Copyright	(C) 2010-2015 Maximilian Bolingbroke 2015 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

Documentation

newtype Divisibility a Source #

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

Constructors

Divisibility
Fields getDivisibility :: a

Instances

Monad Divisibility Source #
Methods (>>=) :: Divisibility a -> (a -> Divisibility b) -> Divisibility b # (>>) :: Divisibility a -> Divisibility b -> Divisibility b # return :: a -> Divisibility a # fail :: String -> Divisibility a #
Functor Divisibility Source #
Methods fmap :: (a -> b) -> Divisibility a -> Divisibility b # (<$) :: a -> Divisibility b -> Divisibility a #
Applicative Divisibility Source #
Methods pure :: a -> Divisibility a # (<>) :: Divisibility (a -> b) -> Divisibility a -> Divisibility b # (>) :: Divisibility a -> Divisibility b -> Divisibility b # (<*) :: Divisibility a -> Divisibility b -> Divisibility a #
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) #
Generic1 Divisibility Source #
Associated Types type Rep1 (Divisibility :: * -> ) :: -> * # Methods from1 :: Divisibility a -> Rep1 Divisibility a # to1 :: Rep1 Divisibility a -> Divisibility a #
Eq a => Eq (Divisibility a) Source #
Methods (==) :: Divisibility a -> Divisibility a -> Bool # (/=) :: Divisibility a -> Divisibility a -> Bool #
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 #
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 #
Read a => Read (Divisibility a) Source #
Methods readsPrec :: Int -> ReadS (Divisibility a) # readList :: ReadS [Divisibility a] # readPrec :: ReadPrec (Divisibility a) # readListPrec :: ReadPrec [Divisibility a] #
Show a => Show (Divisibility a) Source #
Methods showsPrec :: Int -> Divisibility a -> ShowS # show :: Divisibility a -> String # showList :: [Divisibility a] -> ShowS #
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 #
Methods hashWithSalt :: Int -> Divisibility a -> Int # hash :: Divisibility a -> Int #
(Eq a, Integral a) => PartialOrd (Divisibility a) Source #
Methods leq :: Divisibility a -> Divisibility a -> Bool Source # comparable :: Divisibility a -> Divisibility a -> Bool Source #
Integral a => BoundedJoinSemiLattice (Divisibility a) Source #
Methods bottom :: Divisibility a Source #
Integral a => Lattice (Divisibility a) Source #

Integral a => MeetSemiLattice (Divisibility a) Source #
Methods (/\) :: Divisibility a -> Divisibility a -> Divisibility a Source # meet :: Divisibility a -> Divisibility a -> Divisibility a Source #
Integral a => JoinSemiLattice (Divisibility a) Source #
Methods (\/) :: Divisibility a -> Divisibility a -> Divisibility a Source # join :: Divisibility a -> Divisibility a -> Divisibility a Source #
type Rep1 Divisibility Source #
type Rep1 Divisibility = D1 (MetaData "Divisibility" "Algebra.Lattice.Divisibility" "lattices-1.6.0-2oKxOcsrwg99Rpe11Qz7rb" True) (C1 (MetaCons "Divisibility" PrefixI True) (S1 (MetaSel (Just Symbol "getDivisibility") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))
type Rep (Divisibility a) Source #
type Rep (Divisibility a) = D1 (MetaData "Divisibility" "Algebra.Lattice.Divisibility" "lattices-1.6.0-2oKxOcsrwg99Rpe11Qz7rb" True) (C1 (MetaCons "Divisibility" PrefixI True) (S1 (MetaSel (Just Symbol "getDivisibility") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))