diff --git a/src/ControlledOpSet.ts b/src/ControlledOpSet.ts
index ddd4740..dbb434d 100644
--- a/src/ControlledOpSet.ts
+++ b/src/ControlledOpSet.ts
@@ -1,14 +1,8 @@
 import {Timestamp} from "./helper/Timestamp";
-import {
-  asType,
-  mapMapToMap,
-  mapWith,
-  mapWithout,
-  RoArray,
-  RoMap,
-} from "./helper/Collection";
+import {asType, RoArray, RoMap} from "./helper/Collection";
 import {TypedValue} from "./helper/TypedValue";
 import {AssertFailed} from "./helper/Assert";
+import {HashMap} from "prelude-ts";
 
 export class DeviceId extends TypedValue<"DeviceId", string> {}
 
@@ -45,7 +39,7 @@ export type UndoOp<Value, AppliedOp extends AppliedOpBase> = (
 
 type DesiredHeads<Value, AppliedOp extends AppliedOpBase> = (
   value: Value,
-) => RoMap<DeviceId, "open" | OpList<AppliedOp>>;
+) => HashMap<DeviceId, "open" | OpList<AppliedOp>>;
 
 export class ControlledOpSet<Value, AppliedOp extends AppliedOpBase> {
   static create<Value, AppliedOp extends AppliedOpBase>(
@@ -60,7 +54,7 @@ export class ControlledOpSet<Value, AppliedOp extends AppliedOpBase> {
       desiredHeads,
       value,
       undefined,
-      RoMap(),
+      HashMap.empty(),
     );
   }
 
@@ -71,28 +65,31 @@ export class ControlledOpSet<Value, AppliedOp extends AppliedOpBase> {
 
     readonly value: Value,
     readonly appliedHead: AppliedOpList<AppliedOp> | undefined,
-    readonly heads: RoMap<DeviceId, OpList<AppliedOp>>,
+    readonly heads: HashMap<DeviceId, OpList<AppliedOp>>,
   ) {}
 
   update(
-    remoteHeads: RoMap<DeviceId, undefined | OpList<AppliedOp>>,
+    remoteHeads: HashMap<DeviceId, undefined | OpList<AppliedOp>>,
   ): ControlledOpSet<Value, AppliedOp> {
     const abstractDesiredHeads = this.desiredHeads(this.value);
-    const filteredAbstractDesiredHeads = RoMap(
-      Array.from(abstractDesiredHeads.entries()).filter(
-        ([deviceId]) => remoteHeads.get(deviceId) !== undefined,
-      ),
-    );
-    const desiredHeads = mapMapToMap(
-      filteredAbstractDesiredHeads,
-      (deviceId, openOrOp) => [
-        deviceId,
-        asType<OpList<AppliedOp>>(
-          openOrOp === "open" ? remoteHeads.get(deviceId)! : openOrOp,
-        ),
-      ],
+    const filteredAbstractDesiredHeads = abstractDesiredHeads.filterKeys(
+      (deviceId) => remoteHeads.get(deviceId).getOrUndefined() !== undefined,
     );
-    if (ControlledOpSet.headsEqual(desiredHeads, this.heads)) return this;
+    const desiredHeads = filteredAbstractDesiredHeads.map<
+      DeviceId,
+      OpList<AppliedOp>
+    >((deviceId, openOrOp) => [
+      deviceId,
+      asType<OpList<AppliedOp>>(
+        openOrOp === "open"
+          ? remoteHeads
+              .get(deviceId)
+              .getOrThrow("There should be a remote head for this deviceId")!
+          : openOrOp,
+      ),
+    ]);
+
+    if (desiredHeads.equals(this.heads)) return this;
 
     const {value, appliedHead, ops} = ControlledOpSet.commonStateAndDesiredOps(
       this.undoOp,
@@ -131,8 +128,8 @@ export class ControlledOpSet<Value, AppliedOp extends AppliedOpBase> {
     AppliedOp extends AppliedOpBase,
   >(
     undoOp: UndoOp<Value, AppliedOp>,
-    desiredHeads: RoMap<DeviceId, OpList<AppliedOp>>,
-    actualHeads: RoMap<DeviceId, OpList<AppliedOp>>,
+    desiredHeads: HashMap<DeviceId, OpList<AppliedOp>>,
+    actualHeads: HashMap<DeviceId, OpList<AppliedOp>>,
     value: Value,
     appliedHead: undefined | AppliedOpList<AppliedOp>,
   ): {
@@ -142,7 +139,7 @@ export class ControlledOpSet<Value, AppliedOp extends AppliedOpBase> {
   } {
     const ops = new Array<AppliedOp["op"]>();
 
