Add syntax for Bitraverse to allow traversal and sequencing of the le…

…ft side (#2606)

* Add syntax for Bitraverse to allow independent traversal of sides

This adds syntax for:
* traverse
* sequence
* leftTraverse
* leftSequence

I am open to having better names, but I think these would be useful to have in cats-core.

* Add syntax tests and accept prePR's style change

* Fix repeated variables in SyntaxSuite

* Rename bitraverse's traverse and sequence to rightTraverse and rightSequence

* Attempt to make new Bitraverse syntax binary compatible

* Add a new syntax bincompat to let me add new Bitraverse syntax to syntax.all

* Move Bitraverse new syntax into AllSyntaxBinCompat3

* Drop rightTraverse and rightSequence from this PR

* scalafmt

* Add scaladoc on leftSequence/leftTraverse

* Fix doctests for leftTraverse/leftSequence

* Fix doctests for leftTraverse/leftSequence again

* Fix doctests for leftTraverse/leftSequence yet again

core/src/main/scala/cats/syntax/all.scala

@@ -84,3 +84,4 @@ trait AllSyntaxBinCompat4
     with ParallelApplySyntax
     with FoldableSyntaxBinCompat0
     with ReducibleSyntaxBinCompat0
+    with BitraverseSyntaxBinCompat0

core/src/main/scala/cats/syntax/bitraverse.scala

@@ -22,3 +22,64 @@ final class NestedBitraverseOps[F[_, _], G[_], A, B](private val fgagb: F[G[A],
   def bisequence(implicit F: Bitraverse[F], G: Applicative[G]): G[F[A, B]] =
     F.bisequence(fgagb)
 }
+
+trait BitraverseSyntaxBinCompat0 {
+  implicit final def catsSyntaxBitraverseBinCompat0[F[_, _]: Bitraverse, A, B](
+    fab: F[A, B]
+  ): BitraverseOpsBinCompat0[F, A, B] =
+    new BitraverseOpsBinCompat0[F, A, B](fab)
+  implicit final def catsSyntaxLeftNestedBitraverse[F[_, _]: Bitraverse, G[_], A, B](
+    fgab: F[G[A], B]
+  ): LeftNestedBitraverseOps[F, G, A, B] =
+    new LeftNestedBitraverseOps[F, G, A, B](fgab)
+}
+
+final class BitraverseOpsBinCompat0[F[_, _], A, B](val fab: F[A, B]) extends AnyVal {
+
+  /**
+   *  Traverse over the left side of the structure.
+   *  For the right side, use the standard `traverse` from [[cats.Traverse]].
+   *
+   *  Example:
+   *  {{{
+   *  scala> import cats.implicits._
+   *
+   *  scala> val intAndString: (Int, String) = (7, "test")
+   *
+   *  scala> intAndString.leftTraverse(i => Option(i).filter(_ > 5))
+   *  res1: Option[(Int, String)] = Some((7,test))
+   *
+   *  scala> intAndString.leftTraverse(i => Option(i).filter(_ < 5))
+   *  res2: Option[(Int, String)] = None
+   *  }}}
+   */
+  def leftTraverse[G[_], C](f: A => G[C])(implicit F: Bitraverse[F], G: Applicative[G]): G[F[C, B]] =
+    F.bitraverse(fab)(f, G.pure(_))
+}
+
+final class LeftNestedBitraverseOps[F[_, _], G[_], A, B](val fgab: F[G[A], B]) extends AnyVal {
+
+  /**
+   * Sequence the left side of the structure.
+   * For the right side, use the standard `sequence` from [[cats.Traverse]].
+   *
+   * Example:
+   * {{{
+   * scala> import cats.implicits._
+   *
+   * scala> val optionalErrorRight: Either[Option[String], Int] = Either.right(123)
+   * scala> optionalErrorRight.leftSequence
+   * res1: Option[Either[String, Int]] = Some(Right(123))
+   *
+   * scala> val optionalErrorLeftSome: Either[Option[String], Int] = Either.left(Some("something went wrong"))
+   * scala> optionalErrorLeftSome.leftSequence
+   * res2: Option[Either[String, Int]] = Some(Left(something went wrong))
+   *
+   * scala> val optionalErrorLeftNone: Either[Option[String], Int] = Either.left(None)
+   * scala> optionalErrorLeftNone.leftSequence
+   * res3: Option[Either[String,Int]] = None
+   * }}}
+   */
+  def leftSequence(implicit F: Bitraverse[F], G: Applicative[G]): G[F[A, B]] =
+    F.bitraverse(fgab)(identity, G.pure(_))
+}

core/src/main/scala/cats/syntax/package.scala

@@ -11,7 +11,7 @@ package object syntax {
   object bifunctor extends BifunctorSyntax
   object bifoldable extends BifoldableSyntax
   object binested extends BinestedSyntax
-  object bitraverse extends BitraverseSyntax
+  object bitraverse extends BitraverseSyntax with BitraverseSyntaxBinCompat0
   @deprecated("use cats.syntax.semigroupal instead", "1.0.0-RC1")
   object cartesian extends SemigroupalSyntax
   object choice extends ChoiceSyntax

tests/src/test/scala/cats/tests/SyntaxSuite.scala

@@ -307,9 +307,13 @@ object SyntaxSuite
 
     val fab = mock[F[A, B]]
     val gfcd = fab.bitraverse(f, g)
+    val gfcb = fab.leftTraverse(f)
 
     val fgagb = mock[F[G[A], G[B]]]
     val gfab = fgagb.bisequence
+
+    val fgab = mock[F[G[A], B]]
+    val gfab2 = fgab.leftSequence
   }
 
   def testAlternativeMonad[F[_]: Alternative: Monad, G[_]: Foldable, H[_, _]: Bifoldable, A, B]: Unit = {