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LC-187: Type hierarchy for numerics

From: Biron,Paul V <Paul.V.Biron@kp.org>
Date: Thu, 12 Oct 2000 14:47:55 -0700
Message-Id: <376E771642C1D2118DC300805FEAAF4386DF40@pars-exch-1.ca.kp.org>
To: "'GK@Dial.pipex.com'" <GK@Dial.pipex.com>
Cc: "'www-xml-schema-comments'" <www-xml-schema-comments@w3.org>
Dear Graham and members of the XML Schema WG:

The W3C XML Schema Working Group has spent the last several months
working through the comments received from the public on the last-call
draft of the XML Schema specification.  We thank you for the comments
you made on our specification during our last-call comment period, and
want to make sure you know that all comments received during the
last-call comment period have been recorded in our last-call issues
list (http://www.w3.org/2000/05/12-xmlschema-lcissues).

You raised the point registered as issue LC-187, which suggests that
XML Schema be modified such that a single primitive numeric datatype,
rational numbers, be introduced and that the existing numeric types
(float, double and decimal) be derived from rationals.

During the evolution of XML Schema Part 2: Datatypes the numeric
type hierarchy has undergone many revisions, the end result of which
is the hierarchy with decimal, float and double as primitives.  The design
issues that the WG grappled with during this evolution were many, but
can be classified as those pertaining to questions of value space and
those pertaining to questions of lexical space.

As far as the value space questions (which the WG considered the
more import questions), we settled on the current design for a number
of reasons.

First, the value space of the rational numbers requires
representations with infinite precision (e.g., 1/3 is not representable in a
finite number of decimal digits) unless notions of symbolic expression
evaluation is introduced.  The WG made a design decision early on
that expression evaluation was out of scope for XML Schema V1.
Note also that infinite precision representations are quite different
from the arbitrarily large (but finite) precision of our current decimal

Second, sound arguments were put forward within the WG that floating
point numbers are not real numbers (and hence are not rationals).
Among the points made were the following: 1) the relationship between the
sets of numbers in the floating-point and real value spaces is not trivial,
and hence, selecting *semantic* facets that would subset the reals
[or rationals] to the value space of float/double would not be easy;
2) floating-point value spaces contain elements that do not belong
in the real, decimal, or integer value spaces (e.g., +/- Inf, +/-0 and NaN);

The most important lexical space question the WG dealt with was
the proper representation of rationals.  As much as possible, the WG
has tried to create lexical spaces that that a one to one mapping
to value spaces.  It is true that the cases where this general rule was
violated is in the case of the numberic types (e.g., +1 and 1 are both
legal literals for the integer 1).  The particular cases of lexical
we allow are all very well controlled (and supported by most existing
numeric libraries in common programming languages).  However,
the prospect of requiring schema processors to recognize that
1/2, 2/4, 3/6, 4/8, etc. are all literals that map to the same value in
the value space was felt to be too great of a burden on V1 processors
(this is the other side of decision that expression evaluation is out
of scope).

The upshot is that the WG declined to make the change that you

It would be helpful to us to know whether you are satisfied with the
decision taken by the WG on this issue, or wish your dissent from the
WG's decision to be recorded for consideration by the Director of
the W3C.

with best regards,

Paul V. Biron
Co-editor, W3C XML Schema Part 2: Datatypes
Received on Thursday, 12 October 2000 18:11:59 UTC

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