diff --git a/implementations/javascript/package.json b/implementations/javascript/package.json
index 3d7000b..29e6fbb 100644
--- a/implementations/javascript/package.json
+++ b/implementations/javascript/package.json
@@ -9,6 +9,7 @@
   },
   "repository": "gitlab:preserves/preserves",
   "main": "lib/index.js",
+  "types": "lib/index.d.ts",
   "author": "Tony Garnock-Jones <tonyg@leastfixedpoint.com>",
   "devDependencies": {
     "@types/jest": "^26.0.19",
diff --git a/implementations/javascript/src/codec.ts b/implementations/javascript/src/codec.ts
index 7ee522e..c978a8b 100644
--- a/implementations/javascript/src/codec.ts
+++ b/implementations/javascript/src/codec.ts
@@ -4,7 +4,6 @@ import {
     underlying,
     Annotated,
     Dictionary, Set, Bytes, Record, Single, Double,
-    isSet, isDictionary,
     BytesLike,
     Value,
 } from './values';
@@ -117,8 +116,8 @@ export class Decoder {
         return this.includeAnnotations ? new Annotated(v) : v;
     }
 
-    static dictionaryFromArray(vs: Value[]): Dictionary {
-        const d = new Dictionary();
+    static dictionaryFromArray(vs: Value[]): Dictionary<Value> {
+        const d = new Dictionary<Value>();
         if (vs.length % 2) throw new DecodeError("Missing dictionary value");
         for (let i = 0; i < vs.length; i += 2) {
             d.set(vs[i], vs[i+1]);
@@ -294,7 +293,7 @@ export class Encoder {
         this.emitbyte(Tag.End);
     }
 
-    push(v: Value) {
+    push(v: any) {
         if (typeof v === 'object' && v !== null && typeof v[PreserveOn] === 'function') {
             v[PreserveOn](this);
         }
@@ -327,30 +326,6 @@ export class Encoder {
         else if (Array.isArray(v)) {
             this.encodevalues(Tag.Sequence, v);
         }
-        else if (isSet(v)) {
-            if (this.canonical) {
-                const pieces = v._map((_v, k) => encode(k, { canonical: true }));
-                pieces.sort(Bytes.compare);
-                this.encoderawvalues(Tag.Set, pieces);
-            } else {
-                this.encodevalues(Tag.Set, v);
-            }
-        }
-        else if (isDictionary(v)) {
-            if (this.canonical) {
-                const pieces = v._map((v, k) => Bytes.concat([encode(k, { canonical: true }),
-                                                              encode(v, { canonical: true })]));
-                pieces.sort(Bytes.compare);
-                this.encoderawvalues(Tag.Dictionary, pieces);
-            } else {
-                this.emitbyte(Tag.Dictionary);
-                v._forEach((v, k) => {
-                    this.push(k);
-                    this.push(v);
-                });
-                this.emitbyte(Tag.End);
-            }
-        }
         else if (typeof v === 'object' && v !== null && typeof v[Symbol.iterator] === 'function') {
             this.encodevalues(Tag.Sequence, v as Iterable<Value>);
         }
@@ -361,10 +336,10 @@ export class Encoder {
     }
 }
 
-export function encode(v: Value, options?: EncoderOptions): Bytes {
+export function encode(v: any, options?: EncoderOptions): Bytes {
     return new Encoder(options).push(v).contents();
 }
 
