question of decimal pointed literals
Lennart Augustsson
lennart@mail.augustsson.net
Fri, 20 Apr 2001 16:58:42 +0200
"S.D.Mechveliani" wrote:
> Can we solve and close the problem of the meaning of decimal pointed
> leterals?
There is no problem, it's clearly specified by the report.
(There is a problem with Hugs, it doesn't implement literals properly.
Or has that ancient bug been fixed?)
> > "The floating point literal f is equivalent to
> > fromRational (n Ratio.% d), where fromRational is a
> > method in class Fractional and Ratio.% constructs a rational from
> > two integers, as defined in the Ratio library. The integers n and
> > d are chosen so that n/d = f."
>
> By saying "input is in decimal representation (`0.9')"
> I meant that a number `0.9' is written by a programmer keeping in
> mind a decimal representation.
> Further, according to the citation, 0.9 --> fromRational (9%10),
> 0.2 --> fromRational (1%5)
>
> are stored as the values of type Fractional a => a.
The literal itself must be stored as a Rational (i.e. `Ratio Integer'), but the
result of the `fromRational L' has type `(Fractional a) => a' as you said.
> (1) What is this `a' for our example of
> toRational (fromRational (0.9)) == 9%10
> ?
It depends, see below.
>
> (2) Why Haskell does not report an ambiguity error?
Because any ambigous type is subjected to the defaulting mechanism.
If the ambigous type variable belongs to class `Num' it is defaulted
according to the defaults in scope in that module. The standard default
is `(Integer, Double)', so the the pick in this case is Double. So the intermediate
result after fromRational is of type Double. So you will lose precision.
> For `a' may be Rational, Double, Float - just anything of Fractional.
> If we take Lennart's assertion
> > Input in decimal representation is stored as a Rational number.
> > There is absolutely no loss of precision.
>
> then it should be `a' = Rational.
> Then, in particular, toRational (0.d) == d%10 = True
>
> for any decimal literal d and * any other behavior is a bug. *
> Is this really so?
No, since what you wrote is equivalent to
toRational (fromRational (d%10)) == d%10
and as I described it is subject to defaulting. If you do
default (Integer, Rational)
in your module you'll get equality.
-- Lennart