/core/src/main/scala/scalaz/InvariantFunctor.scala
http://github.com/scalaz/scalaz · Scala · 75 lines · 33 code · 16 blank · 26 comment · 0 complexity · 0bc56ea07c21a45a603afd0c9c00861c MD5 · raw file
- package scalaz
- ////
- /**
- * Unary type constructor that supports an `xmap` operation that converts an `F[A]` to an `F[B]` given
- * two functions, `A => B` and `B => A`.
- *
- * An invariant functor must satisfy two laws:
- * - identity - xmap(ma)(identity, identity) == ma
- * - composite - xmap(xmap(ma, f1, g1), f2, g2) == xmap(ma, f2 compose f1, g1, compose g2)
- *
- * Also known as an exponential functor.
- *
- * @see [[https://hackage.haskell.org/packages/archive/invariant/latest/doc/html/Data-Functor-Invariant.html]]
- * @see [[http://comonad.com/reader/2008/rotten-bananas/]]
- *
- * @see [[scalaz.InvariantFunctor.InvariantFunctorLaw]]
- */
- ////
- trait InvariantFunctor[F[_]] { self =>
- ////
- import BijectionT.Bijection
- import Isomorphism.<=>
- /** Converts `ma` to a value of type `F[B]` using the provided functions `f` and `g`. */
- def xmap[A, B](ma: F[A], f: A => B, g: B => A): F[B]
- /** Converts `ma` to a value of type `F[B]` using the provided bijection. */
- def xmapb[A, B](ma: F[A])(b: Bijection[A, B]): F[B] = xmap(ma, b.to, b.from)
- /** Converts `ma` to a value of type `F[B]` using the provided isomorphism. */
- def xmapi[A, B](ma: F[A])(iso: A <=> B): F[B] = xmap(ma, iso.to, iso.from)
- trait InvariantFunctorLaw {
- def invariantIdentity[A](fa: F[A])(implicit FA: Equal[F[A]]): Boolean =
- FA.equal(xmap[A, A](fa, x => x, x => x), fa)
- def invariantComposite[A, B, C](fa: F[A], f1: A => B, g1: B => A, f2: B => C, g2: C => B)(implicit FC: Equal[F[C]]): Boolean =
- FC.equal(xmap(xmap(fa, f1, g1), f2, g2), xmap(fa, f2 compose f1, g1 compose g2))
- }
- def invariantFunctorLaw = new InvariantFunctorLaw {}
- ////
- val invariantFunctorSyntax: scalaz.syntax.InvariantFunctorSyntax[F] =
- new scalaz.syntax.InvariantFunctorSyntax[F] { def F = InvariantFunctor.this }
- }
- object InvariantFunctor {
- @inline def apply[F[_]](implicit F: InvariantFunctor[F]): InvariantFunctor[F] = F
- import Isomorphism._
- def fromIso[F[_], G[_]](D: F <~> G)(implicit E: InvariantFunctor[G]): InvariantFunctor[F] =
- new IsomorphismInvariantFunctor[F, G] {
- override def G: InvariantFunctor[G] = E
- override def iso: F <~> G = D
- }
- ////
- ////
- }
- trait IsomorphismInvariantFunctor[F[_], G[_]] extends InvariantFunctor[F] {
- implicit def G: InvariantFunctor[G]
- ////
- import Isomorphism._
- def iso: F <~> G
- override def xmap[A, B](ma: F[A], f: A => B, g: B => A): F[B] =
- iso.from(G.xmap(iso.to(ma), f, g))
- ////
- }