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Rename “assert” statement to “spec”

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This commit is contained in:
Patrick Lühne
2020-05-22 18:34:59 +02:00
parent 116f74f63e
commit 739cae1f7c
9 changed files with 26 additions and 23 deletions
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2
examples/example-0.spec
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@@ -1,3 +1,3 @@
input: p/2.
assert: exists X, Y p(X, Y) <-> exists X q(X).
spec: exists X, Y p(X, Y) <-> exists X q(X).

2
examples/example-1.spec
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@@ -1,6 +1,6 @@
input: p/1.
assert:
spec:
forall N
(
forall X (p(X) -> exists I exists M (I = M and I = X and I <= N))

2
examples/example-2.spec
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@@ -10,7 +10,7 @@ axiom: forall N1, N2, N3 (N1 > N2 and N3 > 0 -> N1 * N3 > N2 * N3).
# This axiom is necessary because we use Vampire without higher-order reasoning
axiom: (p(0) and forall N (N >= 0 and p(N) -> p(N + 1))) -> (forall N p(N)).
assert: exists N (forall X (q(X) <-> X = N) and N >= 0 and N * N <= n and (N + 1) * (N + 1) > n).
spec: exists N (forall X (q(X) <-> X = N) and N >= 0 and N * N <= n and (N + 1) * (N + 1) > n).

6
examples/example-exact-cover.spec
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@@ -18,8 +18,8 @@ output: in/1.
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).
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
assert: forall X (exists I s(X, I) -> exists I (in(I) and s(X, I))).
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
assert: forall I, J (exists X (s(X, I) and s(X, J)) and in(I) and in(J) -> I = J).
spec: forall I, J (exists X (s(X, I) and s(X, J)) and in(I) and in(J) -> I = J).

8
examples/example-prime.spec
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@@ -13,7 +13,7 @@ lemma(backward): forall N (composite(N) -> (exists N10 (1 <= N and N <= n and 2
lemma: forall X1 (composite(X1) <-> (exists N1, N10 (X1 = N1 and 1 <= N1 and N1 <= n and 2 <= N10 and N10 <= N1 - 1 and exists N11 (N1 = (N10 * N11) and 0 < N11)))).
assert: forall X (composite(X) -> p__is_integer__(X)).
assert: forall N (composite(N) <-> N > 1 and N <= n and exists I, J (I > 1 and J > 1 and I * J = N)).
assert: forall X (prime(X) -> p__is_integer__(X)).
assert: forall N (prime(N) <-> N > 1 and N <= n and not exists I, J (I > 1 and J > 1 and I * J = N)).
#spec: forall X (composite(X) -> p__is_integer__(X)).
#spec: forall N (composite(N) <-> N > 1 and N <= n and exists I, J (I > 1 and J > 1 and I * J = N)).
spec: forall X (prime(X) -> p__is_integer__(X)).
spec: forall N (prime(N) <-> N > 1 and N <= n and not exists I, J (I > 1 and J > 1 and I * J = N)).