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Vincent, Frédéric, P1788 On 7 Sep 2009, at 16:32, Vincent Lefevre wrote:
On 2009-09-07 16:22:08 +0200, Frédéric Goualard wrote:Indeed. Anyway, I wonder how such an undefined behavior would be handledpractically by programming languages that lack exception facilities.External flags (such as the infamous C errno) do not seem that good an option. Should we really put this burden on implementors (the Standard being language agnostic) while identifying [-oo,-oo] and [+oo, +oo] to the empty set appears to have so few drawbacks (correct me on that one:I have seen many discussions in the Motion 7 thread on that topic and may have overlooked some definitive argument against it)?Perhaps, but the question of whether [-oo,-oo] and [+oo,+oo] should be left undefined behavior (e.g. because non consensus is reached) or regarded as some well-defined data (e.g. the empty set or a NaI) could be discussed later. Also this is IMHO more a representation issue (Level 3), while Motion 6 is only about Levels 1 and 2. BTW, I see this as an error (or some ambiguity) in the position paper, which seems to talk about Level-3 issues in a Level-1 section.
I am sorry if the wording of the Motion 6 paper has been ambiguous. But anyone who thinks this [-oo,-oo] and [+oo,+oo] business has ANYTHING to do with level 3 issues is completely wrong.
As I wrote privately to Frédéric yesterday:
On motion 6, however, you are mistaken. The reference to [-oo, -oo]
and [+oo, +oo] is in the Level 1 description. It simply says that
as a matter of mathematical notation, these are semantically
invalid sequences of symbols. That has no connection with, for
instance, what should be returned by a constructor call such as
interval(-Inf,-Inf)
... which is (I believe) a level 2 issue yet to be decided ...or what level 2 datum, if any, is represented by a level 3 interval object if its fields (xlo,xhi) represent the inf and sup of an interval and happen to hold xlo = xhi = -Inf ;
... which is a level 3 issue yet to be decided.In the context of the motion 6 paper, the relevant sentence is deeming [-oo, -oo] and [+oo, +oo] to be invalid math notation for an interval in the same way as ["tuesday", "camembert"] is invalid.
John Pryce