diff --git a/src/hb-iter.hh b/src/hb-iter.hh
index 192347dc0..6954d431b 100644
--- a/src/hb-iter.hh
+++ b/src/hb-iter.hh
@@ -649,15 +649,15 @@ HB_FUNCOBJ (hb_unzip);
 struct
 {
   template <typename Iterable,
-	    typename Val = bool,
+	    typename Pred = decltype ((hb_bool)),
 	    typename Proj = decltype ((hb_identity)),
 	    hb_requires (hb_is_iterable (Iterable))>
   bool operator () (Iterable&& c,
-		    Val v = true,
+		    Pred&& p = hb_bool,
 		    Proj&& f = hb_identity) const
   {
     for (auto it = hb_iter (c); it; ++it)
-      if (!((Val) hb_get (hb_forward<Proj> (f), *it) == v))
+      if (!hb_match (hb_forward<Pred> (p), hb_get (hb_forward<Proj> (f), *it)))
 	return false;
     return true;
   }
@@ -666,15 +666,15 @@ HB_FUNCOBJ (hb_all);
 struct
 {
   template <typename Iterable,
-	    typename Val = bool,
+	    typename Pred = decltype ((hb_bool)),
 	    typename Proj = decltype ((hb_identity)),
 	    hb_requires (hb_is_iterable (Iterable))>
   bool operator () (Iterable&& c,
-		    Val v = true,
+		    Pred&& p = hb_bool,
 		    Proj&& f = hb_identity) const
   {
     for (auto it = hb_iter (c); it; ++it)
-      if (((Val) hb_get (hb_forward<Proj> (f), *it) == v))
+      if (hb_match (hb_forward<Pred> (p), hb_get (hb_forward<Proj> (f), *it)))
 	return true;
     return false;
   }
@@ -683,15 +683,15 @@ HB_FUNCOBJ (hb_any);
 struct
 {
   template <typename Iterable,
-	    typename Val = bool,
+	    typename Pred = decltype ((hb_bool)),
 	    typename Proj = decltype ((hb_identity)),
 	    hb_requires (hb_is_iterable (Iterable))>
   bool operator () (Iterable&& c,
-		    Val v = true,
+		    Pred&& p = hb_bool,
 		    Proj&& f = hb_identity) const
   {
     for (auto it = hb_iter (c); it; ++it)
-      if (((Val) hb_get (hb_forward<Proj> (f), *it) == v))
+      if (hb_match (hb_forward<Pred> (p), hb_get (hb_forward<Proj> (f), *it)))
 	return false;
     return true;
   }
diff --git a/src/test-iter.cc b/src/test-iter.cc
index 70952f3e2..17a1972b3 100644
--- a/src/test-iter.cc
+++ b/src/test-iter.cc
@@ -166,11 +166,13 @@ main (int argc, char **argv)
   assert (true == hb_all (st));
   assert (false == hb_all (st, 42u));
   assert (true == hb_any (st));
-  assert (false == hb_any (st, 14));
-  assert (true == hb_any (st, 15));
+  assert (false == hb_any (st, 14u));
+  assert (true == hb_any (st, 14u, [] (unsigned _) { return _ - 1u; }));
+  assert (true == hb_any (st, [] (unsigned _) { return _ == 15u; }));
+  assert (true == hb_any (st, 15u));
   assert (false == hb_none (st));
-  assert (false == hb_none (st, 15));
-  assert (true == hb_none (st, 17));
+  assert (false == hb_none (st, 15u));
+  assert (true == hb_none (st, 17u));
 
   hb_array_t<hb_vector_t<int>> pa;
   pa->as_array ();