26 lines
1.0 KiB
Python
26 lines
1.0 KiB
Python
# Auxiliary predicate to determine whether a variable is integer
|
|
#axiom: forall X (is_int(X) <-> exists N X = N).
|
|
|
|
# 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.
|
|
|
|
# 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.
|
|
|
|
# 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) -> exists N (Y = N)).
|
|
|
|
# Only valid sets can be included in the solution
|
|
spec: 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
|
|
spec: forall X (exists I s(X, I) -> exists I (in(I) and s(X, I))).
|
|
# Elements may not be covered by two input sets
|
|
spec: forall I, J (exists X (s(X, I) and s(X, J)) and in(I) and in(J) -> I = J).
|