123 lines
3.5 KiB
Python
123 lines
3.5 KiB
Python
import pytest
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import fol
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@pytest.mark.parametrize(['imp', 'res'], [
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('\\exists x (Pre(y) -> Post(y))',
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'\\exists x (~Pre(y) | Post(y))'),
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('Pre(x) -> Post(x)', '~Pre(x) | Post(x)'),
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('Pre(x) -> (Aux(y) -> Post(x))',
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'~Pre(x) | (~Aux(y) | Post(x))'),
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('(Pre(x) & Aux(y)) -> Post(x)', '~(Pre(x) & Aux(y)) | Post(x)')
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])
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def test_cnf_imp(imp, res):
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assert fol.cnf.elim_imp(fol.p(imp)).equals(fol.p(res))
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@pytest.mark.parametrize(['f', 'res'], [
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('~(Pre(x) | Post(y))', '~Pre(x) & ~Post(y)'),
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('~(Pre(x) & Post(y))', '~Pre(x) | ~Post(y)'),
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('~(Pre(x) & (Post(y) | Post(z)))',
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'~Pre(x) | (~Post(y) & ~Post(z))'),
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])
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def test_cnf_neg(f, res):
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assert fol.cnf.neg(fol.p(f)).equals(fol.p(res))
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@pytest.mark.parametrize(['f', 'res'], [
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('Pre(x) -> Post(x)', 'Pre(x0) -> Post(x0)'),
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('Pre(x) -> Post(y)', 'Pre(x0) -> Post(x1)'),
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('Pre(x, y) -> Post(y, x)', 'Pre(x0, x1) -> Post(x1, x0)'),
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('Pre(f(x)) -> Post(g(g(y), x))',
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'Pre(f(x0)) -> Post(g(g(x1), x0))'),
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])
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def test_cnf_normalize(f, res):
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assert fol.cnf.normalize(fol.p(f)).equals(fol.p(res))
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@pytest.mark.parametrize(['f', 'res'], [
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# FOR ALL
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('~(\\forall x Pre(x))', '\\exists x ~Pre(x)'),
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('(\\forall x Pre(x)) & Post(x)',
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'\\forall x (Pre(x) & Post(x))'),
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('(\\forall x Pre(x)) | Post(x)',
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'\\forall x (Pre(x) | Post(x))'),
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('(\\forall x Pre(x)) -> Post(x)',
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'\\exists x (Pre(x) -> Post(x))'),
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('Pre(x) & (\\forall x Post(x))',
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'\\forall x (Pre(x) & Post(x))'),
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('Pre(x) | (\\forall x Post(x))',
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'\\forall x (Pre(x) | Post(x))'),
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('Pre(x) -> (\\forall x Post(x))',
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'\\forall x (Pre(x) -> Post(x))'),
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# EXISTS
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('~(\\exists x Pre(x))', '\\forall x ~Pre(x)'),
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('(\\exists x Pre(x)) & Post(x)',
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'\\exists x (Pre(x) & Post(x))'),
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('(\\exists x Pre(x)) | Post(x)',
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'\\exists x (Pre(x) | Post(x))'),
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('(\\exists x Pre(x)) -> Post(x)',
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'\\forall x (Pre(x) -> Post(x))'),
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('Pre(x) & (\\exists x Post(x))',
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'\\exists x (Pre(x) & Post(x))'),
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('Pre(x) | (\\exists x Post(x))',
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'\\exists x (Pre(x) | Post(x))'),
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('Pre(x) -> (\\exists x Post(x))',
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'\\exists x (Pre(x) -> Post(x))'),
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])
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def test_cnf_prenex(f, res):
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assert fol.cnf.prenex(fol.p(f)).equals(fol.p(res))
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@pytest.mark.parametrize(['imp', 'res'], [
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('\\exists x (Pre(x) -> Post(x))', 'Pre(S0) -> Post(S0)'),
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('\\exists x (\\exists y (Pre(x) -> Post(y)))',
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'Pre(S0) -> Post(S1)'),
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('\\forall a (\\exists x (Pre(a, x) -> Post(x)))',
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'\\forall a (Pre(a, s0(a)) -> Post(s0(a)))'),
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('\\forall a (\\forall b (\\exists x (Pre(a, x) -> Post(x))))',
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'\\forall a (\\forall b (Pre(a, s0(a, b)) -> Post(s0(a, b))))'),
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('\\forall a (\\exists x (\\forall b (Pre(x) -> Post(x))))',
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'\\forall a (\\forall b (Pre(s0(a)) -> Post(s0(a))))'),
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('\\forall a (\\exists x (\\forall b (Pre(x) -> Post(x))))',
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'\\forall a (\\forall b (Pre(s0(a)) -> Post(s0(a))))'),
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])
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def test_cnf_skolem(imp, res):
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assert fol.cnf.skolem(fol.p(imp)).equals(fol.p(res))
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@pytest.mark.parametrize(['f', 'oracle'], [
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('Pre(x) | (Aux(x) & Post(x))',
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'(Pre(x) | Aux(x)) & (Pre(x) | Post(x))'),
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('(Aux(x) & Post(x)) | Pre(x)',
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'(Aux(x) | Pre(x)) & (Post(x) | Pre(x))')
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])
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def test_distrib(oracle, f):
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assert fol.cnf.distrib(fol.p(f)).equals(fol.p(oracle))
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@pytest.mark.parametrize(['f', 'oracle'], [
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('Friend(x, y) -> Friend(y, x)',
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'~Friend(x0, x1) | Friend(x1, x0)')
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])
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def test_cnf(oracle, f):
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assert fol.cnf.cnf(fol.p(f)).equals(fol.p(oracle))
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