Sets

sets.ts

import * as R from 'ramda';

// union and difference are more or less the same except 
// for the operation performed
const abstractSummation = R.curry((operation, a, b) => R.reduce((s, e) => {
  s[operation](e);
  return s;
}, new Set(a), b));
// for the given sets:
//     A={2,4,6,8,10}
//     B={1,2,3,4,5}
// then Union: A∪B = {1,2,3,4,5,6,8,10}
// https://upload.wikimedia.org/wikipedia/commons/3/30/Venn0111.svg
export const union = abstractSummation('add');
// for the given sets:
//     A={2,4,6,8,10}
//     B={1,2,3,4,5}
// then Difference: A-B = {6,8,10}
// https://upload.wikimedia.org/wikipedia/commons/4/46/Venn0110.svg
export const difference = abstractSummation('delete');
// for the given sets:
//     A={2,4,6,8,10}
//     B={1,2,3,4,5}
// then Complement: A^B = {1,3,5}
// https://upload.wikimedia.org/wikipedia/commons/e/eb/Venn1010.svg
export const complement = R.curry((a, b) => difference(b, a));
// for the given sets:
//     A={2,4,6,8,10}
//     B={1,2,3,4,5}
// then Intersection: A∩B = {2,4}
// In this we use De Morgan's Law and some basic juggling to
// remove the need to write a seperate function.
// https://upload.wikimedia.org/wikipedia/commons/9/99/Venn0001.svg
export const intersection = R.curry((a, b) => difference(a, difference(a, b)));