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.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 # 
Instance details

Defined in Algebra.Lattice.Ordered

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 # 
Instance details

Defined in Algebra.Lattice.Ordered

Methods

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

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

Applicative Ordered Source # 
Instance details

Defined in Algebra.Lattice.Ordered

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 # 
Instance details

Defined in Algebra.Lattice.Ordered

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 # 
Instance details

Defined in Algebra.Lattice.Ordered

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 # 
Instance details

Defined in Algebra.Lattice.Ordered

Methods

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

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

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

Defined in Algebra.Lattice.Ordered

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 # 
Instance details

Defined in Algebra.Lattice.Ordered

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 # 
Instance details

Defined in Algebra.Lattice.Ordered

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

Defined in Algebra.Lattice.Ordered

Methods

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

show :: Ordered a -> String #

showList :: [Ordered a] -> ShowS #

Generic (Ordered a) Source # 
Instance details

Defined in Algebra.Lattice.Ordered

Associated Types

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

Methods

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

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

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

Defined in Algebra.Lattice.Ordered

Methods

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

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

Defined in Algebra.Lattice.Ordered

Methods

arbitrary :: Gen (Ordered a) #

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

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

Defined in Algebra.Lattice.Ordered

Methods

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

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

Defined in Algebra.Lattice.Ordered

Methods

rnf :: Ordered a -> () #

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

Defined in Algebra.Lattice.Ordered

Methods

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

hash :: Ordered a -> Int #

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

Defined in Algebra.Lattice.Ordered

Methods

universe :: [Ordered a] #

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

Defined in Algebra.Lattice.Ordered

Ord a => PartialOrd (Ordered a) Source # 
Instance details

Defined in Algebra.Lattice.Ordered

Methods

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

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

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

Defined in Algebra.Lattice.Ordered

Methods

top :: Ordered a Source #

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

Defined in Algebra.Lattice.Ordered

Methods

bottom :: Ordered a Source #

Ord a => Lattice (Ordered a) Source # 
Instance details

Defined in Algebra.Lattice.Ordered

Methods

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

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

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

This is interesting logic, as it satisfies both de Morgan laws; but isn't Boolean: i.e. law of exluded middle doesn't hold.

Negation "smashes" value into minBound or maxBound.

Instance details

Defined in Algebra.Lattice.Ordered

Methods

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

neg :: Ordered a -> Ordered a Source #

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

Generic1 Ordered Source # 
Instance details

Defined in Algebra.Lattice.Ordered

Associated Types

type Rep1 Ordered :: k -> Type #

Methods

from1 :: Ordered a -> Rep1 Ordered a #

to1 :: Rep1 Ordered a -> Ordered a #

type Rep (Ordered a) Source # 
Instance details

Defined in Algebra.Lattice.Ordered

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

Defined in Algebra.Lattice.Ordered

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