algebra.Lattice.Divisibility

Associated Types

type Rep1 Divisibility :: k -> Type

Methods

from1 :: forall (a :: k). Divisibility a -> Rep1 Divisibility a

to1 :: forall (a :: k). Rep1 Divisibility a -> Divisibility a

(Arbitrary a, Num a, Ord a) => Arbitrary (Divisibility a)

Defined in Algebra.Lattice.Divisibility

Methods

arbitrary :: Gen (Divisibility a)

shrink :: Divisibility a -> [Divisibility a]

CoArbitrary a => CoArbitrary (Divisibility a)

Defined in Algebra.Lattice.Divisibility

Methods

coarbitrary :: Divisibility a -> Gen b -> Gen b

Function a => Function (Divisibility a)

Defined in Algebra.Lattice.Divisibility

Methods

function :: (Divisibility a -> b) -> Divisibility a :-> b

Data a => Data (Divisibility a)

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)

Defined in Algebra.Lattice.Divisibility

Associated Types

type Rep (Divisibility a) :: Type -> Type

Methods

from :: Divisibility a -> Rep (Divisibility a) x

to :: Rep (Divisibility a) x -> Divisibility a

Read a => Read (Divisibility a)

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)

Defined in Algebra.Lattice.Divisibility

Methods

showsPrec :: Int -> Divisibility a -> ShowS

show :: Divisibility a -> String

showList :: [Divisibility a] -> ShowS

NFData a => NFData (Divisibility a)

Defined in Algebra.Lattice.Divisibility

Methods

rnf :: Divisibility a -> ()

Eq a => Eq (Divisibility a)

Defined in Algebra.Lattice.Divisibility

Methods

(==) :: Divisibility a -> Divisibility a -> Bool

(/=) :: Divisibility a -> Divisibility a -> Bool

Ord a => Ord (Divisibility a)

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)

Defined in Algebra.Lattice.Divisibility

Methods

hashWithSalt :: Int -> Divisibility a -> Int

hash :: Divisibility a -> Int

Integral a => BoundedJoinSemiLattice (Divisibility a)

Defined in Algebra.Lattice.Divisibility

Methods

bottom :: Divisibility a

Integral a => Lattice (Divisibility a)

Defined in Algebra.Lattice.Divisibility

Methods

(\/) :: Divisibility a -> Divisibility a -> Divisibility a

(/\) :: Divisibility a -> Divisibility a -> Divisibility a

(Eq a, Integral a) => PartialOrd (Divisibility a)

Defined in Algebra.Lattice.Divisibility

Methods

leq :: Divisibility a -> Divisibility a -> Bool

comparable :: Divisibility a -> Divisibility a -> Bool

Finite a => Finite (Divisibility a)

Defined in Algebra.Lattice.Divisibility

Methods

universeF :: [Divisibility a]

cardinality :: Tagged (Divisibility a) Natural

Universe a => Universe (Divisibility a)

Defined in Algebra.Lattice.Divisibility

Methods

universe :: [Divisibility a]

type Rep1 Divisibility

Defined in Algebra.Lattice.Divisibility

type Rep1 Divisibility = D1 ('MetaData "Divisibility" "Algebra.Lattice.Divisibility" "lattices-2.2-ExsECSVnOmtEcARHt0Jtvl" 'True) (C1 ('MetaCons "Divisibility" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDivisibility") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

type Rep (Divisibility a)

Defined in Algebra.Lattice.Divisibility

type Rep (Divisibility a) = D1 ('MetaData "Divisibility" "Algebra.Lattice.Divisibility" "lattices-2.2-ExsECSVnOmtEcARHt0Jtvl" 'True) (C1 ('MetaCons "Divisibility" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDivisibility") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))