lattices-2.1: Fine-grained library for constructing and manipulating lattices
Copyright (C) 2010-2015 Maximilian Bolingbroke 2015-2019 Oleg Grenrus
License BSD-3-Clause (see the file LICENSE)
Maintainer Oleg Grenrus <oleg.grenrus@iki.fi>
Safe Haskell Safe
Language Haskell2010

Algebra.Lattice.Levitated

Description

Synopsis

Documentation

data Levitated a Source #

Graft a distinct top and bottom onto an otherwise unbounded lattice. The top is the absorbing element for the join, and the bottom is the absorbing element for the meet.

Constructors

Bottom
Levitate a
Top

Instances

Instances details
Monad Levitated Source #
Instance details

Defined in Algebra.Lattice.Levitated

Methods

(>>=) :: Levitated a -> (a -> Levitated b) -> Levitated b Source #

(>>) :: Levitated a -> Levitated b -> Levitated b Source #

return :: a -> Levitated a Source #

Functor Levitated Source #
Instance details

Defined in Algebra.Lattice.Levitated

Methods

fmap :: (a -> b) -> Levitated a -> Levitated b Source #

(<$) :: a -> Levitated b -> Levitated a Source #

Applicative Levitated Source #
Instance details

Defined in Algebra.Lattice.Levitated

Methods

pure :: a -> Levitated a Source #

(<*>) :: Levitated (a -> b) -> Levitated a -> Levitated b Source #

liftA2 :: (a -> b -> c) -> Levitated a -> Levitated b -> Levitated c Source #

(*>) :: Levitated a -> Levitated b -> Levitated b Source #

(<*) :: Levitated a -> Levitated b -> Levitated a Source #

Foldable Levitated Source #
Instance details

Defined in Algebra.Lattice.Levitated

Methods

fold :: Monoid m => Levitated m -> m Source #

foldMap :: Monoid m => (a -> m) -> Levitated a -> m Source #

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

foldr :: (a -> b -> b) -> b -> Levitated a -> b Source #

foldr' :: (a -> b -> b) -> b -> Levitated a -> b Source #

foldl :: (b -> a -> b) -> b -> Levitated a -> b Source #

foldl' :: (b -> a -> b) -> b -> Levitated a -> b Source #

foldr1 :: (a -> a -> a) -> Levitated a -> a Source #

foldl1 :: (a -> a -> a) -> Levitated a -> a Source #

toList :: Levitated a -> [a] Source #

null :: Levitated a -> Bool Source #

length :: Levitated a -> Int Source #

elem :: Eq a => a -> Levitated a -> Bool Source #

maximum :: Ord a => Levitated a -> a Source #

minimum :: Ord a => Levitated a -> a Source #

sum :: Num a => Levitated a -> a Source #

product :: Num a => Levitated a -> a Source #

Traversable Levitated Source #
Instance details

Defined in Algebra.Lattice.Levitated

Methods

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

sequenceA :: Applicative f => Levitated (f a) -> f ( Levitated a) Source #

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

sequence :: Monad m => Levitated (m a) -> m ( Levitated a) Source #

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

Defined in Algebra.Lattice.Levitated

Methods

(==) :: Levitated a -> Levitated a -> Bool Source #

(/=) :: Levitated a -> Levitated a -> Bool Source #

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

Defined in Algebra.Lattice.Levitated

Methods

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

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

toConstr :: Levitated a -> Constr Source #

dataTypeOf :: Levitated a -> DataType Source #

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

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

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

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

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

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

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

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

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

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

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

Defined in Algebra.Lattice.Levitated

Methods

compare :: Levitated a -> Levitated a -> Ordering Source #

(<) :: Levitated a -> Levitated a -> Bool Source #

(<=) :: Levitated a -> Levitated a -> Bool Source #

(>) :: Levitated a -> Levitated a -> Bool Source #

(>=) :: Levitated a -> Levitated a -> Bool Source #

max :: Levitated a -> Levitated a -> Levitated a Source #

min :: Levitated a -> Levitated a -> Levitated a Source #

