This is just a small idea, not something I'd argue for strongly...
How about making numbers formatted with decimal points, like "12.34",
read as exact rather than inexact?
The rationale being: decimal point format is a commonplace and very
useful format for writing exact rational numbers, and if one writes a
number like "5.55", there is nothing except an old Scheme convention to
imply that one intends "5.55" to be any less exact than "555/100". (I'm
ignoring any question of precision here, which Scheme does not address
either.)
For example, with this change, the following expression would evaluate
to an exact 5 rather than what it currently does: an inexact
4.999999999999999.
(/ (read (open-input-string "5.55")) 1.11)
The exact 5 result would also be what I imagine is expected by, say,
casual programmers using Racket for financial calculations, which I
think would be a small selling point for Racket.
Python 2.5.2 (r252:60911, Jan 24 2010, 14:53:14)
[GCC 4.3.2] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> 5.55 / 1.11
4.9999999999999991
The only good linguistic argument I can think of against this is that,
when we have Racket *write* (as in the "write" procedure, not "display")
inexact rationals in decimal-point form, they'd need to be written with
an "#i" prefix, so that inexactness is preserved on a *read* of that
same format by Racket. The drawbacks I see to the "#i" on write are
small: (1) visually, it's a little bit more cluttered; (2) it will break
any legacy code that assumes it can do a write of numbers for some
interoperation or UI purpose that doesn't work if the "#i" prefix is
added. "#i" could even be considered helpful, as in a heads-up to the
programmer that they have a number that might be corrupted by IEEE
floating-point operations they didn't expect.
The only implementation efficiency argument I can think of against this
is perhaps wanting numbers to be inexact by default, so that native
floating-point representation and operations can be used more often. If
that is indeed a consideration, I'd prefer to leave adding "#i" prefixes
and "exact->inexact" calls as optimizations that can be added
consciously by programmers, with the default being more exact than
efficient.
--
http://www.neilvandyke.org/
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