Add Semigroupal for Monoidal hierarchy

- Make (new) Semigroupal extend Functor - Add Monoidal and associated tests - Applicative extends Monoidal
typelevel · Jan 10, 2016 · 57824dd · 57824dd
1 parent 0529841
commit 57824dd
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diff --git a/core/src/main/scala/cats/Applicative.scala b/core/src/main/scala/cats/Applicative.scala
@@ -12,7 +12,7 @@ import simulacrum.typeclass
  *
  * Must obey the laws defined in cats.laws.ApplicativeLaws.
  */
-@typeclass trait Applicative[F[_]] extends Apply[F] { self =>
+@typeclass trait Applicative[F[_]] extends Apply[F] with Monoidal[F] { self =>
 
   /**
    * `pure` lifts any value into the Applicative Functor.
@@ -26,7 +26,7 @@ import simulacrum.typeclass
    *
    * This variant supports optional laziness.
    */
-  def pureEval[A](x: Eval[A]): F[A] = pure(x.value)
+  override def pureEval[A](x: Eval[A]): F[A] = pure(x.value)
 
   /**
    * Two sequentially dependent Applicatives can be composed.

diff --git a/core/src/main/scala/cats/Apply.scala b/core/src/main/scala/cats/Apply.scala
@@ -8,7 +8,7 @@ import simulacrum.typeclass
  * Must obey the laws defined in cats.laws.ApplyLaws.
  */
 @typeclass(excludeParents=List("ApplyArityFunctions"))
-trait Apply[F[_]] extends Functor[F] with Monoidal[F] with ApplyArityFunctions[F] { self =>
+trait Apply[F[_]] extends Functor[F] with Semigroupal[F] with ApplyArityFunctions[F] { self =>
 
   /**
    * Given a value and a function in the Apply context, applies the

diff --git a/core/src/main/scala/cats/Monoidal.scala b/core/src/main/scala/cats/Monoidal.scala
@@ -8,8 +8,16 @@ import simulacrum.typeclass
  *
  * It is worth noting that the couple Monoidal and [[Functor]] is interdefinable with [[Apply]].
  */
-@typeclass trait Monoidal[F[_]] {
-  def product[A, B](fa: F[A], fb: F[B]): F[(A, B)]
-}
+@typeclass trait Monoidal[F[_]] extends Semigroupal[F] {
+  /**
+   * `pure` lifts any value into the lax monoidal functor.
+   */
+  def pure[A](x: A): F[A]
 
-object Monoidal extends MonoidalArityFunctions
+  /**
+   * `pureEval` lifts any value into the lax monoidal functor.
+   *
+   * This variant supports optional laziness.
+   */
+  def pureEval[A](x: Eval[A]): F[A] = pure(x.value)
+}
diff --git a/core/src/main/scala/cats/Semigroupal.scala b/core/src/main/scala/cats/Semigroupal.scala
@@ -0,0 +1,16 @@
+package cats
+
+import simulacrum.typeclass
+
+/**
+ * [[Semigroupal]] generalizes [[Functor]] by allowing functions of any
+ * arity to be applied to an effectful value. It encodes this by pairing
+ * together two effectful values (which can then be extended to be three
+ * or more) within a context, which can then be mapped over via the [[Functor]]
+ * instance.
+ */
+@typeclass trait Semigroupal[F[_]] extends Functor[F] {
+  def product[A, B](fa: F[A], fb: F[B]): F[(A, B)]
+}
+
+object Semigroupal extends SemigroupalArityFunctions
diff --git a/core/src/main/scala/cats/syntax/all.scala b/core/src/main/scala/cats/syntax/all.scala
@@ -3,7 +3,6 @@ package syntax
 
 trait AllSyntax
     extends ApplySyntax
-    with MonoidalSyntax
     with BifunctorSyntax
     with CoflatMapSyntax
     with ComonadSyntax
@@ -25,6 +24,7 @@ trait AllSyntax
     with ProfunctorSyntax
     with ReducibleSyntax
     with SemigroupSyntax
+    with SemigroupalSyntax
     with SemigroupKSyntax
     with Show.ToShowOps
     with SplitSyntax

diff --git a/core/src/main/scala/cats/syntax/monoidal.scala b/core/src/main/scala/cats/syntax/monoidal.scala
@@ -1,25 +1,25 @@
 package cats
 package syntax
 
