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

23 %
24 goal(on(b1,b0)).
25 goal(on(b2,b1)).
26 goal(on(b0,table)).
Note that the facts in Line 13–15 and 24–26 specify the initial and the goal state depicted
in Line 9-11 and 19–22, respectively. We here use (uninterpreted) function on/2
to illustrate another important feature available in gringo, clingo, and iclingo,
namely, the possibility of instantiating variables to compound terms.
4.3.2 Problem Encoding
Our Blocks-World Planning encoding for iclingo makes use of declaratives #base,
#cumulative, and #volatile, separating the encoding into a static, a cumulative,
and a volatile (query) part. Each of them can be further refined into Generate, Define,
Test, and Display constituents, as indicated in the comments below:
1 #base.
2 % Define
3 location(table).
4 location(X) :- block(X).
5 holds(F,0) :- init(F).
6 %
7 #cumulative t.
8 % Generate
9 1 { move(X,Y,t) : block(X) : location(Y) : X != Y } 1.
10 % Test
11 :- move(X,Y,t),
12 1 { holds(on(A,X),t-1),
13 holds(on(B,Y),t-1) : B != X : Y != table }.
14 % Define
15 holds(on(X,Y),t) :- move(X,Y,t).
16 holds(on(X,Z),t) :- holds(on(X,Z),t-1),
17 { move(X,Y,t) : Y != Z } 0.
18 %
19 #volatile t.
20 % Test
21 :- goal(F), not holds(F,t).
22 %
23 #base.
24 % Display
25 #hide.
26 #show move/3.
In the initial #base part (Line 1–5), we define blocks and constant table as instances
of predicate location/1. Moreover, we use instances of init/1 to initialize predicate
holds/2 for step 0, thus, defining the conditions before the first incremental step.
Note that variable F is instantiated to compound terms over function on/2.
The #cumulative statement in Line 7 declares constant t as a placeholder for
step numbers in the cumulative encoding part below. Here, the Generate rule in Line 9
states that exactly one block X must be moved to a location Y (different from X) at each
step t. The integrity constraint in Line 11–13 is used to test whether moving block X
38