trait LatticeElement[L] extends Order[L] with Monoid[L] with Show[L]
We define here some domains that can will be useful to build a lattice for most languages.
Linear Supertypes
Known Subclasses
Ordering
- Alphabetic
- By Inheritance
Inherited
- LatticeElement
- Show
- Monoid
- Semigroup
- Order
- Equal
- AnyRef
- Any
Implicitly
- by any2stringadd
- by StringFormat
- by Ensuring
- by ArrowAssoc
- Hide All
- Show All
Visibility
- Public
- All
Type Members
-
trait
EqualLaw extends AnyRef
- Definition Classes
- Equal
- trait LatticeElementLaw extends MonoidLaw with OrderLaw
-
trait
MonoidLaw extends scalaz.Monoid.SemigroupLaw
- Definition Classes
- Monoid
-
trait
OrderLaw extends scalaz.Order.EqualLaw
- Definition Classes
- Order
-
trait
SemigroupApply extends Apply[[α]F]
- Attributes
- protected[this]
- Definition Classes
- Semigroup
-
trait
SemigroupCompose extends Compose[[α, β]F]
- Attributes
- protected[this]
- Definition Classes
- Semigroup
-
trait
SemigroupLaw extends AnyRef
- Definition Classes
- Semigroup
Abstract Value Members
-
abstract
def
bottom: L
The bottom element
- abstract def cardinality(x: L): Cardinality
-
abstract
def
eql[B](x: L, y: L)(implicit arg0: BoolLattice[B]): B
Equality check, returning an abstract result
-
abstract
def
join(x: L, y: ⇒ L): L
The join operation
-
abstract
def
name: String
The name of the lattice
-
abstract
def
order(x: L, y: L): Ordering
- Definition Classes
- Order
-
abstract
def
subsumes(x: L, y: ⇒ L): Boolean
The subsumption relation that defines the ordering of elements
-
abstract
def
top: L
The top element.
Concrete Value Members
-
final
def
!=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
-
final
def
##(): Int
- Definition Classes
- AnyRef → Any
-
def
+(other: String): String
- Implicit
- This member is added by an implicit conversion from LatticeElement[L] to any2stringadd[LatticeElement[L]] performed by method any2stringadd in scala.Predef.
- Definition Classes
- any2stringadd
-
def
->[B](y: B): (LatticeElement[L], B)
- Implicit
- This member is added by an implicit conversion from LatticeElement[L] to ArrowAssoc[LatticeElement[L]] performed by method ArrowAssoc in scala.Predef.
- Definition Classes
- ArrowAssoc
- Annotations
- @inline()
-
final
def
==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
-
final
def
append(x: L, y: ⇒ L): L
- Definition Classes
- LatticeElement → Semigroup
-
final
def
applicative: Applicative[[α]L]
- Definition Classes
- Monoid
-
final
def
apply: Apply[[α]L]
- Definition Classes
- Semigroup
-
def
apply(x: L, y: L): Ordering
- Definition Classes
- Order
-
final
def
asInstanceOf[T0]: T0
- Definition Classes
- Any
-
final
def
category: Category[[α, β]L]
- Definition Classes
- Monoid
-
def
clone(): AnyRef
- Attributes
- protected[java.lang]
- Definition Classes
- AnyRef
- Annotations
- @native() @HotSpotIntrinsicCandidate() @throws( ... )
-
final
def
compose: Compose[[α, β]L]
- Definition Classes
- Semigroup
-
def
contramap[B](f: (B) ⇒ L): Order[B]
- Definition Classes
- Order → Equal
-
def
ensuring(cond: (LatticeElement[L]) ⇒ Boolean, msg: ⇒ Any): LatticeElement[L]
- Implicit
- This member is added by an implicit conversion from LatticeElement[L] to Ensuring[LatticeElement[L]] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
-
def
ensuring(cond: (LatticeElement[L]) ⇒ Boolean): LatticeElement[L]
- Implicit
- This member is added by an implicit conversion from LatticeElement[L] to Ensuring[LatticeElement[L]] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
-
def
ensuring(cond: Boolean, msg: ⇒ Any): LatticeElement[L]
- Implicit
- This member is added by an implicit conversion from LatticeElement[L] to Ensuring[LatticeElement[L]] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
-
def
ensuring(cond: Boolean): LatticeElement[L]
- Implicit
- This member is added by an implicit conversion from LatticeElement[L] to Ensuring[LatticeElement[L]] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
-
final
def
eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
-
def
equal(x: L, y: L): Boolean
- Definition Classes
- Order → Equal
-
def
equalIsNatural: Boolean
- Definition Classes
- Equal
-
def
equalLaw: EqualLaw
- Definition Classes
- Equal
-
val
equalSyntax: EqualSyntax[L]
- Definition Classes
- Equal
-
def
equals(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
-
def
formatted(fmtstr: String): String
- Implicit
- This member is added by an implicit conversion from LatticeElement[L] to StringFormat[LatticeElement[L]] performed by method StringFormat in scala.Predef.