-trait MonoidalSyntax1 {
-  implicit def monoidalSyntaxU[FA](fa: FA)(implicit U: Unapply[Monoidal, FA]): MonoidalOps[U.M, U.A] =
-    new MonoidalOps[U.M, U.A] {
+trait SemigroupalSyntax1 {
+  implicit def monoidalSyntaxU[FA](fa: FA)(implicit U: Unapply[Semigroupal, FA]): SemigroupalOps[U.M, U.A] =
+    new SemigroupalOps[U.M, U.A] {
       val self = U.subst(fa)
       val typeClassInstance = U.TC
     }
 }
 
-trait MonoidalSyntax extends MonoidalSyntax1 {
-  implicit def monoidalSyntax[F[_], A](fa: F[A])(implicit F: Monoidal[F]): MonoidalOps[F, A] =
-    new MonoidalOps[F, A] {
+trait SemigroupalSyntax extends SemigroupalSyntax1 {
+  implicit def monoidalSyntax[F[_], A](fa: F[A])(implicit F: Semigroupal[F]): SemigroupalOps[F, A] =
+    new SemigroupalOps[F, A] {
       val self = fa
       val typeClassInstance = F
     }
 }
 
-abstract class MonoidalOps[F[_], A] extends Monoidal.Ops[F, A] {
-  def |@|[B](fb: F[B]): MonoidalBuilder[F]#MonoidalBuilder2[A, B] =
-    new MonoidalBuilder[F] |@| self |@| fb
+abstract class SemigroupalOps[F[_], A] extends Semigroupal.Ops[F, A] {
+  def |@|[B](fb: F[B]): SemigroupalBuilder[F]#SemigroupalBuilder2[A, B] =
+    new SemigroupalBuilder[F] |@| self |@| fb
 
   def *>[B](fb: F[B])(implicit F: Functor[F]): F[B] = F.map(typeClassInstance.product(self, fb)) { case (a, b) => b }
 

diff --git a/core/src/main/scala/cats/syntax/package.scala b/core/src/main/scala/cats/syntax/package.scala
@@ -3,7 +3,6 @@ package cats
 package object syntax {
   object all extends AllSyntax
   object apply extends ApplySyntax
-  object monoidal extends MonoidalSyntax
   object bifunctor extends BifunctorSyntax
   object coflatMap extends CoflatMapSyntax
   object comonad extends ComonadSyntax
@@ -23,6 +22,7 @@ package object syntax {
   object partialOrder extends PartialOrderSyntax
   object profunctor extends ProfunctorSyntax
   object semigroup extends SemigroupSyntax
+  object semigroupal extends SemigroupalSyntax
   object semigroupk extends SemigroupKSyntax
   object show extends Show.ToShowOps
   object split extends SplitSyntax

diff --git a/laws/src/main/scala/cats/laws/ApplicativeLaws.scala b/laws/src/main/scala/cats/laws/ApplicativeLaws.scala
@@ -7,7 +7,7 @@ import cats.syntax.functor._
 /**
  * Laws that must be obeyed by any `Applicative`.
  */
-trait ApplicativeLaws[F[_]] extends ApplyLaws[F] {
+trait ApplicativeLaws[F[_]] extends ApplyLaws[F] with MonoidalLaws[F] {
   implicit override def F: Applicative[F]
 
   def applicativeIdentity[A](fa: F[A]): IsEq[F[A]] =

diff --git a/laws/src/main/scala/cats/laws/ApplyLaws.scala b/laws/src/main/scala/cats/laws/ApplyLaws.scala
@@ -7,7 +7,7 @@ import cats.syntax.functor._
 /**
  * Laws that must be obeyed by any `Apply`.
  */
-trait ApplyLaws[F[_]] extends FunctorLaws[F] with MonoidalLaws[F] {
+trait ApplyLaws[F[_]] extends FunctorLaws[F] with SemigroupalLaws[F] {
   implicit override def F: Apply[F]
 
   def applyComposition[A, B, C](fa: F[A], fab: F[A => B], fbc: F[B => C]): IsEq[F[C]] = {

diff --git a/laws/src/main/scala/cats/laws/MonoidalLaws.scala b/laws/src/main/scala/cats/laws/MonoidalLaws.scala
@@ -1,18 +1,20 @@
 package cats
 package laws
 
