diff --git a/llama_cpp/llama_grammar.py b/llama_cpp/llama_grammar.py
index c02e656..d8ef563 100644
--- a/llama_cpp/llama_grammar.py
+++ b/llama_cpp/llama_grammar.py
@@ -1432,7 +1432,6 @@ class SchemaConverter:
         return key
 
     def visit(self, schema: Dict[str, Any], name: str) -> str:
-        schema_type: Optional[str] = schema.get("type") # type: ignore
         rule_name = name or "root"
 
         if "$defs" in schema:
@@ -1458,7 +1457,19 @@ class SchemaConverter:
             rule = " | ".join((self._format_literal(v) for v in schema["enum"]))
             return self._add_rule(rule_name, rule)
 
-        elif schema_type == "object" and "properties" in schema:
+        elif "$ref" in schema:
+            ref = schema["$ref"]
+            assert ref.startswith("#/$defs/"), f"Unrecognized schema: {schema}"
+            # inline $defs
+            def_name = ref[len("#/$defs/") :]
+            def_schema = self._defs[def_name]
+            return self.visit(def_schema, f'{name}{"-" if name else ""}{def_name}')
+
+
+        schema_type: Optional[str] = schema.get("type") # type: ignore
+        assert isinstance(schema_type, str), f"Unrecognized schema: {schema}"
+
+        if schema_type == "object" and "properties" in schema:
             # TODO: `required` keyword
             prop_order = self._prop_order
             prop_pairs = sorted(
@@ -1489,14 +1500,6 @@ class SchemaConverter:
             )
             return self._add_rule(rule_name, rule)
 
-        elif "$ref" in schema:
-            ref = schema["$ref"]
-            assert ref.startswith("#/$defs/"), f"Unrecognized schema: {schema}"
-            # inline $defs
-            def_name = ref[len("#/$defs/") :]
-            def_schema = self._defs[def_name]
-            return self.visit(def_schema, f'{name}{"-" if name else ""}{def_name}')
-
         else:
             assert schema_type in PRIMITIVE_RULES, f"Unrecognized schema: {schema}"
             return self._add_rule(
diff --git a/tests/test_grammar.py b/tests/test_grammar.py
index ef9392b..cb22188 100644
--- a/tests/test_grammar.py
+++ b/tests/test_grammar.py
@@ -50,3 +50,29 @@ def test_composed_pydantic_grammar():
     grammar = llama_cpp.LlamaGrammar.from_json_schema(json.dumps(schema))
 
     assert grammar.grammar is not None
+
+
+def test_grammar_anyof():
+    sch = {
+        "properties": {
+            "temperature": {
+                "description": "The temperature mentioned",
+                "type": "number",
+            },
+            "unit": {
+                "anyOf": [
+                    {
+                        "description": "Unit for temperature",
+                        "enum": ["celsius", "fahrenheit"],
+                        "type": "string",
+                    },
+                    {"type": "null"},
+                ],
+            },
+        },
+        "type": "object",
+    }
+
+    grammar = llama_cpp.LlamaGrammar.from_json_schema(json.dumps(sch))
+
+    assert grammar.grammar is not None
\ No newline at end of file