An unordered collection of values that may have duplicates. Formal Definition: A bag has a single query function, numberIn(v, B), which tells how many copies of an element are in the bag, and two modifier functions, add(v, B) and remove(v, B). These may be defined with axiomatic semantics as follows.

1. new() returns a bag
2. numberIn(v, new()) = 0
3. numberIn(v, add(v, B)) = 1 + numberIn(v, B)
4. numberIn(v, add(u, B)) = numberIn(v, B) if v ≠ u
5. remove(v, new()) = new()
6. remove(v, add(v, B)) = B
7. remove(v, add(u, B)) = add(u, remove(v, B)) if v ≠ u