Type classes

Currently, there are five type classes defined in Cats-tagless: FunctorK, ContravariantK, InvariantK, SemigroupalK, and ApplyK. They can be deemed as somewhat higher kinded versions of the corresponding type classes in cats.

FunctorK

  def mapK[F[_], G[_]](af: A[F])(fk: F ~> G): A[G]

For tagless final algebras whose effect F appears only in the covariant position, instance of FunctorK can be auto generated through the autoFunctorK annotation.

ContravariantK

  def contramapK[F[_], G[_]](af: A[F])(fk: G ~> F): A[G]

For tagless final algebras whose effect F appears only in the contravariant position, instance of ContravariantK can be auto generated through the autoContravariantK annotation.

InvariantK

  def imapK[F[_], G[_]](af: A[F])(fk: F ~> G)(gK: G ~> F): A[G]

For tagless final algebras whose effect F appears in both the covariant positions and contravariant positions, instance of InvariantK can be auto generated through the autoInvariantK annotation.

SemigroupalK

 def productK[F[_], G[_]](af: A[F], ag: A[G]): A[Tuple2K[F, G, *]]

For tagless final algebras that

1. has no extra type parameters or abstract type members, and
2. whose effect F appears only in the covariant position for all members,

instance of SemigroupalK can be auto generated through autoSemigroupalK annotation.

ApplyK

 def map2K[F[_], G[_], H[_]](af: A[F], ag: A[G])(f: Tuple2K[F, G, *] ~> H): A[H]

ApplyK extends both SemigroupalK and FunctorK just like their lower kinded counterparts.

For tagless final algebras that

1. has no extra type parameters or abstract type members, and
2. whose effect F appears only in the covariant position for all members,

instance of ApplyK can be auto generated through autoApplyK annotation.

Their laws are defined in cats.tagless.laws. To test your instance (if you decide to roll your own) against these laws please follow the examples in cats.tagless.tests, especially the ones that test against SafeAlg.