Safe Haskell	None
Language	GHC2024

Circuit.Logics.Goedel

Description

Gödel–Dummett fuzzy logic on an ordered unit interval.

Meetjoin are minmax; implication is the standard Gödel rule. Heyting but not Boolean: excluded middle fails for intermediate degrees.

Synopsis

newtype Goedel r = Goedel r
mkGoedel :: (Ord r, Num r) => r -> Goedel r
unGoedel :: Goedel r -> r
godei :: Rational -> Goedel Rational

Documentation

newtype Goedel r Source #

Gödel truth degree, intended in [0,1].

The constructor is strict about bounds via mkGoedel; the newtype is still exposed for zero-cost unwrapping when the invariant is trusted.

Constructors

Goedel r

Instances

Instances details

Eq r => Eq (Goedel r) Source #
Instance details Defined in Circuit.Logics.Goedel Methods (==) :: Goedel r -> Goedel r -> Bool # (/=) :: Goedel r -> Goedel r -> Bool #
Ord r => Ord (Goedel r) Source #
Instance details Defined in Circuit.Logics.Goedel Methods compare :: Goedel r -> Goedel r -> Ordering # (<) :: Goedel r -> Goedel r -> Bool # (<=) :: Goedel r -> Goedel r -> Bool # (>) :: Goedel r -> Goedel r -> Bool # (>=) :: Goedel r -> Goedel r -> Bool # max :: Goedel r -> Goedel r -> Goedel r # min :: Goedel r -> Goedel r -> Goedel r #
Read r => Read (Goedel r) Source #
Instance details Defined in Circuit.Logics.Goedel Methods readsPrec :: Int -> ReadS (Goedel r) # readList :: ReadS [Goedel r] # readPrec :: ReadPrec (Goedel r) # readListPrec :: ReadPrec [Goedel r] #
Show r => Show (Goedel r) Source #
Instance details Defined in Circuit.Logics.Goedel Methods showsPrec :: Int -> Goedel r -> ShowS # show :: Goedel r -> String # showList :: [Goedel r] -> ShowS #
(Ord r, Num r) => Complemented (Goedel r) Source #	Gödel negation as `a ==> bottom` (sharp: only 0 maps to 1).
Instance details Defined in Circuit.Logics.Goedel Methods complement :: Goedel r -> Goedel r Source #
(Ord r, Num r) => Heyting (Goedel r) Source #
Instance details Defined in Circuit.Logics.Goedel Methods (==>) :: Goedel r -> Goedel r -> Goedel r Source #
Ord r => JoinSemiLattice (Goedel r) Source #
Instance details Defined in Circuit.Logics.Goedel Methods (\/) :: Goedel r -> Goedel r -> Goedel r Source #
(Ord r, Num r) => LowerBounded (Goedel r) Source #
Instance details Defined in Circuit.Logics.Goedel Methods bottom :: Goedel r Source #
Ord r => MeetSemiLattice (Goedel r) Source #
Instance details Defined in Circuit.Logics.Goedel Methods (/\) :: Goedel r -> Goedel r -> Goedel r Source #
(Ord r, Num r) => UpperBounded (Goedel r) Source #
Instance details Defined in Circuit.Logics.Goedel Methods top :: Goedel r Source #

mkGoedel :: (Ord r, Num r) => r -> Goedel r Source #

Clamp to the unit interval and wrap.

unGoedel :: Goedel r -> r Source #

godei :: Rational -> Goedel Rational Source #

Alias matching common spelling in the literature.