Add comments to exact cover example

examples/exact-cover.spec

@@ -1,10 +1,23 @@
+# Auxiliary predicate to determine whether a variable is integer. is_int/1 is declared as an input
+# predicate so that anthem doesn’t generate its completed definition
+input: is_int/1.
 axiom: forall X (is_int(X) <-> exists N X = N).
 
-input: n -> integer, s/2, is_int/1.
-
+# Perform the proofs under the assumption that n is a nonnegative integer input constant. n stands
+# for the total number of input sets
+input: n -> integer.
 assume: n >= 0.
+
+# s/2 is the input predicate defining the sets for which the program searches for exact covers
+input: s/2.
+
+# Perform the proofs under the assumption that the second parameter of s/2 (the number of the set)
+# is always an integer
 assume: forall X, Y (s(X, Y) -> is_int(Y)).
 
+# Only valid sets can be included in the solution
 assert: forall X (in(X) -> X >= 1 and X <= n).
+# If an element is contained in an input set, it must be covered by all solutions
 assert: forall X (exists I s(X, I) -> exists I (in(I) and s(X, I))).
+# Elements may not be covered by two input sets
 assert: forall I, J (exists X (s(X, I) and s(X, J)) and in(I) and in(J) -> I = J).