Do not report empty function arities as badarity

lib/elixir/lib/module/types/descr.ex

@@ -1556,18 +1556,23 @@ defmodule Module.Types.Descr do
 
   defp fun_other_non_empty_arities(%{fun: {:union, bdds}}, arity) do
     case :maps.take(arity, bdds) do
-      {_bdd, rest} ->
-        for {a, b} <- rest,
-            not Enum.all?(bdd_to_dnf(b), fn {pos, neg} -> fun_line_empty?(pos, neg) end),
-            do: a
-
-      :error ->
-        []
+      {_bdd, rest} -> bdds_non_empty_arities(rest)
+      :error -> []
     end
   end
 
   defp fun_other_non_empty_arities(_, _), do: []
 
+  # Returns the arities of the given BDD map whose function type is not empty.
+  # An empty bucket carries no value, so it must never be reported as a
+  # supported arity (otherwise we would return :badarity for a function type
+  # that is actually empty, or reject a live arity in favour of a dead one).
+  defp bdds_non_empty_arities(bdds) do
+    for {arity, bdd} <- bdds,
+        not Enum.all?(bdd_to_dnf(bdd), fn {pos, neg} -> fun_line_empty?(pos, neg) end),
+        do: arity
+  end
+
   # Transforms a binary decision diagram (BDD) into the canonical `domain-arrows` pair:
   #
   # 1. **domain**: The union of all domains from positive functions in the BDD
@@ -1602,9 +1607,10 @@ defmodule Module.Types.Descr do
 
         if arrows == [] do
           # The function is empty at the requested arity. Report the *other*
-          # arities (never the called one, which would be self-contradictory),
-          # or :badfun when there are none, i.e. the function is empty.
-          case :maps.keys(rest) do
+          # non-empty arities (never the called one, which would be
+          # self-contradictory), or :badfun when there are none, i.e. the
+          # function is empty.
+          case bdds_non_empty_arities(rest) do
             [] -> :badfun
             other -> {:badarity, other}
           end
@@ -1613,7 +1619,10 @@ defmodule Module.Types.Descr do
         end
 
       :error ->
-        {:badarity, :maps.keys(bdds)}
+        case bdds_non_empty_arities(bdds) do
+          [] -> :badfun
+          other -> {:badarity, other}
+        end
     end
   end
 

lib/elixir/test/elixir/module/types/descr_test.exs

@@ -1459,6 +1459,34 @@ defmodule Module.Types.DescrTest do
       assert fun_apply(fun([integer(), atom()], boolean()), [integer()]) == {:badarity, [2]}
       assert fun_apply(usable_at_2, [integer(), atom()]) == {:ok, boolean()}
 
+      # A function that is empty at *every* arity is :badfun at any arity, even
+      # when other (also empty) arity entries are structurally present. An empty
+      # entry must never be reported as a supported arity.
+      empty_at_1 = opt_difference(fun([integer()], atom()), fun([integer()], term()))
+
+      empty_at_2 =
+        opt_difference(fun([integer(), atom()], atom()), fun([integer(), atom()], term()))
+
+      empty_both = opt_union(empty_at_1, empty_at_2)
+
+      assert empty?(empty_both)
+      assert fun_apply(empty_both, [integer()]) == :badfun
+      assert fun_apply(empty_both, [integer(), atom()]) == :badfun
+
+      # Same when the called arity has no entry at all and the only entries
+      # present are empty ones.
+      assert fun_apply(empty_at_2, [integer()]) == :badfun
+      assert fun_apply(dynamic(empty_at_2), [integer()]) == :badfun
+
+      # An empty static arity must not shadow a live dynamic one: `live_at_2` is
+      # semantically equal to its dynamic arity-2 part, so applying it to two
+      # arguments must succeed instead of reporting the dead arity 1.
+      live_at_2 = opt_union(empty_at_1, dynamic(fun([integer(), atom()], boolean())))
+
+      assert equal?(live_at_2, dynamic(fun([integer(), atom()], boolean())))
+      assert fun_apply(live_at_2, [integer(), atom()]) == {:ok, dynamic(boolean())}
+      assert fun_apply(live_at_2, [integer()]) == {:badarity, [2]}
+
       # Function intersection tests (no overlap)
       fun0 = opt_intersection(fun([integer()], atom()), fun([float()], binary()))
       assert fun_apply(fun0, [integer()]) == {:ok, atom()}