diff --git a/doc/conf.py b/doc/conf.py
index d81510bb019b2a0feb23ebffef0d29739066d1a1..2991a2f4b73a6fbb8708a57fce8ce6a4d9cd84a0 100644
--- a/doc/conf.py
+++ b/doc/conf.py
@@ -26,6 +26,7 @@ intersphinx_mapping = {
     "https://documen.tician.de/loopy/": None,
     "https://documen.tician.de/sumpy/": None,
     "https://documen.tician.de/islpy/": None,
+    "https://pyrsistent.readthedocs.io/en/latest/": None,
 }
 
 import sys
@@ -33,4 +34,6 @@ sys.PYTATO_BUILDING_SPHINX_DOCS = True
 
 nitpick_ignore_regex = [
     ["py:class", r"numpy.(u?)int[\d]+"],
+    ["py:class", r"pyrsistent.typing.(.+)"],
+
 ]
diff --git a/pytato/transform.py b/pytato/transform.py
index d38edc2c72b9018ae34c113645ab92f0316e2ab4..480a377eca1887c070a8c223cfeac5fb015387a6 100644
--- a/pytato/transform.py
+++ b/pytato/transform.py
@@ -44,6 +44,8 @@ from pytato.array import (
 from pytato.loopy import LoopyCall, LoopyCallResult
 from dataclasses import dataclass
 from pytato.tags import ImplStored
+from pyrsistent import pmap
+from pyrsistent.typing import PMap as PMapT
 
 if TYPE_CHECKING:
     from pytato.distributed import DistributedSendRefHolder, DistributedRecv
@@ -1255,15 +1257,16 @@ def get_users(expr: ArrayOrNames) -> Dict[ArrayOrNames,
 
 # {{{ operations on graphs in dict form
 
-def reverse_graph(graph: Dict[ArrayOrNames, Set[ArrayOrNames]]) \
-        -> Dict[ArrayOrNames, Set[ArrayOrNames]]:
-    """Reverses a graph.
+def reverse_graph(graph: Mapping[ArrayOrNames, FrozenSet[ArrayOrNames]]
+                  ) -> PMapT[ArrayOrNames, FrozenSet[ArrayOrNames]]:
+    """
+    Reverses a graph.
 
     :param graph: A :class:`dict` representation of a directed graph, mapping each
         node to other nodes to which it is connected by edges. A possible
         use case for this function is the graph in
         :attr:`UsersCollector.node_to_users`.
-    :returns: A :class:`dict` representing *graph* with edges reversed.
+    :returns: A :class:`pyrsistent.PMap` representing *graph* with edges reversed.
     """
     result: Dict[ArrayOrNames, Set[ArrayOrNames]] = {}
 
@@ -1274,7 +1277,7 @@ def reverse_graph(graph: Dict[ArrayOrNames, Set[ArrayOrNames]]) \
         for other_node_key in edges:
             result.setdefault(other_node_key, set()).add(node_key)
 
-    return result
+    return pmap({k: frozenset(v) for k, v in result.items()})
 
 
 def _recursively_get_all_users(