Replace signed by itv

[proux01]

Motivation for this change

Complete the development of itv.v and use it in place of signed.v

Checklist

• added corresponding entries in CHANGELOG_UNRELEASED.md

• added corresponding documentation in the headers

Reference: How to document

Reminder to reviewers

• Read this Checklist
• Put a milestone if possible
• Check labels

Fixes #879

Fixes #878

[affeldt-aist]

I haven't read in details but since it fixes at least two issues and since once merged the file will again be the object of a port to MathComp, I think it should be merged for the next release.

[proux01]

As you want. I still think it could be good to have a light review about for instance putting things in a Private module, checking that the doc is reasonnable,...

[proux01]

@affeldt-aist thanks for the fix/update but apparently there are still conflicts?

[affeldt-aist]

As you want. I still think it could be good to have a light review about for instance putting things in a Private module, checking that the doc is reasonnable,...

You're right. I'll do that this week-end.

[affeldt-aist]

@affeldt-aist thanks for the fix/update but apparently there are still conflicts?

Indeed. It compiles fine on my machine though (MathComp 2.3.0, HB 1.8.1, Coq 8.20.1).
I might try other configurations as part of my review this week-end.

[affeldt-aist]

There is a number of definitions/lemmas (e.g., map_itv_bound, add_itv, see (non-exhaustive?) list below [1]) that do not depend on the Itv module but only on interval and possibly int. They amount for a sizeable amount of the file (about 20%?) and can be understood independently of the inference infrastructure. What about putting then together at the top of the file as a "preliminaries" section (extending interval.v) so as to lighten the core part of the file and clarify dependencies on section variables?

[1]
map_itv_bound
map_itv_bound_comp
opp_itv_bound
opp_itv_ge0
opp_itv_gt0
opp_itv
add_itv_boundl
add_itv_boundr
add_itv
mul_itv_boundl
mul_itv_boundr
signb
itv_bound_signl
itv_bound_signr
signi
interval_sign
mult_itv
mul_itv_boundrC
mul_itv_boundr_BRight
max_itv
min_itv
keep_pos_itv_bound
exprn_le1_itv_bound
exprn_itv

[proux01]

There is a number of definitions/lemmas (e.g., map_itv_bound, add_itv, see (non-exhaustive?) list below [1]) that do not depend on the Itv module but only on interval and possibly int. They amount for a sizeable amount of the file (about 20%?) and can be understood independently of the inference infrastructure. What about putting then together at the top of the file as a "preliminaries" section (extending interval.v) so as to lighten the core part of the file and clarify dependencies on section variables?

[1] map_itv_bound map_itv_bound_comp opp_itv_bound opp_itv_ge0 opp_itv_gt0 opp_itv add_itv_boundl add_itv_boundr add_itv mul_itv_boundl mul_itv_boundr signb itv_bound_signl itv_bound_signr signi interval_sign mult_itv mul_itv_boundrC mul_itv_boundr_BRight max_itv min_itv keep_pos_itv_bound exprn_le1_itv_bound exprn_itv

Note that most (if not all) of these are now in the Instances module which is not imported (and not meant to be). So it's a kind of private module. So we need to find a solution to not make them too public. Maybe a new IntervalArithmetic module, or even file?

[affeldt-aist]

Should we merge this one for today's release?

[proux01]

Can be merged when CI is green