-export function encodeWithAnnotations(v: Value, options: EncoderOptions = {}): Bytes {
+export function encodeWithAnnotations(v: any, options: EncoderOptions = {}): Bytes {
     return encode(v, { ... options, includeAnnotations: true });
 }
diff --git a/implementations/javascript/src/flex.ts b/implementations/javascript/src/flex.ts
new file mode 100644
index 0000000..1d098d5
--- /dev/null
+++ b/implementations/javascript/src/flex.ts
@@ -0,0 +1,223 @@
+// FlexMap, FlexSet: like built-in Map and Set, but with a
+// canonicalization function which gives us the possibility of a
+// coarser equivalence than the identity equivalence used in Map and
+// Set.
+
+// A Canonicalizer represents the equivalence you have in mind. For
+//
+//    c: Canonicalizer<V>
+//    eqv: Equivalence<V>
+//    v1: V
+//    v2: V
+//
+// where `eqv` is the equivalence you want,
+//
+//     eqv(v1, v2) ⇔ c(v1) === c(v2)
+//
+export type Canonicalizer<V> = (v: V) => string;
+export type Equivalence<V> = (v1: V, v2: V) => boolean;
+
+export type IdentityMap<K, V> = Map<K, V>;
+export type IdentitySet<V> = Set<V>;
+export const IdentityMap = Map;
+export const IdentitySet = Set;
+
+export function _iterMap<S,T>(i: Iterator<S> | undefined, f : (s: S) => T): IterableIterator<T> {
+    if (!i) return void 0;
+    const _f = (r: IteratorResult<S>): IteratorResult<T> => {
+        const { done, value } = r;
+        return { done, value: done ? void 0 : f(value) };
+    };
+    return {
+        next: (v?: any): IteratorResult<T> => _f(i.next(v)),
+        return: (v?: any): IteratorResult<T> => _f(i.return(v)),
+        throw: (e?: any): IteratorResult<T> => _f(i.throw(e)),
+        [Symbol.iterator]() { return this; },
+    };
+}
+
+export class FlexMap<K, V> implements Map<K, V> {
+    readonly items: Map<string, [K, V]>;
+    readonly canonicalizer: Canonicalizer<K>;
+
+    constructor(c: Canonicalizer<K>, items?: Iterable<readonly [K, V]>) {
+        this.canonicalizer = c;
+        this.items = new Map((items === void 0)
+            ? void 0
+            : _iterMap(items[Symbol.iterator](), ([k, v]) => [this._key(k), [k, v]]));
+    }
+
+    _key(k: K): string {
+        return this.canonicalizer(k);
+    }
+
+    get(k: K, defaultValue?: V): V | undefined {
+        const e = this.items.get(this._key(k));
+        return (e === void 0) ? defaultValue : e[1];
+    }
+
+    set(k: K, v: V): this {
+        this.items.set(this._key(k), [k, v]);
+        return this;
+    }
+
+    forEach(f: <T extends Map<K, V>> (v: V, k: K, map: T) => void, thisArg?: any) {
+        this.items.forEach(([k, v]) => f.call(thisArg, v, k, this));
+    }
+
+    entries(): IterableIterator<[K, V]> {
+        return this.items.values();
+    }
+
+    keys(): IterableIterator<K> {
+        return _iterMap(this.items.values(), ([k, _v]) => k);
+    }
+
+    values(): IterableIterator<V> {
+        return _iterMap(this.items.values(), ([_k, v]) => v);
+    }
+
+    delete(k: K): boolean {
+        return this.items.delete(this._key(k));
+    }
+
+    clear() {
+        this.items.clear();
+    }
+
+    has(k: K): boolean {
+        return this.items.has(this._key(k));
+    }
+
+    get size(): number {
+        return this.items.size;
+    }
+
+    [Symbol.iterator](): IterableIterator<[K, V]> {
+        return this.items.values();
+    }
+
+    [Symbol.toStringTag] = 'FlexMap';
+
+    equals(other: any, eqv: Equivalence<V> = (v1, v2) => v1 === v2): boolean {
+        if (!('size' in other && 'has' in other && 'get' in other)) return false;
+        if (this.size !== other.size) return false;
+        for (let [k, v] of this.items.values()) {
+            if (!other.has(k)) return false;
+            if (!eqv(v, other.get(k))) return false;
+        }
+        return true;
+    }
+
+    update(key: K,
+           f: (oldValue?: V) => V | undefined,
+           defaultValue?: V,
+           eqv: Equivalence<V> = (v1, v2) => v1 === v2): number
+    {
+        const ks = this._key(key);
+        if (this.items.has(ks)) {
+            const oldValue = this.items.get(ks)[1];
+            const newValue = f(oldValue);
+            if (newValue === void 0) {
+                this.items.delete(ks);
+                return -1;
+            } else {
+                if (!eqv(newValue, oldValue)) this.items.set(ks, [key, newValue]);
+                return 0;
+            }
+        } else {
+            const newValue = f(defaultValue);
+            if (newValue === void 0) {
+                return 0;
+            } else {
+                this.items.set(ks, [key, newValue]);
+                return 1;
+            }
+        }
+    }
+
+    canonicalKeys(): IterableIterator<string> {
+        return this.items.keys();
+    }
+}
+
+export class FlexSet<V> implements Set<V> {
+    readonly items: Map<string, V>;
+    readonly canonicalizer: Canonicalizer<V>;
+
+    constructor(c: Canonicalizer<V>, items?: Iterable<V>) {
+        this.canonicalizer = c;
+        this.items = new Map((items === void 0)
+            ? void 0
+            : _iterMap(items[Symbol.iterator](), (v) => [this._key(v), v]));
+    }
+
+    _key(v: V): string {
+        return this.canonicalizer(v);
+    }
+
+    has(v: V): boolean {
+        return this.items.has(this._key(v));
+    }
+
+    get(v: V): {item: V} | null {
+        const vs = this._key(v);
+        if (this.items.has(vs)) {
+            return {item: this.items[vs]};
+        } else {
+            return null;
+        }
+    }
+
+    add(v: V): this {
+        this.items[this._key(v)] = v;
+        return this;
+    }
+
+    forEach(f: <T extends Set<V>>(v: V, v2: V, set: T) => void, thisArg?: any) {
+        this.items.forEach((v) => f.call(thisArg, v, v, this));
+    }
+
+    entries(): IterableIterator<[V, V]> {
+        return _iterMap(this.items.values(), (v) => [v, v]);
+    }
+
+    keys(): IterableIterator<V> {
+        return this.items.values();
+    }
+
+    values(): IterableIterator<V> {
+        return this.items.values();
+    }
+
+    delete(v: V): boolean {
+        return this.items.delete(this._key(v));
+    }
+
+    clear() {
+        this.items.clear();
+    }
+
+    get size(): number {
+        return this.items.size;
+    }
+
+    [Symbol.iterator](): IterableIterator<V> {
+        return this.items.values();
+    }
+
+    [Symbol.toStringTag] = 'FlexSet';
+
+    equals(other: any): boolean {
+        if (!('size' in other && 'has' in other)) return false;
+        if (this.size !== other.size) return false;
+        for (let v of this.items.values()) {
+            if (!other.has(v)) return false;
+        }
+        return true;
+    }
+
+    canonicalValues(): IterableIterator<string> {
+        return this.items.keys();
+    }
+}
diff --git a/implementations/javascript/src/index.ts b/implementations/javascript/src/index.ts
index 6926d5b..0f84416 100644
--- a/implementations/javascript/src/index.ts
+++ b/implementations/javascript/src/index.ts
@@ -1,3 +1,4 @@
+export * from './flex';
 export * from './symbols';
 export * from './codec';
 export * from './values';
diff --git a/implementations/javascript/src/text.ts b/implementations/javascript/src/text.ts
index fbbe98d..307b000 100644
--- a/implementations/javascript/src/text.ts
+++ b/implementations/javascript/src/text.ts
@@ -1,10 +1,14 @@
 import { Value } from './values';
 
