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 Timestamp s. Typically this is done in an arbitary, but deterministic manner.

Constructors

Lexicographic !k !v

Instances

Instances details

BoundedJoinSemiLattice k => Monad ( Lexicographic k) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods (>>=) :: Lexicographic k a -> (a -> Lexicographic k b) -> Lexicographic k b Source # (>>) :: Lexicographic k a -> Lexicographic k b -> Lexicographic k b Source # return :: a -> Lexicographic k a Source #
Functor ( Lexicographic k) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods fmap :: (a -> b) -> Lexicographic k a -> Lexicographic k b Source # (<$) :: a -> Lexicographic k b -> Lexicographic k a Source #
BoundedJoinSemiLattice k => Applicative ( Lexicographic k) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods pure :: a -> Lexicographic k a Source # (<>) :: Lexicographic k (a -> b) -> Lexicographic k a -> Lexicographic k b Source # liftA2 :: (a -> b -> c) -> Lexicographic k a -> Lexicographic k b -> Lexicographic k c Source # (>) :: Lexicographic k a -> Lexicographic k b -> Lexicographic k b Source # (<*) :: Lexicographic k a -> Lexicographic k b -> Lexicographic k a Source #
Foldable ( Lexicographic k) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods fold :: Monoid m => Lexicographic k m -> m Source # foldMap :: Monoid m => (a -> m) -> Lexicographic k a -> m Source # foldMap' :: Monoid m => (a -> m) -> Lexicographic k a -> m Source # foldr :: (a -> b -> b) -> b -> Lexicographic k a -> b Source # foldr' :: (a -> b -> b) -> b -> Lexicographic k a -> b Source # foldl :: (b -> a -> b) -> b -> Lexicographic k a -> b Source # foldl' :: (b -> a -> b) -> b -> Lexicographic k a -> b Source # foldr1 :: (a -> a -> a) -> Lexicographic k a -> a Source # foldl1 :: (a -> a -> a) -> Lexicographic k a -> a Source # toList :: Lexicographic k a -> [a] Source # null :: Lexicographic k a -> Bool Source # length :: Lexicographic k a -> Int Source # elem :: Eq a => a -> Lexicographic k a -> Bool Source # maximum :: Ord a => Lexicographic k a -> a Source # minimum :: Ord a => Lexicographic k a -> a Source # sum :: Num a => Lexicographic k a -> a Source # product :: Num a => Lexicographic k a -> a Source #
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) Source # sequenceA :: Applicative f => Lexicographic k (f a) -> f ( Lexicographic k a) Source # mapM :: Monad m => (a -> m b) -> Lexicographic k a -> m ( Lexicographic k b) Source # sequence :: Monad m => Lexicographic k (m a) -> m ( Lexicographic k a) Source #
Generic1 ( Lexicographic k :: Type -> Type ) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Associated Types type Rep1 ( Lexicographic k) :: k -> Type Source # Methods from1 :: forall (a :: k0). Lexicographic k a -> Rep1 ( Lexicographic k) a Source # to1 :: forall (a :: k0). Rep1 ( Lexicographic k) a -> Lexicographic k a Source #
( Eq k, Eq v) => Eq ( Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods (==) :: Lexicographic k v -> Lexicographic k v -> Bool Source # (/=) :: Lexicographic k v -> Lexicographic k v -> Bool Source #
( 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) Source # gunfold :: ( forall b r. Data b => c (b -> r) -> c r) -> ( forall r. r -> c r) -> Constr -> c ( Lexicographic k v) Source # toConstr :: Lexicographic k v -> Constr Source # dataTypeOf :: Lexicographic k v -> DataType Source # dataCast1 :: Typeable t => ( forall d. Data d => c (t d)) -> Maybe (c ( Lexicographic k v)) Source # dataCast2 :: Typeable t => ( forall d e. ( Data d, Data e) => c (t d e)) -> Maybe (c ( Lexicographic k v)) Source # gmapT :: ( forall b. Data b => b -> b) -> Lexicographic k v -> Lexicographic k v Source # gmapQl :: (r -> r' -> r) -> r -> ( forall d. Data d => d -> r') -> Lexicographic k v -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> ( forall d. Data d => d -> r') -> Lexicographic k v -> r Source # gmapQ :: ( forall d. Data d => d -> u) -> Lexicographic k v -> [u] Source # gmapQi :: Int -> ( forall d. Data d => d -> u) -> Lexicographic k v -> u Source # gmapM :: Monad m => ( forall d. Data d => d -> m d) -> Lexicographic k v -> m ( Lexicographic k v) Source # gmapMp :: MonadPlus m => ( forall d. Data d => d -> m d) -> Lexicographic k v -> m ( Lexicographic k v) Source # gmapMo :: MonadPlus m => ( forall d. Data d => d -> m d) -> Lexicographic k v -> m ( Lexicographic k v) Source #
( 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 Source # (<) :: Lexicographic k v -> Lexicographic k v -> Bool Source # (<=) :: Lexicographic k v -> Lexicographic k v -> Bool Source # (>) :: Lexicographic k v -> Lexicographic k v -> Bool Source # (>=) :: Lexicographic k v -> Lexicographic k v -> Bool Source # max :: Lexicographic k v -> Lexicographic k v -> Lexicographic k v Source # min :: Lexicographic k v -> Lexicographic k v -> Lexicographic k v Source #
( Read k, Read v) => Read ( Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods readsPrec :: Int -> ReadS ( Lexicographic k v) Source # readList :: ReadS [ Lexicographic k v] Source # readPrec :: ReadPrec ( Lexicographic k v) Source # readListPrec :: ReadPrec [ Lexicographic k v] Source #
( Show k, Show v) => Show ( Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods showsPrec :: Int -> Lexicographic k v -> ShowS Source # show :: Lexicographic k v -> String Source # showList :: [ Lexicographic k v] -> ShowS Source #
Generic ( Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Associated Types type Rep ( Lexicographic k v) :: Type -> Type Source # Methods from :: Lexicographic k v -> Rep ( Lexicographic k v) x Source # to :: Rep ( Lexicographic k v) x -> Lexicographic k v Source #
( 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 Source #
( Arbitrary k, Arbitrary v) => Arbitrary ( Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods arbitrary :: Gen ( Lexicographic k v) Source # shrink :: Lexicographic k v -> [ Lexicographic k v] Source #
( 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 Source #
( NFData k, NFData v) => NFData ( Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods rnf :: Lexicographic k v -> () Source #
( Hashable k, Hashable v) => Hashable ( Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods hashWithSalt :: Int -> Lexicographic k v -> Int Source # hash :: Lexicographic k v -> Int Source #
( Universe k, Universe v) => Universe ( Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods universe :: [ Lexicographic k v] Source #
( Finite k, Finite v) => Finite ( Lexicographic k v) Source #
Instance details Defined in Algebra.Lattice.Lexicographic Methods universeF :: [ Lexicographic k v] Source # cardinality :: Tagged ( Lexicographic k v) Natural Source #
( 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-2.1-Aj77JapAM1ZIiO74F5gL5i" ' 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-2.1-Aj77JapAM1ZIiO74F5gL5i" ' 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)))