Update examples

This updates the examples to showcase the scope of anthem’s feature set.
New examples are added concerning placeholders, hiding predicates, and
simplifications related to integer variables.

examples/choice-rules.lp

@@ -0,0 +1,2 @@
+p(a).
+{q(a)}.

examples/graph-coloring.lp

@@ -1,10 +1,18 @@
-#external color(1).
+% assign a set of colors to each vertex
-#external edge(2).
-#external vertex(1).
-#show color/2.
-
 {color(V, C)} :- vertex(V), color(C).
+
+% at most one color per vertex
+:- color(V, C1), color(V, C2), C1 != C2.
+
+% at least one color per vertex
 covered(V) :- color(V, _).
 :- vertex(V), not covered(V).
+
+% adjacent vertices don’t share the same color
 :- color(V1, C), color(V2, C), edge(V1, V2).
-:- color(V, C1), color(V, C2), C1 != C2.
+
+#show color/2.
+
+#external vertex(1).
+#external edge(2).
+#external color(1).

examples/letters.lp

@@ -0,0 +1,11 @@
+letter(a).
+letter(b).
+letter(c).
+
+{p(1..3, Y)} :- letter(Y).
+:- p(X1, Y), p(X2, Y), X1 != X2.
+
+q(X) :- p(X, _).
+:- X = 1..3, not q(X).
+
+#show p/2.

examples/prime.lp

@@ -1,4 +1,4 @@
-#show prime/1.
-
 composite(I * J) :- I = 2..n, J = 2..n.
 prime(N) :- N = 2..n, not composite(N).
+
+#show prime/1.

examples/schur-numbers.lp

@@ -1,7 +1,7 @@
-#show in/2.
-
 {in(1..n, 1..r)}.
 covered(I) :- in(I, S).
 
 :- I = 1..n, not covered(I).
 :- in(I, S), in(J, S), in(I + J, S).
+
+#show in/2.

examples/simple-external-show.lp

@@ -0,0 +1,9 @@
+s(X) :- p(X).
+s(X) :- q(X).
+u(X) :- r(X), not s(X).
+
+#show u/1.
+
+#external p(1).
+#external q(1).
+#external r(1).

examples/simple-external.lp

@@ -0,0 +1,5 @@
+s(X) :- p(X).
+s(X) :- q(X).
+
+#external p(1).
+#external q(1).