diff --git a/compiler/ir.py b/compiler/ir.py
index ddc8217..6035c61 100644
--- a/compiler/ir.py
+++ b/compiler/ir.py
@@ -125,12 +125,20 @@ class IRAssignable(IRValue, metaclass=abc.ABCMeta):
 
 
 class IRRegister(IRAssignable):
-    register_id = 0
+    register_id: int = 0
+    registers: dict[int, IRRegister] = {}
 
     def __init__(self, location: SourceLocation):
         super().__init__(location)
         self.id = IRRegister.register_id
         IRRegister.register_id += 1
+        IRRegister.registers[self.id] = self
+
+    def __hash__(self) -> int:
+        return self.id
+
+    def remove(self):
+        del IRRegister.registers[self.id]
 
     def codegen(self):
         return f"%r{self.id}"