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.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

Instances details
Monad Ordered Source #
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Defined in Algebra.Lattice.Ordered

Functor Ordered Source #
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Applicative Ordered Source #
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Foldable Ordered Source #
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Traversable Ordered Source #
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Defined in Algebra.Lattice.Ordered

Eq a => Eq ( Ordered a) Source #
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Defined in Algebra.Lattice.Ordered

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

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

toConstr :: Ordered a -> Constr Source #

dataTypeOf :: Ordered a -> DataType Source #

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

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

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

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

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

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

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

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

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

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

Ord a => Ord ( Ordered a) Source #
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Defined in Algebra.Lattice.Ordered

Read a => Read ( Ordered a) Source #
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Show a => Show ( Ordered a) Source #
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Defined in Algebra.Lattice.Ordered

Generic ( Ordered a) Source #
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Defined in Algebra.Lattice.Ordered

Associated Types

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

Function a => Function ( Ordered a) Source #
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Defined in Algebra.Lattice.Ordered

Arbitrary a => Arbitrary ( Ordered a) Source #
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Defined in Algebra.Lattice.Ordered

CoArbitrary a => CoArbitrary ( Ordered a) Source #
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Defined in Algebra.Lattice.Ordered

NFData a => NFData ( Ordered a) Source #
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Defined in Algebra.Lattice.Ordered

Hashable a => Hashable ( Ordered a) Source #
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Defined in Algebra.Lattice.Ordered

Universe a => Universe ( Ordered a) Source #
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Finite a => Finite ( Ordered a) Source #
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Defined in Algebra.Lattice.Ordered

Ord a => PartialOrd ( Ordered a) Source #
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( Ord a, Bounded a) => BoundedMeetSemiLattice ( Ordered a) Source #
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Defined in Algebra.Lattice.Ordered

( Ord a, Bounded a) => BoundedJoinSemiLattice ( Ordered a) Source #
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Defined in Algebra.Lattice.Ordered

Ord a => Lattice ( Ordered a) Source #
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Defined in Algebra.Lattice.Ordered

( 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 .

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Defined in Algebra.Lattice.Ordered

Generic1 Ordered Source #
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Defined in Algebra.Lattice.Ordered

Associated Types

type Rep1 Ordered :: k -> Type Source #

type Rep ( Ordered a) Source #
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Defined in Algebra.Lattice.Ordered

type Rep ( Ordered a) = D1 (' MetaData "Ordered" "Algebra.Lattice.Ordered" "lattices-2.1-Aj77JapAM1ZIiO74F5gL5i" ' True ) ( C1 (' MetaCons "Ordered" ' PrefixI ' True ) ( S1 (' MetaSel (' Just "getOrdered") ' NoSourceUnpackedness ' NoSourceStrictness ' DecidedLazy ) ( Rec0 a)))
type Rep1 Ordered Source #
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Defined in Algebra.Lattice.Ordered

type Rep1 Ordered = D1 (' MetaData "Ordered" "Algebra.Lattice.Ordered" "lattices-2.1-Aj77JapAM1ZIiO74F5gL5i" ' True ) ( C1 (' MetaCons "Ordered" ' PrefixI ' True ) ( S1 (' MetaSel (' Just "getOrdered") ' NoSourceUnpackedness ' NoSourceStrictness ' DecidedLazy ) Par1 ))