// Arithmetic
// ----------
// Correctness
//    Addition, Multiplication
//       integers
//       real
//       mixed-mode: integers & reals
//    Subtraction
//       integers
//          small - large, large - small, equal
//       real
//          small - large, large - small, equal
//       mixed-mode: integers & reals
//    Division
//       integers
//          large / small, small / large, 
//       real numbers
//          large / small, small / large, 
//       mixed-mode: integers & reals
//    Modulus
//       integers
//          large op small, small op large, equal op equal
//       real - error

4 + 5
3 * 4

2.5 + 1.5
2.5 * 2.0 

3 + 5.5
3.5 * 2

4 - 7
8 - 5
6 - 6

5.5 - 3.0
2.0 - 4.5
4.0 - 4.0

7 - 3.5
4 - 6.5
8 - 8.0

7 / 4
3 / 6

6.0 / 4.0
4.0 / 8.0

6.0 / 4
2.0 / 4

7 % 4
4 % 7
6 % 6

5.0 % 2

// Precedence
//    {Addition, Subtraction} Vs {Multiplication, Division, Modulus}

4 + 3 * 2 + 2
3 + 4 * 2 + 3

5.5 + 2 + 12 / 5
3 + 4.5 + 8 / 3

10 - 6 - 9 / 4 
9 - 5 - 7 / 3

12 + 5 - 6.0 * 4
10 + 4 - 5 * 3.0

10 / 4 + 10.0 / 4.0
15.0 / 6.0 - 15 / 6 

10 % 3 + 3 % 10
12 % 5 + 5 % 12

3 / 7 - 7 / 3 
4 / 9 - 9 / 4 

3 / 6 + 3 % 6
4 / 8 + 4 % 8

12 % 4 - 4.0 * 2.5
15 % 5 - 2.0 * 5.0

// Associativity
//    Subtraction
//       one - two - three
//    Division
//       one / two / three
//    Modulus
//       one % two % three

9 - 5 - 2
11 - 6 - 3

12 / 2 / 2
16 / 8 / 4

9 % 5 % 2
11 % 6 % 3

5 * 4 / 3 % 4
3 * 10 / 4 % 4 



// -------------------------------------------------------------------------
// Precedence - Two Operators only - ALL DONE
// + *, + / (both int and real), + %
// - *, - / (both int and real), - %
// Error for modulus

# 2
Operator.Arithmetic.
>
3 + 4 * 5
>
Type: output
Hardness: 30


4.0 + 6 * 3

6 + 7 / 3
5 + 7.0 / 4.0
4 + 4.0 / 8
3.5 + 7 / 4

3 + 7 % 4
4.0 + 3 % 8

8 - 2 * 5
7 - 1.5 * 2

7 - 4 / 3
9 - 6 / 4.0
7 - 2.0 / 8.0
8.5 - 4 / 6

9 - 4 % 6
8.5 - 8 % 3

5 + 6.0 % 6
8 + 4 % 8.0

9 - 4 % 4.0
7 - 9.0 % 2

// -------------------------------------------------------------------------
// Precedence - 3 Operators
// + + * (int), + * + (real)
// * + *
// + + / (int), + / + (real)
// / + /
// + + % (int), + % +
// % + %
// - - * (int), - * - (real)
// * - *
// - - / (int), - / - (real)
// / - /
// - - % (int), - % -
// % - %
// % with errors





4 + 3 * 2 + 2
3 + 4 * 2 + 3

5.5 + 2 + 12 / 5
3 + 4.5 + 8 / 3

10 - 6 - 9 / 4 
9 - 5 - 7 / 3

12 + 5 - 6.0 * 4
10 + 4 - 5 * 3.0

10 / 4 + 10.0 / 4.0
15.0 / 6.0 - 15 / 6 

10 % 3 + 3 % 10
12 % 5 + 5 % 12

3 / 7 - 7 / 3 
4 / 9 - 9 / 4 

3 / 6 + 3 % 6
4 / 8 + 4 % 8

12 % 4 - 4.0 * 2.5
15 % 5 - 2.0 * 5.0

// -------------------------------------------------------------------------
// Associativity - 2 operators- ALL DONE
// + + +
// - - - 
// * * *
// / / /
// % % %

