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Format exact cover example like in paper

This commit is contained in:
Patrick Lühne 2020-06-05 18:54:17 +02:00
parent f9dbe54918
commit b29422cfbf
Signed by: patrick
GPG Key ID: 05F3611E97A70ABF
2 changed files with 8 additions and 8 deletions
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6
examples/example-exact-cover.lp
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@ -1,5 +1,5 @@
{in(1..n)}.
{in_cover(1..n)}.
:- I != J, in(I), in(J), s(X, I), s(X, J).
covered(X) :- in(I), s(X, I).
:- I != J, in_cover(I), in_cover(J), s(X, I), s(X, J).
covered(X) :- in_cover(I), s(X, I).
:- s(X, I), not covered(X).

10
examples/example-exact-cover.spec
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@ -8,15 +8,15 @@ input: s/2.
# Only the in/1 predicate is an actual output, s/2 is an input and covered/1 and is_int/1 are
# auxiliary
output: in/1.
output: in_cover/1.
# Perform the proofs under the assumption that the second parameter of s/2 (the number of the set)
# is always an integer
assume: forall Y (exists X s(X, Y) -> exists N (Y = N and N >= 1 and N <= n)).
assume: forall Y (exists X s(X, Y) -> exists I (Y = I and I >= 1 and I <= n)).
# Only valid sets can be included in the solution
spec: forall Y (in(Y) -> exists N (Y = N and N >= 1 and N <= n)).
spec: forall Y (in_cover(Y) -> exists I (Y = I and I >= 1 and I <= n)).
# If an element is contained in an input set, it must be covered by all solutions
spec: forall X (exists Y s(X, Y) -> exists Y (in(Y) and s(X, Y))).
spec: forall X (exists Y s(X, Y) -> exists Y (s(X, Y) and in_cover(Y))).
# Elements may not be covered by two input sets
spec: forall Y, Z (exists X (s(X, Y) and s(X, Z)) and in(Y) and in(Z) -> Y = Z).
spec: forall Y, Z (exists X (s(X, Y) and s(X, Z)) and in_cover(Y) and in_cover(Z) -> Y = Z).