Add ContravariantMonoidal #2034

stephen-lazaro · 2017-11-22T05:36:14Z

Adds the Divisible typeclass as discussed in #1935.
I went ahead and opened this against core though it was suggested it might belong more in more, just because there seems to be thoughts and discussion around #1940 still. This way, we can get something that's relatively ready to merge when/if more is a thing. I'd be happy to move things over at that time.

Anyway, some notes:

I switched the names from divide and conquer to contramap2 and unit respectively, since that seems a little more in line with the naming standards in cats. Welcome to bike shedding on that front.
While implementing, I noticed that the only real contribution Divisible gives is the presence of a left and right unit along the diagonal, since in point of fact contramap2 is perfectly well implementable on ContravariantSemigroupal as:

def contramap2[A, B, C](fb: F[B], fc: F[C])(f: A => (B, C)): F[A] =
  contramap(product(fb, fc))(f)

I could see the impedance of adding another typeclass being high enough that maybe it'd be more reasonable just to add some enrichment to ContravariantSemigroupal. I could also see having both, or just Divisible. Not sure what the most desirable outcome would be here.

I did not add an instance for Show because unit seems a little against the spirit of the thing, for that particular instance. The only lawful instance AFAICT is the constantly empty string unit induced by the A => B where B : Monoid.
The branch name is a bit of a misnomer because I decided not to implement Decideable cause honestly I had trouble parsing the laws on that typeclass in the primary source here:
https://hackage.haskell.org/package/contravariant-1.4/docs/Data-Functor-Contravariant-Divisible.html#t:Divisible
I'll probably take another stab at it unless someone beats me to it.
Added some tut documentation, but am happy to drop it entirely if its unwanted.
I couldn't figure out how to the higher arity stuff works in Apply so I didn't take a shot implementing a dual here. If someone points me in the right direction and it is desired, I'd be happy to try.
I added an attribution to ekmett in the Scala doc for Divisible. Hopefully, it satisfies that requirement, but if we have a format I've not met, please do let me know.

First time contributing to this repo so I'm sure I missed something. Thanks preemptively for your solicitous review, as well as your forbearance. :)

Adds Divisible typeclass Adds laws for Divisible and tests for relevant instances Adds documentation for Divisible typeclass Adds instances for: - Const - Nested - Tuple2K - Function with Monoid codomain - ReaderT - Kleisli - IdT - Eq - Equiv - Order - Ordering - OptionT - WriterT - IndexedStateT Adds tests

julienrf · 2017-11-22T07:40:24Z

I did not add an instance for Show because unit seems a little against the spirit of the thing, for that particular instance.

Indeed, for some typeclasses there is no sensible unit implementation. I think this is why we should have both Divisible and ContravariantSemigroupal.

Also, since we don’t use the names divide and conquer I’m not sure the Divisible name makes sense. To me it is more intuitive to think of it as a ContravariantMonoidal (since it extends ContravariantSemigroupal with a unit method).

julienrf · 2017-11-22T07:42:59Z

core/src/main/scala/cats/Divisible.scala

+   * Given two values in the Divisible context, and a function producing a value of both types,
+   * yields an element of the domain of the function lifted into the context.
+   */
+  def contramap2[A, B, C](fb: F[B], fc: F[C])(f: A => (B, C)): F[A]


Why not provide a default implementation in terms of contramap and product? (like we do for covariant semigroupal: https://github.com/typelevel/cats/blob/master/core/src/main/scala/cats/Apply.scala#L44-L50 )

Sure, that makes sense, consistency is pretty valuable. I mostly went this approach based on the primary document.

Renames to ContravariantMonoidal Derives contramap2 from product, contramap Moves contramap2 to ContravariantSemigroupal

stephen-lazaro · 2017-11-23T04:49:00Z

Renamed to ContravariantMonoidal and used product and contramap to implement contramap2 on ContravariantSemigroupal.

julienrf · 2017-11-23T07:46:25Z

core/src/main/scala/cats/Composed.scala

@@ -113,14 +113,17 @@ private[cats] trait ComposedContravariantCovariant[F[_], G[_]] extends Contravar
    F.contramap(fga)(gb => G.map(gb)(f))
 }

-private[cats] trait ComposedApplicativeDivisible[F[_], G[_]] extends Divisible[λ[α => F[G[α]]]] { outer =>
+private[cats] trait ComposedApplicativeContravariantMonoidal[F[_], G[_]] extends ContravariantMonoidal[λ[α => F[G[α]]]] { outer =>


I wouldn’t repeat Monoidal here because Applicative already implies Monoidal since they are equivalent (see also this detailed explanation: https://stackoverflow.com/questions/23316255/lax-monoidal-functors-with-a-different-monoidal-structure).

