Add hunchbacked Quasimonad; both friendly and a monster

build.sbt

@@ -1,11 +1,13 @@
 lazy val root = (project in file("."))
   .settings(noPublishSettings)
   .aggregate(coreJVM, coreJS)
+  .aggregate(quasiJVM, quasiJS)
   .aggregate(testsJVM, testsJS)
   .aggregate(examplesCatsJVM, examplesCatsJS)
   .aggregate(examplesScalazJVM, examplesScalazJS)
   .aggregate(bench)
   .aggregate(corezJVM, corezJS)
+  .aggregate(quasizJVM, quasizJS)
   .aggregate(testszJVM, testszJS)
   .aggregate(readme, docs)
 
@@ -15,8 +17,8 @@ lazy val core = module("core", hideFolder = true)
     flags    = "cats" :: Nil,
     yaxScala = true))
   .crossDepSettings(
-    %%("cats-core"),
-    %%("cats-free"))
+    "org.typelevel" %% "cats-core" % "1.0.0-RC1",
+    "org.typelevel" %% "cats-free" % "1.0.0-RC1")
 
 lazy val coreJVM = core.jvm
 lazy val coreJS  = core.js
@@ -32,6 +34,26 @@ lazy val corez = module("core", hideFolder = true, prefixSuffix = "z")
 lazy val corezJVM = corez.jvm
 lazy val corezJS  = corez.js
 
+lazy val quasi = module("quasi", hideFolder = true)
+  .dependsOn(core)
+  .settings(macroSettings)
+  .settings(yax(file("modules/quasi/src/main/scala"), Compile,
+    flags    = "cats" :: Nil,
+    yaxScala = true))
+
+lazy val quasiJVM = quasi.jvm
+lazy val quasiJS  = quasi.js
+
+lazy val quasiz = module("quasi", hideFolder = true, prefixSuffix = "z")
+  .dependsOn(corez)
+  .settings(macroSettings)
+  .settings(yax(file("modules/quasi/src/main/scala"), Compile,
+    flags    = "scalaz" :: Nil,
+    yaxScala = true))
+
+lazy val quasizJVM = quasiz.jvm
+lazy val quasizJS  = quasiz.js
+
 lazy val tests = module("tests", hideFolder = true)
   .dependsOn(core)
   .settings(noPublishSettings)

