A User's Guide to gringo, clasp, clingo, and iclingo

of the function symbol is compared lexicographically. If again the name differs, then
arguments are compared component wise. Finally, integers are always smaller than
constants and constants are always smaller than function symbols. �
Note that a built-in comparison predicate cannot bind variables, i.e., when checking
whether a rule is safe, comparison predicates are not considered to be positive.
3.1.6 Assignments
The built-in predicates := and = can be used in the body of a rule to unify a term on
their right-hand side to a (non-ground) term or variable on its left-hand side, respectively.
Example 3.4. The next program demonstrates how terms can be assigned to variables: The unique answer set of the
1 num(1). num(2). num(3). num(4). num(5).
program is obtained via call:
gringo -t
3 squares(XX,YY,Z) :-
4 XX := X*X, YY := Y*Y, Z := XX+YY, Y1 := Y+1,
5 Y1*Y1 == Z, num(X), num(Y), X < Y.
Line 3 contains four assignments, where the right-hand sides directly or indirectly depend
on X and Y. These two variables are bound in Line 5 via atoms of predicate num/1.
Also observe the different usage and role of built-in comparison predicate ==. �
Example 3.5. The second program demonstrates the usage of :=, which allows for
terms on the left hand side: The unique answer set of the
1 sym(f(a,1,2)). sym(f(a,1,3)). sym(f(b,d)).
2 sym((a,1,2)). sym((a,1,3)). sym((b,d)).
4 unifyf(X) :- f(a,X,X+1) := F, sym(F).
5 unifyt(X) :- (a,X,X+1) := T, sym(T).
Here the term f(a,X,X+1) is unified with every function symbol provided by sym/1.
Note the usage of X+1 in the term. gringo does not try to unify any term containing
arithmetic but in this example X occurs also directly as second argument of the argument
and can thus be unified with. The term X + 1 is merely a test that is deferred and
checked later. For example, the fourth line is equivalent to:
6 unifyf(X) :- f(a,X,Y) := F, sym(F), Y == X + 1.
Note that assignments to some extent can bind variables. Of course cyclic assignments
cannot bind variables. For example the rule p(X) :- X = Y, Y = X. is rejected
by gringo. Either X or Y has to be provided by some positive predicate in this case.
Additionally, unification is restricted to ground terms on the right hand side of the
assignment, that is, all variables on the right hand side have to be bound by some other
predicate.
3.1.7 Intervals
In Line 1 of Example 3.4, there are five facts num(k) over consecutive integers k. For
a more compact representation, gringo and clingo support integer intervals of the
14
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program is obtained via call:
gringo -t