# Terminology Questions: Data-structure consisting of lists without repetitions

I've google around and have been unsuccessful in finding a name for a data-structure consisting of a list whose elements are unique.

I've seen "unique sorted lists", but I'm looking into the more general, not necessarily sorted, case.

Does anyone know a name and a source for such things? --e.g., a one word name for them.

Moreover, lists may be construed as initial algebras or the solutions to a family of recursive equations involving constructors, say, nil and cons. What possible equational algebra gives rise to lists without repetitions? That is, do they pop-out as a solution to some family or are they an algebraic data type that has certain equational constraints, if so which ones?

• This is similar to an ordered dictionary. You might call it an ordered set. – Yuval Filmus Jul 31 '18 at 13:51
• As mentioned above, I'm specifically avoiding the particular case of things being ordered. – Musa Al-hassy Jul 31 '18 at 15:48
• In that case, you're interested in the set data structure. – Yuval Filmus Jul 31 '18 at 15:50
• An order statistic tree is a tree that supports efficient select and rank queries (log n) which means it is an effcient list implementation. It is implemented on top a of a bst set data structure. – SoloNasus Jul 31 '18 at 17:02
• In that case, you're interested in an ordered set. We can continue this back and forth for a few more rounds, but the end result would be either an ordered set or a (regular) set. – Yuval Filmus Aug 1 '18 at 15:42