[racket-dev] (round), etc. in Typed Racket

At Mon, 13 Dec 2010 16:43:58 +0100,
Jos Koot wrote:
> Would we not have the same problem with 'rational?'.
> All reals, both exact and inexact ones are rationals (for the obvious reason
> that we cannot represent every irrational number in finite memory)
> Would we not need the same distinction between 'exact-rational?' and
> 'inexact-rational?'. May be 'rational?' should mean 'exact-rational?' and
> 'real?' should mean 'inexact-real?' or 'inexact-rational?'.

I like that, it's consistent with exact-integer -> integer.

> And how about exact and inexact 'complex?'?

It's a bit more tricky, since there are potentially 4 kinds of
complexes, each part could be exact or inexact. However, I'm not sure
that complex numbers of the shape exact+inexact*i are of any use, and
apart from the special case inexact+0i (inexact reals), I don't see
much use for inexact+exact*i either.

> I have the feeling that the numeric tower is tilting like that of Pisa.

Sounds more like straightening it up to me.

> When it comes to efficiency, flonums may be preferred, but it is not
> difficult to enforce a function to do all its computations with flonums.

It can be tricky if you mix exacts and inexacts, the result is not
always inexact:
(* 3.4 0) -> 0 ; not 0.0

Vincent