Utilities for comparing sets
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can-set is a utility for comparing sets that are represented by the parameters commonly passed to service requests.

For example, the set {type: "critical"} might represent all critical todos. It is a superset of the set {type: "critical", due: "today"} which might represent all critical todos due today.

can-set is useful for building caching and other data-layer optimizations. It can be used in client or server environments. can-connect uses can-set to create data modeling utilities and middleware for the client.

Play around in this JSBin!


Use npm to install can-set:

npm install can-set --save


Use require in Node/Browserify workflows to import can-set like:

var set = require('can-set');

Use define, require or import in StealJS workflows to import can-set like:

import set from 'can-set'

Once you've imported set into your project, use it to create a set.Algebra and then use that to compare and perform operations on sets.

// create an algebra
var algebra = new set.Algebra(
    // specify the unique identifier on data
    // specify that completed can be true, false or undefined
    // specify properties that define pagination
    // specify the property that controls sorting

// compare two sets
algebra.subset({start: 2, end: 3}, {start: 1, end: 4}) //-> true
algebra.difference({} , {completed: true}) //-> {completed: false}

// perform operations on sets
algebra.getSubset({start: 2,end: 3},{start: 1,end: 4},
            [{id: 1},{id: 2},{id: 3},{id: 4}])
//-> [{id: 2},{id: 3}]

Once you have the basics, you can use set algebra to all sorts of intelligent caching and performance optimizations. The following example defines a getTodos function that gets todo data from a memory cache or from the server.

var algebra = new set.Algebra(
var cache = [];

// `params` might look like `{complete: true}`
var getTodos = function(set, cb) {

  // Check cache for a superset of what we are looking for.
  for(var i = 0 ; i < cache.length; i++) {
    var cacheEntry = cache[i];
    if(algebra.subset( set, cacheEntry.set ) ) {

      // If a match is found get those items.
      var matchingTodos = algebra.getSubset(set, cacheEntry.set, cacheEntry.items)
      return cb(matchingTodos);

  // not in cache, get and save in cache
  $.get("/todos",set, function(todos){
      set: set,
      items: todos


new set.Algebra(compares...)

Creates an object that can perform binary operations on sets with an awareness of how certain properties represent the set.

var set = require("can-set");
var algebra = new set.Algebra(
  1. compares {Compares}: Each argument is a compares. These are returned by the functions on props or can be created manually.

Compares {Object\<String,Prop()\>}

An object of property names and prop functions.

  // return `true` if the values should be considered the same:
  lastName: function(aValue, bValue){
    return (""+aValue).toLowerCase() === (""+bValue).toLowerCase();

prop(aValue, bValue, a, b, prop, algebra)

A prop function returns algebra values for two values for a given property.

  1. aValue {*}: The value of A's property in a set difference A and B (A B).
  2. bValue {*}: The value of A's property in a set difference A and B (A B).
  3. a {*}: The A set in a set difference A and B (A B).
  4. b {*}: The B set in a set difference A and B (A B).

  • returns {Object|Boolean}: A prop function should either return a Boolean which indicates if aValue and bValue are equal or an AlgebraResult object that details information about the union, intersection, and difference of aValue and bValue.

    An AlgebraResult object has the following values:

    • union - A value the represents the union of A and B.
    • intersection - A value that represents the intersection of A and B.
    • difference - A value that represents all items in A that are not in B.
    • count - The count of the items in A.

    For example, if you had a colors property and A is ["Red","Blue"] and B is ["Green","Yellow","Blue"], the AlgebraResult object might look like:

      union: ["Red","Blue","Green","Yellow"],
      intersection: ["Blue"],
      difference: ["Red"],
      count: 2000

    The count is 2000 because there might be 2000 items represented by colors "Red" and "Blue". Often the real number can not be known.

algebra.difference(a, b)

Returns a set that represents the difference of sets A and B (A \ B), or returns if a difference exists.

algebra1 = new set.Algebra(set.props.boolean("completed"));
algebra2 = new set.Algebra();

// A has all of B
algebra1.difference( {} , {completed: true} ) //-> {completed: false}

// A has all of B, but we can't figure out how to create a set object
algebra2.difference( {} , {completed: true} ) //-> true

// A is totally inside B
algebra2.difference( {completed: true}, {} )  //-> false
  1. a {Set}: A set.
  2. b {Set}: A set.

