RON.Semilattice

Documentation

class Semigroup a => Semilattice a where

A semilattice.

It may be a join-semilattice, or meet-semilattice, it doesn't matter.

If it matters for you, use package lattices.

In addition to Semigroup, Semilattice defines these laws:

commutativity

x <> y == y <> x

idempotency

x <> x == x

relation-operation equivalence

x ≼ y == (x <> y == y) x <> y == minimum z -> x ≼ z && y ≼ z

Minimal complete definition

Nothing

Methods

(≼) :: a -> a -> Bool

Semilattice relation.

default (≼) :: Eq a => a -> a -> Bool

Instances

Semilattice a => Semilattice (Maybe a)

Defined in RON.Semilattice

Methods

(≼) :: Maybe a -> Maybe a -> Bool

Ord a => Semilattice (Max a)

Defined in RON.Semilattice

Methods

(≼) :: Max a -> Max a -> Bool

Ord a => Semilattice (Set a)

Defined in RON.Semilattice

Methods

(≼) :: Set a -> Set a -> Bool

type BoundedSemilattice a = (Monoid a, Semilattice a)

A bounded semilattice.

Bounded semilattice laws are already defined by Monoid and Semilattice, so we don't define an explicit class here.