Algebra.Lattice.ZeroHalfOne

Documentation

data ZeroHalfOne

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

Arbitrary ZeroHalfOne

Defined in Algebra.Lattice.ZeroHalfOne

Methods

arbitrary :: Gen ZeroHalfOne

shrink :: ZeroHalfOne -> [ZeroHalfOne]

CoArbitrary ZeroHalfOne

Defined in Algebra.Lattice.ZeroHalfOne

Methods

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

Function ZeroHalfOne

Defined in Algebra.Lattice.ZeroHalfOne

Methods

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

Data ZeroHalfOne

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

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 :: forall r r'. (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

Bounded ZeroHalfOne

Defined in Algebra.Lattice.ZeroHalfOne

Methods

minBound :: ZeroHalfOne

maxBound :: ZeroHalfOne

Enum ZeroHalfOne

Defined in Algebra.Lattice.ZeroHalfOne

Methods

succ :: ZeroHalfOne -> ZeroHalfOne

pred :: ZeroHalfOne -> ZeroHalfOne

toEnum :: Int -> ZeroHalfOne

fromEnum :: ZeroHalfOne -> Int

enumFrom :: ZeroHalfOne -> [ZeroHalfOne]

enumFromThen :: ZeroHalfOne -> ZeroHalfOne -> [ZeroHalfOne]

enumFromTo :: ZeroHalfOne -> ZeroHalfOne -> [ZeroHalfOne]

enumFromThenTo :: ZeroHalfOne -> ZeroHalfOne -> ZeroHalfOne -> [ZeroHalfOne]

Generic ZeroHalfOne

Defined in Algebra.Lattice.ZeroHalfOne

Associated Types

type Rep ZeroHalfOne :: Type -> Type

Methods

from :: ZeroHalfOne -> Rep ZeroHalfOne x

to :: Rep ZeroHalfOne x -> ZeroHalfOne

Read ZeroHalfOne

Defined in Algebra.Lattice.ZeroHalfOne

Methods

readsPrec :: Int -> ReadS ZeroHalfOne

readList :: ReadS [ZeroHalfOne]

readPrec :: ReadPrec ZeroHalfOne

readListPrec :: ReadPrec [ZeroHalfOne]

Show ZeroHalfOne

Defined in Algebra.Lattice.ZeroHalfOne

Methods

showsPrec :: Int -> ZeroHalfOne -> ShowS

show :: ZeroHalfOne -> String

showList :: [ZeroHalfOne] -> ShowS

NFData ZeroHalfOne

Defined in Algebra.Lattice.ZeroHalfOne

Methods

rnf :: ZeroHalfOne -> ()

Eq ZeroHalfOne

Defined in Algebra.Lattice.ZeroHalfOne

Methods

(==) :: ZeroHalfOne -> ZeroHalfOne -> Bool

(/=) :: ZeroHalfOne -> ZeroHalfOne -> Bool

Ord ZeroHalfOne

Defined in Algebra.Lattice.ZeroHalfOne

Methods

compare :: ZeroHalfOne -> ZeroHalfOne -> Ordering

(<) :: ZeroHalfOne -> ZeroHalfOne -> Bool

(<=) :: ZeroHalfOne -> ZeroHalfOne -> Bool

(>) :: ZeroHalfOne -> ZeroHalfOne -> Bool

(>=) :: ZeroHalfOne -> ZeroHalfOne -> Bool

max :: ZeroHalfOne -> ZeroHalfOne -> ZeroHalfOne

min :: ZeroHalfOne -> ZeroHalfOne -> ZeroHalfOne

Hashable ZeroHalfOne

Defined in Algebra.Lattice.ZeroHalfOne

Methods

hashWithSalt :: Int -> ZeroHalfOne -> Int

hash :: ZeroHalfOne -> Int

Heyting ZeroHalfOne

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

Defined in Algebra.Lattice.ZeroHalfOne

Methods

(==>) :: ZeroHalfOne -> ZeroHalfOne -> ZeroHalfOne

neg :: ZeroHalfOne -> ZeroHalfOne

(<=>) :: ZeroHalfOne -> ZeroHalfOne -> ZeroHalfOne

BoundedJoinSemiLattice ZeroHalfOne

Defined in Algebra.Lattice.ZeroHalfOne

Methods

bottom :: ZeroHalfOne

BoundedMeetSemiLattice ZeroHalfOne

Defined in Algebra.Lattice.ZeroHalfOne

Methods

top :: ZeroHalfOne

Lattice ZeroHalfOne

Defined in Algebra.Lattice.ZeroHalfOne

Methods

(\/) :: ZeroHalfOne -> ZeroHalfOne -> ZeroHalfOne

(/\) :: ZeroHalfOne -> ZeroHalfOne -> ZeroHalfOne

PartialOrd ZeroHalfOne

Defined in Algebra.Lattice.ZeroHalfOne

Methods

leq :: ZeroHalfOne -> ZeroHalfOne -> Bool

comparable :: ZeroHalfOne -> ZeroHalfOne -> Bool

Finite ZeroHalfOne

Defined in Algebra.Lattice.ZeroHalfOne

Methods

universeF :: [ZeroHalfOne]

cardinality :: Tagged ZeroHalfOne Natural

Universe ZeroHalfOne

Defined in Algebra.Lattice.ZeroHalfOne

Methods

universe :: [ZeroHalfOne]

type Rep ZeroHalfOne

Defined in Algebra.Lattice.ZeroHalfOne

type Rep ZeroHalfOne = D1 ('MetaData "ZeroHalfOne" "Algebra.Lattice.ZeroHalfOne" "lattices-2.2-ExsECSVnOmtEcARHt0Jtvl" '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)))