Safe Haskell	Safe-Inferred
Language	Haskell2010

Lattices.UnitIntervalStructures.Product

Synopsis

newtype UIProduct = UIProduct UnitInterval
class RealFrac l => BoundedLattice l where
- (/\) :: l -> l -> l
- (\/) :: l -> l -> l
- top :: l
- bot :: l
- mkLattice :: Double -> l
mkProductUnitInterval :: Double -> UIProduct
fromProductUnitInterval :: UIProduct -> Double

Documentation

newtype UIProduct Source #

Constructors

UIProduct UnitInterval

Instances

Instances details

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

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 #

mkProductUnitInterval :: Double -> UIProduct Source #

fromProductUnitInterval :: UIProduct -> Double Source #