lattices-1.7.1: 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.Ordered

Description

 

Synopsis

Documentation

newtype Ordered a Source #

A total order gives rise to a lattice. Join is max, meet is min.

Constructors

Ordered 

Fields

Instances

Monad Ordered Source # 

Methods

(>>=) :: Ordered a -> (a -> Ordered b) -> Ordered b #

(>>) :: Ordered a -> Ordered b -> Ordered b #

return :: a -> Ordered a #

fail :: String -> Ordered a #

Functor Ordered Source # 

Methods

fmap :: (a -> b) -> Ordered a -> Ordered b #

(<$) :: a -> Ordered b -> Ordered a #

Applicative Ordered Source # 

Methods

pure :: a -> Ordered a #

(<*>) :: Ordered (a -> b) -> Ordered a -> Ordered b #

liftA2 :: (a -> b -> c) -> Ordered a -> Ordered b -> Ordered c #

(*>) :: Ordered a -> Ordered b -> Ordered b #

(<*) :: Ordered a -> Ordered b -> Ordered a #

Foldable Ordered Source # 

Methods

fold :: Monoid m => Ordered m -> m #

foldMap :: Monoid m => (a -> m) -> Ordered a -> m #

foldr :: (a -> b -> b) -> b -> Ordered a -> b #

foldr' :: (a -> b -> b) -> b -> Ordered a -> b #

foldl :: (b -> a -> b) -> b -> Ordered a -> b #

foldl' :: (b -> a -> b) -> b -> Ordered a -> b #

foldr1 :: (a -> a -> a) -> Ordered a -> a #

foldl1 :: (a -> a -> a) -> Ordered a -> a #

toList :: Ordered a -> [a] #

null :: Ordered a -> Bool #

length :: Ordered a -> Int #

elem :: Eq a => a -> Ordered a -> Bool #

maximum :: Ord a => Ordered a -> a #

minimum :: Ord a => Ordered a -> a #

sum :: Num a => Ordered a -> a #

product :: Num a => Ordered a -> a #

Traversable Ordered Source # 

Methods

traverse :: Applicative f => (a -> f b) -> Ordered a -> f (Ordered b) #

sequenceA :: Applicative f => Ordered (f a) -> f (Ordered a) #

mapM :: Monad m => (a -> m b) -> Ordered a -> m (Ordered b) #

sequence :: Monad m => Ordered (m a) -> m (Ordered a) #

Eq a => Eq (Ordered a) Source # 

Methods

(==) :: Ordered a -> Ordered a -> Bool #

(/=) :: Ordered a -> Ordered a -> Bool #

Data a => Data (Ordered a) Source # 

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Ordered a -> c (Ordered a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Ordered a) #

toConstr :: Ordered a -> Constr #

dataTypeOf :: Ordered a -> DataType #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Ordered a)) #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Ordered a)) #

gmapT :: (forall b. Data b => b -> b) -> Ordered a -> Ordered a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Ordered a -> r #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Ordered a -> r #

gmapQ :: (forall d. Data d => d -> u) -> Ordered a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Ordered a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Ordered a -> m (Ordered a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Ordered a -> m (Ordered a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Ordered a -> m (Ordered a) #

Ord a => Ord (Ordered a) Source # 

Methods

compare :: Ordered a -> Ordered a -> Ordering #

(<) :: Ordered a -> Ordered a -> Bool #

(<=) :: Ordered a -> Ordered a -> Bool #

(>) :: Ordered a -> Ordered a -> Bool #

(>=) :: Ordered a -> Ordered a -> Bool #

max :: Ordered a -> Ordered a -> Ordered a #

min :: Ordered a -> Ordered a -> Ordered a #

Read a => Read (Ordered a) Source # 
Show a => Show (Ordered a) Source # 

Methods

showsPrec :: Int -> Ordered a -> ShowS #

show :: Ordered a -> String #

showList :: [Ordered a] -> ShowS #

Generic (Ordered a) Source # 

Associated Types

type Rep (Ordered a) :: * -> * #

Methods

from :: Ordered a -> Rep (Ordered a) x #

to :: Rep (Ordered a) x -> Ordered a #

NFData a => NFData (Ordered a) Source # 

Methods

rnf :: Ordered a -> () #

Hashable a => Hashable (Ordered a) Source # 

Methods

hashWithSalt :: Int -> Ordered a -> Int #

hash :: Ordered a -> Int #

Ord a => PartialOrd (Ordered a) Source # 

Methods

leq :: Ordered a -> Ordered a -> Bool Source #

comparable :: Ordered a -> Ordered a -> Bool Source #

(Ord a, Bounded a) => BoundedLattice (Ordered a) Source # 
(Ord a, Bounded a) => BoundedMeetSemiLattice (Ordered a) Source # 

Methods

top :: Ordered a Source #

(Ord a, Bounded a) => BoundedJoinSemiLattice (Ordered a) Source # 

Methods

bottom :: Ordered a Source #

Ord a => Lattice (Ordered a) Source # 
Ord a => MeetSemiLattice (Ordered a) Source # 

Methods

(/\) :: Ordered a -> Ordered a -> Ordered a Source #

meet :: Ordered a -> Ordered a -> Ordered a Source #

Ord a => JoinSemiLattice (Ordered a) Source # 

Methods

(\/) :: Ordered a -> Ordered a -> Ordered a Source #

join :: Ordered a -> Ordered a -> Ordered a Source #

Generic1 * Ordered Source # 

Associated Types

type Rep1 Ordered (f :: Ordered -> *) :: k -> * #

Methods

from1 :: f a -> Rep1 Ordered f a #

to1 :: Rep1 Ordered f a -> f a #

type Rep (Ordered a) Source # 
type Rep (Ordered a) = D1 * (MetaData "Ordered" "Algebra.Lattice.Ordered" "lattices-1.7.1-JS0VzTZGaXfIhOiyIFy1o0" True) (C1 * (MetaCons "Ordered" PrefixI True) (S1 * (MetaSel (Just Symbol "getOrdered") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))
type Rep1 * Ordered Source # 
type Rep1 * Ordered = D1 * (MetaData "Ordered" "Algebra.Lattice.Ordered" "lattices-1.7.1-JS0VzTZGaXfIhOiyIFy1o0" True) (C1 * (MetaCons "Ordered" PrefixI True) (S1 * (MetaSel (Just Symbol "getOrdered") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))