modules/quasi/src/main/scala/iota/quasi/quasi/package.scala

@@ -0,0 +1,240 @@
+package iota  //#=cats
+package iotaz //#=scalaz
+
+import cats._  //#=cats
+import scalaz._ //#=scalaz
+
+import TListK.::
+
+package object quasi {
+
+  type Quasi[S[_], A] = quasiImpl.Quasi[S, A]
+  type Concur[S[_], A] = quasiImpl.Concur[S, A]
+  type Subseq[S[_], A] = quasiImpl.Subseq[S, A]
+
+  implicit final class QuasiOps[S[_], A](val quasi: Quasi[S, A]) extends AnyVal {
+    def concur: Concur[S, A] = quasiImpl.toConcur(quasi)
+    def subseq: Subseq[S, A] = quasiImpl.toSubseq(quasi)
+  }
+
+  final implicit class ConcurOps[S[_], A](val concur: Concur[S, A]) extends AnyVal {
+    def quasi: Quasi[S, A] = quasiImpl.fromConcur(concur)
+    def subseq: Subseq[S, A] = quasi.subseq
+
+    def ap[B](f: Concur[S, A => B]): Concur[S, B] =
+      quasiImpl.ap(f.quasi)(concur.quasi).concur
+
+    def map[B](f: A => B): Concur[S, B] = ap(Quasi.pure(f).concur)
+  }
+
+  final implicit class SubseqOps[S[_], A](val subseq: Subseq[S, A]) extends AnyVal {
+    def quasi: Quasi[S, A] = quasiImpl.fromSubseq(subseq)
+    def concur: Concur[S, A] = quasi.concur
+
+    def map[B](f: A => B): Subseq[S, B] =
+      flatMap(a => Quasi.pure(f(a)).subseq)
+
+    def flatMap[B](f: A => Subseq[S, B]): Subseq[S, B] =
+      quasiImpl.flatMap(subseq.quasi)(f.andThen(_.quasi)).subseq
+  }
+
+  implicit def subseqMonad[S[_]]: Monad[Subseq[S, ?]] = new Monad[Subseq[S, ?]] {
+    def pure[A](a: A): Subseq[S, A] = Quasi.pure(a).subseq
+    def flatMap[A, B](fa: Subseq[S, A])(f: A => Subseq[S, B]): Subseq[S, B] =
+      fa.flatMap(f)
+
+    def tailRecM[A, B](a: A)(f: A => Subseq[S, Either[A, B]]): Subseq[S, B] = ???
+  }
+
+  implicit def concurApplicative[S[_]]: Applicative[Concur[S, ?]] = new Applicative[Concur[S, ?]] {
+    def pure[A](a: A): Concur[S, A] = Quasi.pure(a).concur
+    def ap[A, B](ff: Concur[S, A => B])(fa: Concur[S, A]): Concur[S, B] =
+      fa.ap(ff)
+  }
+
+  implicit def subseqConcurParallel[S[_]]: Parallel[Subseq[S, ?], Concur[S, ?]] =
+    new Parallel[Subseq[S, ?], Concur[S, ?]] {
+      val parallel: Subseq[S, ?] ~> Concur[S, ?] =
+        λ[Subseq[S, ?] ~> Concur[S, ?]](_.quasi.concur)
+      val sequential: Concur[S, ?] ~> Subseq[S, ?] =
+        λ[Concur[S, ?] ~> Subseq[S, ?]](_.quasi.subseq)
+      val applicative: Applicative[Concur[S, ?]] = Applicative[Concur[S, ?]]
+      val monad: Monad[Subseq[S, ?]] = Monad[Subseq[S, ?]]
+    }
+
+  object Quasi {
+
+    def pure[S[_], A](a: A): Quasi[S, A] = quasiImpl.pure(a)
+    def liftF[S[_], A](value: S[A]): Quasi[S, A] = quasiImpl.suspend(value)
+
+    def toConcur[S[_]]: Quasi[S, ?] ~> Concur[S, ?] =
+      λ[Quasi[S, ?] ~> Concur[S, ?]](_.concur)
+
+    def toSubseq[S[_]]: Quasi[S, ?] ~> Subseq[S, ?] =
+      λ[Quasi[S, ?] ~> Subseq[S, ?]](_.subseq)
+
+    def foldMap[S[_], M[_], A](quasi: Quasi[S, A])(f: S ~> M)(implicit M: Parallel[M, M]): M[A] =
+      quasiImpl.evaluator(f, M.monad, M.applicative)(quasi)
+  }
+
+  private[quasi] sealed trait QuasiImpl {
+    type Quasi [S[_], A]
+    type Concur[S[_], A]
+    type Subseq[S[_], A]
+
+    type Evaluator[S[_], M[_]] = Quasi[S, ?] ~> M
+
+    def toConcur[S[_], A](quasi: Quasi[S, A]): Concur[S, A]
+    def fromConcur[S[_], A](subseq: Concur[S, A]): Quasi[S, A]
+    def toSubseq[S[_], A](quasi: Quasi[S, A]): Subseq[S, A]
+    def fromSubseq[S[_], A](subseq: Subseq[S, A]): Quasi[S, A]
+
+    def pure[S[_], A](a: A): Quasi[S, A]
+    def suspend[S[_], A](value: S[A]): Quasi[S, A]
+    def flatMap[S[_], A, B](fa: Quasi[S, A])(f: A => Quasi[S, B]): Quasi[S, B]
+    def ap[S[_], A, B](ff: Quasi[S, A => B])(fa: Quasi[S, A]): Quasi[S, B]
+
+    def evaluator[S[_], Z[_]](
+      f: S ~> Z,
+      Zm: Monad[Z],
+      Za: Applicative[Z]
+    ): Evaluator[S, Z]
+  }
+
+  private[quasi] val quasiImpl: QuasiImpl = new QuasiImpl {
+    type Quasi [S[_], A] = CopK[Effects[S], A]
+    type Concur[S[_], A] = CopK[Effects[S], A]
+    type Subseq[S[_], A] = CopK[Effects[S], A]
+
+    type Effects[S[_]] =
+      Pure    [S,    ?] ::
+      Suspend [S,    ?] ::
+      FlatMap [S, _, ?] ::
+      Ap      [S, _, ?] ::
+      Raise   [S, _, ?] ::
