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

Bounded ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods minBound :: ZeroHalfOne # maxBound :: ZeroHalfOne #
Enum ZeroHalfOne Source #
Instance details 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] #
Eq ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods (==) :: ZeroHalfOne -> ZeroHalfOne -> Bool # (/=) :: ZeroHalfOne -> ZeroHalfOne -> Bool #
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 # 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 #
Instance details 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 #
Read ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods readsPrec :: Int -> ReadS ZeroHalfOne # readList :: ReadS [ZeroHalfOne] # readPrec :: ReadPrec ZeroHalfOne # readListPrec :: ReadPrec [ZeroHalfOne] #
Show ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods showsPrec :: Int -> ZeroHalfOne -> ShowS # show :: ZeroHalfOne -> String # showList :: [ZeroHalfOne] -> ShowS #
Generic ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Associated Types type Rep ZeroHalfOne :: Type -> Type # Methods from :: ZeroHalfOne -> Rep ZeroHalfOne x # to :: Rep ZeroHalfOne x -> ZeroHalfOne #
Function ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods function :: (ZeroHalfOne -> b) -> ZeroHalfOne :-> b #
Arbitrary ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods arbitrary :: Gen ZeroHalfOne # shrink :: ZeroHalfOne -> [ZeroHalfOne] #
CoArbitrary ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods coarbitrary :: ZeroHalfOne -> Gen b -> Gen b #
NFData ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods rnf :: ZeroHalfOne -> () #
Hashable ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods hashWithSalt :: Int -> ZeroHalfOne -> Int # hash :: ZeroHalfOne -> Int #
Universe ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods universe :: [ZeroHalfOne] #
Finite ZeroHalfOne Source #
Instance details Defined in Algebra.Lattice.ZeroHalfOne Methods universeF :: [ZeroHalfOne] # cardinality :: Tagged ZeroHalfOne Natural #
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-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)))