another dumb question about numbers

[Alan Bawden <bawden@parc.xerox.com>]

    Date: Thu, 2 Nov 89 17:57:49 est
    From: Hal Abelson <hal@zurich.ai.mit.edu>
    Why not have round, floor, ceiling, and truncate produce exact
    integers, and provide some other names for the analogous (more
    primitive?) operations that do not force exactness?

Suppose you were porting your program from a Scheme that supported exact
rationals to a scheme that only supported exact integers.  Suppose that in
the case where (/ P Q) is not an integer the latter Scheme implementation
returned an inexact number (perhaps represented using floating-point).
Then if FLOOR did a silent coercion, (FLOOR (/ P Q)), where P and Q are
exact integers in both implementations, might return different exact
integers as answers -- the correct answer in the first Scheme, and an
incorrect answer in the second.  Again the "silent coercion" has silently
introduced a potential bug.  If you -expected- an inexact quotient, then
you probably should have written (INEXACT->EXACT (FLOOR (/ P Q))).

I think we already had an analogous discussion about MAX and MIN.