-trait MonoidalLaws[F[_]] {
+trait MonoidalLaws[F[_]] extends SemigroupalLaws[F] {
 
   implicit def F: Monoidal[F]
 
-  def monoidalAssociativity[A, B, C](fa: F[A], fb: F[B], fc: F[C]): (F[(A, (B, C))], F[((A, B), C)]) =
-    (F.product(fa, F.product(fb, fc)), F.product(F.product(fa, fb), fc))
+  def leftIdentity[A](fa: F[A]): IsEq[F[A]] =
+    F.map(F.product(F.pure(()), fa))(_._2) <-> fa
 
+  def rightIdentity[A](fa: F[A]): IsEq[F[A]] =
+    F.map(F.product(fa, F.pure(())))(_._1) <-> fa
 }
 
 object MonoidalLaws {
 
   def apply[F[_]](implicit ev: Monoidal[F]): MonoidalLaws[F] =
     new MonoidalLaws[F] { val F = ev }
 
-}
+}
diff --git a/laws/src/main/scala/cats/laws/SemigroupalLaws.scala b/laws/src/main/scala/cats/laws/SemigroupalLaws.scala
@@ -0,0 +1,18 @@
+package cats
+package laws
+
+trait SemigroupalLaws[F[_]] {
+
+  implicit def F: Semigroupal[F]
+
+  def semigroupalAssociativity[A, B, C](fa: F[A], fb: F[B], fc: F[C]): (F[(A, (B, C))], F[((A, B), C)]) =
+    (F.product(fa, F.product(fb, fc)), F.product(F.product(fa, fb), fc))
+
+}
+
+object SemigroupalLaws {
+
+  def apply[F[_]](implicit ev: Semigroupal[F]): SemigroupalLaws[F] =
+    new SemigroupalLaws[F] { val F = ev }
+
+}
diff --git a/laws/src/main/scala/cats/laws/discipline/AlternativeTests.scala b/laws/src/main/scala/cats/laws/discipline/AlternativeTests.scala
@@ -2,7 +2,7 @@ package cats
 package laws
 package discipline
 
-import cats.laws.discipline.MonoidalTests.Isomorphisms
+import cats.laws.discipline.SemigroupalTests.Isomorphisms
 import org.scalacheck.Arbitrary
 import org.scalacheck.Prop
 import Prop._

diff --git a/laws/src/main/scala/cats/laws/discipline/ApplicativeTests.scala b/laws/src/main/scala/cats/laws/discipline/ApplicativeTests.scala
@@ -2,12 +2,12 @@ package cats
 package laws
 package discipline
 
-import cats.laws.discipline.MonoidalTests.Isomorphisms
+import cats.laws.discipline.SemigroupalTests.Isomorphisms
 import org.scalacheck.Arbitrary
 import org.scalacheck.Prop
 import Prop._
 
-trait ApplicativeTests[F[_]] extends ApplyTests[F] {
+trait ApplicativeTests[F[_]] extends ApplyTests[F] with MonoidalTests[F] {
   def laws: ApplicativeLaws[F]
 
   def applicative[A: Arbitrary, B: Arbitrary, C: Arbitrary](implicit
@@ -22,13 +22,17 @@ trait ApplicativeTests[F[_]] extends ApplyTests[F] {
     EqFABC: Eq[F[(A, B, C)]],
     iso: Isomorphisms[F]
   ): RuleSet = {
-    new DefaultRuleSet(
-      name = "applicative",
-      parent = Some(apply[A, B, C]),
-      "applicative identity" -> forAll(laws.applicativeIdentity[A] _),
-      "applicative homomorphism" -> forAll(laws.applicativeHomomorphism[A, B] _),
-      "applicative interchange" -> forAll(laws.applicativeInterchange[A, B] _),
-      "applicative map" -> forAll(laws.applicativeMap[A, B] _))
+    new RuleSet {
+      def name: String = "applicative"
+      def bases: Seq[(String, RuleSet)] = Nil
+      def parents: Seq[RuleSet] = Seq(apply[A, B, C], monoidal[A, B, C])
+      def props: Seq[(String, Prop)] = Seq(
+        "applicative identity" -> forAll(laws.applicativeIdentity[A] _),
+        "applicative homomorphism" -> forAll(laws.applicativeHomomorphism[A, B] _),
+        "applicative interchange" -> forAll(laws.applicativeInterchange[A, B] _),
+        "applicative map" -> forAll(laws.applicativeMap[A, B] _)
+      )
+    }
   }
 }
 

diff --git a/laws/src/main/scala/cats/laws/discipline/ApplyTests.scala b/laws/src/main/scala/cats/laws/discipline/ApplyTests.scala
@@ -2,12 +2,12 @@ package cats
 package laws
 package discipline
 
