diff --git a/loopy/kernel.py b/loopy/kernel.py
index 8ac9c12045e29c3969ab0f5133db5aafb2798765..24ca824e73b5bc1da793031573ea910a03c6944f 100644
--- a/loopy/kernel.py
+++ b/loopy/kernel.py
@@ -299,7 +299,7 @@ class Instruction(Record):
     """
     def __init__(self,
             id, assignee, expression,
-            forced_iname_deps=set(), insn_deps=set(), boostable=None,
+            forced_iname_deps=frozenset(), insn_deps=set(), boostable=None,
             boostable_into=None,
             temp_var_type=None, duplicate_inames_and_tags=[]):
 
@@ -309,7 +309,7 @@ class Instruction(Record):
         if isinstance(expression, str):
             assignee = parse(expression)
 
-        assert isinstance(forced_iname_deps, set)
+        assert isinstance(forced_iname_deps, frozenset)
         assert isinstance(insn_deps, set)
 
         Record.__init__(self,
@@ -738,10 +738,10 @@ class LoopKernel(Record):
                 if groups["iname_deps_and_tags"] is not None:
                     inames_and_tags = parse_iname_and_tag_list(
                             groups["iname_deps_and_tags"])
-                    forced_iname_deps = set(iname for iname, tag in inames_and_tags)
+                    forced_iname_deps = frozenset(iname for iname, tag in inames_and_tags)
                     iname_to_tag_requests.update(dict(inames_and_tags))
                 else:
-                    forced_iname_deps = set()
+                    forced_iname_deps = frozenset()
 
                 if groups["duplicate_inames_and_tags"] is not None:
                     duplicate_inames_and_tags = parse_iname_and_tag_list(
diff --git a/loopy/symbolic.py b/loopy/symbolic.py
index c7376b4d652156bdf953bae3eaba84dcb63f5065..92629cc160ab8c0482e8a400a117ba58680f46b5 100644
--- a/loopy/symbolic.py
+++ b/loopy/symbolic.py
@@ -691,7 +691,7 @@ def get_dependencies(expr):
     from loopy.symbolic import DependencyMapper
     dep_mapper = DependencyMapper(composite_leaves=False)
 
-    return set(dep.name for dep in dep_mapper(expr))
+    return frozenset(dep.name for dep in dep_mapper(expr))