On 2020-08-01 21:14 +0200, Marc Nieper-Wißkirchen wrote:
> >     It is an error if (zero? (modulo (- end start) step)) => #f.
>
> Why do you need such a constraint at all? By the way, it would only
> make sense if multiplication would be the exact inverse of division,
> which it isn't for inexact numbers.

The really important thing is that the range created by numeric-range
have a valid length, that is, that (- end start) satisfies both
positive? and integer?.

I'm not sure if dropping the divisibility-by-step constraint would
break anything, but it's certainly confusing to allow uses like

    (numeric-range 0 10 11),  ; => 0, 11, 22, ...

in which the `end' parameter is meaningless.  So I'm in favor of
John's Scheme rewording of the constraint, s/modulo/floor-remainder/.

> >> So range-split-at has to use a custom
> >> indexer for the second subrange.
> >
> > On the above view, it does not.
>
> It does because the root cause is not related to numerics but to the
> fact that indexers do not have the following constraint:
>
> "(indexer lower-bound (+ k l)) is equal to (indexer (indexer lower-bound k) l)"

I do think this is related to numerics, in that it hinges on whether
we are talking about ranges of numbers or of their floating-point
representations.  Provided we're talking about the former, we can
certainly require that the above constraint holds without breaking
numeric-range.

I do think that we've gone into something of a rat-hole in trying to
take into account the possible behavior of inexact numbers under range
operations.  The original reason for proposing some constraints on
indexers was to ensure that they "generate a sequence", for some
precise but not-too-arcane understanding of that phrase.  I think this
is as much as we need.

--
Wolfgang Corcoran-Mathe  <xxxxxx@sigwinch.xyz>

"Most learning is not the result of instruction.  It is rather the
result of unhampered participation in a meaningful setting."
--Ivan Illich