-    while (!ControlledOpSet.headsEqual(desiredHeads, actualHeads)) {
+    while (!desiredHeads.equals(actualHeads)) {
       const {heads: nextRemainingDesiredHeads, op: desiredOp} =
         ControlledOpSet.undoHeadsOnce(desiredHeads);
       const {heads: nextActualHeads, op: actualOp} =
@@ -205,25 +202,25 @@ export class ControlledOpSet<Value, AppliedOp extends AppliedOpBase> {
   }
 
   private static undoHeadsOnce<AppliedOp extends AppliedOpBase>(
-    heads: RoMap<DeviceId, OpList<AppliedOp>>,
+    heads: HashMap<DeviceId, OpList<AppliedOp>>,
   ): {
     op: undefined | AppliedOp["op"];
-    heads: RoMap<DeviceId, OpList<AppliedOp>>;
+    heads: HashMap<DeviceId, OpList<AppliedOp>>;
   } {
-    if (heads.size === 0) return {op: undefined, heads};
+    if (heads.length() === 0) return {op: undefined, heads};
 
-    const [newestDeviceId, newestOpList] = Array.from(heads.entries()).reduce(
-      (winner, current) => {
+    const [newestDeviceId, newestOpList] = heads
+      .reduce((winner, current) => {
         return winner[1].op.timestamp > current[1].op.timestamp
           ? winner
           : current;
-      },
-    );
+      })
+      .getOrThrow("Reducing over empty heads");
     return {
       op: newestOpList.op,
       heads: newestOpList.prev
-        ? mapWith(heads, newestDeviceId, newestOpList.prev)
-        : mapWithout(heads, newestDeviceId),
+        ? heads.put(newestDeviceId, newestOpList.prev)
+        : heads.remove(newestDeviceId),
     };
   }
 
diff --git a/src/PermissionedTree.monkey.test.ts b/src/PermissionedTree.monkey.test.ts
index 2b70409..ca24535 100644
--- a/src/PermissionedTree.monkey.test.ts
+++ b/src/PermissionedTree.monkey.test.ts
@@ -1,12 +1,5 @@
 import seedRandom from "seed-random";
-import {
-  asType,
-  definedOrThrow,
-  mapMapToMap,
-  mapWith,
-  RoArray,
-  RoMap,
-} from "./helper/Collection";
+import {asType, definedOrThrow, RoArray} from "./helper/Collection";
 import {
   AppliedOp,
   createPermissionedTree,
@@ -16,6 +9,7 @@ import {
 import {DeviceId} from "./ControlledOpSet";
 import {Clock} from "./helper/Clock";
 import {Timestamp} from "./helper/Timestamp";
+import {HashMap} from "prelude-ts";
 import {expectPreludeEqual} from "./helper/Shared.testing";
 
 type OpType = "add" | "move" | "update";
@@ -86,11 +80,11 @@ describe("PermissionedTree.monkey", function () {
       priority: -1,
       status: "open",
     });
-    let devices = RoMap<DeviceId, PermissionedTree>(
-      Array.from(Array(4).keys()).map((index) => [
-        DeviceId.create(`device${index}`),
-        initialTree,
-      ]),
+    let devices = HashMap<DeviceId, PermissionedTree>.of(
+      [DeviceId.create("device1"), initialTree],
+      [DeviceId.create("device2"), initialTree],
+      [DeviceId.create("device3"), initialTree],
+      [DeviceId.create("device4"), initialTree],
     );
 
     for (let turn = 0; turn < 10000; turn++) {
@@ -107,38 +101,42 @@ describe("PermissionedTree.monkey", function () {
 
       // Update a device.
       {
-        const device = randomInArray(rand, Array.from(devices.keys()))!;
-        const tree = devices.get(device)!;
+        const device = randomInArray(rand, Array.from(devices.keySet()))!;
+        const tree = devices.get(device).getOrThrow("Device should be listed");
         const opType = randomOpType(rand);
 
         log(`turn ${turn}, device ${device}, op type ${opType}`);
         if (opType === "update") {
-          const remoteHeads = mapMapToMap(devices, (device, tree) => [
+          const remoteHeads = devices.map((device, tree) => [
             device,
-            tree.heads.get(device),
+            tree.heads
+              .get(device)
+              .getOrThrow("Couldn't get device in tree heads"),
           ]);
           const tree1 = tree.update(remoteHeads);
-          devices = mapWith(devices, device, tree1);
+          devices = devices.put(device, tree1);
         } else {
           const op = opForOpType(clock, log, rand, opType, tree);
           const tree1 = applyNewOp(tree, device, op);
-          devices = mapWith(devices, device, tree1);
+          devices = devices.put(device, tree1);
         }
       }
 
