diff --git a/src/jsonata/functions.py b/src/jsonata/functions.py
index 262ee21..e6a42fd 100644
--- a/src/jsonata/functions.py
+++ b/src/jsonata/functions.py
@@ -224,14 +224,18 @@ def validate_input(arg: Optional[Any]) -> None:
     #     
     @staticmethod
     def substring(string: Optional[str], start: Optional[float], length: Optional[float]) -> Optional[str]:
+        if string is utils.Utils.NULL_VALUE or start is utils.Utils.NULL_VALUE or length is utils.Utils.NULL_VALUE:
+            raise jexception.JException("T0410", -1)
+
         # undefined inputs always return undefined
         if string is None:
             return None
 
-        if string is utils.Utils.NULL_VALUE:
-            raise jexception.JException("T0410", -1)
+        # match JS: undefined start returns the whole string, or "" if a length is given
+        if start is None:
+            return string if length is None else ""
 
-        start = int(start) if start is not None else None
+        start = int(start)
         length = int(length) if length is not None else None
 
         # not used: var strArray = stringToArray(string)
@@ -308,13 +312,13 @@ def substr(string: str, start: int, length: int) -> str:
     #     
     @staticmethod
     def substring_before(string: Optional[str], chars: Optional[str]) -> Optional[str]:
+        if string is utils.Utils.NULL_VALUE or chars is utils.Utils.NULL_VALUE:
+            raise jexception.JException("T0410", -1)
+
         # undefined inputs always return undefined
         if string is None:
             return None
 
-        if string is utils.Utils.NULL_VALUE:
-            raise jexception.JException("T0410", -1)
-
         if chars is None:
             return string
 
@@ -332,12 +336,15 @@ def substring_before(string: Optional[str], chars: Optional[str]) -> Optional[st
     #     
     @staticmethod
     def substring_after(string: Optional[str], chars: Optional[str]) -> Optional[str]:
+        if string is utils.Utils.NULL_VALUE or chars is utils.Utils.NULL_VALUE:
+            raise jexception.JException("T0410", -1)
+
         # undefined inputs always return undefined
         if string is None:
             return None
 
-        if string is utils.Utils.NULL_VALUE:
-            raise jexception.JException("T0410", -1)
+        if chars is None:
+            return string
 
         pos = string.find(chars)
         if pos > -1:
@@ -433,22 +440,25 @@ def trim(string: Optional[str]) -> Optional[str]:
     #     
     @staticmethod
     def pad(string: Optional[str], width: Optional[int], char: Optional[str]) -> Optional[str]:
+        if string is utils.Utils.NULL_VALUE or width is utils.Utils.NULL_VALUE or char is utils.Utils.NULL_VALUE:
+            raise jexception.JException("T0410", -1)
+
         # undefined inputs always return undefined
         if string is None:
             return None
 
-        if string is utils.Utils.NULL_VALUE:
-            raise jexception.JException("T0410", -1)
-
         if char is None or not char:
             char = " "
 
+        # match JS: undefined width adds no padding
+        if width is None:
+            return string
+
         # match JS: truncate width to integer
-        if width is not None:
-            try:
-                width = int(width)
-            except Exception:
-                width = 0
+        try:
+            width = int(width)
+        except Exception:
+            width = 0
 
         if width < 0:
             result = Functions.left_pad(string, -width, char)
diff --git a/tests/string_test.py b/tests/string_test.py
index 7f20608..cae54e6 100644
--- a/tests/string_test.py
+++ b/tests/string_test.py
@@ -1,4 +1,5 @@
 import jsonata
+import pytest
 from jsonata.regex_engine import default_regex_engine
 
 
@@ -147,6 +148,23 @@ def test_trim(self):
         assert jsonata.Jsonata("$trim(\"\")").evaluate(None) == ""
         assert jsonata.Jsonata("$trim(notthere)").evaluate(None) is None
 
+    def test_undefined_args(self):
+        assert jsonata.Jsonata("$substring('abc', $nothing)").evaluate(None) == "abc"
+        assert jsonata.Jsonata("$substring('abc', $nothing, 1)").evaluate(None) == ""
+        assert jsonata.Jsonata("$substring(?, $nothing)('abc')").evaluate(None) == "abc"
+        assert jsonata.Jsonata("$substringAfter('abc', $nothing)").evaluate(None) == "abc"
+        assert jsonata.Jsonata("$pad('abc', $nothing)").evaluate(None) == "abc"
+
+    def test_null_args(self):
+        for expr in ["$substring('abc', null)", "$substring('abc', 1, null)", "$substring('abc', $nothing, null)",
+                     "$substring($nothing, null)", "$substring($nothing, 1, null)",
+                     "$pad('abc', null)", "$pad('abc', 5, null)", "$pad($nothing, null)",
+                     "$substringBefore('abc', null)", "$substringBefore($nothing, null)",
+                     "$substringAfter('abc', null)", "$substringAfter($nothing, null)"]:
+            with pytest.raises(jsonata.JException) as exc_info:
+                jsonata.Jsonata(expr).evaluate(None)
+            assert exc_info.value.error == "T0410"
+
     def test_match_limit(self):
         res = jsonata.Jsonata("$match('ababab', /ab/)").evaluate(None)
         assert res is not None