-export function stringify(x: Value): string {
+export function stringify(x: any): string {
     if (typeof x === 'object' && x !== null && 'asPreservesText' in x) {
         return x.asPreservesText();
     } else {
-        return JSON.stringify(x);
+        try {
+            return JSON.stringify(x);
+        } catch (_e) {
+            return ('' + x).asPreservesText();
+        }
     }
 }
 
diff --git a/implementations/javascript/src/values.ts b/implementations/javascript/src/values.ts
index c48e358..090d081 100644
--- a/implementations/javascript/src/values.ts
+++ b/implementations/javascript/src/values.ts
@@ -3,13 +3,15 @@
 import { PreserveOn, AsPreserve } from './symbols';
 import { Tag } from './constants';
 import { Encoder, encode } from './codec';
+import { stringify } from './text';
+import { _iterMap, FlexMap, FlexSet, IdentityMap, IdentitySet } from './flex';
 
 const textEncoder = new TextEncoder();
 const textDecoder = new TextDecoder();
 
 export type Value = Atom | Compound | Annotated;
 export type Atom = boolean | Single | Double | number | string | Bytes | symbol;
-export type Compound = Record | Array<Value> | Set | Dictionary;
+export type Compound = Record | Array<Value> | Set | Dictionary<Value>;
 
 export function isRecord(x: any): x is Record {
     return Array.isArray(x) && 'label' in x;
@@ -517,12 +519,14 @@ export interface RecordConstructorInfo {
     arity: number;
 }
 
-export function is(a: Value, b: Value): boolean {
+export function is(a: any, b: any): boolean {
+    if (isAnnotated(a)) a = a.item;
+    if (isAnnotated(b)) b = b.item;
     if (Object.is(a, b)) return true;
     if (typeof a !== typeof b) return false;
     if (typeof a === 'object') {
         if (a === null || b === null) return false;
-        if ('equals' in a) return a.equals(b);
+        if ('equals' in a) return a.equals(b, is);
         if (Array.isArray(a) && Array.isArray(b)) {
             if (a.length !== b.length) return false;
             for (let i = 0; i < a.length; i++) if (!is(a[i], b[i])) return false;
@@ -542,176 +546,119 @@ export function isClassOf(ci: RecordConstructorInfo, v: any): v is Record {
 
 export type DictionaryType = 'Dictionary' | 'Set';
 
