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.Lexicographic

Description

Synopsis

data Lexicographic k v = Lexicographic !k !v

Documentation

data Lexicographic k v Source #

A pair lattice with a lexicographic ordering. This means in a join the second component of the resulting pair is the second component of the pair with the larger first component. If the first components are equal, then the second components will be joined. The meet is similar only it prefers the smaller first component.

An application of this type is versioning. For example, a Last-Writer-Wins register would look like Lexicographic (Ordered Timestamp) v where the lattice structure handles the, presumably rare, case of matching Timestamps. Typically this is done in an arbitary, but deterministic manner.

Constructors

Lexicographic !k !v

Instances

BoundedJoinSemiLattice k => Monad (Lexicographic k) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods (>>=) :: Lexicographic k a -> (a -> Lexicographic k b) -> Lexicographic k b # (>>) :: Lexicographic k a -> Lexicographic k b -> Lexicographic k b # return :: a -> Lexicographic k a # fail :: String -> Lexicographic k a #
Functor (Lexicographic k) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods fmap :: (a -> b) -> Lexicographic k a -> Lexicographic k b # (<$) :: a -> Lexicographic k b -> Lexicographic k a #
BoundedJoinSemiLattice k => Applicative (Lexicographic k) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods pure :: a -> Lexicographic k a # (<>) :: Lexicographic k (a -> b) -> Lexicographic k a -> Lexicographic k b # liftA2 :: (a -> b -> c) -> Lexicographic k a -> Lexicographic k b -> Lexicographic k c # (>) :: Lexicographic k a -> Lexicographic k b -> Lexicographic k b # (<*) :: Lexicographic k a -> Lexicographic k b -> Lexicographic k a #
Foldable (Lexicographic k) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods fold :: Monoid m => Lexicographic k m -> m # foldMap :: Monoid m => (a -> m) -> Lexicographic k a -> m # foldr :: (a -> b -> b) -> b -> Lexicographic k a -> b # foldr' :: (a -> b -> b) -> b -> Lexicographic k a -> b # foldl :: (b -> a -> b) -> b -> Lexicographic k a -> b # foldl' :: (b -> a -> b) -> b -> Lexicographic k a -> b # foldr1 :: (a -> a -> a) -> Lexicographic k a -> a # foldl1 :: (a -> a -> a) -> Lexicographic k a -> a # toList :: Lexicographic k a -> [a] # null :: Lexicographic k a -> Bool # length :: Lexicographic k a -> Int # elem :: Eq a => a -> Lexicographic k a -> Bool # maximum :: Ord a => Lexicographic k a -> a # minimum :: Ord a => Lexicographic k a -> a # sum :: Num a => Lexicographic k a -> a # product :: Num a => Lexicographic k a -> a #
Traversable (Lexicographic k) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods traverse :: Applicative f => (a -> f b) -> Lexicographic k a -> f (Lexicographic k b) # sequenceA :: Applicative f => Lexicographic k (f a) -> f (Lexicographic k a) # mapM :: Monad m => (a -> m b) -> Lexicographic k a -> m (Lexicographic k b) # sequence :: Monad m => Lexicographic k (m a) -> m (Lexicographic k a) #
Generic1 (Lexicographic k :: Type -> Type) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Associated Types type Rep1 (Lexicographic k) :: k -> Type # Methods from1 :: Lexicographic k a -> Rep1 (Lexicographic k) a # to1 :: Rep1 (Lexicographic k) a -> Lexicographic k a #
(Eq k, Eq v) => Eq (Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods (==) :: Lexicographic k v -> Lexicographic k v -> Bool # (/=) :: Lexicographic k v -> Lexicographic k v -> Bool #
(Data k, Data v) => Data (Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Lexicographic k v -> c (Lexicographic k v) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Lexicographic k v) # toConstr :: Lexicographic k v -> Constr # dataTypeOf :: Lexicographic k v -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Lexicographic k v)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Lexicographic k v)) # gmapT :: (forall b. Data b => b -> b) -> Lexicographic k v -> Lexicographic k v # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Lexicographic k v -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Lexicographic k v -> r # gmapQ :: (forall d. Data d => d -> u) -> Lexicographic k v -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Lexicographic k v -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Lexicographic k v -> m (Lexicographic k v) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Lexicographic k v -> m (Lexicographic k v) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Lexicographic k v -> m (Lexicographic k v) #
