lattices-2.2.1.1: 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

Instances details
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

Functor Op Source # 
Instance details

Defined in Algebra.Lattice.Op

Methods

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

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

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

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

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)

Generic1 Op Source # 
Instance details

Defined in Algebra.Lattice.Op

Associated Types

type Rep1 Op 
Instance details

Defined in Algebra.Lattice.Op

type Rep1 Op = D1 ('MetaData "Op" "Algebra.Lattice.Op" "lattices-2.2.1.1-DOiSBgvrTjdFgPaGHAnlJl" 'True) (C1 ('MetaCons "Op" 'PrefixI 'True) (S1 ('MetaSel ('Just "getOp") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

Methods

from1 :: Op a -> Rep1 Op a

to1 :: Rep1 Op a -> Op a

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

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

Defined in Algebra.Lattice.Op

Methods

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

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

Defined in Algebra.Lattice.Op

Methods

rnf :: Op a -> ()

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 :: forall r r'. (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)

Generic (Op a) Source # 
Instance details

Defined in Algebra.Lattice.Op

Associated Types

type Rep (Op a) 
Instance details

Defined in Algebra.Lattice.Op

type Rep (Op a) = D1 ('MetaData "Op" "Algebra.Lattice.Op" "lattices-2.2.1.1-DOiSBgvrTjdFgPaGHAnlJl" 'True) (C1 ('MetaCons "Op" 'PrefixI 'True) (S1 ('MetaSel ('Just "getOp") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Methods

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

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

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

Defined in Algebra.Lattice.Op

Methods

readsPrec :: Int -> ReadS (Op a)

readList :: ReadS [Op a]

readPrec :: ReadPrec (Op a)

readListPrec :: ReadPrec [Op a]

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

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

Defined in Algebra.Lattice.Op

Methods

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

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

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

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

Defined in Algebra.Lattice.Op

Methods

hashWithSalt :: Int -> Op a -> Int

hash :: Op a -> Int

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

Defined in Algebra.Lattice.Op

Methods

bottom :: Op a Source #

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

Defined in Algebra.Lattice.Op

Methods

top :: 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 #

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 #

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

Defined in Algebra.Lattice.Op

Methods

universeF :: [Op a]

cardinality :: Tagged (Op a) Natural

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

Defined in Algebra.Lattice.Op

Methods

universe :: [Op a]

type Rep1 Op Source # 
Instance details

Defined in Algebra.Lattice.Op

type Rep1 Op = D1 ('MetaData "Op" "Algebra.Lattice.Op" "lattices-2.2.1.1-DOiSBgvrTjdFgPaGHAnlJl" 'True) (C1 ('MetaCons "Op" 'PrefixI 'True) (S1 ('MetaSel ('Just "getOp") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
type Rep (Op a) Source # 
Instance details

Defined in Algebra.Lattice.Op

type Rep (Op a) = D1 ('MetaData "Op" "Algebra.Lattice.Op" "lattices-2.2.1.1-DOiSBgvrTjdFgPaGHAnlJl" 'True) (C1 ('MetaCons "Op" 'PrefixI 'True) (S1 ('MetaSel ('Just "getOp") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))