Safe Haskell	Safe-Inferred
Language	Haskell2010

Lattices.UnitIntervalStructures.Lukasiewicz

Synopsis

newtype UILukasiewicz = UILukasiewicz UnitInterval
class RealFrac l => BoundedLattice l where
- (/\) :: l -> l -> l
- (\/) :: l -> l -> l
- top :: l
- bot :: l
- mkLattice :: Double -> l
mkLukasiewiczUnitInterval :: Double -> UILukasiewicz
fromLukasiewiczUnitInterval :: UILukasiewicz -> Double

Documentation

newtype UILukasiewicz Source #

Constructors

UILukasiewicz UnitInterval

Instances

Instances details

Num UILukasiewicz Source #
Instance details Defined in Lattices.UnitIntervalStructures.Lukasiewicz Methods (+) :: UILukasiewicz -> UILukasiewicz -> UILukasiewicz (-) :: UILukasiewicz -> UILukasiewicz -> UILukasiewicz (*) :: UILukasiewicz -> UILukasiewicz -> UILukasiewicz negate :: UILukasiewicz -> UILukasiewicz abs :: UILukasiewicz -> UILukasiewicz signum :: UILukasiewicz -> UILukasiewicz fromInteger :: Integer -> UILukasiewicz
Fractional UILukasiewicz Source #
Instance details Defined in Lattices.UnitIntervalStructures.Lukasiewicz Methods (/) :: UILukasiewicz -> UILukasiewicz -> UILukasiewicz recip :: UILukasiewicz -> UILukasiewicz fromRational :: Rational -> UILukasiewicz
Real UILukasiewicz Source #
Instance details Defined in Lattices.UnitIntervalStructures.Lukasiewicz Methods toRational :: UILukasiewicz -> Rational
RealFrac UILukasiewicz Source #
Instance details Defined in Lattices.UnitIntervalStructures.Lukasiewicz Methods properFraction :: Integral b => UILukasiewicz -> (b, UILukasiewicz) truncate :: Integral b => UILukasiewicz -> b round :: Integral b => UILukasiewicz -> b ceiling :: Integral b => UILukasiewicz -> b floor :: Integral b => UILukasiewicz -> b
Show UILukasiewicz Source #
Instance details Defined in Lattices.UnitIntervalStructures.Lukasiewicz Methods showsPrec :: Int -> UILukasiewicz -> ShowS show :: UILukasiewicz -> String showList :: [UILukasiewicz] -> ShowS
BoundedLattice UILukasiewicz Source #
Instance details Defined in Lattices.UnitIntervalStructures.Lukasiewicz Methods (/\) :: UILukasiewicz -> UILukasiewicz -> UILukasiewicz Source # (\/) :: UILukasiewicz -> UILukasiewicz -> UILukasiewicz Source # top :: UILukasiewicz Source # bot :: UILukasiewicz Source # mkLattice :: Double -> UILukasiewicz Source #
ResiduatedLattice UILukasiewicz Source #	Łukasiewicz structure of truth values
Instance details Defined in Lattices.UnitIntervalStructures.Lukasiewicz Methods (-->) :: UILukasiewicz -> UILukasiewicz -> UILukasiewicz Source # (<--) :: UILukasiewicz -> UILukasiewicz -> UILukasiewicz Source # (<-->) :: UILukasiewicz -> UILukasiewicz -> UILukasiewicz Source # tnorm :: UILukasiewicz -> UILukasiewicz -> UILukasiewicz Source # negation :: UILukasiewicz -> UILukasiewicz Source # power :: UILukasiewicz -> Nat -> UILukasiewicz Source #
Eq UILukasiewicz Source #
Instance details Defined in Lattices.UnitIntervalStructures.Lukasiewicz Methods (==) :: UILukasiewicz -> UILukasiewicz -> Bool (/=) :: UILukasiewicz -> UILukasiewicz -> Bool
Ord UILukasiewicz Source #
Instance details Defined in Lattices.UnitIntervalStructures.Lukasiewicz Methods compare :: UILukasiewicz -> UILukasiewicz -> Ordering (<) :: UILukasiewicz -> UILukasiewicz -> Bool (<=) :: UILukasiewicz -> UILukasiewicz -> Bool (>) :: UILukasiewicz -> UILukasiewicz -> Bool (>=) :: UILukasiewicz -> UILukasiewicz -> Bool max :: UILukasiewicz -> UILukasiewicz -> UILukasiewicz min :: UILukasiewicz -> UILukasiewicz -> UILukasiewicz

class RealFrac l => BoundedLattice l where Source #

Lattice is an algebraic structure with join and meet operations. BoundedLattice has Top and Bottom elements Lattice satisfies following laws:

Associativity

x \/ (y \/ z) ≡ (x \/ y) \/ z
x /\ (y /\ z) ≡ (x /\ y) /\ z

Commutativity

x \/ y ≡ y \/ x
x /\ y ≡ y /\ x

Idempotency

x \/ x ≡ x
x /\ x ≡ x

Absorption

a \/ (a /\ b) ≡ a
a /\ (a \/ b) ≡ a

Methods

(/\) :: l -> l -> l Source #

meet

(\/) :: l -> l -> l Source #

join

top :: l Source #

also called upper bound

bot :: l Source #

also called lower bound

mkLattice :: Double -> l Source #

constructor for lattice

Instances

Instances details

BoundedLattice UnitInterval Source #
Instance details Defined in Lattices.UnitInterval Methods (/\) :: UnitInterval -> UnitInterval -> UnitInterval Source # (\/) :: UnitInterval -> UnitInterval -> UnitInterval Source # top :: UnitInterval Source # bot :: UnitInterval Source # mkLattice :: Double -> UnitInterval Source #
BoundedLattice UIGodel Source #
Instance details Defined in Lattices.UnitIntervalStructures.Godel Methods (/\) :: UIGodel -> UIGodel -> UIGodel Source # (\/) :: UIGodel -> UIGodel -> UIGodel Source # top :: UIGodel Source # bot :: UIGodel Source # mkLattice :: Double -> UIGodel Source #
BoundedLattice UILukasiewicz Source #
Instance details Defined in Lattices.UnitIntervalStructures.Lukasiewicz Methods (/\) :: UILukasiewicz -> UILukasiewicz -> UILukasiewicz Source # (\/) :: UILukasiewicz -> UILukasiewicz -> UILukasiewicz Source # top :: UILukasiewicz Source # bot :: UILukasiewicz Source # mkLattice :: Double -> UILukasiewicz Source #
BoundedLattice UIProduct Source #
Instance details Defined in Lattices.UnitIntervalStructures.Product Methods (/\) :: UIProduct -> UIProduct -> UIProduct Source # (\/) :: UIProduct -> UIProduct -> UIProduct Source # top :: UIProduct Source # bot :: UIProduct Source # mkLattice :: Double -> UIProduct Source #

mkLukasiewiczUnitInterval :: Double -> UILukasiewicz Source #

fromLukasiewiczUnitInterval :: UILukasiewicz -> Double Source #