Safe Haskell	None
Language	GHC2024

Circuit.Logics.Boolean2Ring

Description

Boolean algebra re-read as a ring of characteristic 2.

(+)  = XOR   (symmetric difference)
(*)  = AND
zero = false
one  = true
negate = id

Keeps Boolean and ring APIs separate while documenting the bridge — relevant if numhask ever wants an explicit Boolean↔Ring story.

Synopsis

newtype Boolean2Ring b = Boolean2Ring {
- getBoolean2Ring :: b
}
xorBool :: Complemented b => b -> b -> b

Documentation

newtype Boolean2Ring b Source #

Carrier wrapper: same Boolean values, ring operations.

Constructors

Boolean2Ring
Fields getBoolean2Ring :: b

Instances

Instances details

Eq b => Eq (Boolean2Ring b) Source #
Instance details Defined in Circuit.Logics.Boolean2Ring Methods (==) :: Boolean2Ring b -> Boolean2Ring b -> Bool # (/=) :: Boolean2Ring b -> Boolean2Ring b -> Bool #
Ord b => Ord (Boolean2Ring b) Source #
Instance details Defined in Circuit.Logics.Boolean2Ring Methods compare :: Boolean2Ring b -> Boolean2Ring b -> Ordering # (<) :: Boolean2Ring b -> Boolean2Ring b -> Bool # (<=) :: Boolean2Ring b -> Boolean2Ring b -> Bool # (>) :: Boolean2Ring b -> Boolean2Ring b -> Bool # (>=) :: Boolean2Ring b -> Boolean2Ring b -> Bool # max :: Boolean2Ring b -> Boolean2Ring b -> Boolean2Ring b # min :: Boolean2Ring b -> Boolean2Ring b -> Boolean2Ring b #
(MeetSemiLattice b, Complemented b, LowerBounded b, UpperBounded b) => Num (Boolean2Ring b) Source #
Instance details Defined in Circuit.Logics.Boolean2Ring Methods (+) :: Boolean2Ring b -> Boolean2Ring b -> Boolean2Ring b # (-) :: Boolean2Ring b -> Boolean2Ring b -> Boolean2Ring b # (*) :: Boolean2Ring b -> Boolean2Ring b -> Boolean2Ring b # negate :: Boolean2Ring b -> Boolean2Ring b # abs :: Boolean2Ring b -> Boolean2Ring b # signum :: Boolean2Ring b -> Boolean2Ring b # fromInteger :: Integer -> Boolean2Ring b #
Read b => Read (Boolean2Ring b) Source #
Instance details Defined in Circuit.Logics.Boolean2Ring Methods readsPrec :: Int -> ReadS (Boolean2Ring b) # readList :: ReadS [Boolean2Ring b] # readPrec :: ReadPrec (Boolean2Ring b) # readListPrec :: ReadPrec [Boolean2Ring b] #
Show b => Show (Boolean2Ring b) Source #
Instance details Defined in Circuit.Logics.Boolean2Ring Methods showsPrec :: Int -> Boolean2Ring b -> ShowS # show :: Boolean2Ring b -> String # showList :: [Boolean2Ring b] -> ShowS #

xorBool :: Complemented b => b -> b -> b Source #

XOR on a complemented meet-semilattice with bounds.