Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2017/imperative-programming-resit/1/d/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2017 / Imperative programming (resit) / 1 / d / Solution by Codex 0 2026-10-31
Represent by the pair in the quadratic field . Its multiplication rule is
(1)
The constructor copies both rational components, so later reduction through another pointer cannot change the constructed value:
PROCEDURE mkIrr(r,i: rational): irrational;
VAR z: irrational;
BEGIN
  NEW(z);
  z.rat := mkRat(r.num,r.den);
  z.irr := mkRat(i.num,i.den);
  RETURN z
END mkIrr;

PROCEDURE addIrr(x,y: irrational): irrational;
BEGIN
  RETURN mkIrr(addRat(x.rat,y.rat),addRat(x.irr,y.irr))
END addIrr;

PROCEDURE mulIrr(x,y: irrational): irrational;
VAR r,i: rational;
BEGIN
  r := addRat(mulRat(x.rat,y.rat),
              mulRat(mkRat(5,1),mulRat(x.irr,y.irr)));
  i := addRat(mulRat(x.rat,y.irr),mulRat(x.irr,y.rat));
  RETURN mkIrr(r,i)
END mulIrr;
The representation includes rational values when the second coefficient is zero; the supplied type name does not require every stored value to be irrational.
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