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 '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)

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)

Methods

fmap :: (a -> b) -> Lexicographic k a -> Lexicographic k b

(<$) :: a -> Lexicographic k b -> Lexicographic k a

BoundedJoinSemiLattice k => Applicative (Lexicographic k)

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)

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)

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)

Associated Types

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

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)

Methods

(==) :: Lexicographic k v -> Lexicographic k v -> Bool

(/=) :: Lexicographic k v -> Lexicographic k v -> Bool

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

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)

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)

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)

Methods

showsPrec :: Int -> Lexicographic k v -> ShowS

show :: Lexicographic k v -> String

showList :: [Lexicographic k v] -> ShowS

Generic (Lexicographic k v)

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)

Methods

rnf :: Lexicographic k v -> ()

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

Methods

hashWithSalt :: Int -> Lexicographic k v -> Int

hash :: Lexicographic k v -> Int

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

Methods

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

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

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

Methods

top :: Lexicographic k v

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

Methods

bottom :: Lexicographic k v

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

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

Methods

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

meet :: Lexicographic k v -> Lexicographic k v -> Lexicographic k v

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

Methods

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

join :: Lexicographic k v -> Lexicographic k v -> Lexicographic k v

type Rep1 (Lexicographic k)

type Rep (Lexicographic k v)