= Solution
Extend the data <linked list node> type by a <real number> field and compare that field through an <Oberon> <type guard>.
``
TYPE RealNode = RECORD (Node) value: REAL END;
RealTail = POINTER TO RealNode;
PROCEDURE RealLess(p, q: Tail): BOOLEAN;
BEGIN
RETURN p(RealTail).value < q(RealTail).value
END RealLess;
``
Construct the data chain from `RealTail` nodes, retain the ordinary `Header` for its header, set its count correctly, and call
``
MergeSort(RealLess, p)
``
Only data nodes reach `RealLess`, so the header needs no real-valued field. Its <precondition> is that every data node has the `RealNode` extension. With ordinary <real numbers>, the comparison supplies a <total order>; machine values such as `NaN` must be excluded if the machine <floating-point number> type admits them.
$$
\boxed{\mathrm{RealLess}(p,q)\iff p.\mathrm{value}<q.\mathrm{value};\quad\mathrm{MergeSort}(\mathrm{RealLess},p).}
$$
Back to article page
