Multisets

What Are Multisets

A multiset is a datatype for storing a set of objects where objects can occur more than once, but the ordering of objects does not matter. Multisets have attributes and a single domain. A multiset can be defined for both GroundDomain and UnresolvedDomain.

Attributes

• A cardinality attribute, as a range; size, minSize, maxSize.
• An occurrence attribute, as a range; minOccur, maxOccur.

In the original conjure implementation, a multiset was infinite without size, maxSize, or maxOccur. In the new conjure-oxide implementation, a variable’s domain is ground if it is fully-bounded (i.e. has a minSize and maxSize).

$ Valid
find foo: multiset (maxSize 5, minOccur 2) of int(1..10)
find bar: multiset (size 3) of int(1..4)


$ Invalid
find fizz: multiset of int(1..10)               $ there must be a upper-bounded size attribute
find buzz: multiset (minSize 3) of int(1..10)   $ this is a lower bound, there is no upper bound on the size attribute

Operators

There are four operators which are defined on functions. These are represented as Expressions in Conjure-Oxide.

• hist(m) - histogram of multi-set m
• max(m) - largest element in ordered multiset m
• min(m) - largest element in ordered multiset m
• freq(m,e) - counts occurrences of element e in multiset m

As of 29th April 2026, Min and Max have been added as Expressions, but Hist and Freq have not. There is no support for rewriting rules or solving.