       // Check the devices.
       if (turn % 10 === 0) {
-        const remoteHeads = mapMapToMap(devices, (device, tree) => [
+        const remoteHeads = devices.map((device, tree) => [
           device,
-          tree.heads.get(device),
+          tree.heads
+            .get(device)
+            .getOrThrow("Couldn't retrieve device from tree heads"),
         ]);
-        const devices1 = mapMapToMap(devices, (device, tree) => [
+        const devices1 = devices.map((device, tree) => [
           device,
           tree.update(remoteHeads),
         ]);
-        // for (const [, tree] of devices1) {
-        //   expectPreludeEqual(tree, Array.from(devices1.values())[0]);
-        // }
+        for (const [, tree] of devices1) {
+          expectPreludeEqual(tree, Array.from(devices1.values())[0]);
+        }
       }
     }
   });
@@ -190,7 +188,10 @@ function applyNewOp(
   device: DeviceId,
   op: AppliedOp["op"],
 ): PermissionedTree {
-  const opList1 = {prev: tree.heads.get(device), op};
-  const heads1 = mapWith(tree.heads, device, opList1);
+  const opList1 = {
+    prev: tree.heads.get(device).getOrThrow("Couldn't construct op list 1"),
+    op,
+  };
+  const heads1 = tree.heads.put(device, opList1);
   return tree.update(heads1);
 }
diff --git a/src/PermissionedTree.ts b/src/PermissionedTree.ts
index 29dd2bc..10efde7 100644
--- a/src/PermissionedTree.ts
+++ b/src/PermissionedTree.ts
@@ -1,10 +1,4 @@
-import {
-  asType,
-  definedOrThrow,
-  mapMapToMap,
-  mapWith,
-  RoMap,
-} from "./helper/Collection";
+import {asType} from "./helper/Collection";
 import {ControlledOpSet, DeviceId, OpList} from "./ControlledOpSet";
 import {Timestamp} from "./helper/Timestamp";
 import {TypedValue} from "./helper/TypedValue";
@@ -45,11 +39,27 @@ class ParentPos {
   }
 }
 
+class PriorityStatus {
+  public priority: number;
+  public status: "open" | OpList<AppliedOp>;
+  constructor(priority: number, status: "open" | OpList<AppliedOp>) {
+    this.priority = priority;
+    this.status = status;
+  }
+  equals(other: PriorityStatus | undefined): boolean {
+    if (!other) return false;
+    return (
+      areEqual(this.priority, other.priority) &&
+      areEqual(this.status, other.status)
+    );
+  }
+  hashCode(): number {
+    return fieldsHashCode(this.priority, this.status);
+  }
+}
+
 type PermissionedTreeValue = {
-  writers: RoMap<
-    DeviceId,
-    {priority: number; status: "open" | OpList<AppliedOp>}
-  >;
+  writers: HashMap<DeviceId, PriorityStatus>;
   nodes: HashMap<NodeId, ParentPos>;
 };
 export class NodeId extends TypedValue<"NodeId", string> {}
@@ -78,21 +88,22 @@ export function createPermissionedTree(owner: DeviceId): PermissionedTree {
   return ControlledOpSet<PermissionedTreeValue, AppliedOp>.create(
     persistentDoOpFactory((value, op) => {
       if (op.type === "set writer") {
-        const devicePriority = definedOrThrow(
-          value.writers.get(op.device),
-          "Cannot find writer entry for op author",
-        ).priority;
-        const writerPriority = value.writers.get(op.targetWriter)?.priority;
+        const devicePriority = value.writers
+          .get(op.device)
+          .getOrThrow("Cannot find writer entry for op author").priority;
+        const writerPriority = value.writers
+          .get(op.targetWriter)
+          .getOrUndefined()?.priority;
         if (writerPriority !== undefined && writerPriority >= devicePriority)
           return value;
         if (op.priority >= devicePriority) return value;
 
         return {
           ...value,
-          writers: mapWith(value.writers, op.targetWriter, {
-            priority: op.priority,
-            status: op.status,
-          }),
+          writers: value.writers.put(
+            op.targetWriter,
+            new PriorityStatus(op.priority, op.status),
+          ),
         };
       } else {
         if (ancestor(value.nodes, op.node, op.parent)) return value;
@@ -106,10 +117,9 @@ export function createPermissionedTree(owner: DeviceId): PermissionedTree {
       }
     }),
     persistentUndoOp,
-    (value) =>
-      mapMapToMap(value.writers, (device, info) => [device, info.status]),
+    (value) => value.writers.mapValues((info) => info.status),
     asType<PermissionedTreeValue>({
-      writers: RoMap([[owner, {priority: 0, status: "open"}]]),
+      writers: HashMap.of([owner, new PriorityStatus(0, "open")]),
       nodes: HashMap.empty(),
     }),
   );
diff --git a/src/helper/TypedValue.ts b/src/helper/TypedValue.ts
index 6f09c40..3bf81fc 100644
--- a/src/helper/TypedValue.ts
+++ b/src/helper/TypedValue.ts
@@ -1,4 +1,6 @@
-export class TypedValue<Name extends string, T> {
+import {HasEquals} from "prelude-ts";
+
+export class TypedValue<Name extends string, T> implements HasEquals {
   static create<Name extends string, T>(
     this: new (raw: T) => TypedValue<Name, T>,
     raw: T,