lattices-2.2.1: Fine-grained library for constructing and manipulating lattices
Copyright(C) 2010-2015 Maximilian Bolingbroke 2015-2019 Oleg Grenrus
LicenseBSD-3-Clause (see the file LICENSE)
MaintainerOleg Grenrus <oleg.grenrus@iki.fi>
Safe HaskellSafe
LanguageHaskell2010

Algebra.Lattice.Divisibility

Description

 
Synopsis

Documentation

newtype Divisibility a Source #

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

Constructors

Divisibility 

Fields

Instances

Instances details
Foldable Divisibility Source # 
Instance details

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 # 
Instance details

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 Source # 
Instance details

Defined in Algebra.Lattice.Divisibility

Functor Divisibility Source # 
Instance details

Defined in Algebra.Lattice.Divisibility

Methods

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

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

Monad Divisibility Source # 
Instance details

Defined in Algebra.Lattice.Divisibility

Generic1 Divisibility Source # 
Instance details

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) Source # 
Instance details

Defined in Algebra.Lattice.Divisibility

CoArbitrary a => CoArbitrary (Divisibility a) Source # 
Instance details

Defined in Algebra.Lattice.Divisibility

Methods

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

Function a => Function (Divisibility a) Source # 
Instance details

Defined in Algebra.Lattice.Divisibility

Methods

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

Data a => Data (Divisibility a) Source # 
Instance details

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 # 
Instance details

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) Source # 
Instance details

Defined in Algebra.Lattice.Divisibility

Show a => Show (Divisibility a) Source # 
Instance details

Defined in Algebra.Lattice.Divisibility

NFData a => NFData (Divisibility a) Source # 
Instance details

Defined in Algebra.Lattice.Divisibility

Methods

rnf :: Divisibility a -> () #

Eq a => Eq (Divisibility a) Source # 
Instance details

Defined in Algebra.Lattice.Divisibility

Ord a => Ord (Divisibility a) Source # 
Instance details

Defined in Algebra.Lattice.Divisibility

Hashable a => Hashable (Divisibility a) Source # 
Instance details

Defined in Algebra.Lattice.Divisibility

Integral a => BoundedJoinSemiLattice (Divisibility a) Source # 
Instance details

Defined in Algebra.Lattice.Divisibility

Integral a => Lattice (Divisibility a) Source # 
Instance details

Defined in Algebra.Lattice.Divisibility

(Eq a, Integral a) => PartialOrd (Divisibility a) Source # 
Instance details

Defined in Algebra.Lattice.Divisibility

Finite a => Finite (Divisibility a) Source # 
Instance details

Defined in Algebra.Lattice.Divisibility

Universe a => Universe (Divisibility a) Source # 
Instance details

Defined in Algebra.Lattice.Divisibility

Methods

universe :: [Divisibility a] #

type Rep1 Divisibility Source # 
Instance details

Defined in Algebra.Lattice.Divisibility

type Rep1 Divisibility = D1 ('MetaData "Divisibility" "Algebra.Lattice.Divisibility" "lattices-2.2.1-83qrGPcFdIWCf2lUVrFvrH" 'True) (C1 ('MetaCons "Divisibility" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDivisibility") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
type Rep (Divisibility a) Source # 
Instance details

Defined in Algebra.Lattice.Divisibility

type Rep (Divisibility a) = D1 ('MetaData "Divisibility" "Algebra.Lattice.Divisibility" "lattices-2.2.1-83qrGPcFdIWCf2lUVrFvrH" 'True) (C1 ('MetaCons "Divisibility" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDivisibility") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))