(Ord k, Ord v) => Ord (Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods compare :: Lexicographic k v -> Lexicographic k v -> Ordering # (<) :: Lexicographic k v -> Lexicographic k v -> Bool # (<=) :: Lexicographic k v -> Lexicographic k v -> Bool # (>) :: Lexicographic k v -> Lexicographic k v -> Bool # (>=) :: Lexicographic k v -> Lexicographic k v -> Bool # max :: Lexicographic k v -> Lexicographic k v -> Lexicographic k v # min :: Lexicographic k v -> Lexicographic k v -> Lexicographic k v #
(Read k, Read v) => Read (Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods readsPrec :: Int -> ReadS (Lexicographic k v) # readList :: ReadS [Lexicographic k v] # readPrec :: ReadPrec (Lexicographic k v) # readListPrec :: ReadPrec [Lexicographic k v] #
(Show k, Show v) => Show (Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods showsPrec :: Int -> Lexicographic k v -> ShowS # show :: Lexicographic k v -> String # showList :: [Lexicographic k v] -> ShowS #
Generic (Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Associated Types type Rep (Lexicographic k v) :: Type -> Type # Methods from :: Lexicographic k v -> Rep (Lexicographic k v) x # to :: Rep (Lexicographic k v) x -> Lexicographic k v #
(Function k, Function v) => Function (Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods function :: (Lexicographic k v -> b) -> Lexicographic k v :-> b #
(Arbitrary k, Arbitrary v) => Arbitrary (Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods arbitrary :: Gen (Lexicographic k v) # shrink :: Lexicographic k v -> [Lexicographic k v] #
(CoArbitrary k, CoArbitrary v) => CoArbitrary (Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods coarbitrary :: Lexicographic k v -> Gen b -> Gen b #
(NFData k, NFData v) => NFData (Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods rnf :: Lexicographic k v -> () #
(Hashable k, Hashable v) => Hashable (Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods hashWithSalt :: Int -> Lexicographic k v -> Int # hash :: Lexicographic k v -> Int #
(Universe k, Universe v) => Universe (Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods universe :: [Lexicographic k v] #
(Finite k, Finite v) => Finite (Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods universeF :: [Lexicographic k v] # cardinality :: Tagged (Lexicographic k v) Natural #
(PartialOrd k, PartialOrd v) => PartialOrd (Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods leq :: Lexicographic k v -> Lexicographic k v -> Bool Source # comparable :: Lexicographic k v -> Lexicographic k v -> Bool Source #
(PartialOrd k, BoundedMeetSemiLattice k, BoundedJoinSemiLattice v, BoundedMeetSemiLattice v) => BoundedMeetSemiLattice (Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods top :: Lexicographic k v Source #
(PartialOrd k, BoundedJoinSemiLattice k, BoundedJoinSemiLattice v, BoundedMeetSemiLattice v) => BoundedJoinSemiLattice (Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods bottom :: Lexicographic k v Source #
(PartialOrd k, Lattice k, BoundedJoinSemiLattice v, BoundedMeetSemiLattice v) => Lattice (Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods (\/) :: Lexicographic k v -> Lexicographic k v -> Lexicographic k v Source # (/\) :: Lexicographic k v -> Lexicographic k v -> Lexicographic k v Source #
type Rep1 (Lexicographic k :: Type -> Type) Source #
Instance details Defined in Algebra.Lattice.Lexicographic type Rep1 (Lexicographic k :: Type -> Type) = D1 (MetaData "Lexicographic" "Algebra.Lattice.Lexicographic" "lattices-2-GNwPiglY2qIELYMTNuLIEL" False) (C1 (MetaCons "Lexicographic" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 k) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1))
type Rep (Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic type Rep (Lexicographic k v) = D1 (MetaData "Lexicographic" "Algebra.Lattice.Lexicographic" "lattices-2-GNwPiglY2qIELYMTNuLIEL" False) (C1 (MetaCons "Lexicographic" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 k) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 v)))