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import scala.annotation.tailrec
/**
* Symbolic aliases for various types are defined here.
*/
package object cats {
type ~>[F[_], G[_]] = arrow.FunctionK[F, G]
type ⊥ = Nothing
type ⊤ = Any
/** [[cats.InjectK]][F, G] */
type :<:[F[_], G[_]] = InjectK[F, G]
/** [[cats.InjectK]][F, G] */
type ::[F[_], G[_]] = InjectK[F, G]
/**
* Identity, encoded as `type Id[A] = A`, a convenient alias to make
* identity instances well-kinded.
*
* The identity monad can be seen as the ambient monad that encodes
* the effect of having no effect. It is ambient in the sense that
* plain pure values are values of `Id`.
*
* For instance, the [[cats.Functor]] instance for `[[cats.Id]]`
* allows us to apply a function `A => B` to an `Id[A]` and get an
* `Id[B]`. However, an `Id[A]` is the same as `A`, so all we're doing
* is applying a pure function of type `A => B` to a pure value of
* type `A` to get a pure value of type `B`. That is, the instance
* encodes pure unary function application.
*/
type Id[A] = A
type Endo[A] = A => A
implicit val catsInstancesForId: Bimonad[Id] with CommutativeMonad[Id] with Comonad[Id] with NonEmptyTraverse[Id] with Distributive[Id] =
new Bimonad[Id] with CommutativeMonad[Id] with Comonad[Id] with NonEmptyTraverse[Id] with Distributive[Id] {
def pure[A](a: A): A = a
def extract[A](a: A): A = a
def flatMap[A, B](a: A)(f: A => B): B = f(a)
def coflatMap[A, B](a: A)(f: A => B): B = f(a)
@tailrec def tailRecM[A, B](a: A)(f: A => Either[A, B]): B = f(a) match {
case Left(a1) => tailRecM(a1)(f)
case Right(b) => b
}
override def distribute[F[_], A, B](fa: F[A])(f: A => B)(implicit F: Functor[F]): Id[F[B]] = F.map(fa)(f)
override def map[A, B](fa: A)(f: A => B): B = f(fa)
override def ap[A, B](ff: A => B)(fa: A): B = ff(fa)
override def flatten[A](ffa: A): A = ffa
override def map2[A, B, Z](fa: A, fb: B)(f: (A, B) => Z): Z = f(fa, fb)
override def lift[A, B](f: A => B): A => B = f
override def imap[A, B](fa: A)(f: A => B)(fi: B => A): B = f(fa)
def foldLeft[A, B](a: A, b: B)(f: (B, A) => B) = f(b, a)
def foldRight[A, B](a: A, lb: Eval[B])(f: (A, Eval[B]) => Eval[B]): Eval[B] =
f(a, lb)
def nonEmptyTraverse[G[_], A, B](a: A)(f: A => G[B])(implicit G: Apply[G]): G[B] =
f(a)
override def foldMap[A, B](fa: Id[A])(f: A => B)(implicit B: Monoid[B]): B = f(fa)
override def reduce[A](fa: Id[A])(implicit A: Semigroup[A]): A =
fa
def reduceLeftTo[A, B](fa: Id[A])(f: A => B)(g: (B, A) => B): B =
f(fa)
override def reduceLeft[A](fa: Id[A])(f: (A, A) => A): A =
fa
override def reduceLeftToOption[A, B](fa: Id[A])(f: A => B)(g: (B, A) => B): Option[B] =
Some(f(fa))
override def reduceRight[A](fa: Id[A])(f: (A, Eval[A]) => Eval[A]): Eval[A] =
Now(fa)
def reduceRightTo[A, B](fa: Id[A])(f: A => B)(g: (A, Eval[B]) => Eval[B]): Eval[B] =
Now(f(fa))
override def reduceRightToOption[A, B](fa: Id[A])(f: A => B)(g: (A, Eval[B]) => Eval[B]): Eval[Option[B]] =
Now(Some(f(fa)))
override def reduceMap[A, B](fa: Id[A])(f: A => B)(implicit B: Semigroup[B]): B = f(fa)
override def size[A](fa: Id[A]): Long = 1L
override def get[A](fa: Id[A])(idx: Long): Option[A] =
if (idx == 0L) Some(fa) else None
override def isEmpty[A](fa: Id[A]): Boolean = false
}
/**
* Witness for: Id[A] <-> Unit => A
*/
implicit val catsRepresentableForId: Representable.Aux[Id, Unit] = new Representable[Id] {
override type Representation = Unit
override val F: Functor[Id] = Functor[Id]
override def tabulate[A](f: Unit => A): Id[A] = f(())
override def index[A](f: Id[A]): Unit => A = (_: Unit) => f
}
implicit val catsParallelForId: Parallel[Id, Id] = Parallel.identity
type Eq[A] = cats.kernel.Eq[A]
type PartialOrder[A] = cats.kernel.PartialOrder[A]
type Comparison = cats.kernel.Comparison
type Order[A] = cats.kernel.Order[A]
type Hash[A] = cats.kernel.Hash[A]
type Semigroup[A] = cats.kernel.Semigroup[A]
type Monoid[A] = cats.kernel.Monoid[A]
type Group[A] = cats.kernel.Group[A]
val Eq = cats.kernel.Eq
val PartialOrder = cats.kernel.PartialOrder
val Order = cats.kernel.Order
val Comparison = cats.kernel.Comparison
val Hash = cats.kernel.Hash
val Semigroup = cats.kernel.Semigroup
val Monoid = cats.kernel.Monoid
val Group = cats.kernel.Group
@deprecated("renamed to Semigroupal", "1.0.0-RC1")
type Cartesian[F[_]] = Semigroupal[F]
}