lattices-2: Fine-grained library for constructing and manipulating lattices

Copyright(C) 2010-2015 Maximilian Bolingbroke 2015-2019 Oleg Grenrus
LicenseBSD-3-Clause (see the file LICENSE)
MaintainerOleg Grenrus <oleg.grenrus@iki.fi>
Safe HaskellSafe
LanguageHaskell2010

Algebra.Lattice.Op

Description

 
Synopsis

Documentation

newtype Op a Source #

The opposite lattice of a given lattice. That is, switch meets and joins.

Constructors

Op 

Fields

Instances
Monad Op Source # 
Instance details

Defined in Algebra.Lattice.Op

Methods

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

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

return :: a -> Op a #

fail :: String -> Op a #

Functor Op Source # 
Instance details

Defined in Algebra.Lattice.Op

Methods

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

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

Applicative Op Source # 
Instance details

Defined in Algebra.Lattice.Op

Methods

pure :: a -> Op a #

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

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

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

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

Foldable Op Source # 
Instance details

Defined in Algebra.Lattice.Op

Methods

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

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

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

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

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

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

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

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

toList :: Op a -> [a] #

null :: Op a -> Bool #

length :: Op a -> Int #

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

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

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

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

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

Traversable Op Source # 
Instance details

Defined in Algebra.Lattice.Op

Methods

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

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

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

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

Eq a => Eq (Op a) Source # 
Instance details

Defined in Algebra.Lattice.Op

Methods

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

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

Data a => Data (Op a) Source # 
Instance details

Defined in Algebra.Lattice.Op

Methods

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

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

toConstr :: Op a -> Constr #

dataTypeOf :: Op a -> DataType #

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

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

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

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

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

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

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

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

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

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

Ord a => Ord (Op a) Source # 
Instance details

Defined in Algebra.Lattice.Op

Methods

compare :: Op a -> Op a -> Ordering #

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

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

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

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

max :: Op a -> Op a -> Op a #

min :: Op a -> Op a -> Op a #

Read a => Read (Op a) Source # 
Instance details

Defined in Algebra.Lattice.Op

Show a => Show (Op a) Source # 
Instance details

Defined in Algebra.Lattice.Op

Methods

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

show :: Op a -> String #

showList :: [Op a] -> ShowS #

Generic (Op a) Source # 
Instance details

Defined in Algebra.Lattice.Op

Associated Types

type Rep (Op a) :: Type -> Type #

Methods

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

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

Function a => Function (Op a) Source # 
Instance details

Defined in Algebra.Lattice.Op

Methods

function :: (Op a -> b) -> Op a :-> b #

Arbitrary a => Arbitrary (Op a) Source # 
Instance details

Defined in Algebra.Lattice.Op

Methods

arbitrary :: Gen (Op a) #

shrink :: Op a -> [Op a] #

CoArbitrary a => CoArbitrary (Op a) Source # 
Instance details

Defined in Algebra.Lattice.Op

Methods

coarbitrary :: Op a -> Gen b -> Gen b #

NFData a => NFData (Op a) Source # 
Instance details

Defined in Algebra.Lattice.Op

Methods

rnf :: Op a -> () #

Hashable a => Hashable (Op a) Source # 
Instance details

Defined in Algebra.Lattice.Op

Methods

hashWithSalt :: Int -> Op a -> Int #

hash :: Op a -> Int #

Universe a => Universe (Op a) Source # 
Instance details

Defined in Algebra.Lattice.Op

Methods

universe :: [Op a] #

Finite a => Finite (Op a) Source # 
Instance details

Defined in Algebra.Lattice.Op

Methods

universeF :: [Op a] #

cardinality :: Tagged (Op a) Natural #

PartialOrd a => PartialOrd (Op a) Source # 
Instance details

Defined in Algebra.Lattice.Op

Methods

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

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

BoundedJoinSemiLattice a => BoundedMeetSemiLattice (Op a) Source # 
Instance details

Defined in Algebra.Lattice.Op

Methods

top :: Op a Source #

BoundedMeetSemiLattice a => BoundedJoinSemiLattice (Op a) Source # 
Instance details

Defined in Algebra.Lattice.Op

Methods

bottom :: Op a Source #

Lattice a => Lattice (Op a) Source # 
Instance details

Defined in Algebra.Lattice.Op

Methods

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

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

Generic1 Op Source # 
Instance details

Defined in Algebra.Lattice.Op

Associated Types

type Rep1 Op :: k -> Type #

Methods

from1 :: Op a -> Rep1 Op a #

to1 :: Rep1 Op a -> Op a #

type Rep (Op a) Source # 
Instance details

Defined in Algebra.Lattice.Op

type Rep (Op a) = D1 (MetaData "Op" "Algebra.Lattice.Op" "lattices-2-GNwPiglY2qIELYMTNuLIEL" True) (C1 (MetaCons "Op" PrefixI True) (S1 (MetaSel (Just "getOp") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Rep1 Op Source # 
Instance details

Defined in Algebra.Lattice.Op

type Rep1 Op = D1 (MetaData "Op" "Algebra.Lattice.Op" "lattices-2-GNwPiglY2qIELYMTNuLIEL" True) (C1 (MetaCons "Op" PrefixI True) (S1 (MetaSel (Just "getOp") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))