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Add comments to exact cover example

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Patrick Lühne 2020-05-12 06:39:50 +02:00
parent f39393ebce
commit 37f0fff09f
Signed by: patrick
GPG Key ID: 05F3611E97A70ABF
1 changed files with 15 additions and 2 deletions
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examples/exact-cover.spec
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@ -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). 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. 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)). 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). 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))). 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). assert: forall I, J (exists X (s(X, I) and s(X, J)) and in(I) and in(J) -> I = J).