-export function is_Dictionary(x: any, t: DictionaryType): x is _Dictionary {
-    return typeof x === 'object' && x !== null &&
-        '_items' in x &&
-        '_dictionaryType' in x &&
-        x._dictionaryType() === t;
+export function is_Dictionary(x: any, t: DictionaryType): boolean {
+    return typeof x === 'object' && x !== null && x[Symbol.toStringTag] === t;
 }
 
-export const isDictionary = (x: any): x is Dictionary => is_Dictionary(x, 'Dictionary');
+export const isDictionary = <T> (x: any): x is Dictionary<T> => is_Dictionary(x, 'Dictionary');
 export const isSet = (x: any): x is Set => is_Dictionary(x, 'Set');
 
-export type DictionaryEntry = [Value, Value];
+export function _canonicalString(item: Value): string {
+    const bs = encode(item, { canonical: true })._view;
+    const s = String.fromCharCode.apply(null, bs);
+    return s;
+}
 
-export abstract class _Dictionary {
-    _items: { [key: string]: DictionaryEntry } = {};
-
-    _key(key: Value): string {
-        const bs = encode(key, { canonical: true })._view;
-        const s = String.fromCharCode.apply(null, bs);
-        return s;
-    }
-
-    _lookup(key: Value): DictionaryEntry | null {
-        const k = this._key(key);
-        return k in this._items ? this._items[k] : null;
-    }
-
-    _set(key: Value, value: Value) {
-        this._items[this._key(key)] = [key, value];
-    }
-
-    _get(key: Value, defaultValue?: Value): Value {
-        const k = this._key(key);
-        return k in this._items ? this._items[k][1] : defaultValue;
-    }
-
-    _delete(key: Value) {
-        delete this._items[this._key(key)];
-    }
-
-    _forEach(f: (value: Value, key: Value) => void) {
-        for (let ks in this._items) {
-            const [k, v] = this._items[ks];
-            f(v, k);
+export class Dictionary<T> extends FlexMap<Value, T> {
+    static fromJS(x: object): Dictionary<Value> {
+        if (isDictionary(x)) return x as Dictionary<Value>;
+        const d = new Dictionary<Value>();
+        for (let key in x) {
+            const value = x[key];
+            d.set(key, fromJS(value));
         }
+        return d;
     }
 
-    _map<T>(f: (value: Value, key: Value) => T): Array<T> {
-        const result = [];
-        for (let ks in this._items) {
-            const [k, v] = this._items[ks];
-            result.push(f(v, k));
+    constructor(items?: Iterable<readonly [any, T]>) {
+        super(_canonicalString, _iterMap(items?.[Symbol.iterator](), ([k,v]) => [fromJS(k), v]));
+    }
+
+    mapEntries<R>(f: (entry: [Value, T]) => [Value, R]): Dictionary<R> {
+        const result = new Dictionary<R>();
+        for (let oldEntry of this.entries()) {
+            const newEntry = f(oldEntry);
+            result.set(newEntry[0], newEntry[1])
         }
         return result;
     }
 
-    equals(other: any): boolean {
-        if (!Object.is(other.constructor, this.constructor)) return false;
-        const es1 = Object.entries(this._items);
-        if (es1.length !== Object.entries(other._items).length) return false;
-        for (let [ks1, e1] of es1) {
-            const e2 = other._items[ks1];
-            if (!is(e1[1], e2[1])) return false;
-        }
-        return true;
+    asPreservesText(): string {
+        return '{' +
+            Array.from(_iterMap(this.entries(), ([k, v]) =>
+                k.asPreservesText() + ': ' + stringify(v))).join(', ') +
+            '}';
+    }
+
+    clone(): Dictionary<T> {
+        return new Dictionary(this);
     }
 
     toString(): string {
         return this.asPreservesText();
     }
 
-    abstract asPreservesText(): string;
-    abstract _dictionaryType(): DictionaryType;
-}
+    [Symbol.toStringTag] = 'Dictionary';
 
