ContravariantMonoidal

trivial produces an instance of F for any type A that is trivial with respect to contramap2 along the diagonal

Compose Invariant F[_] and G[_] then produce Invariant[F[G[_]]] using their imap.

Example:

scala> import cats.implicits._
scala> import scala.concurrent.duration._

scala> val durSemigroupList: Semigroup[List[FiniteDuration]] =
    | Invariant[Semigroup].compose[List].imap(Semigroup[List[Long]])(Duration.fromNanos)(_.toNanos)
scala> durSemigroupList.combine(List(2.seconds, 3.seconds), List(4.seconds))
res1: List[FiniteDuration] = List(2 seconds, 3 seconds, 4 seconds)

Compose Invariant F[_] and Contravariant G[_] then produce Invariant[F[G[_]]] using F's imap and G's contramap.

Example:

scala> import cats.implicits._
scala> import scala.concurrent.duration._

scala> type ToInt[T] = T => Int
scala> val durSemigroupToInt: Semigroup[ToInt[FiniteDuration]] =
    | Invariant[Semigroup]
    |   .composeContravariant[ToInt]
    |   .imap(Semigroup[ToInt[Long]])(Duration.fromNanos)(_.toNanos)
// semantically equal to (2.seconds.toSeconds.toInt + 1) + (2.seconds.toSeconds.toInt * 2) = 7
scala> durSemigroupToInt.combine(_.toSeconds.toInt + 1, _.toSeconds.toInt * 2)(2.seconds)
res1: Int = 7

Lifts natural subtyping contravariance of contravariant Functors. could be implemented as contramap(identity), but the Functor laws say this is equivalent

point lifts any value into a Monoidal Functor.

Example:

scala> import cats.implicits._

scala> InvariantMonoidal[Option].point(10)
res0: Option[Int] = Some(10)

Combine an F[A] and an F[B] into an F[(A, B)] that maintains the effects of both fa and fb.

Example:

scala> import cats.implicits._

scala> val noneInt: Option[Int] = None
scala> val some3: Option[Int] = Some(3)
scala> val noneString: Option[String] = None
scala> val someFoo: Option[String] = Some("foo")

scala> Semigroupal[Option].product(noneInt, noneString)
res0: Option[(Int, String)] = None

scala> Semigroupal[Option].product(noneInt, someFoo)
res1: Option[(Int, String)] = None

scala> Semigroupal[Option].product(some3, noneString)
res2: Option[(Int, String)] = None

scala> Semigroupal[Option].product(some3, someFoo)
res3: Option[(Int, String)] = Some((3,foo))