Copyright | (C) 2010-2015 Maximilian Bolingbroke 2015 Oleg Grenrus |
---|---|

License | BSD-3-Clause (see the file LICENSE) |

Maintainer | Oleg Grenrus <oleg.grenrus@iki.fi> |

Safe Haskell | Safe |

Language | Haskell2010 |

## Synopsis

- data Lifted a
- retractLifted :: BoundedJoinSemiLattice a => Lifted a -> a

# Documentation

Graft a distinct bottom onto an otherwise unbounded lattice. As a bonus, the bottom will be an absorbing element for the meet.

## Instances

Monad Lifted Source # | |

Functor Lifted Source # | |

Applicative Lifted Source # | |

Foldable Lifted Source # | |

Defined in Algebra.Lattice.Lifted fold :: Monoid m => Lifted m -> m # foldMap :: Monoid m => (a -> m) -> Lifted a -> m # foldr :: (a -> b -> b) -> b -> Lifted a -> b # foldr' :: (a -> b -> b) -> b -> Lifted a -> b # foldl :: (b -> a -> b) -> b -> Lifted a -> b # foldl' :: (b -> a -> b) -> b -> Lifted a -> b # foldr1 :: (a -> a -> a) -> Lifted a -> a # foldl1 :: (a -> a -> a) -> Lifted a -> a # elem :: Eq a => a -> Lifted a -> Bool # maximum :: Ord a => Lifted a -> a # minimum :: Ord a => Lifted a -> a # | |

Traversable Lifted Source # | |

Eq a => Eq (Lifted a) Source # | |

Data a => Data (Lifted a) Source # | |

Defined in Algebra.Lattice.Lifted gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Lifted a -> c (Lifted a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Lifted a) # toConstr :: Lifted a -> Constr # dataTypeOf :: Lifted a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Lifted a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Lifted a)) # gmapT :: (forall b. Data b => b -> b) -> Lifted a -> Lifted a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Lifted a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Lifted a -> r # gmapQ :: (forall d. Data d => d -> u) -> Lifted a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Lifted a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Lifted a -> m (Lifted a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Lifted a -> m (Lifted a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Lifted a -> m (Lifted a) # | |

Ord a => Ord (Lifted a) Source # | |

Defined in Algebra.Lattice.Lifted | |

Read a => Read (Lifted a) Source # | |

Show a => Show (Lifted a) Source # | |

Generic (Lifted a) Source # | |

NFData a => NFData (Lifted a) Source # | |

Defined in Algebra.Lattice.Lifted | |

Hashable a => Hashable (Lifted a) Source # | |

Defined in Algebra.Lattice.Lifted | |

BoundedLattice a => BoundedLattice (Lifted a) Source # | |

Defined in Algebra.Lattice.Lifted | |

BoundedMeetSemiLattice a => BoundedMeetSemiLattice (Lifted a) Source # | |

Defined in Algebra.Lattice.Lifted | |

JoinSemiLattice a => BoundedJoinSemiLattice (Lifted a) Source # | |

Defined in Algebra.Lattice.Lifted | |

Lattice a => Lattice (Lifted a) Source # | |

Defined in Algebra.Lattice.Lifted | |

MeetSemiLattice a => MeetSemiLattice (Lifted a) Source # | |

JoinSemiLattice a => JoinSemiLattice (Lifted a) Source # | |

Generic1 Lifted Source # | |

type Rep (Lifted a) Source # | |

Defined in Algebra.Lattice.Lifted type Rep (Lifted a) = D1 (MetaData "Lifted" "Algebra.Lattice.Lifted" "lattices-1.7.1.1-KHhCTNp0Jlu7lPrYOy5eaF" False) (C1 (MetaCons "Lift" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) :+: C1 (MetaCons "Bottom" PrefixI False) (U1 :: * -> *)) | |

type Rep1 Lifted Source # | |

Defined in Algebra.Lattice.Lifted type Rep1 Lifted = D1 (MetaData "Lifted" "Algebra.Lattice.Lifted" "lattices-1.7.1.1-KHhCTNp0Jlu7lPrYOy5eaF" False) (C1 (MetaCons "Lift" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1) :+: C1 (MetaCons "Bottom" PrefixI False) (U1 :: * -> *)) |

retractLifted :: BoundedJoinSemiLattice a => Lifted a -> a Source #

Interpret

using the `Lifted`

a`BoundedJoinSemiLattice`

of `a`

.