// add adds two rational numbers

add([n1, d1], [n2, d2]) =>
  normalize([n1*d2 + n2*d1, d1*d2]);

// sub subtracts the second rational number from the first
sub([n1, d1], [n2, d2]) =>
  normalize([n1*d2 - n2*d1, d1*d2]);

// mult multiplies two rational numbers
mult([n1, d1], [n2, d2]) =>
  normalize([n1*n2, d1*d2]);

// div divides the first number by the second
div([n1, d1], [n2, d2]) =>
  normalize([n1*d2, n2*d1]);


// normalize normalizes the number, i.e. reduces it to lowest terms

normalize([n, d]) => 
  g = gcd(n, d),
  [n/g, d/g];


// sum adds together the elements of a list.  The unit is [0, 1], i.e. 0.

sum(L) = reduce(add, [0, 1], L);


// prod multiplies the elements of a list.  The unit is [1, 1], i.e. 1.

prod(L) = reduce(mult, [1, 1], L);