| Safe Haskell | Safe-Inferred |
|---|---|
| Language | GHC2021 |
NumHask.Algebra.Lattice
Description
Synopsis
- class Eq a => JoinSemiLattice a where
- (\/) :: a -> a -> a
- joinLeq :: JoinSemiLattice a => a -> a -> Bool
- (<\) :: JoinSemiLattice a => a -> a -> Bool
- class Eq a => MeetSemiLattice a where
- (/\) :: a -> a -> a
- meetLeq :: MeetSemiLattice a => a -> a -> Bool
- (</) :: MeetSemiLattice a => a -> a -> Bool
- class JoinSemiLattice a => BoundedJoinSemiLattice a where
- bottom :: a
- class MeetSemiLattice a => BoundedMeetSemiLattice a where
- top :: a
- type Lattice a = (JoinSemiLattice a, MeetSemiLattice a)
- type BoundedLattice a = (JoinSemiLattice a, MeetSemiLattice a, BoundedJoinSemiLattice a, BoundedMeetSemiLattice a)
Documentation
class Eq a => JoinSemiLattice a where Source #
A algebraic structure with element joins: See Semilattice
Associativity: x \/ (y \/ z) == (x \/ y) \/ z Commutativity: x \/ y == y \/ x Idempotency: x \/ x == x
Instances
joinLeq :: JoinSemiLattice a => a -> a -> Bool Source #
The partial ordering induced by the join-semilattice structure
(<\) :: JoinSemiLattice a => a -> a -> Bool infixr 6 Source #
The partial ordering induced by the join-semilattice structure
class Eq a => MeetSemiLattice a where Source #
A algebraic structure with element meets: See Semilattice
Associativity: x /\ (y /\ z) == (x /\ y) /\ z Commutativity: x /\ y == y /\ x Idempotency: x /\ x == x
Instances
meetLeq :: MeetSemiLattice a => a -> a -> Bool Source #
The partial ordering induced by the meet-semilattice structure
(</) :: MeetSemiLattice a => a -> a -> Bool infixr 6 Source #
The partial ordering induced by the meet-semilattice structure
class JoinSemiLattice a => BoundedJoinSemiLattice a where Source #
Instances
class MeetSemiLattice a => BoundedMeetSemiLattice a where Source #
Instances
type Lattice a = (JoinSemiLattice a, MeetSemiLattice a) Source #
The combination of two semi lattices makes a lattice if the absorption law holds: see Absorption Law and Lattice
Absorption: a \/ (a /\ b) == a /\ (a \/ b) == a
type BoundedLattice a = (JoinSemiLattice a, MeetSemiLattice a, BoundedJoinSemiLattice a, BoundedMeetSemiLattice a) Source #
Lattices with both bounds