diff --git a/pytools/persistent_dict.py b/pytools/persistent_dict.py
index 4090cb438f7007ecabfc143a04b40106ecc77028..13d8b10ea48367286e6bc1d435b5b09ed4c0be86 100644
--- a/pytools/persistent_dict.py
+++ b/pytools/persistent_dict.py
@@ -480,6 +480,9 @@ class KeyBuilder:
 
     # }}}
 
+    def update_for_function(self, key_hash: Hash, key: Any) -> None:
+        self.rec(key_hash, key.__module__ + key.__qualname__)
+
     # }}}
 
 # }}}
diff --git a/pytools/test/test_persistent_dict.py b/pytools/test/test_persistent_dict.py
index d53fcfd7ad1d0fa2e05fb62bad3c986531ce60e9..578b6addf9ba767a521af0e11dd361e5e0ddd0b3 100644
--- a/pytools/test/test_persistent_dict.py
+++ b/pytools/test/test_persistent_dict.py
@@ -719,6 +719,44 @@ def test_xdg_cache_home() -> None:
         shutil.rmtree(xdg_dir)
 
 
+def global_fun():
+    pass
+
+
+def global_fun2():
+    pass
+
+
+def test_hash_function() -> None:
+    keyb = KeyBuilder()
+
+    assert keyb(global_fun) == keyb(global_fun) == \
+        "51b5980dd3a8aa13f6e83869e4a04c22973d7aaf96cb22899abdfdc55e15c9b2"
+    assert keyb(global_fun) != keyb(global_fun2)
+
+    def local_fun():
+        pass
+
+    def local_fun2():
+        pass
+
+    assert keyb(local_fun) == keyb(local_fun) == \
+        "fc58f5b0130df821913c848749eb03f5dcd4da7a568c6130f1c0cfb96ed0d12d"
+    assert keyb(local_fun) != keyb(local_fun2)
+
+    class C1:
+        def method(self):
+            pass
+
+    class C2:
+        def method(self):
+            pass
+
+    assert keyb(C1.method) == keyb(C1.method) == \
+        "3013eb424dac133a57bd70cb6084d2a2f349a247714efc508fe3b10b99b6f717"
+    assert keyb(C1.method) != keyb(C2.method)
+
+
 if __name__ == "__main__":
     if len(sys.argv) > 1:
         exec(sys.argv[1])