How to encode normalized(A,B) properly? - clingo

Question

I am using clingo to solve a homework problem and stumbled upon something I can't explain:
normalized(0,0).
normalized(A,1) :-
A != 0.
normalized(10).
In my opinion, normalized should be 0 when the first parameter is 0 or 1 in every other case.
Running clingo on that, however, produces the following:
test.pl:2:1-3:12: error: unsafe variables in:
normalized(A,1):-[#inc_base];A!=0.
test.pl:2:12-13: note: 'A' is unsafe
Why is A unsafe here?
According to Programming with CLINGO
Some error messages say that the program
has “unsafe variables.” Such a message usually indicates that the head of one of
the rules includes a variable that does not occur in its body; stable models of such
programs may be infinite.
But in this example A is present in the body.
Will clingo produce an infinite set consisting of answers for all numbers here?
I tried adding number(_) around the first parameter and pattern matching on it to avoid this situation but with the same result:
normalized(number(0),0).
normalized(A,1) :-
A=number(B),
B != 0.
normalized(number(10)).
How would I write normalized properly?

Answer 1

With "variables occuring in the body" actually means in a positive literal in the body. I can recommend the official guide: https://github.com/potassco/guide/releases/
The second thing, ASP is not prolog. Your rules get grounded, i.e. each first order variable is replaced with its domain. In your case A has no domain.
What would be the expected outcome of your program ?
normalized(12351,1).
normalized(my_mom,1).
would all be valid replacements for A so you create an infinite program. This is why 'A' has to be bounded by a domain. For example:
dom(a). dom(b). dom(c). dom(100).
normalized(0,0).
normalized(A,1) :- dom(A).
would produce
normalize(0,0).
normalize(a,1).
normalize(b,1).
normalize(c,1).
normalize(100,1).
Also note that there is no such thing as number/1. ASP is a typefree language.
Also,
normalized(10).
is a different predicate with only one parameter, I do not know how this will fit in your program.
Maybe your are looking for something like this:
dom(1..100).
normalize(0,0).
normalize(X,1) :- dom(X).
foo(43).
bar(Y) :- normalize(X,Y), foo(X).