Prolog constraint

Question

I have 3 Constraints for a List:

1. list ins 1..9
2. all_different(list)

3. lists in the list --> I get some lists from the list. every list from the list has to fulfill the constraint to be gapless. for example:

   List1 = [1,3,2,4];
   List2=[3,2,1];
   List3= [5,7,6]
   WRONG: List4=[1,4,3]
   

1 Question: You have an idea to set constraint 3? I would sort the lists and check for: Element1=Element2+1?

After all i want to use labeling([ff],list)

2 Question: I get a solution with labeling if i set contraint 3 like my idea?

Answer 1

I think this is along the lines of what you're looking for...

:- use_module(library(clpfd)).

foo(L) :-
    Len in 1..9,    % lists of length 1 through 9
    length(L, Len),
    L ins 1..9,
    label(L),
    msort(L, LS),
    series(LS).

series([_]).
series([X,Y|T]) :- Y #= X + 1, series([Y|T]).

Since you are already constraining the list to a specific series behavior, indicating all_different would be redundant.

Another approach could be:

foo(L) :-
    [Fst,Lst] ins 1..9,
    Fst #=< Lst,
    Len #= Lst - Fst + 1,
    length(L, Len),
    label([Fst,Lst]),
    L ins Fst..Lst,
    all_different(L),
    label(L).

These predicates generate all possible lists meeting the criteria, and should succeed if and only if the given list meets the criteria.