OrderPreservingSemigroup

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.

The binary operation to combine f1 and f2.

Implementations should not evaluate the by-name parameter f2 if result can be determined by f1.

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.

For n = 0, value For n = 1, append(value, value) For n = 2, append(append(value, value), value)

The default definition uses peasant multiplication, exploiting associativity to only require O(log n) uses of append

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.