-import cats.laws.discipline.MonoidalTests.Isomorphisms
+import cats.laws.discipline.SemigroupalTests.Isomorphisms
 import org.scalacheck.Arbitrary
 import org.scalacheck.Prop
 import Prop._
 
-trait ApplyTests[F[_]] extends FunctorTests[F] with MonoidalTests[F] {
+trait ApplyTests[F[_]] extends FunctorTests[F] with SemigroupalTests[F] {
   def laws: ApplyLaws[F]
 
   def apply[A: Arbitrary, B: Arbitrary, C: Arbitrary](implicit
@@ -22,7 +22,7 @@ trait ApplyTests[F[_]] extends FunctorTests[F] with MonoidalTests[F] {
     iso: Isomorphisms[F]
   ): RuleSet = new RuleSet {
     val name = "apply"
-    val parents = Seq(functor[A, B, C], monoidal[A, B, C])
+    val parents = Seq(functor[A, B, C], semigroupal[A, B, C])
     val bases = Seq.empty
     val props = Seq("apply composition" -> forAll(laws.applyComposition[A, B, C] _))
   }

diff --git a/laws/src/main/scala/cats/laws/discipline/BimonadTests.scala b/laws/src/main/scala/cats/laws/discipline/BimonadTests.scala
@@ -2,7 +2,7 @@ package cats
 package laws
 package discipline
 
-import cats.laws.discipline.MonoidalTests.Isomorphisms
+import cats.laws.discipline.SemigroupalTests.Isomorphisms
 import org.scalacheck.Arbitrary
 import org.scalacheck.Prop
 import Prop._

diff --git a/laws/src/main/scala/cats/laws/discipline/FlatMapTests.scala b/laws/src/main/scala/cats/laws/discipline/FlatMapTests.scala
@@ -2,7 +2,7 @@ package cats
 package laws
 package discipline
 
-import cats.laws.discipline.MonoidalTests.Isomorphisms
+import cats.laws.discipline.SemigroupalTests.Isomorphisms
 import org.scalacheck.Arbitrary
 import org.scalacheck.Prop
 import Prop._

diff --git a/laws/src/main/scala/cats/laws/discipline/MonadCombineTests.scala b/laws/src/main/scala/cats/laws/discipline/MonadCombineTests.scala
@@ -2,7 +2,7 @@ package cats
 package laws
 package discipline
 
-import cats.laws.discipline.MonoidalTests.Isomorphisms
+import cats.laws.discipline.SemigroupalTests.Isomorphisms
 import org.scalacheck.Arbitrary
 import org.scalacheck.Prop
 import Prop._

diff --git a/laws/src/main/scala/cats/laws/discipline/MonadErrorTests.scala b/laws/src/main/scala/cats/laws/discipline/MonadErrorTests.scala
@@ -3,7 +3,7 @@ package laws
 package discipline
 
 import cats.data.{ Xor, XorT }
-import cats.laws.discipline.MonoidalTests.Isomorphisms
+import cats.laws.discipline.SemigroupalTests.Isomorphisms
 import cats.laws.discipline.arbitrary._
 import cats.laws.discipline.eq.unitEq
 import org.scalacheck.{Arbitrary, Prop}

diff --git a/laws/src/main/scala/cats/laws/discipline/MonadFilterTests.scala b/laws/src/main/scala/cats/laws/discipline/MonadFilterTests.scala
@@ -2,7 +2,7 @@ package cats
 package laws
 package discipline
 
-import cats.laws.discipline.MonoidalTests.Isomorphisms
+import cats.laws.discipline.SemigroupalTests.Isomorphisms
 import org.scalacheck.Arbitrary
 import org.scalacheck.Prop
 import Prop._

diff --git a/laws/src/main/scala/cats/laws/discipline/MonadReaderTests.scala b/laws/src/main/scala/cats/laws/discipline/MonadReaderTests.scala
@@ -2,7 +2,7 @@ package cats
 package laws
 package discipline
 
