Re: clp with intervals

Joost Geurts wrote:
> Dear people,
> 
> I have the following CLP program which fails although I do not really
> understand why. It fails in SWI-prolog at exactly the same point so I
> assume it is me who made a mistake. Maybe somebody can explain, and
> possibly suggest a way to solve it.
...
> The last constraint, CX2 #= MinX2 fails. My guess is it has something to
> do with the minlist constraint. I am using eclipse 5.7 with the ic
> library.

Indeed it does.

...
>         % set size for A , B
...
>         WB = 120,
>         
>         % width A,B
...
>         WB #= BX2 - BX1,                        

This constrains BX2 to equal BX1 + 120

>         % A before B
>         AX2 #=< BX1,

This constrains BX1 to be no less than AX2, and thus BX2 to be no less 
than AX2 + 120.

>         % C contains A&B
...
>         BX1 #>= CX1, BX2 #=< CX2,

This constrains CX2 to be no less than BX2.

>         % find minimum  of A & B
...
>         minlist([AX2,BX2],MinX2),        

This constraints MinX2 to equal the minimum of AX2 and BX2, i.e. AX2 
since BX2 is already constrained to be no less than AX2 + 120.

...
>         % C fits tightly
...
>         CX2 #= MinX2, % This constraint fails!

And this constrains CX2 to equal MinX2, i.e. AX2. Since CX2 must be no 
less than BX2 this can only succeed if BX2 =< AX2, but BX2 is no less 
than AX2 + 120. What you need is not to find the minimum of A & B, but 
the extent of A & B, i.e.

	minlist([AX1,BX1],MinX1),
	maxlist([AX2,BX2],MaxX2),

and then

	CX2 #= MaxX2,

if you want tightest fit.

-- 
Andrew Eremin
Research Assistant                   Tel: +44 (0)20 7594 8299
IC-Parc, Imperial College London     Fax: +44 (0)20 7594 8432
London SW7 2AZ                       Email: a.eremin@icparc.ic.ac.uk