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Better readability could be achieved using array.filter, since it creates the array for you and all you have to do is return true or false. No need to create an array, do the comparison and push yourself.

In the same way when checking for the values, Object.keys can be used with array.every to iterate through your constraints and see if each of the current item's keys match the constraint.

Also, I wouldn't call it source. It's not a source of anything. It's more of a "constraint" for your collection. So I'd call it that way instead.

In terms of performance, array iteration functions are slower than your average for loop (older APIs will tend to be more optimized). However, in terms of readability, these array APIs really shorten your code.

function where(collection, constraint){
  // filter creates an array of items whose callback returns true for them
  return collection.filter(function(collectionItem){
    // every returns true when every item's callback returns true
    return Object.keys(constraint).every(function(key){
      return collectionItem.hasOwnProperty(key) && constraint[key] === collectionItem[key];
    });
  });
}

var a = where([{ "a": 1 }, { "a": 1 }, { "a": 1, "b": 3 }], { "a": 1});
var b = where([{ "a": 1, "b": 2 }, { "a": 1 }, { "a": 1, "b": 2, "c": 2 }], { "a": 1, "b": 2 })

document.write(JSON.stringify(a));
document.write('<br>');
document.write(JSON.stringify(b));