-export class Dictionary extends _Dictionary {
-    static fromJS(x: object): Dictionary {
-        if (isDictionary(x)) return x;
-        const d = new Dictionary();
-        for (let key in x) {
-            const value = x[key];
-            d._set(key, fromJS(value));
+    [PreserveOn](encoder: Encoder) {
+        if (encoder.canonical) {
+            const pieces = Array.from(this).map(([k, v]) =>
+                Bytes.concat([encode(k, { canonical: true }),
+                              encode(v, { canonical: true })]));
+            pieces.sort(Bytes.compare);
+            encoder.encoderawvalues(Tag.Dictionary, pieces);
+        } else {
+            encoder.emitbyte(Tag.Dictionary);
+            this.forEach((v, k) => {
+                encoder.push(k);
+                encoder.push(v);
+            });
+            encoder.emitbyte(Tag.End);
         }
-        return d;
-    }
-
-    _dictionaryType(): DictionaryType {
-        return 'Dictionary';
-    }
-
-    set(key: Value, value: Value) {
-        this._set(key, value);
-    }
-
-    get(key: Value, defaultValue?: Value): Value {
-        return this._get(key, defaultValue);
-    }
-
-    delete(key: Value) {
-        this._delete(key);
-    }
-
-    mapEntries(f: (entry: DictionaryEntry) => DictionaryEntry): Dictionary {
-        const result = new Dictionary();
-        for (let ks in this._items) {
-            const oldEntry = this._items[ks];
-            const newEntry = f(oldEntry);
-            result._set(newEntry[0], newEntry[1])
-        }
-        return result;
-    }
-
-    forEach(f: (value: Value, key: Value) => void) {
-        this._forEach(f);
-    }
-
-    asPreservesText(): string {
-        return '{' +
-            this._map((v, k) => k.asPreservesText() + ': ' + v.asPreservesText()).join(', ') +
-            '}';
     }
 }
 
-export class Set extends _Dictionary implements Iterable<Value> {
-    constructor(items: Iterable<any> = []) {
-        super();
-        for (let item of items) this.add(fromJS(item));
-    }
-
-    _dictionaryType(): DictionaryType {
-        return 'Set';
-    }
-
-    add(v: Value) {
-        this._set(v, true);
-    }
-
-    delete(v: Value) {
-        this._delete(v);
-    }
-
-    includes(key: Value) {
-        return this._lookup(key) !== null;
-    }
-
-    forEach(f: (value: Value) => void) {
-        this._forEach((_v, k) => f(k));
+export class Set extends FlexSet<Value> {
+    constructor(items?: Iterable<any>) {
+        super(_canonicalString, _iterMap(items?.[Symbol.iterator](), fromJS));
     }
 
     map(f: (value: Value) => Value): Set {
-        const result = new Set();
-        for (let ks in this._items) {
-            const k = this._items[ks][0];
-            result._set(f(k), true);
-        }
-        return result;
+        return new Set(_iterMap(this[Symbol.iterator](), f));
     }
 
-    [Symbol.iterator](): Iterator<Value> {
-        return this._map((_v, k) => k)[Symbol.iterator]();
+    filter(f: (value: Value) => boolean): Set {
+        const result = new Set();
+        for (let k of this) if (f(k)) result.add(k);
+        return result;
     }
 
     asPreservesText(): string {
         return '#{' +
-            this._map((_v, k) => k.asPreservesText()).join(', ') +
+            Array.from(_iterMap(this.values(), v => v.asPreservesText())).join(', ') +
             '}';
     }
+
+    clone(): Set {
+        return new Set(this);
+    }
+
+    [Symbol.toStringTag] = 'Set';
+
+    [PreserveOn](encoder: Encoder) {
+        if (encoder.canonical) {
+            const pieces = Array.from(this).map(k => encode(k, { canonical: true }));
+            pieces.sort(Bytes.compare);
+            encoder.encoderawvalues(Tag.Set, pieces);
+        } else {
+            encoder.encodevalues(Tag.Set, this);
+        }
+    }
 }
 
 export function isAnnotated(x: any): x is Annotated {
     return typeof x === 'object' && x !== null &&
+        x.constructor.name === 'Annotated' &&
         'annotations' in x &&
         'item' in x;
 }
@@ -740,7 +687,7 @@ export class Annotated {
     }
 
     equals(other: any): boolean {
-        return isAnnotated(other) && is(this.item, other.item);
+        return is(this.item, isAnnotated(other) ? other.item : other);
     }
 
     hashCode(): number {
diff --git a/implementations/javascript/test/codec.test.ts b/implementations/javascript/test/codec.test.ts
index 0147453..a132a79 100644
--- a/implementations/javascript/test/codec.test.ts
+++ b/implementations/javascript/test/codec.test.ts
@@ -132,7 +132,7 @@ describe('common test suite', () => {
         });
     }
 
-    const tests = peel(TestCases._.cases(peel(samples))) as Dictionary;
+    const tests = peel(TestCases._.cases(peel(samples))) as Dictionary<Value>;
     tests.forEach((t0: Value, tName0: Value) => {
         const tName = Symbol.keyFor(strip(tName0) as symbol);
         const t = peel(t0) as Record;