diff --git a/reasoning_gym/cognition/sequences.py b/reasoning_gym/cognition/sequences.py
index 8dfb4649..c1d6d4f0 100644
--- a/reasoning_gym/cognition/sequences.py
+++ b/reasoning_gym/cognition/sequences.py
@@ -40,9 +40,10 @@ class SequenceConfig:
 class PatternRule:
     """Represents a composable sequence pattern rule"""
 
-    def __init__(self, operations: List[Operation], parameters: List[int]):
+    def __init__(self, operations: List[Operation], parameters: List[int], subrules: List['PatternRule'] = None):
         self.operations = operations
         self.parameters = parameters
+        self.subrules = subrules or []
 
     def apply(self, sequence: List[int], position: int) -> int:
         """Apply the rule to generate the next number"""
@@ -62,9 +63,20 @@ class PatternRule:
             elif op == Operation.PREV_PLUS:
                 if position > 0:
                     result += sequence[position - 1]
+            elif op == Operation.COMPOSE:
+                # Apply each subrule in sequence
+                temp_sequence = sequence[:position + 1]
+                temp_sequence[-1] = result  # Use current result as input
+                for subrule in self.subrules:
+                    result = subrule.apply(temp_sequence, position)
 
         return result
 
+    @classmethod
+    def compose(cls, rules: List['PatternRule']) -> 'PatternRule':
+        """Create a new rule that composes multiple rules together"""
+        return cls([Operation.COMPOSE], [0], subrules=rules)
+
     def to_string(self) -> str:
         """Convert rule to human-readable string"""
         parts = []
diff --git a/tests/test_sequences.py b/tests/test_sequences.py
index 1d6c3a97..6d383284 100644
--- a/tests/test_sequences.py
+++ b/tests/test_sequences.py
@@ -23,11 +23,17 @@ def test_pattern_rule():
     # Test simple addition
     rule = PatternRule([Operation.ADD], [2])
     assert rule.apply([1, 3], 1) == 5
-
+    
     # Test composition
     rule = PatternRule([Operation.DOUBLE, Operation.ADD], [0, 3])
     assert rule.apply([1, 4], 1) == 11  # (4 * 2) + 3
 
+    # Test rule composition
+    rule1 = PatternRule([Operation.DOUBLE], [0])  # Double the number
+    rule2 = PatternRule([Operation.ADD], [3])     # Add 3
+    composed = PatternRule.compose([rule1, rule2])
+    assert composed.apply([1, 4], 1) == 11  # (4 * 2) + 3
+
 
 def test_sequence_dataset_deterministic():
     """Test that dataset generates same items with same seed"""