def setUp(self):
self.p = UnnamedOpetopicSet.Typing(
UnnamedOpetopicSet.Variable("p", UnnamedOpetope.Point()),
UnnamedOpetopicSet.Type(UnnamedOpetopicSet.PastingDiagram.point(),
None))
self.a = UnnamedOpetopicSet.Typing(
UnnamedOpetopicSet.Variable("a",
UnnamedOpetope.OpetopicInteger(0)),
UnnamedOpetopicSet.Type(
UnnamedOpetopicSet.PastingDiagram.degeneratePastingDiagram(
UnnamedOpetope.OpetopicInteger(0), "p"),
UnnamedOpetopicSet.Variable("p", UnnamedOpetope.Arrow())))
self.b = UnnamedOpetopicSet.Typing(
UnnamedOpetopicSet.Variable("b",
UnnamedOpetope.OpetopicInteger(0)),
UnnamedOpetopicSet.Type(
UnnamedOpetopicSet.PastingDiagram.degeneratePastingDiagram(
UnnamedOpetope.OpetopicInteger(0), "p"),
UnnamedOpetopicSet.Variable("p", UnnamedOpetope.Arrow())))
self.c = UnnamedOpetopicSet.Typing(
UnnamedOpetopicSet.Variable("c",
UnnamedOpetope.OpetopicInteger(2)),
UnnamedOpetopicSet.Type(
UnnamedOpetopicSet.PastingDiagram.nonDegeneratePastingDiagram(
UnnamedOpetope.OpetopicInteger(2), {
UnnamedOpetope.Address.epsilon(1): "x",
UnnamedOpetope.Address.epsilon(0).shift(): "y"
}), UnnamedOpetopicSet.Variable("z",
UnnamedOpetope.Arrow())))
self.ctx = UnnamedOpetopicSet.Context() + self.p + self.a + self.c
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_shape(self):
self.assertEqual(self.a.shape, UnnamedOpetope.Arrow().eval().source)
self.assertEqual(self.b.shape, UnnamedOpetope.Arrow().eval().source)
self.assertEqual(self.i1.shape,
UnnamedOpetope.OpetopicInteger(1).eval().source)
self.assertEqual(self.i2.shape,
UnnamedOpetope.OpetopicInteger(2).eval().source)
self.assertEqual(self.i3.shape,
UnnamedOpetope.OpetopicInteger(3).eval().source)
def test_shapeTarget(self):
self.assertEqual(self.a.shapeTarget(),
UnnamedOpetope.Point().eval().source)
self.assertEqual(self.b.shapeTarget(),
UnnamedOpetope.Point().eval().source)
self.assertEqual(self.i1.shapeTarget(),
UnnamedOpetope.Arrow().eval().source)
self.assertEqual(self.i2.shapeTarget(),
UnnamedOpetope.Arrow().eval().source)
self.assertEqual(self.i3.shapeTarget(),
UnnamedOpetope.Arrow().eval().source)
self.assertEqual(self.c.shapeTarget(),
UnnamedOpetope.OpetopicInteger(3).eval().source)
def setUp(self):
self.a = UnnamedOpetopicSet.Variable("a", UnnamedOpetope.Arrow())
self.b = UnnamedOpetopicSet.Variable("b", UnnamedOpetope.Arrow())
self.i1 = UnnamedOpetopicSet.Variable(
"i1", UnnamedOpetope.OpetopicInteger(1))
self.i2 = UnnamedOpetopicSet.Variable(
"i2", UnnamedOpetope.OpetopicInteger(2))
self.i3 = UnnamedOpetopicSet.Variable(
"i3", UnnamedOpetope.OpetopicInteger(3))
self.c = UnnamedOpetopicSet.Variable(
"c",
UnnamedOpetope.Graft(
UnnamedOpetope.Shift(UnnamedOpetope.OpetopicInteger(2)),
UnnamedOpetope.OpetopicInteger(2),
UnnamedOpetope.Address.fromList([['*']], 2)))
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.t = UnnamedOpetopicSet.Type(
UnnamedOpetopicSet.PastingDiagram.nonDegeneratePastingDiagram(
UnnamedOpetope.OpetopicInteger(2), {
UnnamedOpetope.Address.epsilon(1): "a",
UnnamedOpetope.Address.epsilon(0).shift(): "b"
}), UnnamedOpetopicSet.Variable("t", UnnamedOpetope.Arrow()))
def type_arrow(
self, src: str,
tgt: UnnamedOpetopicSet.Variable) -> UnnamedOpetopicSet.Type:
"""
Convenient function to define the type of an arrow shaped cell
"""
return UnnamedOpetopicSet.Type(
UnnamedOpetopicSet.PastingDiagram.nonDegeneratePastingDiagram(
UnnamedOpetope.Arrow(),
{UnnamedOpetope.Address.epsilon(0): src}), tgt)
def test___init__(self):
UnnamedOpetopicSet.Type(
self.s, UnnamedOpetopicSet.Variable("t", UnnamedOpetope.Arrow()))
with self.assertRaises(DerivationError):
UnnamedOpetopicSet.Type(
self.s, UnnamedOpetopicSet.Variable("t",
UnnamedOpetope.Point()))
UnnamedOpetopicSet.Type(UnnamedOpetopicSet.PastingDiagram.point(),
None)
with self.assertRaises(DerivationError):
UnnamedOpetopicSet.Type(self.s, None)
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"
}))
def test_ProofTree(self):
self.assertEqual(
UnnamedOpetope.ProofTree({}).eval(),
UnnamedOpetope.Point().eval())
self.assertEqual(
UnnamedOpetope.ProofTree({
UnnamedOpetope.address('*'): {}
}).eval(),
UnnamedOpetope.Arrow().eval())
self.assertEqual(
UnnamedOpetope.ProofTree({
None: {}
}).eval(),
UnnamedOpetope.OpetopicInteger(0).eval())
self.assertEqual(
UnnamedOpetope.ProofTree({
UnnamedOpetope.address([], 1): {
UnnamedOpetope.address('*'): {}
},
UnnamedOpetope.address(['*']): {
UnnamedOpetope.address('*'): {}
}
}).eval(),
UnnamedOpetope.OpetopicInteger(2).eval())
with self.assertRaises(DerivationError):
UnnamedOpetope.ProofTree({
UnnamedOpetope.address(['*']): {
UnnamedOpetope.address('*'): {}
}
})
with self.assertRaises(DerivationError):
UnnamedOpetope.ProofTree({
UnnamedOpetope.address([], 1): {
UnnamedOpetope.address('*'): {}
},
UnnamedOpetope.address(['*', '*']): {
UnnamedOpetope.address('*'): {}
}
}).eval()