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

Defined in Algebra.Lattice.Levitated

Methods

readsPrec :: Int -> ReadS ( Levitated a) Source #

readList :: ReadS [ Levitated a] Source #

readPrec :: ReadPrec ( Levitated a) Source #

readListPrec :: ReadPrec [ Levitated a] Source #

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

Defined in Algebra.Lattice.Levitated

Methods

showsPrec :: Int -> Levitated a -> ShowS Source #

show :: Levitated a -> String Source #

showList :: [ Levitated a] -> ShowS Source #

Generic ( Levitated a) Source #
Instance details

Defined in Algebra.Lattice.Levitated

Associated Types

type Rep ( Levitated a) :: Type -> Type Source #

Methods

from :: Levitated a -> Rep ( Levitated a) x Source #

to :: Rep ( Levitated a) x -> Levitated a Source #

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

Defined in Algebra.Lattice.Levitated

Methods

function :: ( Levitated a -> b) -> Levitated a :-> b Source #

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

Defined in Algebra.Lattice.Levitated

Methods

arbitrary :: Gen ( Levitated a) Source #

shrink :: Levitated a -> [ Levitated a] Source #

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

Defined in Algebra.Lattice.Levitated

Methods

coarbitrary :: Levitated a -> Gen b -> Gen b Source #

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

Defined in Algebra.Lattice.Levitated

Methods

rnf :: Levitated a -> () Source #

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

Defined in Algebra.Lattice.Levitated

Methods

hashWithSalt :: Int -> Levitated a -> Int Source #

hash :: Levitated a -> Int Source #

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

Defined in Algebra.Lattice.Levitated

Methods

universe :: [ Levitated a] Source #

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

Defined in Algebra.Lattice.Levitated

Methods

universeF :: [ Levitated a] Source #

cardinality :: Tagged ( Levitated a) Natural Source #

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

Defined in Algebra.Lattice.Levitated

Methods

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

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

Lattice a => BoundedMeetSemiLattice ( Levitated a) Source #
Instance details

Defined in Algebra.Lattice.Levitated

Methods

top :: Levitated a Source #

Lattice a => BoundedJoinSemiLattice ( Levitated a) Source #
Instance details

Defined in Algebra.Lattice.Levitated

Methods

bottom :: Levitated a Source #

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

Defined in Algebra.Lattice.Levitated

Methods

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

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

Generic1 Levitated Source #
Instance details

Defined in Algebra.Lattice.Levitated

Associated Types

type Rep1 Levitated :: k -> Type Source #

Methods

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

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

type Rep ( Levitated a) Source #
Instance details

Defined in Algebra.Lattice.Levitated

type Rep ( Levitated a) = D1 (' MetaData "Levitated" "Algebra.Lattice.Levitated" "lattices-2.1-Aj77JapAM1ZIiO74F5gL5i" ' False ) ( C1 (' MetaCons "Bottom" ' PrefixI ' False ) ( U1 :: Type -> Type ) :+: ( C1 (' MetaCons "Levitate" ' PrefixI ' False ) ( S1 (' MetaSel (' Nothing :: Maybe Symbol ) ' NoSourceUnpackedness ' NoSourceStrictness ' DecidedLazy ) ( Rec0 a)) :+: C1 (' MetaCons "Top" ' PrefixI ' False ) ( U1 :: Type -> Type )))
type Rep1 Levitated Source #
Instance details

Defined in Algebra.Lattice.Levitated

type Rep1 Levitated = D1 (' MetaData "Levitated" "Algebra.Lattice.Levitated" "lattices-2.1-Aj77JapAM1ZIiO74F5gL5i" ' False ) ( C1 (' MetaCons "Bottom" ' PrefixI ' False ) ( U1 :: Type -> Type ) :+: ( C1 (' MetaCons "Levitate" ' PrefixI ' False ) ( S1 (' MetaSel (' Nothing :: Maybe Symbol ) ' NoSourceUnpackedness ' NoSourceStrictness ' DecidedLazy ) Par1 ) :+: C1 (' MetaCons "Top" ' PrefixI ' False ) ( U1 :: Type -> Type )))

retractLevitated :: ( BoundedMeetSemiLattice a, BoundedJoinSemiLattice a) => Levitated a -> a Source #

Interpret Levitated a using the BoundedLattice of a .

foldLevitated :: b -> (a -> b) -> b -> Levitated a -> b Source #

Fold Levitated .