diff --git a/artiq/compiler/ir.py b/artiq/compiler/ir.py
index c6b00869c..292d42427 100644
--- a/artiq/compiler/ir.py
+++ b/artiq/compiler/ir.py
@@ -48,7 +48,7 @@ class Value:
         self.uses, self.type = set(), typ.find()
 
     def replace_all_uses_with(self, value):
-        for user in self.uses:
+        for user in set(self.uses):
             user.replace_uses_of(self, value)
 
 class Constant(Value):
@@ -126,11 +126,11 @@ class User(NamedValue):
         self.set_operands([])
 
     def replace_uses_of(self, value, replacement):
-        assert value in operands
+        assert value in self.operands
 
-        for index, operand in enumerate(operands):
+        for index, operand in enumerate(self.operands):
             if operand == value:
-                operands[index] = replacement
+                self.operands[index] = replacement
 
         value.uses.remove(self)
         replacement.uses.add(self)
@@ -851,6 +851,9 @@ class Closure(Instruction):
 class Call(Instruction):
     """
     A function call operation.
+
+    :ivar static_target_function: (:class:`Function` or None)
+        statically resolved callee
     """
 
     """
@@ -861,6 +864,7 @@ class Call(Instruction):
         assert isinstance(func, Value)
         for arg in args: assert isinstance(arg, Value)
         super().__init__([func] + args, func.type.ret, name)
+        self.static_target_function = None
 
     def opcode(self):
         return "call"
@@ -871,6 +875,12 @@ class Call(Instruction):
     def arguments(self):
         return self.operands[1:]
 
+    def __str__(self):
+        result = super().__str__()
+        if self.static_target_function is not None:
+            result += " ; calls {}".format(self.static_target_function.name)
+        return result
+
 class Select(Instruction):
     """
     A conditional select instruction.
@@ -1080,6 +1090,9 @@ class Reraise(Terminator):
 class Invoke(Terminator):
     """
     A function call operation that supports exception handling.
+
+    :ivar static_target_function: (:class:`Function` or None)
+        statically resolved callee
     """
 
     """
@@ -1094,6 +1107,7 @@ class Invoke(Terminator):
         assert isinstance(normal, BasicBlock)
         assert isinstance(exn, BasicBlock)
         super().__init__([func] + args + [normal, exn], func.type.ret, name)
+        self.static_target_function = None
 
     def opcode(self):
         return "invoke"
@@ -1116,6 +1130,12 @@ class Invoke(Terminator):
                                             self.operands[-1].as_operand())
         return result
 
+    def __str__(self):
+        result = super().__str__()
+        if self.static_target_function is not None:
+            result += " ; calls {}".format(self.static_target_function.name)
+        return result
+
 class LandingPad(Terminator):
     """
     An instruction that gives an incoming exception a name and
diff --git a/artiq/compiler/module.py b/artiq/compiler/module.py
index 0dff76786..0e607fa4d 100644
--- a/artiq/compiler/module.py
+++ b/artiq/compiler/module.py
@@ -68,10 +68,9 @@ class Module:
         iodelay_estimator.visit_fixpoint(src.typedtree)
         devirtualization.visit(src.typedtree)
         self.artiq_ir = artiq_ir_generator.visit(src.typedtree)
+        artiq_ir_generator.annotate_calls(devirtualization)
         dead_code_eliminator.process(self.artiq_ir)
         local_access_validator.process(self.artiq_ir)
-        # for f in self.artiq_ir:
-        #     print(f)
 
     def build_llvm_ir(self, target):
         """Compile the module to LLVM IR for the specified target."""
diff --git a/artiq/compiler/transforms/artiq_ir_generator.py b/artiq/compiler/transforms/artiq_ir_generator.py
index 11ca96d52..3daadd8e2 100644
--- a/artiq/compiler/transforms/artiq_ir_generator.py
+++ b/artiq/compiler/transforms/artiq_ir_generator.py
@@ -63,6 +63,18 @@ class ARTIQIRGenerator(algorithm.Visitor):
         the basic block to which ``return`` will transfer control
     :ivar unwind_target: (:class:`ir.BasicBlock` or None)
         the basic block to which unwinding will transfer control
+
+    There is, additionally, some global state that is used to translate
+    the results of analyses on AST level to IR level:
+
+    :ivar function_map: (map of :class:`ast.FunctionDefT` to :class:`ir.Function`)
+        the map from function definition nodes to IR functions
+    :ivar variable_map: (map of :class:`ast.NameT` to :class:`ir.GetLocal`)
+        the map from variable name nodes to instructions retrieving
+        the variable values
+    :ivar method_map: (map of :class:`ast.AttributeT` to :class:`ir.GetAttribute`)
+        the map from method resolution nodes to instructions retrieving
+        the called function inside a translated :class:`ast.CallT` node
     """
 
     _size_type = builtins.TInt(types.TValue(32))
@@ -86,6 +98,19 @@ class ARTIQIRGenerator(algorithm.Visitor):
         self.continue_target = None
         self.return_target = None
         self.unwind_target = None
+        self.function_map = dict()
+        self.variable_map = dict()
+        self.method_map = dict()
+
+    def annotate_calls(self, devirtualization):
+        for var_node in devirtualization.variable_map:
+            callee_node = devirtualization.variable_map[var_node]
+            callee      = self.function_map[callee_node]
+            call_target = self.variable_map[var_node]
+            for use in call_target.uses:
+                if isinstance(use, (ir.Call, ir.Invoke)) and \
+                        use.target_function() == call_target:
+                    use.static_target_function = callee
 
     def add_block(self, name=""):
         block = ir.BasicBlock([], name)
@@ -204,6 +229,9 @@ class ARTIQIRGenerator(algorithm.Visitor):
             self.functions.append(func)
             old_func, self.current_function = self.current_function, func
 
+            if not is_lambda:
+                self.function_map[node] = func
+
             entry = self.add_block()
             old_block, self.current_block = self.current_block, entry
 
@@ -701,7 +729,9 @@ class ARTIQIRGenerator(algorithm.Visitor):
 
     def visit_NameT(self, node):
         if self.current_assign is None:
-            return self._get_local(node.id)
+            insn = self._get_local(node.id)
+            self.variable_map[node] = insn
+            return insn
         else:
             return self._set_local(node.id, self.current_assign)