Add ability to constraint variables to binary or integer values.

[stelmo]

Allows construction of MILPs

[stelmo]

/format

[github-actions]

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (250bf55) 100.00% compared to head (df4e357) 100.00%.

Additional details and impacted files

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  Lines          196       196           
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[exaexa]

a few comments, will fix/merge later

[exaexa]

OK so, this is gonna be harder:

• JuMP and other systems don't really seem to support actual integer CONSTRAINTS, just integer VARIABLES. That kinda sucks from the algebraic point of view but what can we do, solver reality is harsh.
• there are very many thinkable types of constraints and their interpretations -- I can think of few representations just for the integers: (bool, choice from vector, choice from range, free integer, powers of 2, approximate free integer with error term on it, .......)

In the long term I suggest we remove the closed type family Bound and convert it to open, just as was done for Value. That prevents us from forcing a given MILP representation to people, and allows everyone to treat the MILPs as they seem fit. The modification of actual CT source code will thus stay minimal and the functionality will be preserved.

For the current state, I think the easiest way of supporting integer constraints is to just smash in an extra JuMP variable and an equality bound (in the end that would be the same). That should go to the tutorial.

Also, we should re-think the Floatiness of the whole CTs at that point (people might just want to get integers out).

[stelmo]

Okay, I think opening it to integer constraints is definitely more general.

[exaexa]

@stelmo can you review here?

edit: technically you can't for M$ reasons, pls just ack. :D

[stelmo]

This all looks good to me!