Arguments are not sufficiently instantiated on list sum - list

Question

I am trying to constraint the sum of a list, but my code fails at label().
.pl:
:- use_module(library(clpfd)).
solve(L, Dim) :-
length(L, 5), % define 5 diagonals
SkipVars is Dim - 2, % to skip variables
init_sublists_above_center(L, Dim, SkipVars),
init_center(L, 2, Dim),
init_sublists_below_center(L, 3, Dim, 1),
flatten(L, FlatL),
collect_vars(FlatL, _),
writeln("list="+L),
constraint_sum(L, 38).
collect_vars([], NewL):-
all_different(NewL).
collect_vars([H|T], NewL) :-
H == 0,
collect_vars(T, NewL).
collect_vars([H|T], NewL) :-
append(NewL, [H], NewestL),
collect_vars(T, NewestL).
constraint_sum([], _).
constraint_sum([H|T], Sum) :-
writeln(H),
label(H),
sum_list(H, Sum),
constraint_sum(T, Sum).
init_sublists_above_center([H|T], Dim, SkipVars) :-
length(H, Dim),
init_zeroes(H, SkipVars),
NewSkipVars is SkipVars + 1,
NewSkipVars =< Dim,
init_sublists_above_center(T, Dim, NewSkipVars).
init_sublists_above_center(_, _, _).
init_sublists_below_center(_, _, Dim, Fill) :-
End is Dim - 2,
Fill == End.
init_sublists_below_center([H|T], ToSkip, Dim, Fill) :-
ToSkip == 0,
length(H, Dim),
init_zeroes_start(H, Fill),
NewFill is Fill + 1,
init_sublists_below_center(T, 0, Dim, NewFill).
init_sublists_below_center([_|T], ToSkip, Dim, Fill) :-
NewToSkip is ToSkip - 1,
init_sublists_below_center(T, NewToSkip, Dim, Fill).
init_center(_, ToSkip, _) :-
ToSkip == -1.
init_center([H|_], ToSkip, Dim) :-
ToSkip == 0,
length(H, Dim),
init_center(_, -1, _).
init_center([_|T], ToSkip, Dim) :-
NewToSkip is ToSkip - 1,
init_center(T, NewToSkip, Dim).
init_zeroes([], _).
init_zeroes([H|T], Fill) :-
Fill == 0,
H is 0,
init_zeroes(T, Fill).
init_zeroes([_|T], Fill) :-
NewFill is Fill - 1,
init_zeroes(T, NewFill).
init_zeroes_start(_, Fill) :-
Fill == 0.
init_zeroes_start([H|T], Fill) :-
H is 0,
NewFill is Fill - 1,
init_zeroes_start(T, NewFill).
Output:
7 ?- solve(L, 5).
list= + [[_G15351,_G15407,_G15466,0,0],[_G15525,_G15584,_G15643,_G15702,0],[_G15761,_G15820,_G15879,_G15938,_G15997],[0,_G16056,_G16115,_G16174,_G16233],[0,0,_G16292,_G16351,_G16410]]
[_G15351,_G15407,_G15466,0,0]
ERROR: Arguments are not sufficiently instantiated
Any ideas please?
EDIT:
After running the debugger:, I think that the error is inside label(), at this point:
finite_domain(Var) :-
( fd_get(Var, Dom, _) ->
( domain_infimum(Dom, n(_)), domain_supremum(Dom, n(_)) -> true
; instantiation_error(Var)
)
; integer(Var) -> true
; must_be(integer, Var)
).

Answer 1

Use the graphical debugger to step through your code:
?- gtrace, solve(L, 5).
As you will see, label/1 has nothing whatsoever to do with this error.
Instead of sum_list/2, use the CLP(FD) constraint sum/3: It works in all directions and lets you see answers for your query.
That being said, I recommend you take a huge step back and really consider what you are doing here.
For example, why are you mixing side-effects (write/1) with pure code? Focus on a clear declarative description of the problem, and let the toplevel do the reporting for you.
Also, it is highly unusual to need extra-logical predicates like (==)/2 so frequently. For example, write:
sublists_below_center(_, _, Dim, End) :-
End #= Dim - 2.
to make the relation between the arguments perfectly clear without resorting to extra-logical language elements.
Using flatten/2 is almost always a bad idea and typically indicates a problem in your data structure design. Use append/2 to remove one level of nesting.
Why are you still using primitive arithmetic if you are already importing the CLP(FD) library? Use (#=)/2 etc. throughout.
Also your predicate names indicate that you are thinking way too imperatively about your problem. Focus on a pure declarative description of what a solution of your problem looks like, and Prolog will do the rest for you. Avoid imperative names. Instead, use names that describe what holds under what conditions.