Add filterFold and collectFold to Foldable

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

@@ -158,4 +158,33 @@ final class FoldableOps[F[_], A](val fa: F[A]) extends AnyVal {
       case Some((a, src)) => G.map(p(a))(if (_) Right(Some(a)) else Left(src.value))
       case None => G.pure(Right(None))
     })
+
+  /**
+    * Tear down a subset of this structure using a `PartialFunction`.
+    *{{{
+    * scala> import cats.implicits._
+    * scala> val xs = List(1, 2, 3, 4)
+    * scala> xs.collectFold { case n if n % 2 == 0 => n }
+    * res0: Int = 6
+    *}}}
+    */
+  def collectFold[M](f: PartialFunction[A, M])(implicit F: Foldable[F], M: Monoid[M]): M =
+    F.foldLeft(fa, M.empty)((acc, a) ⇒ M.combine(acc, f.applyOrElse(a, (_: A) ⇒ M.empty)))
+
+  /**
+    * Tear down a subset of this structure using a `A => Option[M]`.
+    *{{{
+    * scala> import cats.implicits._
+    * scala> val xs = List(1, 2, 3, 4)
+    * scala> def f(n: Int): Option[Int] = if (n % 2 == 0) Some(n) else None
+    * scala> xs.filterFold(f)
+    * res0: Int = 6
+    *}}}
+    */
+  def filterFold[M](f: A ⇒ Option[M])(implicit F: Foldable[F], M: Monoid[M]): M =
+    F.foldLeft(fa, M.empty)((acc, a) ⇒ f(a) match {
+      case Some(x) ⇒ M.combine(acc, x)
+      case None    ⇒ acc
+    })
+
 }

tests/src/test/scala/cats/tests/FoldableSuite.scala

@@ -85,6 +85,20 @@ abstract class FoldableSuite[F[_]: Foldable](name: String)(
     }
   }
 
+  test(s"Foldable[$name] partial summation") {
+    forAll { (fa: F[String], f: String ⇒ Boolean) ⇒
+      val m: Monoid[String] = Monoid[String]
+
+      val pf: PartialFunction[String, String] = {
+        case n if f(n) ⇒ n
+      }
+      fa.collectFold(pf) should === (fa.toList.collect(pf).fold(m.empty)(m.combine))
+
+      def g(a: String): Option[String] = Some(a).filter(f)
+      fa.filterFold(g) should === (fa.toList.filter(f).fold(m.empty)(m.combine))
+    }
+  }
+
   test(s"Foldable[$name].find/exists/forall/findM/existsM/forallM/filter_/dropWhile_") {
     forAll { (fa: F[Int], n: Int) =>
       fa.find(_ > n)   should === (iterator(fa).find(_ > n))