def test_graft(self):
with self.assertRaises(DerivationError):
UnnamedOpetopicSet.graft(
UnnamedOpetopicSet.Sequent(),
UnnamedOpetopicSet.PastingDiagram.degeneratePastingDiagram(
UnnamedOpetope.OpetopicInteger(0), "x"))
with self.assertRaises(DerivationError):
UnnamedOpetopicSet.graft(
UnnamedOpetopicSet.Sequent(),
UnnamedOpetopicSet.PastingDiagram.nonDegeneratePastingDiagram(
UnnamedOpetope.Arrow(),
{UnnamedOpetope.Address.epsilon(0): "x"}))
# Incorrect grafting: ab on top of cd
with self.assertRaises(DerivationError):
UnnamedOpetopicSet.graft(
self.seq,
UnnamedOpetopicSet.PastingDiagram.nonDegeneratePastingDiagram(
UnnamedOpetope.OpetopicInteger(2), {
UnnamedOpetope.Address.epsilon(1): "cd",
UnnamedOpetope.Address.epsilon(0).shift(): "ab"
}))
# Correct grafting: ab on top of bc
UnnamedOpetopicSet.graft(
self.seq,
UnnamedOpetopicSet.PastingDiagram.nonDegeneratePastingDiagram(
UnnamedOpetope.OpetopicInteger(2), {
UnnamedOpetope.Address.epsilon(1): "bc",
UnnamedOpetope.Address.epsilon(0).shift(): "ab"
}))
def setUp(self):
self.type_point = UnnamedOpetopicSet.Type(
UnnamedOpetopicSet.PastingDiagram.point(), None)
self.a = UnnamedOpetopicSet.Variable("a", UnnamedOpetope.Point())
self.b = UnnamedOpetopicSet.Variable("b", UnnamedOpetope.Point())
self.c = UnnamedOpetopicSet.Variable("c", UnnamedOpetope.Point())
self.d = UnnamedOpetopicSet.Variable("d", UnnamedOpetope.Point())
self.ab = UnnamedOpetopicSet.Variable("ab", UnnamedOpetope.Arrow())
self.ac = UnnamedOpetopicSet.Variable("ac", UnnamedOpetope.Arrow())
self.bc = UnnamedOpetopicSet.Variable("bc", UnnamedOpetope.Arrow())
self.cd = UnnamedOpetopicSet.Variable("cd", UnnamedOpetope.Arrow())
self.seq = UnnamedOpetopicSet.Sequent()
self.seq.context = UnnamedOpetopicSet.Context() + \
UnnamedOpetopicSet.Typing(self.a, self.type_point) + \
UnnamedOpetopicSet.Typing(self.b, self.type_point) + \
UnnamedOpetopicSet.Typing(self.c, self.type_point) + \
UnnamedOpetopicSet.Typing(self.d, self.type_point) + \
UnnamedOpetopicSet.Typing(
self.ab, self.type_arrow("a", self.b)) + \
UnnamedOpetopicSet.Typing(
self.ac, self.type_arrow("a", self.c)) + \
UnnamedOpetopicSet.Typing(
self.bc, self.type_arrow("b", self.c)) + \
UnnamedOpetopicSet.Typing(
self.cd, self.type_arrow("c", self.d))
def test_point(self):
s = UnnamedOpetopicSet.point(UnnamedOpetopicSet.Sequent(), "x")
s = UnnamedOpetopicSet.point(s, "y")
self.assertEqual(len(s.context), 2)
with self.assertRaises(DerivationError):
UnnamedOpetopicSet.point(s, "x")
s.pastingDiagram = UnnamedOpetopicSet.PastingDiagram.point()
with self.assertRaises(DerivationError):
UnnamedOpetopicSet.point(s, "z")
def test_degen(self):
s = UnnamedOpetopicSet.point(UnnamedOpetopicSet.Sequent(), "x")
with self.assertRaises(DerivationError):
UnnamedOpetopicSet.degen(s, "y")
s = UnnamedOpetopicSet.degen(s, "x")
self.assertIsNotNone(s.pastingDiagram.degeneracy)
self.assertEqual(s.pastingDiagram.degeneracy, "x")
self.assertIsNone(s.pastingDiagram.nodes)
with self.assertRaises(DerivationError):
UnnamedOpetopicSet.degen(s, "x")