Re: clpfd: Correlation between domains

>> Hello,
>>
>> take the following two clpfd - constraints:
>>
>> 1) A #>= 2, A #=< 3, B #>= 1, B #=< 3, C #>= 1, C #=< 2.
>>
>> 2) A #>= 2, A #=< 4, B #>= A, B #=< 3, C #= A + 1, C #= B + 1.
>>
>> In 2) you have corelations between the domains, i.e. B #>= A
>>
>> In 1) there are no correlations between each other. Every domain  
>> has a
>> number as inf and sup.
>>
>> Now can I find out in a statement when a domain has correlations to  
>> other
>> domains and when not?
>>
>> I.e. in 1) correlated(A) -> false
>>
>> in 2) correlated(A) -> true because of B references to A
>
> You mean probably that X and Y are correlated in
>
> ?- X #= K*Y.
>
> Except for K = 0.  Sometimes clpfd is clever enough to realize this.
> Sometimes not.
>
> ?- X #= (A-B)*Y, A #>= B, B #>= A.
> _G2745*Y#=X,
> _G2745+B#=A,
> B#>=A,
> A#>=B.
>
> ?- X #= (A-B)*Y, A #>= B, B #>= A, A = B.
> X = 0,
> A = B,
> B in inf..sup,
> Y in inf..sup.
>
> The general problem behind is undecidable, so you have to go for some
> kind of approximation.  The simplest one would be start investigating
> the neighbor variables that are attached to the same constraints.
> copy_term/3 should suffice.  Finding a better form of approximation
> seems to be the most difficult task here.