lattices-2.1: 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.Wide

Description

 
Synopsis

Documentation

data Wide a Source #

Graft a distinct top and bottom onto any type. The Top is identity for /\ and the absorbing element for \/. The Bottom is the identity for \/ and and the absorbing element for /\. Two Middle values join to top, unless they are equal.

Constructors

Top 
Middle a 
Bottom 

Instances

Instances details
Foldable Wide Source # 
Instance details

Defined in Algebra.Lattice.Wide

Methods

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

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

foldMap' :: Monoid m => (a -> m) -> Wide a -> m #

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

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

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

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

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

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

toList :: Wide a -> [a] #

null :: Wide a -> Bool #

length :: Wide a -> Int #

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

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

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

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

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

Traversable Wide Source # 
Instance details

Defined in Algebra.Lattice.Wide

Methods

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

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

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

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

Applicative Wide Source # 
Instance details

Defined in Algebra.Lattice.Wide

Methods

pure :: a -> Wide a #

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

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

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

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

Functor Wide Source # 
Instance details

Defined in Algebra.Lattice.Wide

Methods

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

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

Monad Wide Source # 
Instance details

Defined in Algebra.Lattice.Wide

Methods

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

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

return :: a -> Wide a #

Generic1 Wide Source # 
Instance details

Defined in Algebra.Lattice.Wide

Associated Types

type Rep1 Wide :: k -> Type #

Methods

from1 :: forall (a :: k). Wide a -> Rep1 Wide a #

to1 :: forall (a :: k). Rep1 Wide a -> Wide a #

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

Defined in Algebra.Lattice.Wide

Methods

arbitrary :: Gen (Wide a) #

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

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

Defined in Algebra.Lattice.Wide

Methods

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

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

Defined in Algebra.Lattice.Wide

Methods

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

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

Defined in Algebra.Lattice.Wide

Methods

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

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

toConstr :: Wide a -> Constr #

dataTypeOf :: Wide a -> DataType #

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

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

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

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

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

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

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

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

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

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

Generic (Wide a) Source # 
Instance details

Defined in Algebra.Lattice.Wide

Associated Types

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

Methods

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

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

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

Defined in Algebra.Lattice.Wide

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

Defined in Algebra.Lattice.Wide

Methods

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

show :: Wide a -> String #

showList :: [Wide a] -> ShowS #

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

Defined in Algebra.Lattice.Wide

Methods

rnf :: Wide a -> () #

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

Defined in Algebra.Lattice.Wide

Methods

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

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

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

Defined in Algebra.Lattice.Wide

Methods

compare :: Wide a -> Wide a -> Ordering #

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

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

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

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

max :: Wide a -> Wide a -> Wide a #

min :: Wide a -> Wide a -> Wide a #

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

Defined in Algebra.Lattice.Wide

Methods

hashWithSalt :: Int -> Wide a -> Int #

hash :: Wide a -> Int #

Eq a => BoundedJoinSemiLattice (Wide a) Source # 
Instance details

Defined in Algebra.Lattice.Wide

Methods

bottom :: Wide a Source #

Eq a => BoundedMeetSemiLattice (Wide a) Source # 
Instance details

Defined in Algebra.Lattice.Wide

Methods

top :: Wide a Source #

Eq a => Lattice (Wide a) Source # 
Instance details

Defined in Algebra.Lattice.Wide

Methods

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

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

Eq a => PartialOrd (Wide a) Source # 
Instance details

Defined in Algebra.Lattice.Wide

Methods

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

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

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

Defined in Algebra.Lattice.Wide

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

Defined in Algebra.Lattice.Wide

Methods

universe :: [Wide a] #

type Rep1 Wide Source # 
Instance details

Defined in Algebra.Lattice.Wide

type Rep1 Wide = D1 ('MetaData "Wide" "Algebra.Lattice.Wide" "lattices-2.1-FTYhZPoI65oIdMkyt1I5F1" 'False) (C1 ('MetaCons "Top" 'PrefixI 'False) (U1 :: Type -> Type) :+: (C1 ('MetaCons "Middle" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1) :+: C1 ('MetaCons "Bottom" 'PrefixI 'False) (U1 :: Type -> Type)))
type Rep (Wide a) Source # 
Instance details

Defined in Algebra.Lattice.Wide

type Rep (Wide a) = D1 ('MetaData "Wide" "Algebra.Lattice.Wide" "lattices-2.1-FTYhZPoI65oIdMkyt1I5F1" 'False) (C1 ('MetaCons "Top" 'PrefixI 'False) (U1 :: Type -> Type) :+: (C1 ('MetaCons "Middle" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: C1 ('MetaCons "Bottom" 'PrefixI 'False) (U1 :: Type -> Type)))