# Sets Sets are persistent hash sets: unordered collections of unique values. Build them with the `^{ ... }` literal, and combine them with the operations below, which return new sets and leave their inputs unchanged. Literal syntax, membership (`in?`), iteration, and conversion are covered in Collections; this page is the operation catalogue. All five functions are stdlib natives available without an import. ## Functions | Function | Purpose | |---|---| | `union a b` | Set of all elements from both sets | | `intersection a b` | Elements common to both sets | | `difference a b` | Elements in `a` but not in `b` | | `subset? a b` | `true` when every element of `a` is also in `b` | | `superset? a b` | `true` when `a` contains every element of `b` | Notes: - The three set operations return a new set; the inputs are never mutated. - `subset?` and `superset?` are relation predicates returning booleans. Every set is a subset and superset of itself, and the empty set is a subset of every set. - Duplicates collapse at construction: `^{ :a :a :b }` is `^{:a :b}`. - Membership uses `in?` (`[in? $roles :admin]`), and `into ^{}` builds a set from any sequence. ## Examples

def a ^{ 1 2 3 }
def b ^{ 2 3 4 }

[union $a $b]                 # => ^{1 2 3 4}
[intersection $a $b]          # => ^{2 3}
[difference $a $b]            # => ^{1}

[subset? ^{ 1 2 } $a]         # => true
[superset? $a ^{ 1 2 }]       # => true
[subset? $a $b]               # => false
[superset? ^{ 1 2 } ^{ 1 2 }] # => true

# Membership and construction
[in? ^{ :admin :user } :admin]              # => true
[into ^{} [map { $it }] @{ 1 2 2 }]         # => ^{1 2}
^{ :a :a :b }                               # => ^{:a :b}

# Comparing capabilities
def editors ^{ :read :write }
def admins  ^{ :read :write :delete }
[subset? $editors $admins]                  # => true
[difference $admins $editors]               # => ^{:delete}

## See Also - Collections — set literals, `in?`, and iteration - Lists — persistent list operations - Maps — persistent map operations