Problem Statement

A   set   is a collection (container) of certain values, without any particular order, and no repeated values. It corresponds with a finite set in mathematics. A set can be implemented as an associative array (partial mapping) in which the value of each key-value pair is ignored. Given a set S, the power set (or powerset) of S, written P(S), or 2S, is the set of all subsets of S.

By using a library or built-in set type, or by defining a set type with necessary operations, write a function with a set S as input that yields the power set 2S of S.

For example, the power set of     {1,2,3,4}     is For a set which contains n elements, the corresponding power set has 2n elements, including the edge cases of empty set. The power set of the empty set is the set which contains itself (20 = 1): And the power set of the set which contains only the empty set, has two subsets, the empty set and the set which contains the empty set (21 = 2):

Extra credit: Demonstrate that your language supports these last two powersets.

Let's start with the solution:

import Set;

public set[set[&T]] PowerSet(set[&T] s) = power(s);

rascal>PowerSet({1,2,3,4})
set[set[int]]: {
  {4,3},
  {4,2,1},
  {4,3,1},
  {4,2},
  {4,3,2},
  {4,1},
  {4,3,2,1},
  {4},
  {3},
  {2,1},
  {3,1},
  {2},
  {3,2},
  {1},
  {3,2,1},
  {}
}