four issues for R5RS meeting at Xerox PARC

[Aubrey Jaffer <jaffer@martigny.ai.mit.edu>]

   Date: Mon, 18 May 92 13:42:28 -0400
   From: "Chris Hanson" <cph@martigny.ai.mit.edu>

      Date: Sun, 17 May 92 14:24:59 -0400
      From: Aubrey Jaffer <jaffer@martigny.ai.mit.edu>

       <1>
      Section 6.5.3 should be clearer about what (/ 5 3) should do in an
      integers only implementation and in the case of an implementation with
      inexeacts but no rational numbers.

	Implementations are encouraged, but not required, ... and to
	implement the above procedures and the / procedure in such a way
	that they always return exact results when given exact arguments.
	If one of these procedures is unable to deliver an exact result when
	given exact arguments, then it may either report a violation of an
	implementation restriction or it may silently coerce its result to
	an inexact number.  Such a coercion may cause an error later.

      As stated, (/ 5 3) should return 1 even if the implementation had
      inexact numbers.  It should say something about the Mathematically
      expected result (as it does for the other functions in the paragraph
      before the one I quoted).  There was some discussion of this last year
      but I can't find copies of the messages.

   The IEEE standard has different wording for this paragraph that limits
   the implementation options:

       Implementations should support exact integers and exact rationals
       of practically unlimited size and precision, and to implement
       [sic] the above procedures and the / procedure in such a way that
       they always return exact results when given exact arguments.  If
       one of these procedures is unable to deliver an exact result when
       given exact arguments, then it may either report a violation of
       an implementation restriction or it may silently coerce its
       result to an inexact number.  Such a coercion may cause an error
       later.

The only difference between these paragraphs is the substitution of
the word "should" for the phrase "are encouraged, but not required,
to".  This does not substantially change the meaning of the paragraph.
Other paragraphs in the same section in the IEEE standard use the
words "shall" and "must" to state requirements.

   This requires an exact answer, an inexact answer, or violation of an
   implementation restriction.  Under no circumstances may `(/ 5 3)'
   return `1'; it may return `5/3' or `1.' or some other inexact number,
   or signal an error.

There is no prohibiting (/ 5 3) from returning 1.  For the arithmatic
functions other than / the sentence from the paragraph previous to the
one quoted applies:

   "Finally, the procedures listed below shall return an exact integer
   result provided all the arguments are exact integers and the
   mathematically expected result is representable as an exact integer
   within the implementation:"

Were / part of the list referred to by this sentence then (/ 5 3)
would be restrained from returning 1.  As it is, (/ 5 3) "should"
return an exact number.

SCM used to signal an error for (/ 5 3) which caused no end of
complaints from users.  In a system without rational numbers the only
other possibility I read R4RS as allowing is an integer.