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.Lexicographic

Description

Synopsis

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 'Lexicographc (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 #
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 #
Methods fmap :: (a -> b) -> Lexicographic k a -> Lexicographic k b # (<$) :: a -> Lexicographic k b -> Lexicographic k a #
BoundedJoinSemiLattice k => Applicative (Lexicographic k) Source #
Methods pure :: a -> Lexicographic k a # (<>) :: Lexicographic k (a -> b) -> Lexicographic k a -> Lexicographic k b # (>) :: Lexicographic k a -> Lexicographic k b -> Lexicographic k b # (<*) :: Lexicographic k a -> Lexicographic k b -> Lexicographic k a #
Foldable (Lexicographic k) Source #
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 #
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) Source #
Associated Types type Rep1 (Lexicographic k :: * -> ) :: -> * # Methods from1 :: Lexicographic k a -> Rep1 (Lexicographic k) a # to1 :: Rep1 (Lexicographic k) a -> Lexicographic k a #
(Eq v, Eq k) => Eq (Lexicographic k v) Source #
Methods (==) :: Lexicographic k v -> Lexicographic k v -> Bool # (/=) :: Lexicographic k v -> Lexicographic k v -> Bool #
(Data v, Data k) => Data (Lexicographic k v) Source #
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 v, Ord k) => Ord (Lexicographic k v) Source #
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 v, Read k) => Read (Lexicographic k v) Source #
Methods readsPrec :: Int -> ReadS (Lexicographic k v) # readList :: ReadS [Lexicographic k v] # readPrec :: ReadPrec (Lexicographic k v) # readListPrec :: ReadPrec [Lexicographic k v] #
(Show v, Show k) => Show (Lexicographic k v) Source #
Methods showsPrec :: Int -> Lexicographic k v -> ShowS # show :: Lexicographic k v -> String # showList :: [Lexicographic k v] -> ShowS #
Generic (Lexicographic k v) Source #
Associated Types type Rep (Lexicographic k v) :: * -> * # Methods from :: Lexicographic k v -> Rep (Lexicographic k v) x # to :: Rep (Lexicographic k v) x -> Lexicographic k v #
(NFData k, NFData v) => NFData (Lexicographic k v) Source #
Methods rnf :: Lexicographic k v -> () #
(Hashable k, Hashable v) => Hashable (Lexicographic k v) Source #
Methods hashWithSalt :: Int -> Lexicographic k v -> Int # hash :: Lexicographic k v -> Int #
(PartialOrd k, PartialOrd v) => PartialOrd (Lexicographic k v) Source #
Methods leq :: Lexicographic k v -> Lexicographic k v -> Bool Source # comparable :: Lexicographic k v -> Lexicographic k v -> Bool Source #
(PartialOrd k, BoundedLattice k, BoundedLattice v) => BoundedLattice (Lexicographic k v) Source #

(PartialOrd k, BoundedMeetSemiLattice k, BoundedMeetSemiLattice v) => BoundedMeetSemiLattice (Lexicographic k v) Source #
Methods top :: Lexicographic k v Source #
(PartialOrd k, BoundedJoinSemiLattice k, BoundedJoinSemiLattice v) => BoundedJoinSemiLattice (Lexicographic k v) Source #
Methods bottom :: Lexicographic k v Source #
(PartialOrd k, Lattice k, BoundedLattice v) => Lattice (Lexicographic k v) Source #

(PartialOrd k, MeetSemiLattice k, BoundedMeetSemiLattice v) => MeetSemiLattice (Lexicographic k v) Source #
Methods (/\) :: Lexicographic k v -> Lexicographic k v -> Lexicographic k v Source # meet :: Lexicographic k v -> Lexicographic k v -> Lexicographic k v Source #
(PartialOrd k, JoinSemiLattice k, BoundedJoinSemiLattice v) => JoinSemiLattice (Lexicographic k v) Source #
Methods (\/) :: Lexicographic k v -> Lexicographic k v -> Lexicographic k v Source # join :: Lexicographic k v -> Lexicographic k v -> Lexicographic k v Source #
type Rep1 (Lexicographic k) Source #
type Rep1 (Lexicographic k) = D1 (MetaData "Lexicographic" "Algebra.Lattice.Lexicographic" "lattices-1.6.0-2oKxOcsrwg99Rpe11Qz7rb" False) (C1 (MetaCons "Lexicographic" PrefixI False) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 k)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1)))
type Rep (Lexicographic k v) Source #
type Rep (Lexicographic k v) = D1 (MetaData "Lexicographic" "Algebra.Lattice.Lexicographic" "lattices-1.6.0-2oKxOcsrwg99Rpe11Qz7rb" False) (C1 (MetaCons "Lexicographic" PrefixI False) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 k)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 v))))