Collection operations

The Cartesian product of two collections (finite sets, lists, or bags) can be found using the >< operator. See the Cartiesian product page for more information.

Disco> {1,2,3} >< {'x','y'}
{(1, 'x'), (1, 'y'), (2, 'x'), (2, 'y'), (3, 'x'), (3, 'y')}

The union or intersection of two finite sets can be found using the union and intersect operators, or using the Unicode notation ∪ and ∩.

Disco> {1,2,3} union {2,3,4}
{1, 2, 3, 4}
Disco> {1,2,3} intersect {2,3,4}
{2, 3}

We can also find the union of two bags, which works by adding multiplicities:

Disco> bag [1,2,3] union bag [2,3,4]
⟅1, 2 # 2, 3 # 2, 4⟆

The difference of two sets or bags can be found using the difference operator, written \:

Disco> {7 .. 12} \ {1 .. 10}
{11, 12}
Disco> bag [1,2,2,3] \ bag [2,3,4]
⟅1, 2⟆

You can check whether one set or bag is a subset of another using the subset operator (or the Unicode symbol ⊆):

Disco> {2,3,4} subset {1 .. 10}
T
Disco> {7 .. 11} subset {1 .. 10}
F
Disco> (bag [1,2,2,3]) subset (bag [2,3,2,2,4,1])
T

Note that Disco does not support the set complement operation, since the complement of a finite set is infinite whenever the domain is infinite.