-import cats.laws.discipline.MonoidalTests.Isomorphisms
+import cats.laws.discipline.SemigroupalTests.Isomorphisms
 import org.scalacheck.{Arbitrary, Prop}
 import org.scalacheck.Prop.forAll
 

diff --git a/laws/src/main/scala/cats/laws/discipline/MonadStateTests.scala b/laws/src/main/scala/cats/laws/discipline/MonadStateTests.scala
@@ -2,7 +2,7 @@ package cats
 package laws
 package discipline
 
-import cats.laws.discipline.MonoidalTests.Isomorphisms
+import cats.laws.discipline.SemigroupalTests.Isomorphisms
 import eq.unitEq
 import org.scalacheck.{Arbitrary, Prop}
 import org.scalacheck.Prop.forAll

diff --git a/laws/src/main/scala/cats/laws/discipline/MonadTests.scala b/laws/src/main/scala/cats/laws/discipline/MonadTests.scala
@@ -2,7 +2,7 @@ package cats
 package laws
 package discipline
 
-import cats.laws.discipline.MonoidalTests.Isomorphisms
+import cats.laws.discipline.SemigroupalTests.Isomorphisms
 import org.scalacheck.Arbitrary
 import org.scalacheck.Prop
 import Prop._

diff --git a/laws/src/main/scala/cats/laws/discipline/MonoidalTests.scala b/laws/src/main/scala/cats/laws/discipline/MonoidalTests.scala
@@ -7,40 +7,27 @@ import org.scalacheck.Prop
 import Prop._
 import org.typelevel.discipline.Laws
 
-trait MonoidalTests[F[_]] extends Laws {
+trait MonoidalTests[F[_]] extends SemigroupalTests[F] {
   def laws: MonoidalLaws[F]
 
   def monoidal[A : Arbitrary, B : Arbitrary, C : Arbitrary](implicit
-    iso: MonoidalTests.Isomorphisms[F],
+    iso: SemigroupalTests.Isomorphisms[F],
     ArbFA: Arbitrary[F[A]],
     ArbFB: Arbitrary[F[B]],
     ArbFC: Arbitrary[F[C]],
+    EqFA: Eq[F[A]],
     EqFABC: Eq[F[(A, B, C)]]
   ): RuleSet = {
     new DefaultRuleSet(
       name = "monoidal",
-      parent = None,
-      "monoidal associativity" -> forAll((fa: F[A], fb: F[B], fc: F[C]) => iso.associativity(laws.monoidalAssociativity(fa, fb, fc)))
+      parent = Some(semigroupal[A, B, C]),
+      "monoidal left identity" -> forAll(laws.leftIdentity[A] _),
+      "monoidal right identity" -> forAll(laws.rightIdentity[A] _)
     )
   }
 }
 
 object MonoidalTests {
-  def apply[F[_] : Monoidal](implicit ev: Isomorphisms[F]): MonoidalTests[F] =
+  def apply[F[_] : Monoidal](implicit ev: SemigroupalTests.Isomorphisms[F]): MonoidalTests[F] =
     new MonoidalTests[F] { val laws: MonoidalLaws[F] = MonoidalLaws[F] }
-
-  trait Isomorphisms[F[_]] {
-    def associativity[A, B, C](fs: (F[(A, (B, C))], F[((A, B), C)]))(implicit EqFABC: Eq[F[(A, B, C)]]): Prop
-  }
-
-  object Isomorphisms {
-    import algebra.laws._
-    implicit def invariant[F[_]](implicit F: functor.Invariant[F]): Isomorphisms[F] =
-      new Isomorphisms[F] {
-        def associativity[A, B, C](fs: (F[(A, (B, C))], F[((A, B), C)]))(implicit EqFABC: Eq[F[(A, B, C)]]) =
-          F.imap(fs._1) { case (a, (b, c)) => (a, b, c) } { case (a, b, c) => (a, (b, c)) } ?==
-          F.imap(fs._2) { case ((a, b), c) => (a, b, c) } { case (a, b, c) => ((a, b), c) }
-      }
-  }
-
-}
+}