- Definition Classes
- StringFormat
- Annotations
- @inline()
-
final
def
getClass(): Class[_]
- Definition Classes
- AnyRef → Any
- Annotations
- @native() @HotSpotIntrinsicCandidate()
-
def
greaterThan(x: L, y: L): Boolean
- Definition Classes
- Order
-
def
greaterThanOrEqual(x: L, y: L): Boolean
- Definition Classes
- Order
-
def
hashCode(): Int
- Definition Classes
- AnyRef → Any
- Annotations
- @native() @HotSpotIntrinsicCandidate()
-
final
def
ifEmpty[B](a: L)(t: ⇒ B)(f: ⇒ B)(implicit eq: Equal[L]): B
- Definition Classes
- Monoid
-
final
def
isInstanceOf[T0]: Boolean
- Definition Classes
- Any
-
def
isMZero(a: L)(implicit eq: Equal[L]): Boolean
- Definition Classes
- Monoid
- def latticeElementLaw: LatticeElementLaw
-
def
lessThan(x: L, y: L): Boolean
- Definition Classes
- Order
-
def
lessThanOrEqual(x: L, y: L): Boolean
- Definition Classes
- Order
-
def
max(x: L, y: L): L
- Definition Classes
- Order
-
def
min(x: L, y: L): L
- Definition Classes
- Order
-
def
monoidLaw: MonoidLaw
- Definition Classes
- Monoid
-
val
monoidSyntax: MonoidSyntax[L]
- Definition Classes
- Monoid
-
def
multiply(value: L, n: Int): L
- Definition Classes
- Monoid
-
def
multiply1(value: L, n: Int): L
- Definition Classes
- Semigroup
-
final
def
ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
-
final
def
notify(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native() @HotSpotIntrinsicCandidate()
-
final
def
notifyAll(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native() @HotSpotIntrinsicCandidate()
-
final
def
onEmpty[A, B](a: L)(v: ⇒ B)(implicit eq: Equal[L], mb: Monoid[B]): B
- Definition Classes
- Monoid
-
final
def
onNotEmpty[B](a: L)(v: ⇒ B)(implicit eq: Equal[L], mb: Monoid[B]): B
- Definition Classes
- Monoid
-
def
orderLaw: OrderLaw
- Definition Classes
- Order
-
val
orderSyntax: OrderSyntax[L]
- Definition Classes
- Order
-
def
reverseOrder: Order[L]
- Definition Classes
- Order
-
def
semigroupLaw: SemigroupLaw
- Definition Classes
- Semigroup
-
val
semigroupSyntax: SemigroupSyntax[L]
- Definition Classes
- Semigroup
-
def
show(f: L): Cord
- Definition Classes
- Show
-
val
showSyntax: ShowSyntax[L]
- Definition Classes
- Show
-
def
shows(f: L): String
- Definition Classes
- Show
-
def
sort(x: L, y: L): (L, L)
- Definition Classes
- Order
-
final
def
synchronized[T0](arg0: ⇒ T0): T0
- Definition Classes
- AnyRef
-
def
toScalaOrdering: Ordering[L]
- Definition Classes
- Order
-
def
toString(): String
- Definition Classes
- AnyRef → Any
-
final
def
wait(arg0: Long, arg1: Int): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
-
final
def
wait(arg0: Long): Unit
- Definition Classes
- AnyRef
- Annotations
- @native() @throws( ... )
-
final
def
wait(): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
-
final
def
zero: L
- Definition Classes
- LatticeElement → Monoid
-
def
→[B](y: B): (LatticeElement[L], B)
- Implicit
- This member is added by an implicit conversion from LatticeElement[L] to ArrowAssoc[LatticeElement[L]] performed by method ArrowAssoc in scala.Predef.
- Definition Classes
- ArrowAssoc