Safe Haskell	None
Language	GHC2024

Circuit.Logics.Lattice

Description

Order lattices for truth-value carriers.

Naming follows numhask's lattice vocabulary (/, /\, bounds) so a future alignment is a thin instance layer, not a redesign. This package owns its hierarchy so it stays an optional compile target.

Synopsis

class Eq a => JoinSemiLattice a where
- (\/) :: a -> a -> a
class Eq a => MeetSemiLattice a where
- (/\) :: a -> a -> a
type Lattice a = (JoinSemiLattice a, MeetSemiLattice a)
class JoinSemiLattice a => LowerBounded a where
- bottom :: a
class MeetSemiLattice a => UpperBounded a where
- top :: a
type BoundedLattice a = (JoinSemiLattice a, MeetSemiLattice a, LowerBounded a, UpperBounded a)

Documentation

class Eq a => JoinSemiLattice a where Source #

Join-semilattice (disjunction / least upper bound).

Associativity: x \/ (y \/ z) == (x \/ y) \/ z
Commutativity: x \/ y == y \/ x
Idempotency:   x \/ x == x

Methods

(\/) :: a -> a -> a infixr 5 Source #

Instances

Instances details

JoinSemiLattice H3 Source #
Instance details Defined in Circuit.Logics.H3 Methods (\/) :: H3 -> H3 -> H3 Source #
JoinSemiLattice K3 Source #
Instance details Defined in Circuit.Logics.K3 Methods (\/) :: K3 -> K3 -> K3 Source #
JoinSemiLattice Bool Source #
Instance details Defined in Circuit.Logics.Lattice Methods (\/) :: Bool -> Bool -> Bool Source #
Ord r => JoinSemiLattice (Goedel r) Source #
Instance details Defined in Circuit.Logics.Goedel Methods (\/) :: Goedel r -> Goedel r -> Goedel r Source #

class Eq a => MeetSemiLattice a where Source #

Meet-semilattice (conjunction / greatest lower bound).

Associativity: x /\ (y /\ z) == (x /\ y) /\ z
Commutativity: x /\ y == y /\ x
Idempotency:   x /\ x == x

Methods

(/\) :: a -> a -> a infixr 6 Source #

Instances

Instances details

MeetSemiLattice H3 Source #
Instance details Defined in Circuit.Logics.H3 Methods (/\) :: H3 -> H3 -> H3 Source #
MeetSemiLattice K3 Source #
Instance details Defined in Circuit.Logics.K3 Methods (/\) :: K3 -> K3 -> K3 Source #
MeetSemiLattice Bool Source #
Instance details Defined in Circuit.Logics.Lattice Methods (/\) :: Bool -> Bool -> Bool Source #
Ord r => MeetSemiLattice (Goedel r) Source #
Instance details Defined in Circuit.Logics.Goedel Methods (/\) :: Goedel r -> Goedel r -> Goedel r Source #

type Lattice a = (JoinSemiLattice a, MeetSemiLattice a) Source #

Lattice when absorption holds:

a \/ (a /\ b) == a
a /\ (a \/ b) == a

class JoinSemiLattice a => LowerBounded a where Source #

Methods

bottom :: a Source #

Instances

Instances details

LowerBounded H3 Source #
Instance details Defined in Circuit.Logics.H3 Methods bottom :: H3 Source #
LowerBounded K3 Source #
Instance details Defined in Circuit.Logics.K3 Methods bottom :: K3 Source #
LowerBounded Bool Source #
Instance details Defined in Circuit.Logics.Lattice Methods bottom :: Bool Source #
(Ord r, Num r) => LowerBounded (Goedel r) Source #
Instance details Defined in Circuit.Logics.Goedel Methods bottom :: Goedel r Source #

class MeetSemiLattice a => UpperBounded a where Source #

Methods

top :: a Source #

Instances

Instances details

UpperBounded H3 Source #
Instance details Defined in Circuit.Logics.H3 Methods top :: H3 Source #
UpperBounded K3 Source #
Instance details Defined in Circuit.Logics.K3 Methods top :: K3 Source #
UpperBounded Bool Source #
Instance details Defined in Circuit.Logics.Lattice Methods top :: Bool Source #
(Ord r, Num r) => UpperBounded (Goedel r) Source #
Instance details Defined in Circuit.Logics.Goedel Methods top :: Goedel r Source #

type BoundedLattice a = (JoinSemiLattice a, MeetSemiLattice a, LowerBounded a, UpperBounded a) Source #