Safe Haskell	Safe-Inferred
Language	Haskell2010

Lattices.UnitIntervalStructures.Godel

Synopsis

newtype UIGodel = UIGodel UnitInterval
class RealFrac l => BoundedLattice l where
- (/\) :: l -> l -> l
- (\/) :: l -> l -> l
- top :: l
- bot :: l
- mkLattice :: Double -> l
mkGodelUnitInterval :: Double -> UIGodel
fromGodelUnitInterval :: UIGodel -> Double

Documentation

newtype UIGodel Source #

Constructors

UIGodel UnitInterval

Instances

Instances details

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

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 #

mkGodelUnitInterval :: Double -> UIGodel Source #

fromGodelUnitInterval :: UIGodel -> Double Source #