IsomorphismBand

trait IsomorphismBand[F, G] extends Band[F] with IsomorphismSemigroup[F, G]
trait Band[F]
trait Semigroup[F]
class Object
trait Matchable
class Any

Type members

Inherited classlikes

trait BandLaw

Band instances must satisfy scalaz.Semigroup.SemigroupLaw and 1 additional law:

Band instances must satisfy scalaz.Semigroup.SemigroupLaw and 1 additional law:

  • '''idempotency''': forall a. append(a, a) == a
Inherited from
Band

A semigroup in type F must satisfy two laws:

A semigroup in type F must satisfy two laws:

  • '''closure''': ∀ a, b in F, append(a, b) is also in F. This is enforced by the type system.
  • '''associativity''': ∀ a, b, c in F, the equation append(append(a, b), c) = append(a, append(b , c)) holds.
Inherited from
Semigroup

Value members

Inherited methods

def append(f1: F, f2: => F): F
Inherited from
IsomorphismSemigroup
final
def apply: Apply[[α] =>> F]

An scalaz.Apply, that implements ap with append. Note that the type parameter α in Apply[λ[α => F]] is discarded; it is a phantom type. As such, the functor cannot support scalaz.Bind.

An scalaz.Apply, that implements ap with append. Note that the type parameter α in Apply[λ[α => F]] is discarded; it is a phantom type. As such, the functor cannot support scalaz.Bind.

Inherited from
Semigroup
Inherited from
Band
final
def compose: Compose[[α, β] =>> F]

Every Semigroup gives rise to a scalaz.Compose, for which the type parameters are phantoms.

Every Semigroup gives rise to a scalaz.Compose, for which the type parameters are phantoms.

Note

compose.semigroup = this

Inherited from
Semigroup
def iso: IsoSet[F, G]
Inherited from
IsomorphismSemigroup
override
def multiply1(value: F, n: Int): F

The default definition exploits idempotency to optimise to O(1)

The default definition exploits idempotency to optimise to O(1)

Definition Classes
Inherited from
Band
def unfoldlSumOpt[S](seed: S)(f: S => Maybe[(S, F)]): Maybe[F]

Unfold seed to the left and sum using append. Semigroups with right absorbing elements may override this method to not unfold more than is necessary to determine the result.

Unfold seed to the left and sum using append. Semigroups with right absorbing elements may override this method to not unfold more than is necessary to determine the result.

Inherited from
Semigroup
def unfoldrSumOpt[S](seed: S)(f: S => Maybe[(F, S)]): Maybe[F]

Unfold seed to the right and sum using append. Semigroups with left absorbing elements may override this method to not unfold more than is necessary to determine the result.

Unfold seed to the right and sum using append. Semigroups with left absorbing elements may override this method to not unfold more than is necessary to determine the result.

Inherited from
Semigroup

Inherited fields

Inherited from
Band

Implicits

Implicits

implicit
def G: Band[G]