  • returns {Set|Boolean}: If an object is returned, it is difference of sets A and B (A \ B).

    If true is returned, that means that B is a subset of A, but no set object can be returned that represents that set.

    If false is returned, that means there is no difference or the sets are not comparable.

algebra.equal(a, b)

Returns true if the two sets the exact same.

  algebra.equal({type: "critical"}, {type: "critical"}) //-> true
  1. a {Set}: A set.
  2. b {Set}: A set.

  • returns {Boolean}: True if the two sets are equal.

algebra.getSubset(a, b, bData)

Gets a set's items given a super set b and its items.

  {type: "dog"},
  [{id: 1, type:"cat"},
   {id: 2, type: "dog"},
   {id: 3, type: "dog"},
   {id: 4, type: "zebra"}]
) //-> [{id: 2, type: "dog"},{id: 3, type: "dog"}]
  1. a {Set}: The set whose data will be returned.
  2. b {Set}: A superset of set a.
  3. bData {Array<Object>}: The data in set b.

  • returns {Array<Object>}: The data in set a.

algebra.getUnion(a, b, aItems, bItems)

Unifies items from set A and setB into a single array of items.

algebra = new set.Algebra(
  {start: 1,end: 2},
  {start: 2,end: 4},
  [{id: 1},{id: 2}],
  [{id: 2},{id: 3},{id: 4}]);
  //-> [{id: 1},{id: 2},{id: 3},{id: 4}]
  1. a {Set}: A set.
  2. b {Set}: A set.
  3. aItems {Array<Object>}: Set a's items.
  4. bItems {Array<Object>}: Set b's items.

  • returns {Array<Object>}: Returns items in both set a and set b.

algebra.index(set, items, item)

Returns where item should be inserted into items which is represented by set.

algebra = new set.Algebra(
  {orderBy: "age"},
  [{id: 1, age: 3},{id: 2, age: 5},{id: 3, age: 8},{id: 4, age: 10}],
  {id: 6, age: 3}
)  //-> 2

The default sort property is what is specified by id. This means if that if the sort property is not specified, it will assume the set is sorted by the specified id property.

  1. set {Set}: The set that describes items.
  2. items {Array<Object>}: An array of data objects.
  3. item {Object}: The data object to be inserted.

  • returns {Number}: The position to insert item.


Returns the number of items that might be loaded by the set. This makes use of set.Algebra's By default, this returns Infinity.

var algebra =  new set.Algebra({
  set.props.rangeInclusive("start", "end")
algebra.count({start: 10, end: 19}) //-> 10
algebra.count({}) //-> Infinity
  1. set {Set}: [description]

  • returns {Number}: The number of items in the set if known, Infinity if unknown.

algebra.has(set, props)

Used to tell if the set contains the instance object props.

var algebra = new set.Algebra(
  new set.Translate("where","$where")
  {"$where": {playerId: 5}},
  {id: 5, type: "3pt", playerId: 5, gameId: 7}
) //-> true
  1. set {Set}: A set.
  2. props {Object}: An instance's raw data.

  • returns {Boolean}: Returns true if props belongs in set and false it not.

algebra.properSubset(a, b)

Returns true if A is a strict subset of B (AB).

algebra.properSubset({type: "critical"}, {}) //-> true
algebra.properSubset({}, {}) //-> false
  1. a {Set}: A set.
  2. b {Set}: A set.