Edit: sorry I was wrong. This trait composes a covariant applicative with a contravariant one, so the naming is correct, you can ignore my comment.

The SO was a good read, anyway, it clarified some of the points on different Monoidal structures for me, so thank you.

julienrf · 2017-11-23T07:50:49Z

laws/src/main/scala/cats/laws/ContravariantMonoidalLaws.scala

+    (F.unit).contramap2(fa)(f) <-> fa.contramap(f andThen (_._2))
+
+  def contravariantMonoidalContramap2DiagonalAssociates[A](m: F[A], n: F[A], o: F[A]): IsEq[F[A]] =
+    (m.contramap2(n)(delta[A])).contramap2(o)(delta[A]) <-> m.contramap2(n.contramap2(o)(delta[A]))(delta[A])


I think this law could go to ContravariantSemigroupal

LukaJCB · 2017-11-25T08:17:56Z

core/src/main/scala/cats/Composed.scala

+    F.map(fa)(G.contramap(_)(f))
+
+  override def product[A, B](fa: F[G[A]], fb: F[G[B]]) =
+    F.map2(fa, fb)(G.product(_,_))


We need a space after the comma here :)

LukaJCB · 2017-11-25T08:18:24Z

core/src/main/scala/cats/Composed.scala

+
+  override def unit[A]: F[G[A]] = F.pure(G.unit)
+
+  override def contramap[A, B](fa: F[G[A]])(f: B => A) =


Can you add type annotations here and for product? :)

LukaJCB · 2017-11-25T09:31:39Z

docs/src/main/tut/typeclasses/contravariantsemigroupal.md

+      (a: A) => f(a) match {
+        case (b, c) => fb.run(b) && fc.run(c)
+      })
+  }


tut fails here, because contramap2 is missing an override modifier and contramap and product are unimplemented.

Good catch, thank you. Nice to have tut catch these things.

LukaJCB · 2017-11-25T09:38:11Z

core/src/main/scala/cats/ContravariantSemigroupal.scala

@@ -12,4 +12,7 @@ import simulacrum.typeclass
      def F = self
      def G = Functor[G]
    }
+
+  def contramap2[A, B, C](fb: F[B], fc: F[C])(f: A => (B, C)): F[A] =


I'm not exactly sure if we need this definition here, as we already have contramap2- contramap22 in the auto-generated SemigroupalArityFunctions. WDYT?

We could mix in the SemigroupalArityFunctions into the companion object of ContravariantSemigroupal maybe?

Ah, yes! I agree. I didn't realize they were in SemigroupalArityFunctions. I'll do that.

LukaJCB

I've left a couple of comments, I think it looks really good already, so thank you very much! Also thanks a lot to @julienrf for reviewing! :)

LukaJCB · 2017-11-25T13:14:11Z

docs/src/main/tut/typeclasses/contravariantsemigroupal.md

+source: "core/src/main/scala/cats/ContravariantSemigroupal.scala"
+scaladoc: "#cats.ContravariantSemigroupal"
+---
+# Contravariant Semigroupal


We're kind of mixing the Monoidal and the Semigroupal in this doc. Maybe we should fix it all to be ContravariantMonoidal?

Sounds good to me, I'll pin it all to ContravariantMonoidal.

stephen-lazaro · 2017-11-27T06:23:46Z

Switched everything over to use the SemigroupalArityFunctions and the TupleSemigroupalSyntax.
Thanks for reviewing, both @julienrf and @LukaJCB.
(And thank you for lending a hand on the MIMA exceptions @LukaJCB, hadn't seen that before).

LukaJCB · 2017-11-27T08:39:09Z

Seems there's still some binary compatibly issues:

Cats core: found 2 potential binary incompatibilities while checking against org.typelevel:cats-core_2.10:1.0.0-RC1  (filtered 177)�[0m
�[0m[�[31merror�[0m] �[0m * abstract method catsSyntaxContravariantSemigroupal(java.lang.Object,cats.ContravariantSemigroupal)cats.ContravariantSemigroupal#Ops in trait cats.syntax.ContravariantSemigroupalSyntax is inherited by class AllSyntax in current version.�[0m
�[0m[�[31merror�[0m] �[0m   filter with: ProblemFilters.exclude[InheritedNewAbstractMethodProblem]("cats.syntax.ContravariantSemigroupalSyntax.catsSyntaxContravariantSemigroupal")�[0m
�[0m[�[31merror�[0m] �[0m * abstract method catsSyntaxContravariantMonoidal(java.lang.Object,cats.ContravariantMonoidal)cats.syntax.ContravariantMonoidalOps in trait cats.syntax.ContravariantMonoidalSyntax is inherited by class AllSyntax in current version.�[0m
�[0m[�[31merror�[0m] �[0m   filter with: ProblemFilters.exclude[InheritedNewAbstractMethodProblem]("cats.syntax.ContravariantMonoidalSyntax.catsSyntaxContravariantMonoidal")�

If you could add those two to the build.sbt, I think we're done. Thanks again!

