lattices-2: Fine-grained library for constructing and manipulating lattices

Copyright(C) 2019 Oleg Grenrus
LicenseBSD-3-Clause (see the file LICENSE)
MaintainerOleg Grenrus <oleg.grenrus@iki.fi>
Safe HaskellSafe
LanguageHaskell2010

Algebra.Lattice.ZeroHalfOne

Description

 
Synopsis

Documentation

data ZeroHalfOne Source #

The simplest Heyting algebra that is not already a Boolean algebra is the totally ordered set \(\{ 0, \frac{1}{2}, 1 \}\).

Constructors

Zero 
Half 
One 
Instances
Bounded ZeroHalfOne Source # 
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Enum ZeroHalfOne Source # 
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Eq ZeroHalfOne Source # 
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Data ZeroHalfOne Source # 
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Methods

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

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

toConstr :: ZeroHalfOne -> Constr #

dataTypeOf :: ZeroHalfOne -> DataType #

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

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

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

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

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

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

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

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

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

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

Ord ZeroHalfOne Source # 
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Read ZeroHalfOne Source # 
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Show ZeroHalfOne Source # 
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Generic ZeroHalfOne Source # 
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Associated Types

type Rep ZeroHalfOne :: Type -> Type #

Function ZeroHalfOne Source # 
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Methods

function :: (ZeroHalfOne -> b) -> ZeroHalfOne :-> b #

Arbitrary ZeroHalfOne Source # 
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CoArbitrary ZeroHalfOne Source # 
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Methods

coarbitrary :: ZeroHalfOne -> Gen b -> Gen b #

NFData ZeroHalfOne Source # 
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Methods

rnf :: ZeroHalfOne -> () #

Hashable ZeroHalfOne Source # 
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Universe ZeroHalfOne Source # 
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Methods

universe :: [ZeroHalfOne] #

Finite ZeroHalfOne Source # 
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PartialOrd ZeroHalfOne Source # 
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BoundedMeetSemiLattice ZeroHalfOne Source # 
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BoundedJoinSemiLattice ZeroHalfOne Source # 
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Lattice ZeroHalfOne Source # 
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Heyting ZeroHalfOne Source #

Not boolean: neg Half \/ Half = Half /= One

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type Rep ZeroHalfOne Source # 
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type Rep ZeroHalfOne = D1 (MetaData "ZeroHalfOne" "Algebra.Lattice.ZeroHalfOne" "lattices-2-GNwPiglY2qIELYMTNuLIEL" False) (C1 (MetaCons "Zero" PrefixI False) (U1 :: Type -> Type) :+: (C1 (MetaCons "Half" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "One" PrefixI False) (U1 :: Type -> Type)))