Problem Statement

Create a reasonably complete implementation of rational arithmetic in the particular language using the idioms of the language.

Define a new type called frac with binary operator "//" of two integers that returns a structure made up of the numerator and the denominator (as per a rational number). Further define the appropriate rational unary operators abs and '-', with the binary operators for addition '+', subtraction '-', multiplication '×', division '/', integer division '÷', modulo division, the comparison operators (e.g. '<', '≤', '>', & '≥') and equality operators (e.g. '=' & '≠'). Define standard coercion operators for casting int to frac etc. If space allows, define standard increment and decrement operators (e.g. '+:=' & '-:=' etc.). Finally test the operators: Use the new type frac to find all perfect numbers less than 219 by summing the reciprocal of the factors.

Let's start with the solution:

1/2 + 2/3
// 7/6 (approx. 1.1666666666666667)

1/2 + 1/2
// 1

5/sextillion + 3/quadrillion
// 600001/200000000000000000000 (exactly 3.000005e-15)

8^(1/3)
// 2    (note the exact integer result.)