diff --git a/library.lua b/library.lua
index 4a6b59d..ba93082 100644
--- a/library.lua
+++ b/library.lua
@@ -2,10 +2,12 @@
 local function_library = {}
 
 local function library_function ( func_def )
-	-- TODO: Add clause requiring that func_def.func is a builtin.
-	if func_def.func then
-		function_library[func_def.func] = func_def
-	end
+	if not func_def.func then  return false  end
+
+	local is_func_builtin  =  not debug or not debug.getinfo or (debug.getinfo(func_def.func, 'S').what == 'C')
+	if not is_func_builtin then  return false  end
+
+	function_library[func_def.func] = func_def
 end
 
 --------------------------------------------------------------------------------
@@ -1334,7 +1336,7 @@ end
 --------------------------------------------------------------------------------
 -- FFI
 
--- TODO
+-- TODO: Add FFI documentation
 -- Documentation is here: http://luajit.org/ext_ffi_api.html
 
 --------------------------------------------------------------------------------
diff --git a/pretty.lua b/pretty.lua
index 1beefbc..415ea5d 100644
--- a/pretty.lua
+++ b/pretty.lua
@@ -462,10 +462,9 @@ local TYPE_TO_FORMAT_FUNC = {
     ['thread']   =  format_coroutine,
     ['table']    =  format_table,
 
-    -- TODO
-    ['function'] =  format_function,
-    ['userdata'] =  format_primitive,
-    ['cdata']    =  format_primitive,  -- Luajit exclusive ?
+    ['function'] =  format_function,   -- TODO: Improve a little
+    ['userdata'] =  format_primitive,  -- TODO
+    ['cdata']    =  format_primitive,  -- TODO & Luajit only
 }
 
 function format_value (value, _, depth, l)
diff --git a/test/test_pretty.lua b/test/test_pretty.lua
index 4ae1db1..829f1bd 100644
--- a/test/test_pretty.lua
+++ b/test/test_pretty.lua
@@ -124,7 +124,7 @@ format_test {
 --------------------------------------------------------------------------------
 -- Userdata printing
 
--- TODO. First off figure out a way to test this stuff.
+-- TODO: Figure out a way to print userdata.
 -- Maybe look into using the one available debug.getupvalue(pairs, 1)
 
 --------------------------------------------------------------------------------
diff --git a/test/test_resilience.lua b/test/test_resilience.lua
index 305ae22..16a6fca 100644
--- a/test/test_resilience.lua
+++ b/test/test_resilience.lua
@@ -57,7 +57,7 @@ end)
 SUITE:addTest('a_very_small_part_of_math', function ()
     -- This tests whether one could load the library with an empty env, without
     -- an error.
-    local env = { math = { abs = math.abs } }
+    local env = { debug = debug, math = { abs = math.abs } }
     local library = setfenv(loadfile('./library.lua'), env)()
 
     assert( library[math.abs], 'Why is math.abs not defined in the library?' )
@@ -66,13 +66,24 @@ end)
 SUITE:addTest('redefined part of math', function ()
     -- This tests whether the library ignores a redefined function of an
     -- builtin, when defining documentation.
-    local env  =  { setfenv = setfenv, loadfile = function() end }
+    local env  =  { debug = debug, setfenv = setfenv, loadfile = function() end }
     local library = setfenv(loadfile('./library.lua'), env)()
 
     assert(     library[env.setfenv],  'Why is setfenv not defined in the library?' )
     assert( not library[env.loadfile], 'Why is loadfile defined in the library?' )
 end)
 
+SUITE:addTest('redefined part of math 2', function ()
+    -- This tests whether the library allows a redefined function of an
+    -- builtin, when defining documentation, due to not being able to determine
+    -- the origin of the function.
+    local env  =  { setfenv = setfenv, loadfile = function() end }
+    local library = setfenv(loadfile('./library.lua'), env)()
+
+    assert( library[env.setfenv],  'Why is setfenv not defined in the library?' )
+    assert( library[env.loadfile], 'Why is loadfile not defined in the library?' )
+end)
+
 --------------------------------------------------------------------------------
 
 return SUITE