Copyright	(C) 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.ZeroHalfOne

Description

Synopsis

data ZeroHalfOne
- = Zero
- | Half
- | One

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

Instances details

Bounded ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods minBound :: ZeroHalfOne Source # maxBound :: ZeroHalfOne Source #
Enum ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods succ :: ZeroHalfOne -> ZeroHalfOne Source # pred :: ZeroHalfOne -> ZeroHalfOne Source # toEnum :: Int -> ZeroHalfOne Source # fromEnum :: ZeroHalfOne -> Int Source # enumFrom :: ZeroHalfOne -> [ ZeroHalfOne ] Source # enumFromThen :: ZeroHalfOne -> ZeroHalfOne -> [ ZeroHalfOne ] Source # enumFromTo :: ZeroHalfOne -> ZeroHalfOne -> [ ZeroHalfOne ] Source # enumFromThenTo :: ZeroHalfOne -> ZeroHalfOne -> ZeroHalfOne -> [ ZeroHalfOne ] Source #
Eq ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods (==) :: ZeroHalfOne -> ZeroHalfOne -> Bool Source # (/=) :: ZeroHalfOne -> ZeroHalfOne -> Bool Source #
Data ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods gfoldl :: ( forall d b. Data d => c (d -> b) -> d -> c b) -> ( forall g. g -> c g) -> ZeroHalfOne -> c ZeroHalfOne Source # gunfold :: ( forall b r. Data b => c (b -> r) -> c r) -> ( forall r. r -> c r) -> Constr -> c ZeroHalfOne Source # toConstr :: ZeroHalfOne -> Constr Source # dataTypeOf :: ZeroHalfOne -> DataType Source # dataCast1 :: Typeable t => ( forall d. Data d => c (t d)) -> Maybe (c ZeroHalfOne ) Source # dataCast2 :: Typeable t => ( forall d e. ( Data d, Data e) => c (t d e)) -> Maybe (c ZeroHalfOne ) Source # gmapT :: ( forall b. Data b => b -> b) -> ZeroHalfOne -> ZeroHalfOne Source # gmapQl :: (r -> r' -> r) -> r -> ( forall d. Data d => d -> r') -> ZeroHalfOne -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> ( forall d. Data d => d -> r') -> ZeroHalfOne -> r Source # gmapQ :: ( forall d. Data d => d -> u) -> ZeroHalfOne -> [u] Source # gmapQi :: Int -> ( forall d. Data d => d -> u) -> ZeroHalfOne -> u Source # gmapM :: Monad m => ( forall d. Data d => d -> m d) -> ZeroHalfOne -> m ZeroHalfOne Source # gmapMp :: MonadPlus m => ( forall d. Data d => d -> m d) -> ZeroHalfOne -> m ZeroHalfOne Source # gmapMo :: MonadPlus m => ( forall d. Data d => d -> m d) -> ZeroHalfOne -> m ZeroHalfOne Source #
Ord ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods compare :: ZeroHalfOne -> ZeroHalfOne -> Ordering Source # (<) :: ZeroHalfOne -> ZeroHalfOne -> Bool Source # (<=) :: ZeroHalfOne -> ZeroHalfOne -> Bool Source # (>) :: ZeroHalfOne -> ZeroHalfOne -> Bool Source # (>=) :: ZeroHalfOne -> ZeroHalfOne -> Bool Source # max :: ZeroHalfOne -> ZeroHalfOne -> ZeroHalfOne Source # min :: ZeroHalfOne -> ZeroHalfOne -> ZeroHalfOne Source #
Read ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods readsPrec :: Int -> ReadS ZeroHalfOne Source # readList :: ReadS [ ZeroHalfOne ] Source # readPrec :: ReadPrec ZeroHalfOne Source # readListPrec :: ReadPrec [ ZeroHalfOne ] Source #
Show ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods showsPrec :: Int -> ZeroHalfOne -> ShowS Source # show :: ZeroHalfOne -> String Source # showList :: [ ZeroHalfOne ] -> ShowS Source #
Generic ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Associated Types type Rep ZeroHalfOne :: Type -> Type Source # Methods from :: ZeroHalfOne -> Rep ZeroHalfOne x Source # to :: Rep ZeroHalfOne x -> ZeroHalfOne Source #
Function ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods function :: ( ZeroHalfOne -> b) -> ZeroHalfOne :-> b Source #
Arbitrary ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods arbitrary :: Gen ZeroHalfOne Source # shrink :: ZeroHalfOne -> [ ZeroHalfOne ] Source #
CoArbitrary ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods coarbitrary :: ZeroHalfOne -> Gen b -> Gen b Source #
NFData ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods rnf :: ZeroHalfOne -> () Source #
Hashable ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods hashWithSalt :: Int -> ZeroHalfOne -> Int Source # hash :: ZeroHalfOne -> Int Source #
Universe ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods universe :: [ ZeroHalfOne ] Source #
Finite ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods universeF :: [ ZeroHalfOne ] Source # cardinality :: Tagged ZeroHalfOne Natural Source #
PartialOrd ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods leq :: ZeroHalfOne -> ZeroHalfOne -> Bool Source # comparable :: ZeroHalfOne -> ZeroHalfOne -> Bool Source #
BoundedMeetSemiLattice ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods top :: ZeroHalfOne Source #
BoundedJoinSemiLattice ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods bottom :: ZeroHalfOne Source #
Lattice ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods (\/) :: ZeroHalfOne -> ZeroHalfOne -> ZeroHalfOne Source # (/\) :: ZeroHalfOne -> ZeroHalfOne -> ZeroHalfOne Source #
Heyting ZeroHalfOne Source #	Not boolean: `neg Half \/ Half = Half /= One`
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods (==>) :: ZeroHalfOne -> ZeroHalfOne -> ZeroHalfOne Source # neg :: ZeroHalfOne -> ZeroHalfOne Source # (<=>) :: ZeroHalfOne -> ZeroHalfOne -> ZeroHalfOne Source #
type Rep ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne type Rep ZeroHalfOne = D1 (' MetaData "ZeroHalfOne" "Algebra.Lattice.ZeroHalfOne" "lattices-2.1-Aj77JapAM1ZIiO74F5gL5i" ' 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 )))