Packages

trait BoolLatticeLaw extends LatticeElementLaw

Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. BoolLatticeLaw
  2. LatticeElementLaw
  3. OrderLaw
  4. EqualLaw
  5. MonoidLaw
  6. SemigroupLaw
  7. AnyRef
  8. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
  1. Hide All
  2. Show All
Visibility
  1. Public
  2. All

Value Members

  1. def antisymmetric(f1: B, f2: B): Boolean
    Definition Classes
    OrderLaw
  2. def associative(f1: B, f2: B, f3: B)(implicit F: Equal[B]): Boolean
    Definition Classes
    SemigroupLaw
  3. def bottomLowerBound(a: B): Boolean

    Bottom is the lower bound ∀ a: ⊥ ⊑ a

    Bottom is the lower bound ∀ a: ⊥ ⊑ a

    Definition Classes
    LatticeElementLaw
  4. def bottomNotTrueNorFalse: Boolean

    Bottom is neither true nor false ¬isTrue(⊥) ∧ ¬isFalse(⊥)

  5. def commutative(f1: B, f2: B): Boolean
    Definition Classes
    EqualLaw
  6. def eqlIsTrue(a: B): Boolean

    Equal elements are always eql if they're not bottom.

    Equal elements are always eql if they're not bottom. ∀ a: a = bottom ∨ isTrue(eql(a, a))

    Definition Classes
    LatticeElementLaw
  7. def injectPreservesTruthiness: Boolean

    Inject preserves truthiness isTrue(inject(true)) ∧ isFalse(inject(false))

  8. def joinAssociative(a: B, b: B, c: B): Boolean

    Join is associative ∀ a, b, c: (a ⊔ b) ⊔ c = a ⊔ (b ⊔ c)

    Join is associative ∀ a, b, c: (a ⊔ b) ⊔ c = a ⊔ (b ⊔ c)

    Definition Classes
    LatticeElementLaw
  9. def joinCommutative(a: B, b: B): Boolean

    Join is commutative ∀ a, b: a ⊔ b = b ⊔ a

    Join is commutative ∀ a, b: a ⊔ b = b ⊔ a

    Definition Classes
    LatticeElementLaw
  10. def joinIdempotent(a: B): Boolean

    Join is idempotent ∀ a: a ⊔ a = a

    Join is idempotent ∀ a: a ⊔ a = a

    Definition Classes
    LatticeElementLaw
  11. def joinSubsumesCompatible(a: B, b: B): Boolean

    Join and subsumes are compatible ∀ a, b: a ⊑ b ⇒ a ⊔ b = b

    Join and subsumes are compatible ∀ a, b: a ⊑ b ⇒ a ⊔ b = b

    Definition Classes
    LatticeElementLaw
  12. def leftIdentity(a: B)(implicit F: Equal[B]): Boolean
    Definition Classes
    MonoidLaw
  13. def naturality(f1: B, f2: B): Boolean
    Definition Classes
    EqualLaw
  14. def notInvolutive(a: B): Boolean

    Not is involutive ∀ a: not(not(a)) == a

  15. def notReversesTruthiness(a: B): Boolean

    Not reverses truthiness ∀ a: isTrue(a) ⇒ isFalse(not(a)) ∧ isFalse(a) ⇒ isTrue(not(a))

  16. def orderAndEqualConsistent(f1: B, f2: B): Boolean
    Definition Classes
    OrderLaw
  17. def reflexive(f: B): Boolean
    Definition Classes
    EqualLaw
  18. def rightIdentity(a: B)(implicit F: Equal[B]): Boolean
    Definition Classes
    MonoidLaw
  19. def topTrueAndFalse: Boolean

    Top is both true and false (when defined) isTrue(⊤) ∧ isFalse(⊤)

  20. def topUpperBound(a: B): Boolean

    Top is the upper bound (when defined) ∀ a: a ⊑ ⊤

    Top is the upper bound (when defined) ∀ a: a ⊑ ⊤

    Definition Classes
    LatticeElementLaw
  21. def transitive(f1: B, f2: B, f3: B): Boolean
    Definition Classes
    EqualLaw
  22. def transitiveOrder(f1: B, f2: B, f3: B): Boolean
    Definition Classes
    OrderLaw