CustomEqualitySet.js

const BACKING_MAP = Symbol('Backing map for CustomEqualitySet');
const HASH_FUNCTION = Symbol('Hash function for CustomEqualitySet');

export default class CustomEqualitySet extends Set {
  constructor(iterable=[], hashFunction=val=>val) {
    super();
    this[BACKING_MAP] = new Map();
    this[HASH_FUNCTION] = hashFunction;
    for(const el of iterable) {
      this.add(el);
    }
  }
  has(value) {
    return this[BACKING_MAP].has(this[HASH_FUNCTION](value));
  }
  add(value) {
    const hash = this[HASH_FUNCTION](value);
    if (!this[BACKING_MAP].has(hash)) {
      this[BACKING_MAP].set(hash, value)
    }
    return this;
  }
  delete(value) {
    const hash = this[HASH_FUNCTION](value);
    return this[BACKING_MAP].delete(hash);
  }
  
  *entries() {
    for(const value of this[BACKING_MAP].values()) {
      yield [value, value];
    } 
  }
  *keys() {
    for(const value of this[BACKING_MAP].values()) {
      yield value;
    } 
  }
  
  *values() {
    yield* this.keys();
  }
  
  *[Symbol.iterator]() {
    yield* this.keys();
  }
  
  get size() {
    return this[BACKING_MAP].size;
  }

}

Example usage:

function Person(name) {
   this.name = name;
}
var set = new CustomEqualitySet([], a=>a.name);
set
    .add(new Person('Joe'))
    .add(new Person('Ann'))
    .add(new Person('Joe'))
console.log(set.size === 2);
console.log(Array.from(set).length === 2)
console.log(Array.from(set.values()).length === 2);
set.delete(new Person('Joe'));
console.log(set.size === 1);