3 + 4 + 5
2 + 5 + 3.0

9 - 5 - 2.0
11 - 3.0 - 6

2 * 3 * 1.5
4 * 1.5 * 2

12 / 2 / 2
16 / 8 / 4

10 / 2.5 / 2
9 / 3 / 2.0

9 % 5 % 2
10 % 6 % 3

10 % 4 % 3.0
15 % 6.0 % 2
15.0 % 2.5 % 4

// -------------------------------------------------------------------------
// Associativity - 3 operators
// + - + and - + -
// * / * - both int and real 
// / * / - both int and real <<< CONTINUE HERE
// * % * and % * %
// / % / and % / %
// * / %, * % /, / * %, / % *, % * /, % / *

3 + 4 - 2 + 5
2 + 5 - 3 + 6.0

9 - 5 + 7 - 4
8 - 3 + 4.0 - 6

5 * 2 / 4 * 3
3 * 3 / 5 * 1.5
2 * 5 / 4.0 * 2
3 * 4.0 / 5 * 4

/ * /

4 * 3 % 5 * 2
3 * 6 % 5 * 1.5

10 / 2 % 2 / 2
12 / 2 % 4 / 4

/ % /


5 * 4 / 3 % 4
3 * 10 / 4 % 4 

// -------------------------------------------------------------------------
// Precedence & Associativity - more than 3 operators
// 


// Precedence & Associativity
// 




// Relational
// ----------
// Correctness
//    LessThan, GreaterThan
//       small op large,  large op small, equal op equal
//    LessEquals, GreaterEquals
//       small op large,  large op small, equal op equal
//    Equals, NotEquals
//       integers, reals
//          small op large,  large op small, equal op equal
//       integers, boolean
//          small op large,  large op small, equal op equal
// 
// Precedence
//    {LessThan, GreaterThan, LessEquals, GreaterEquals} Vs {Equals, NotEquals}
// 
// Associativity
//    LessThan, GreaterThan      
//       small op medium op large, large op medium op small, 
//       small op large op medium, medium op large op small, 
//       large op small op medium, medium op small op large, 
//       equal op equal op equal, equal op equal op true/false 
//    LessEquals, GreaterEquals
//       small op medium op large, large op medium op small, 
//       small op large op medium, medium op large op small, 
//       large op small op medium, medium op small op large, 
//       equal op equal op equal, equal op equal op true/false 
//    Equals, NotEquals
//       small op medium op large, large op medium op small, 
//       small op large op medium, medium op large op small, 
//       large op small op medium, medium op small op large, 
//       equal op equal op equal, equal op equal op true/false 

// Precedence & Associativity


3 < 7
9 < 4
4 < 4

3 > 7
9 > 4
4 > 4

3 <= 7
9 <= 4
4 <= 4

3 >= 7
9 >= 4
4 >= 4

3 == 7
9 == 4
4 == 4

3 != 7
9 != 4
4 != 4


3 >= 4 == 4 >= 0
5 >= 7 == 7 >= 0

3 < 7 != 7 < 3
4 < 9 != 9 < 4

9 < 5 < 3
8 < 6 < 4

9 < 3 < 5
8 < 4 < 6

9 > 5 > 3
8 > 6 > 4

9 <= 5 <= 0
7 <= 4 <= 0

4 <= 4 <= 1
7 >= 7 >= 1

9 >= 5 >= 3
8 >= 6 >= 2

4 >= 4 >= 4
7 >= 7 >= 7

9 == 3 == 0
7 == 4 == 0

4 == 4 == 1
5 == 5 == 1

3 != 9 != 1
7 != 4 != 1

4 != 4 != 4
7 != 7 != 7

2 == 3 == 4 == 5
3 == 7 == 5 == 9

1 != 3 != 5 != 7
2 != 4 != 6 != 8



// Arithmetic & Relational
// -----------------------

{+, -, *, /, %} X {<, <=, >, >=}
{+, -, *, /, %} X {==. !=}

10 / 4 < 10 / 4.0



// Boolean
// -------
// Arithmetic & Boolean
// 
// Relational & Boolean
// 
// Arithmetic, Relational & Boolean