Bagtype

Bagtype is a type and concept used to represent a bag, or multiset, in which elements may occur more than once and the order of elements is not significant. In a bagtype, each element has an associated nonnegative multiplicity that counts how many times it appears in the collection.

A typical bagtype is implemented as a mapping from elements to their multiplicities. Core operations usually include: add(e) to increase the multiplicity of e, remove(e) to decrease it (down to zero), and count(e) to return the current multiplicity of e. The cardinality (or size) of a bag is the sum of multiplicities across all elements. Contains(e) checks whether e is present (multiplicity greater than zero). Iteration over a bag yields elements with multiplicities, meaning each element is produced as many times as it occurs in the bag. Equality of two bagtypes requires identical multiplicities for every element. A bag can also support emptiness tests and methods to clear all contents.

Bagtype supports multiset operations that differ from those on sets. Union combines multiplicities by summing counts for each element. Intersection takes the minimum multiplicity for each element. Difference subtracts multiplicities of one bag from another, floored at zero. Subset relations are defined by comparing multiplicities element-wise: bag A is a subset of bag B if every multiplicity in A does not exceed that in B.

Common uses include counting-based computations, inventory tracking, word or item frequency analysis, and multiset algebra in combinatorics. In programming libraries, Bag/Multiset types are often exposed with similar but sometimes language-specific APIs, where the exact method names and mutability semantics vary. Bagtype provides a simple, order-insensitive model of collections where duplicates matter, enabling precise representation of frequency-based data.