Safe Haskell	None
Language	GHC2024

Circuit.Logics.H3

Description

H3 — smallest Heyting algebra that is not Boolean.

Values: true false unknown. Implication is defined so Heyting laws hold; excluded middle fails at HUnknown.

Epistemic reading: "do we know enough to assert?" — a natural output alphabet for Process obs H3.

Synopsis

data H3
- = HFalse
- | HUnknown
- | HTrue

Documentation

data H3 Source #

Three-valued Heyting algebra (intuitionistic toy model).

Constructors

HFalse	Known false / bottom.
HUnknown	Open / undecided.
HTrue	Known true / top.

Instances

Instances details

Eq H3 Source #
Instance details Defined in Circuit.Logics.H3 Methods (==) :: H3 -> H3 -> Bool # (/=) :: H3 -> H3 -> Bool #
Ord H3 Source #
Instance details Defined in Circuit.Logics.H3 Methods compare :: H3 -> H3 -> Ordering # (<) :: H3 -> H3 -> Bool # (<=) :: H3 -> H3 -> Bool # (>) :: H3 -> H3 -> Bool # (>=) :: H3 -> H3 -> Bool # max :: H3 -> H3 -> H3 # min :: H3 -> H3 -> H3 #
Bounded H3 Source #
Instance details Defined in Circuit.Logics.H3 Methods minBound :: H3 # maxBound :: H3 #
Enum H3 Source #
Instance details Defined in Circuit.Logics.H3 Methods succ :: H3 -> H3 # pred :: H3 -> H3 # toEnum :: Int -> H3 # fromEnum :: H3 -> Int # enumFrom :: H3 -> [H3] # enumFromThen :: H3 -> H3 -> [H3] # enumFromTo :: H3 -> H3 -> [H3] # enumFromThenTo :: H3 -> H3 -> H3 -> [H3] #
Read H3 Source #
Instance details Defined in Circuit.Logics.H3 Methods readsPrec :: Int -> ReadS H3 # readList :: ReadS [H3] # readPrec :: ReadPrec H3 # readListPrec :: ReadPrec [H3] #
Show H3 Source #
Instance details Defined in Circuit.Logics.H3 Methods showsPrec :: Int -> H3 -> ShowS # show :: H3 -> String # showList :: [H3] -> ShowS #
Complemented H3 Source #	Pseudo-complement `a ==> HFalse`. Not a Boolean complement: `HUnknown \ complement HUnknown = HTrue`.
Instance details Defined in Circuit.Logics.H3 Methods complement :: H3 -> H3 Source #
Heyting H3 Source #
Instance details Defined in Circuit.Logics.H3 Methods (==>) :: H3 -> H3 -> H3 Source #
JoinSemiLattice H3 Source #
Instance details Defined in Circuit.Logics.H3 Methods (\/) :: H3 -> H3 -> H3 Source #
LowerBounded H3 Source #
Instance details Defined in Circuit.Logics.H3 Methods bottom :: H3 Source #
MeetSemiLattice H3 Source #
Instance details Defined in Circuit.Logics.H3 Methods (/\) :: H3 -> H3 -> H3 Source #
UpperBounded H3 Source #
Instance details Defined in Circuit.Logics.H3 Methods top :: H3 Source #