Edit:
I quickly added it myself :)

codecov-io · 2017-11-27T10:20:44Z

Codecov Report

Merging #2034 into master will decrease coverage by 0.6%.
The diff coverage is 90.42%.

@@            Coverage Diff             @@
##           master    #2034      +/-   ##
==========================================
- Coverage   95.25%   94.64%   -0.61%     
==========================================
  Files         305      318      +13     
  Lines        5179     5363     +184     
  Branches      126      127       +1     
==========================================
+ Hits         4933     5076     +143     
- Misses        246      287      +41

Impacted Files	Coverage Δ
...src/main/scala/cats/ContravariantSemigroupal.scala	`66.66% <ø> (ø)`	⬆️
...n/scala/cats/syntax/contravariantSemigroupal.scala	`0% <0%> (ø)`
...main/scala/cats/syntax/contravariantMonoidal.scala	`0% <0%> (ø)`
...re/src/main/scala/cats/ContravariantMonoidal.scala	`0% <0%> (ø)`
...s/laws/discipline/ContravariantMonoidalTests.scala	`100% <100%> (ø)`
core/src/main/scala/cats/data/IdT.scala	`97.61% <100%> (+0.25%)`	⬆️
core/src/main/scala/cats/data/Tuple2K.scala	`95% <100%> (+0.55%)`	⬆️
...in/scala/cats/laws/ContravariantMonoidalLaws.scala	`100% <100%> (ø)`
core/src/main/scala/cats/data/Nested.scala	`95.23% <100%> (+0.41%)`	⬆️
core/src/main/scala/cats/data/WriterT.scala	`93.13% <100%> (-1.55%)`	⬇️
... and 50 more

Continue to review full report at Codecov.

Legend - Click here to learn more
Δ = absolute <relative> (impact), ø = not affected, ? = missing data
Powered by Codecov. Last update ab5433e...6e7a1b5. Read the comment docs.

LukaJCB · 2017-11-27T10:36:29Z

core/src/main/scala/cats/ContravariantSemigroupal.scala

@@ -13,3 +13,5 @@ import simulacrum.typeclass
      def G = Functor[G]
    }
 }
+object ContravariantSemigroupal extends SemigroupalArityFunctions {


nitpick, but can we get rid of these curly braces? :)

Hah, yeah, for sure.

LukaJCB · 2017-11-27T10:44:30Z

I wonder, can we create instances for EitherK in the way we can for Applicative?

LukaJCB · 2017-11-27T16:20:27Z

docs/src/main/tut/typeclasses/contravariantmonoidal.md

+```tut:book:silent
+import cats.Contravariant
+
+trait ContravariantMonoidal[F[_]] extends Contravariant[F] {


Maybe we shouldn't use tut here as it shadows the real ContravariantMonoidal.

we could still use tut here then add a tut:reset after (explained here) so that it has no effect after.

stephen-lazaro · 2017-11-27T17:59:53Z

Yeah, that seems like a no brainer. I'll do that. Thanks for taking care of the binary compatibility issues. I think I'm not running the check correctly locally, because it keeps telling me it passes 🤔

EDIT: Doesn't look like EitherK is in the having, product breaks down since there's no sensible way to combine F[A] and G[B] in the mixed Right/Left case. Will leave to someone cleverer ;)

LukaJCB · 2017-11-27T18:34:08Z

Yeah, you probably need to switch to scala 2.11.11 to see the breakage.

kailuowang · 2017-11-27T21:26:17Z

we squash merge, did you see my comment on using tut:reset?

stephen-lazaro · 2017-11-27T21:26:41Z

Just did, will do 👍 Thanks for the pointer.

kailuowang · 2017-11-27T22:27:38Z

docs/src/main/tut/typeclasses/contravariantmonoidal.md

+The `ContravariantMonoidal` type class is for [`Contravariant`](contravariant.html) functors that can define a
+`product` function and a `unit` function.
+
+```tut:reset


Sorry I didn't make it clear. I was suggesting using a tut:silent here and tut:reset:silent for the next block at line 41.