+      Handle  [S, _, ?] ::
+      TNilK
+
+    type Pure[S[_], A] = A
+    type Suspend[S[_], A] = S[A]
+    final case class FlatMap[S[_], A, B](fa: Quasi[S, A], f: A => Quasi[S, B])
+    final case class Ap[S[_], A, B](ff: Quasi[S, A => B], fa: Quasi[S, A])
+    type Raise[S[_], E, A] = E
+    final case class Handle[S[_], E, A](fe: E => Quasi[S, A])
+    //type Handle[S[_], E, A] = E => Quasi[S, A]
+
+    def toConcur[S[_], A](quasi: Quasi[S, A]): Concur[S, A] = quasi
+    def fromConcur[S[_], A](subseq: Concur[S, A]): Quasi[S, A] = subseq
+    def toSubseq[S[_], A](quasi: Quasi[S, A]): Subseq[S, A] = quasi
+    def fromSubseq[S[_], A](subseq: Subseq[S, A]): Quasi[S, A] = subseq
+
+    def pure[S[_], A](a: A): Quasi[S, A] =
+      CopK.unsafeApply[Effects[S], Pure[S, ?], A](0, a)
+
+    def suspend[S[_], A](value: S[A]): Quasi[S, A] =
+      CopK.unsafeApply[Effects[S], Suspend[S, ?], A](1, value)
+
+    def flatMap[S[_], A, B](fa: Quasi[S, A])(f: A => Quasi[S, B]): Quasi[S, B] =
+      CopK.unsafeApply[Effects[S], FlatMap[S, A, ?], B](2, FlatMap[S, A, B](fa, f))
+
+    def ap[S[_], A, B](ff: Quasi[S, A => B])(fa: Quasi[S, A]): Quasi[S, B] =
+      CopK.unsafeApply[Effects[S], Ap[S, A, ?], B](3, Ap[S, A, B](ff, fa))
+
+    def evaluator[S[_], Z[_]](
+      f: S ~> Z,
+      Zm: Monad[Z],
+      Za: Applicative[Z]
+    ): Evaluator[S, Z] = new Evaluator[S, Z] {
+      def apply[A](quasi: Quasi[S, A]): Z[A] =
+        Zm.tailRecM(quasi)(q => (q.index: @scala.annotation.switch) match {
+          case 0 =>
+            val a: A = q.value.asInstanceOf[A]
+            Zm.pure(Right(a))
+          case 1 =>
+            val sa: S[A] = q.value.asInstanceOf[S[A]]
+            Zm.map(f(sa))(Right(_))
+          case 2 =>
+            val n: FlatMap[S, Any, A] = q.value.asInstanceOf[FlatMap[S, Any, A]]
+            Zm.map(this(n.fa))(z => Left(n.f(z)))
+          case 3 =>
+            val n: Ap[S, Any, A] = q.value.asInstanceOf[Ap[S, Any, A]]
+            Zm.map(Za.ap(this(n.ff))(this(n.fa)))(Right(_))
+          case _ => scala.Predef.???
+        })
+    }
+
+  }
+
+}
+
+// example
+//#+cats
+import cats.implicits._
+package quasi {
+
+  object Example {
+
+    def main(args: Array[String]): Unit = {
+
+      trait MathOp[A]
+      case class ConstInt(value: Int) extends MathOp[Int]
+      case class Add(x: Int, y: Int) extends MathOp[Int]
+      case class Neg(x: Int) extends MathOp[Int]
+
+      trait Math[F[_]] { underlying =>
+        def const(value: Int): F[Int]
+        def add(x: Int, y: Int): F[Int]
+        def neg(x: Int): F[Int]
+
+        final def mapK[G[_]](f: F ~> G): Math[G] = new Math[G] {
+          def const(value: Int): G[Int] = f(underlying.const(value))
+          def add(x: Int, y: Int): G[Int] = f(underlying.add(x, y))
+          def neg(x: Int): G[Int] = f(underlying.neg(x))
+        }
+      }
+
+      object Math {
+        def quasi: Math[Quasi[MathOp, ?]] = new Math[Quasi[MathOp, ?]] {
+          def const(value: Int): Quasi[MathOp, Int] = Quasi.liftF(ConstInt(value))
+          def add(x: Int, y: Int): Quasi[MathOp, Int] = Quasi.liftF(Add(x, y))
+          def neg(x: Int): Quasi[MathOp, Int] = Quasi.liftF(Neg(x))
+        }
+
+        def concur: Math[Concur[MathOp, ?]] = quasi.mapK[Concur[MathOp, ?]](Quasi.toConcur)
+        def subseq: Math[Subseq[MathOp, ?]] = quasi.mapK[Subseq[MathOp, ?]](Quasi.toSubseq)
+      }
+
+      val interp: MathOp ~> Id = λ[MathOp ~> Id] {
+        case ConstInt(value) => value
+        case Add(x, y) => x + y
+        case Neg(x) => -x
+      }
+
+      val math = Math.subseq
+
+      val program0 = for {
+        x <- math.const(1)
+        y <- math.const(2)
+        z <- math.add(x, y)
+      } yield z + 10
+
+      val program1 = for {
+        a <- math.const(100)
+        b <- math.neg(a)
+      } yield a + b
+
+      val program2 = for {
+        foo <- math.const(0)
+        bar <- List(program0, program1).parSequence
+      } yield bar.foldLeft(foo)(_ + _)
+
+      scala.Predef.println(program2)
+
+      val res = Quasi.foldMap(program2.quasi)(interp)
+      scala.Predef.println(res)
+
+    }
+
+  }
+}
+//#-cats