  • returns {Boolean}: true if a is a subset of b and not equal to b.

algebra.subset(a, b)

Returns true if A is a subset of B or A is equal to B (AB).

algebra.subset({type: "critical"}, {}) //-> true
algebra.subset({}, {}) //-> true
  1. a {Set}: A set.
  2. b {Set}: A set.

  • returns {Boolean}: true if a is a subset of b.

algebra.union(a, b)

Returns a set that represents the union of A and B (AB).

  {start: 0, end: 99},
  {start: 100, end: 199},
) //-> {start: 0, end: 199}
  1. a {Set}: A set.
  2. b {Set}: A set.

  • returns {Set|undefined}: If an object is returned, it is the union of A and B (AB).

    If undefined is returned, it means a union can't be created.

props {Object}

Contains a collection of prop generating functions. The following functions create compares objects that can be mixed together to create a set Algebra.

var set = require("can-set");
var algebra = new set.Algebra(
    // ignore this property in set algebra
    sessionId:  function(){ return true }


Makes a compare object with a property function that has the following logic:

A(true) ∪ B(false) = undefined

A(undefined) \ B(true) = false
A(undefined) \ B(false) = true

It understands that true and false are complementary sets that combined to undefined. Another way to think of this is that if you load {complete: false} and {complete: true} you've loaded {}.

  1. property {String}: The name of the boolean property.
  2. A {Compares}: Compares object that can be an argument to Algebra

set.props.rangeInclusive(startIndexProperty, endIndexProperty)

Makes a prop for two ranged properties that specify a range of items that includes both the startIndex and endIndex. For example, a range of [0,20] loads 21 items.

  1. startIndexProperty {String}: The starting property name
  2. endIndexProperty {String}: The ending property name

set.props.enum(property, propertyValues)

Makes a prop for a set of values.

var compare = set.props.enum("type", ["new","accepted","pending","resolved"])

set.props.sort(prop, [sortFunc])

Defines the sortable property and behavior.

var algebra = new set.Algebra(set.props.sort("sortBy"));
  {sortBy: "name desc"},
  [{name: "Meyer"}],
  {name: "Adams"}) //-> 1

  {sortBy: "name"},
  [{name: "Meyer"}],
  {name: "Adams"}) //-> 0
  1. prop {String}: The sortable property.
  2. sortFunc {function(sortPropValue, item1, item2)}: The sortable behavior. The default behavior assumes the sort property value looks like PROPERTY DIRECTION (ex: name desc).

  • returns {Compares}: Returns a compares that can be used to create a set.Algebra.


Defines the property name on items that uniquely identifies them. This is the default sorted property if no sort is provided.

var algebra = new set.Algebra(set.props.id("_id"));
  {sortBy: "name desc"},
  [{name: "Meyer"}],
  {name: "Adams"}) //-> 1

  {sortBy: "name"},
  [{name: "Meyer"}],
  {name: "Adams"}) //-> 0
  1. prop {String}: The property name that defines the unique property id.

  • returns {Compares}: Returns a compares that can be used to create a set.Algebra.

new set.Translate(clauseType, propertyName)

Localizes a clause's properties within another nested property.

var algebra = new set.Algebra(
  new set.Translate("where","$where")
  {$where: {complete: true}},
  {id: 5, complete: true}
) //-> true

This is useful when filters (which are where clauses) are within a nested object.

  1. clause {String}: A clause type. One of 'where', 'order', 'paginate', 'id'.
  2. propertyName {String|Object}: The property name which contains the clauses's properties.

  • returns {Compares}: A set compares object that can do the translation.


To setup your dev environment:

  1. Clone and fork this repo.
  2. Run npm install.
  3. Open test.html in your browser. Everything should pass.
  4. Run npm test. Everything should pass.
  5. Run npm run-script build. Everything should build ok.

To publish:

  1. Update the version number in package.json and commit and push this.
  2. Run npm publish. This should generate the dist folder.
  3. Create and checkout a "release" branch.
  4. Run git add -f dist.
  5. Commit the addition and tag it git tag v0.2.0. Push the tag git push origin --tags.