def degen(seq: Sequent, name: str) -> Sequent:
"""
The :math:`\\textbf{OptSet${}^?$}` :math:`\\texttt{degen}` rule.
"""
if seq.pastingDiagram is not None:
raise DerivationError("degen rule",
"Sequent cannot have a pasting diagram")
res = deepcopy(seq)
res.pastingDiagram = PastingDiagram.degeneratePastingDiagram(
UnnamedOpetope.Degen(seq.context[name].variable.shapeProof), name)
return res
def test_OpetopicTree(self):
self.assertEqual(
UnnamedOpetope.OpetopicTree(None).eval(),
UnnamedOpetope.Degen(UnnamedOpetope.Arrow()).eval())
for i in range(5):
self.assertEqual(
UnnamedOpetope.OpetopicTree([None] * i).eval(),
UnnamedOpetope.Shift(UnnamedOpetope.OpetopicInteger(i)).eval())
for i in range(5):
tree = [None] * i + [[None]] + [None] * (4 - i)
self.assertEqual(
UnnamedOpetope.OpetopicTree(tree).eval(),
UnnamedOpetope.Graft(
UnnamedOpetope.Shift(UnnamedOpetope.OpetopicInteger(5)),
UnnamedOpetope.OpetopicInteger(1),
UnnamedOpetope.address([['*'] * i], 2)).eval())
def test___eq__(self):
self.assertEqual(
UnnamedOpetopicSet.pastingDiagram(
UnnamedOpetope.OpetopicInteger(0), "a"),
UnnamedOpetopicSet.pastingDiagram(
UnnamedOpetope.OpetopicInteger(0), "a"))
self.assertNotEqual(
UnnamedOpetopicSet.pastingDiagram(
UnnamedOpetope.OpetopicInteger(0), "a"),
UnnamedOpetopicSet.pastingDiagram(
UnnamedOpetope.OpetopicInteger(0), "b"))
self.assertNotEqual(
UnnamedOpetopicSet.pastingDiagram(
UnnamedOpetope.OpetopicInteger(0), "a"),
UnnamedOpetopicSet.pastingDiagram(
UnnamedOpetope.Degen(UnnamedOpetope.Arrow()), "a"))
self.assertNotEqual(
UnnamedOpetopicSet.pastingDiagram(
UnnamedOpetope.OpetopicInteger(1),
{UnnamedOpetope.address([], 1): "a"}),
UnnamedOpetopicSet.pastingDiagram(
UnnamedOpetope.OpetopicInteger(1),
{UnnamedOpetope.address([], 1): "b"}))
self.assertNotEqual(
UnnamedOpetopicSet.pastingDiagram(
UnnamedOpetope.OpetopicInteger(1),
{UnnamedOpetope.address([], 1): "a"}),
UnnamedOpetopicSet.pastingDiagram(
UnnamedOpetope.OpetopicInteger(2), {
UnnamedOpetope.address([], 1): "a",
UnnamedOpetope.address(['*']): "a"
}))
self.assertEqual(
UnnamedOpetopicSet.pastingDiagram(
UnnamedOpetope.OpetopicInteger(2), {
UnnamedOpetope.address([], 1): "a",
UnnamedOpetope.address(['*']): "b"
}),
UnnamedOpetopicSet.pastingDiagram(
UnnamedOpetope.OpetopicInteger(2), {
UnnamedOpetope.address(['*']): "b",
UnnamedOpetope.address([], 1): "a"
}))