lattices-1.7.1.1: Fine-grained library for constructing and manipulating lattices

Copyright(C) 2010-2015 Maximilian Bolingbroke 2015 Oleg Grenrus
LicenseBSD-3-Clause (see the file LICENSE)
MaintainerOleg Grenrus <oleg.grenrus@iki.fi>
Safe HaskellSafe
LanguageHaskell2010

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 # 
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 :: * -> *) Source # 
Instance details

Defined in Algebra.Lattice.Lexicographic

Associated Types

type Rep1 (Lexicographic k) :: 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) 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

(Read k, Read v) => Read (Lexicographic k v) Source # 
Instance details

Defined in Algebra.Lattice.Lexicographic

(Show k, Show v) => Show (Lexicographic k v) Source # 
Instance details

Defined in Algebra.Lattice.Lexicographic

Generic (Lexicographic k v) Source # 
Instance details

Defined in Algebra.Lattice.Lexicographic

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 # 
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 #

(PartialOrd k, PartialOrd v) => PartialOrd (Lexicographic k v) Source # 
Instance details

Defined in Algebra.Lattice.Lexicographic

(PartialOrd k, BoundedLattice k, BoundedLattice v) => BoundedLattice (Lexicographic k v) Source # 
Instance details

Defined in Algebra.Lattice.Lexicographic

(PartialOrd k, BoundedMeetSemiLattice k, 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) => BoundedJoinSemiLattice (Lexicographic k v) Source # 
Instance details

Defined in Algebra.Lattice.Lexicographic

(PartialOrd k, Lattice k, BoundedLattice v) => Lattice (Lexicographic k v) Source # 
Instance details

Defined in Algebra.Lattice.Lexicographic

(PartialOrd k, MeetSemiLattice k, BoundedMeetSemiLattice v) => MeetSemiLattice (Lexicographic k v) Source # 
Instance details

Defined in Algebra.Lattice.Lexicographic

(PartialOrd k, JoinSemiLattice k, BoundedJoinSemiLattice v) => JoinSemiLattice (Lexicographic k v) Source # 
Instance details

Defined in Algebra.Lattice.Lexicographic

type Rep1 (Lexicographic k :: * -> *) Source # 
Instance details

Defined in Algebra.Lattice.Lexicographic

type Rep1 (Lexicographic k :: * -> *) = D1 (MetaData "Lexicographic" "Algebra.Lattice.Lexicographic" "lattices-1.7.1.1-KHhCTNp0Jlu7lPrYOy5eaF" 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-1.7.1.1-KHhCTNp0Jlu7lPrYOy5eaF" 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)))