Project 2 – Sets and Set Operations

Setup

1. Install Stack
2. Clone this repository

   ~/Some/Dir git clone https://github.com/edgarlepe/Math200Project

Running

1. From the project root directory run:

   ~/Some/Dir/Math200Project stack build
   ~/Some/Dir/Math200Project stack exec Math200Project-exe
   

Using the Application

The application is an interpreter for basic set operations. Sets can be a combination of any of the following types:

• Integer
• Real
• Character
• String
• Boolean

Running the program will start a REPL (Read, Eval, Print Loop):

~/Some/Dir/Math200Project stack exec Math200Project-exe
Interpreter>

The interpreter supports the following operations:

• Assignment:

  Interpreter> A = {1,2,3}
  => A = {1, 2, 3}
  Interpreter> B = {'a','b','c'}
  => B = {'a', 'b', 'c'}
  Interpreter> C = {3,4,5,6}
  => C = {3, 4, 5, 6}
  

• Union of sets:

  Interpreter> A ∪ B
  => {1, 2, 3, 'a', 'b', 'c'}
  Interpreter> Union(A,C)
  => {1, 2, 3, 4, 5, 6}
  Interpreter> A ∪ B ∪ C
  => {1, 2, 3, 4, 5, 6, 'a', 'b', 'c'}  
  

• Intersection of sets:

  Interpreter> A ∩ B
  => {}
  Interpreter> A ∩ C
  => {3}
  Interpreter> Intersection(A,C)
  => {3}
  

• Difference of sets:

  Interpreter> A - B
  => {1, 2, 3}
  Interpreter> A - C
  => {1, 2}
  Interpreter> Difference(A,C)
  => {1, 2}
  

• Cartesian Product of sets: (A × B or CartesianProduct(A,B))

  Interpreter> A × B
  => {(1,'a'), (1,'b'), (1,'c'), (2,'a'), (2,'b'), (2,'c'), (3,'a'), (3,'b'), (3,'c')}
  Interpreter> CartesianProduct(A,C)
  =>{(1,3), (1,4), (1,5), (1,6), (2,3), (2,4), (2,5), (2,6), (3,3), (3,4), (3,5), (3,6)}
  

• Cardinality of set:

  Interpreter> |A|
  => 3
  

• Power Set:

  Interpreter> P(A)
  => {{1, 2, 3}, {1, 2}, {1, 3}, {1}, {2, 3}, {2}, {3}, {}}
  

• Cardinality:

  Interpreter> |A|
  => 3
  

• Adding an element to a set:

  Interpreter> Add(4,A)
  => {1, 2, 3, 4}
  Interpreter> A
  => {1, 2, 3, 4}
  

• Removing an element from a set:

  Interpreter> Remove('c',B)
  => {'a', 'b'}
  Interpreter> B
  => {'a', 'b'}
  

• Any combination of unions, intersections, differences, and cartesian products:

  Interpreter> A ∪ B ∪ C ∩ B - {3} × B
  => {('a','a'), ('a','b'), ('a','c'), ('b','a'), ('b','b'), ('b','c'), ('c','a'), ('c','b'), ('c','c')}
  

• Checking if A is a subset of B:

  Interpreter> Subset(A,B)
  => False
  Interpreter> Subset({1,2},A)
  => True