IsomorphismBand

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

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

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.

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.

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

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

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 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.