Ah, I see, I was just starting to debug this. Ok, cool, sorry about this, I'm not used to testing against multiple versions of the compiler. I'll fix shortly.

Ok, checked it against 2.10.6, 2.11.11, and 2.12.3 and the docs all compile with that recommendation. So we should be GTG.

LukaJCB · 2017-11-27T23:35:47Z

I was sort of negative on this being in cats-core before, but I think it makes a lot of sense especially how we formulated it. It really makes the relationship between Semigroups/Monoids and Semigroupals/Monoidals/Applicatives much clearer for me. So kudos to all! 🎉

stephen-lazaro · 2017-11-27T23:46:55Z

Awesome! Thanks for the help all involved. Was fun to try my hand at something like this.

kailuowang · 2017-11-28T16:36:18Z

core/src/main/scala/cats/ContravariantMonoidal.scala

+  def liftContravariant[A, B](f: A => B): F[B] => F[A] =
+    ContravariantMonoidal.contramap2(unit[B], _: F[B])(((b: B) => (b, b)) compose f)(self, self)
+
+  // Technically, this is not correct, as the Applicative is composed with the ContravariantMonoidal, not the other way around


Would you mind elaborate a bit more (or point to a more detailed discussion/explanation) here?

Sure, I can also just change the name and move this possibly. The point here is mostly that I didn't want to add anything to Applicative about ContravariantMonoidal since this might live in cats.more, so I ended up having this composition live here in ContravariantMonoidal even though the composition is Applicative compose ContravariantMonoidal, so the name and the signature are a little out of sync with what I saw in the rest of the repository.

ah, I propose we rename and move it to Applicative

Got it, will do. Thanks.

kailuowang · 2017-11-28T22:23:29Z

core/src/main/scala/cats/data/Kleisli.scala

@@ -165,6 +165,9 @@ private[data] sealed abstract class KleisliInstances1 extends KleisliInstances2
 private[data] sealed abstract class KleisliInstances2 extends KleisliInstances3 {
  implicit def catsDataAlternativeForKleisli[F[_], A](implicit F0: Alternative[F]): Alternative[Kleisli[F, A, ?]] =
    new KleisliAlternative[F, A] { def F: Alternative[F] = F0 }
+
+  implicit def catsDataContravariantMonoidalForKleisli[F[_], A](implicit F0: ContravariantMonoidal[F]): ContravariantMonoidal[Kleisli[F, A, ?]] =


The convention in cats is that instances that are more specific should be at higher priority. I.E. instance of ContravariantMonoidal should be lower in the inheritance chain than Contravariant and ContravriantSemigroupal and Semigroupal.

Gotcha, will fix.

kailuowang · 2017-11-29T19:00:18Z

The code looks good for me. But I don't know the area well enough to be comfortable for my sign-off to be the final one for merge. @iravid @julienrf @adelbertc would anyone of you guys give a quick review? (You guys can focus just on the API the laws)

julienrf · 2017-11-29T20:23:24Z

laws/src/main/scala/cats/laws/ContravariantMonoidalLaws.scala

+    (F.unit[B], fa).contramapN(f) <-> fa.contramap(f andThen (_._2))
+
+  def contravariantMonoidalContramap2DiagonalAssociates[A](m: F[A], n: F[A], o: F[A]): IsEq[F[A]] =
+    ((m, n).contramapN(delta[A]), o).contramapN(delta[A]) <-> (m, (n, o).contramapN(delta[A])).contramapN(delta[A])


Why can’t we move this law to ContravariantSemigroupal? It seems that we don’t need unit here.

Ah, we probably could. It'll just involve adding a ContravariantSemigroupal laws trait and so forth. Looks like I overlooked your prior comment, sorry about that. I can move that over.

iravid

This is great stuff. Thanks for implementing this @stephen-lazaro.

I left some comments inline; they're mostly around efficiency and consistency.

iravid · 2017-11-30T07:22:22Z

core/src/main/scala/cats/ContravariantMonoidal.scala

+   */
+  def unit[A]: F[A]
+
+  def liftContravariant[A, B](f: A => B): F[B] => F[A] =


This can actually be moved to Contravariant, no? (as it's just a curried contramap)

iravid · 2017-11-30T07:29:00Z

core/src/main/scala/cats/instances/eq.scala


      def product[A, B](fa: Eq[A], fb: Eq[B]): Eq[(A, B)] =
-        Eq.instance { (left, right) => fa.eqv(left._1, right._1) && fb.eqv(left._2, right._2) }
+        Eq.instance { (l, r) =>


