<: "until goal"

[Raphael Collet]

Dear Kilian,

I scratched my head quite a bit yesterday, and I just found a nice 
solution to your problem.  The idea is to avoid reification, because 
propagation is too poor in that case.

Kilian Sprotte wrote:
> I am looking for a way to constrain a sequence to be "ascending towards 
> a goal". The goal is determined before posting, let's say its 5, so a 
> solution could be:
> 
> [1 2 4 5 5]

Let us call this sequence S.  It can be defined as:

	declare
	Goal=5
	N=5
	S={FD.list N 1#Goal}

The issue is that S is strictly increasing, except when values reach the 
goal.  My idea is to combine the propagators <: and FD.min.  Consider 
another sequence, say T, that is strictly increasing, and where values 
may be greater than the goal:

	declare
	T={FD.list N 1#(Goal+N-1)}
	for A in T  B in T.2 do A <: B end   % strictly increasing

The link with S is done by taking the minimum between the Goal and each 
element of T:

	for X in S  Y in T do X={FD.min Goal Y} end

Both propagators <: and FD.min will propagate of the variables' domains, 
and propagates exactly as you wanted:

>  [1#5 2#5 3#5 4#5 5]

Try to constrain the 3rd element of S to value 4 in the example, and you 
will see that the 4th element is constrained to 5.


Cheers,
raph