Use as rather than map and discard

core/src/main/scala/cats/Apply.scala

@@ -73,7 +73,7 @@ trait Apply[F[_]] extends Functor[F] with InvariantSemigroupal[F] with ApplyArit
    * }}}
    */
   def productR[A, B](fa: F[A])(fb: F[B]): F[B] =
-    ap(map(fa)(_ => (b: B) => b))(fb)
+    ap(as(fa, { (b: B) => b }))(fb)
 
   /**
    * Compose two actions, discarding any value produced by the second.

core/src/main/scala/cats/FlatMap.scala

@@ -80,7 +80,7 @@ import scala.annotation.implicitNotFound
    * scala> assert(count == 1)
    * }}}
    */
-  def productLEval[A, B](fa: F[A])(fb: Eval[F[B]]): F[A] = flatMap(fa)(a => map(fb.value)(_ => a))
+  def productLEval[A, B](fa: F[A])(fb: Eval[F[B]]): F[A] = flatMap(fa)(a => as(fb.value, a))
 
   @deprecated("Use productLEval instead.", "1.0.0-RC2")
   @noop private[cats] def forEffectEval[A, B](fa: F[A])(fb: Eval[F[B]]): F[A] = productLEval(fa)(fb)
@@ -169,7 +169,7 @@ import scala.annotation.implicitNotFound
   def foreverM[A, B](fa: F[A]): F[B] = {
     // allocate two things once for efficiency.
     val leftUnit = Left(())
-    val stepResult: F[Either[Unit, B]] = map(fa)(_ => leftUnit)
+    val stepResult: F[Either[Unit, B]] = as(fa, leftUnit)
     tailRecM(())(_ => stepResult)
   }
 

core/src/main/scala/cats/Monad.scala

@@ -51,9 +51,7 @@ import scala.annotation.implicitNotFound
     val b = Eval.later(body)
     tailRecM(())(_ =>
       ifM(p)(
-        ifTrue = {
-          map(b.value)(_ => continue)
-        },
+        ifTrue = as(b.value, continue),
         ifFalse = stop
       )
     )