Declaring

Sets are unordered collections of values of the same type, like lists are ordered collections. Like the mathematical sets and lists, sets can be empty and, if not, elements of sets in LIGO are unique, whereas they can be repeated in a list.

Like lists, the type of sets is parameterised over the type of its elements. Like list elements, set elements must all have the same type.

Ordinary sets are fine for contracts with a finite lifespan or a bounded number of users. For many contracts however, the intention is to have a set holding many entries, potentially millions of them. The cost of loading those entries into the environment each time a user executes the contract would eventually become too expensive were it not for big sets. Big sets in LIGO are based on big maps, a data structure offered by Michelson which handles the scaling concerns for us. The interface for big sets closer to that of big maps than ordinary sets (for example, it would defeat the purpose to request the size of a big set).

The type of big sets is big_set<elt> or, equivalently, Big_set.t<elt>, where elt is the type of the elements of the big set. It is defined as follows in the standard library:

type t<elt> = big_map<elt, unit>

The empty big set is denoted by the predefined value Big_set.empty. In some contexts, it is useful to annotate it with its type, for example: (empty as Big_set.t<int>).

A non-empty big set can be built by using the function Big_set.literal which takes a list of elements and returns a set containing them, and only them.

const empty_big_set: big_set<int> = Big_set.empty;

const big_set1: big_set<int> = Big_set.literal([3, 2, 2, 1]);

Note: The element 2 is repeated in the list, but not in the set made from it.

If you want to build a big set from an arbitrary list of arbitrary values (not just literal values), then you must use Big_set.of_list instead of Big_set.literal:

const two = 2;

const big_set2 : big_set<int> = Big_set.of_list([3, two, two, 1]);

Set elements are internally sorted by increasing values, so the type of the elements must be comparable, that is, they obey a total order (any two elements can be compared).