If I am not mistaken, the previous version allocates at least one tuple less (although it is admittedly uglier :-))

I guess that's true, I sort of forgot that aspect of things. 👍

iravid · 2017-11-30T07:29:34Z

core/src/main/scala/cats/instances/eq.scala

+       * Note: resulting instances are law-abiding only when the functions used are injective (represent a one-to-one mapping)
+       */
+      def contramap[A, B](fa: Eq[A])(f: B => A): Eq[B] =
+        Eq.instance { (l: B, r: B) =>


Any reason not to delegate to Eq.by, just for consistency?

iravid · 2017-11-30T07:30:05Z

core/src/main/scala/cats/instances/equiv.scala

        }

      def product[A, B](fa: Equiv[A], fb: Equiv[B]): Equiv[(A, B)] =
        new Equiv[(A, B)] {
-          def equiv(x: (A, B), y: (A, B)): Boolean =
-            fa.equiv(x._1, y._1) && fb.equiv(x._2, y._2)


Same comment re allocations

iravid · 2017-11-30T12:41:00Z

core/src/main/scala/cats/instances/order.scala

-            val z = fa.compare(x._1, y._1)
-            if (z == 0) fb.compare(x._2, y._2) else z
-          }
+          def compare(x: (A, B), y: (A, B)): Int =


Same comment re allocations

iravid · 2017-11-30T12:41:13Z

core/src/main/scala/cats/instances/order.scala

      /** Derive an `Order` for `B` given an `Order[A]` and a function `B => A`.
       *
       * Note: resulting instances are law-abiding only when the functions used are injective (represent a one-to-one mapping)
       */
-      def contramap[A, B](fa: Order[A])(f: B => A): Order[B] = Order.by[B, A](f)(fa)
+      def contramap[A, B](fa: Order[A])(f: B => A): Order[B] =
+        new Order[B] {


Same re delegation to Order.by

iravid · 2017-11-30T12:41:34Z

core/src/main/scala/cats/instances/ordering.scala

+      }
+
+      def contramap[A, B](fa: Ordering[A])(f: B => A): Ordering[B] =
+        new Ordering[B] {


Same re delegation to on

iravid · 2017-11-30T12:41:40Z

core/src/main/scala/cats/instances/ordering.scala

-            val z = fa.compare(x._1, y._1)
-            if (z == 0) fb.compare(x._2, y._2) else z
+          def compare(x: (A, B), y: (A, B)): Int = (x, y) match {
+            case ((aL, bL), (aR, bR)) => {


Same re allocations

stephen-lazaro · 2017-11-30T21:51:37Z

Thanks @iravid! I'll take care of those tonight.

kailuowang · 2017-12-01T13:10:17Z

Thanks so much @stephen-lazaro for this awesome contribution!

stephen-lazaro · 2017-12-01T17:33:54Z

🎉 Thanks everyone for the assistance!

julienrf reviewed Nov 22, 2017

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stephen-lazaro changed the title ~~Add Divisible~~ Add ContravariantMonoidal Nov 22, 2017

Rename to ContravariantMonoidal, Base on product

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Renames to ContravariantMonoidal Derives contramap2 from product, contramap Moves contramap2 to ContravariantSemigroupal

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LukaJCB added 2 commits November 25, 2017 09:24

Make scalastyle happy

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Add mima exceptions

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Get ready for RC2 #2044

Merged

3 tasks

stephen-lazaro added 2 commits November 26, 2017 21:27

Use SemigroupalArityFunctions and TupleSemigroupal

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Clean up ContravariantMonoidal documentation

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Add missing mima exclusions

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Increase WriterT coverage, tut:reset

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Use tut:reset correctly

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stephen-lazaro added 2 commits November 28, 2017 14:35

Move composition functions into Applicative

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Reorder instances to be more standard

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Tighten test code for Contravariant derivatives

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Remove extra allocations, use on and by

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kailuowang merged commit e431b72 into typelevel:master Dec 1, 2017

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LukaJCB mentioned this pull request Jun 9, 2018

Add Divisible and Decideable (contravariant Applicative and co.) #1935

Open


		override def unit[A]: F[G[A]] = F.pure(G.unit)

		override def contramap[A, B](fa: F[G[A]])(f: B => A) =

Add ContravariantMonoidal #2034

Add ContravariantMonoidal #2034

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LukaJCB commented Nov 27, 2017 •

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codecov-io commented Nov 27, 2017 •

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stephen-lazaro commented Nov 27, 2017 •

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kailuowang commented Nov 29, 2017 •

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stephen-lazaro Nov 29, 2017 •

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