lattices-1.7.1: Fine-grained library for constructing and manipulating lattices

Copyright(C) 2010-2015 Maximilian Bolingbroke 2015 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

Monad Divisibility Source # 
Functor Divisibility Source # 

Methods

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

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

Applicative Divisibility Source # 
Foldable Divisibility Source # 

Methods

fold :: Monoid m => Divisibility m -> 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 # 

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) #

Eq a => Eq (Divisibility a) Source # 
Data a => Data (Divisibility a) Source # 

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 :: (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) #

Ord a => Ord (Divisibility a) Source # 
Read a => Read (Divisibility a) Source # 
Show a => Show (Divisibility a) Source # 
Generic (Divisibility a) Source # 

Associated Types

type Rep (Divisibility a) :: * -> * #

Methods

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

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

NFData a => NFData (Divisibility a) Source # 

Methods

rnf :: Divisibility a -> () #

Hashable a => Hashable (Divisibility a) Source # 
(Eq a, Integral a) => PartialOrd (Divisibility a) Source # 
Integral a => BoundedJoinSemiLattice (Divisibility a) Source # 
Integral a => Lattice (Divisibility a) Source # 
Integral a => MeetSemiLattice (Divisibility a) Source # 
Integral a => JoinSemiLattice (Divisibility a) Source # 
Generic1 * Divisibility Source # 

Associated Types

type Rep1 Divisibility (f :: Divisibility -> *) :: k -> * #

Methods

from1 :: f a -> Rep1 Divisibility f a #

to1 :: Rep1 Divisibility f a -> f a #

type Rep (Divisibility a) Source # 
type Rep (Divisibility a) = D1 * (MetaData "Divisibility" "Algebra.Lattice.Divisibility" "lattices-1.7.1-JS0VzTZGaXfIhOiyIFy1o0" True) (C1 * (MetaCons "Divisibility" PrefixI True) (S1 * (MetaSel (Just Symbol "getDivisibility") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))
type Rep1 * Divisibility Source # 
type Rep1 * Divisibility = D1 * (MetaData "Divisibility" "Algebra.Lattice.Divisibility" "lattices-1.7.1-JS0VzTZGaXfIhOiyIFy1o0" True) (C1 * (MetaCons "Divisibility" PrefixI True) (S1 * (MetaSel (Just Symbol "getDivisibility") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))