kits.Applicative.scala Maven / Gradle / Ivy
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package kits
import kits.std._
trait Applicative[F[_]] extends Functor[F] { F =>
def pure[A](a: A): F[A]
def ap[A, B](fa: F[A])(f: F[A => B]): F[B]
override def map[A, B](fa: F[A])(f: A => B): F[B] = ap(fa)(pure(f))
def map2[A, B, C](fa: F[A], fb: F[B])(f: (A, B) => C): F[C] = ap(fb)(map(fa)(a => f(a, _)))
def map3[A, B, C, D](fa: F[A], fb: F[B], fc: F[C])(f: (A, B, C) => D): F[D] = ap(fc)(map2(fa, fb)((a, b) => f(a, b, _)))
def compose[G[_]](implicit G: Applicative[G]): Applicative[({ type H[A] = F[G[A]] })#H] =
new Applicative[({ type H[A] = F[G[A]] })#H] {
def pure[A](a: A): F[G[A]] = F.pure(G.pure(a))
def ap[A, B](fga: F[G[A]])(f: F[G[A => B]]): F[G[B]] = F.map2(fga, f)(G.ap(_)(_))
}
}
object Applicative extends ApplicativeFunctions[Applicative] {
implicit def Either[E](implicit E: Monoid[E]): Applicative[({ type F[A] = Either[E, A] })#F] = new EitherApplicative[E] with EitherFunctor[E] { val monoid = E }
}
trait ApplicativeFunctions[T[F[_]] <: Applicative[F]] extends FunctorFunctions[T] {
def ap[F[_], A, B](fa: F[A])(f: F[A => B])(implicit F: T[F]): F[B] = F.ap(fa)(f)
def map2[F[_], A, B, C](fa: F[A], fb: F[B])(f: (A, B) => C)(implicit F: T[F]): F[C] = F.map2(fa, fb)(f)
def map3[F[_], A, B, C, D](fa: F[A], fb: F[B], fc: F[C])(f: (A, B, C) => D)(implicit F: T[F]): F[D] = F.map3(fa, fb, fc)(f)
}