Algebra.Lattice.Lexicographic

Documentation

data Lexicographic k v

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

Defined in Algebra.Lattice.Lexicographic

Methods

function :: (Lexicographic k v -> b) -> Lexicographic k v :-> b

(Arbitrary k, Arbitrary v) => Arbitrary (Lexicographic k v)

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)

Defined in Algebra.Lattice.Lexicographic

Methods

coarbitrary :: Lexicographic k v -> Gen b -> Gen b

(NFData k, NFData v) => NFData (Lexicographic k v)

Defined in Algebra.Lattice.Lexicographic

Methods

rnf :: Lexicographic k v -> ()

(Hashable k, Hashable v) => Hashable (Lexicographic k v)

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)

Defined in Algebra.Lattice.Lexicographic

Methods

universe :: [Lexicographic k v]

(Finite k, Finite v) => Finite (Lexicographic k v)

Defined in Algebra.Lattice.Lexicographic

Methods

universeF :: [Lexicographic k v]

cardinality :: Tagged (Lexicographic k v) Natural

(PartialOrd k, PartialOrd v) => PartialOrd (Lexicographic k v)

Defined in Algebra.Lattice.Lexicographic

Methods

leq :: Lexicographic k v -> Lexicographic k v -> Bool

comparable :: Lexicographic k v -> Lexicographic k v -> Bool

(PartialOrd k, BoundedMeetSemiLattice k, BoundedJoinSemiLattice v, BoundedMeetSemiLattice v) => BoundedMeetSemiLattice (Lexicographic k v)

Defined in Algebra.Lattice.Lexicographic

Methods

top :: Lexicographic k v

(PartialOrd k, BoundedJoinSemiLattice k, BoundedJoinSemiLattice v, BoundedMeetSemiLattice v) => BoundedJoinSemiLattice (Lexicographic k v)

Defined in Algebra.Lattice.Lexicographic

Methods

bottom :: Lexicographic k v

(PartialOrd k, Lattice k, BoundedJoinSemiLattice v, BoundedMeetSemiLattice v) => Lattice (Lexicographic k v)

Defined in Algebra.Lattice.Lexicographic

Methods

(\/) :: Lexicographic k v -> Lexicographic k v -> Lexicographic k v

(/\) :: Lexicographic k v -> Lexicographic k v -> Lexicographic k v

type Rep1 (Lexicographic k :: Type -> Type)

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)

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)))