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 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___init__(self):
UnnamedOpetopicSet.Typing(
UnnamedOpetopicSet.Variable("x",
UnnamedOpetope.OpetopicInteger(2)),
self.t)
with self.assertRaises(DerivationError):
UnnamedOpetopicSet.Typing(
UnnamedOpetopicSet.Variable("x",
UnnamedOpetope.OpetopicInteger(3)),
self.t)
def test___getitem__(self):
d = UnnamedOpetopicSet.PastingDiagram.degeneratePastingDiagram(
UnnamedOpetope.OpetopicInteger(0), "d")
p = UnnamedOpetopicSet.PastingDiagram.nonDegeneratePastingDiagram(
UnnamedOpetope.OpetopicInteger(2), {
UnnamedOpetope.Address.epsilon(1): "a",
UnnamedOpetope.Address.epsilon(0).shift(): "b"
})
with self.assertRaises(DerivationError):
d[UnnamedOpetope.Address.epsilon(0)]
self.assertEqual(p[UnnamedOpetope.Address.epsilon(1)], "a")
self.assertEqual(p[UnnamedOpetope.Address.epsilon(0).shift()], "b")
def test_nonDegeneratePastingDiagram(self):
UnnamedOpetopicSet.PastingDiagram.nonDegeneratePastingDiagram(
UnnamedOpetope.OpetopicInteger(2), {
UnnamedOpetope.Address.epsilon(1): "a",
UnnamedOpetope.Address.epsilon(0).shift(): "b"
})
with self.assertRaises(DerivationError):
UnnamedOpetopicSet.PastingDiagram.nonDegeneratePastingDiagram(
UnnamedOpetope.OpetopicInteger(0), {})
with self.assertRaises(DerivationError):
UnnamedOpetopicSet.PastingDiagram.nonDegeneratePastingDiagram(
UnnamedOpetope.OpetopicInteger(2),
{UnnamedOpetope.Address.epsilon(1): "a"})
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 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 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_shift(self):
s = UnnamedOpetopicSet.graft(
self.seq,
UnnamedOpetopicSet.PastingDiagram.nonDegeneratePastingDiagram(
UnnamedOpetope.OpetopicInteger(1),
{UnnamedOpetope.Address.epsilon(1): "ac"}))
with self.assertRaises(DerivationError):
UnnamedOpetopicSet.shift(s, "ab", "A")
with self.assertRaises(DerivationError):
UnnamedOpetopicSet.shift(s, "bc", "A")
UnnamedOpetopicSet.shift(s, "ac", "A")
def test_graft(self):
i2 = UnnamedOpetope.OpetopicInteger(2).eval()
i3 = UnnamedOpetope.OpetopicInteger(3).eval()
s = UnnamedOpetope.shift(i3)
s = UnnamedOpetope.graft(s, i2,
UnnamedOpetope.Address.fromList([['*']], 2))
s = UnnamedOpetope.graft(
s, i2, UnnamedOpetope.Address.fromList([['*', '*']], 2))
r = s.context
self.assertEqual(r(UnnamedOpetope.Address.fromList([[]], 2)),
UnnamedOpetope.Address.fromList([], 1))
self.assertEqual(r(UnnamedOpetope.Address.fromList([['*'], []], 2)),
UnnamedOpetope.Address.fromList(['*'], 1))
self.assertEqual(r(UnnamedOpetope.Address.fromList([['*'], ['*']], 2)),
UnnamedOpetope.Address.fromList(['*', '*'], 1))
self.assertEqual(
r(UnnamedOpetope.Address.fromList([['*', '*'], []], 2)),
UnnamedOpetope.Address.fromList(['*', '*', '*'], 1))
self.assertEqual(
r(UnnamedOpetope.Address.fromList([['*', '*'], ['*']], 2)),
UnnamedOpetope.Address.fromList(['*', '*', '*', '*'], 1))
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 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()
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 test_degeneratePastingDiagram(self):
UnnamedOpetopicSet.PastingDiagram.degeneratePastingDiagram(
UnnamedOpetope.OpetopicInteger(0), "d")
with self.assertRaises(DerivationError):
UnnamedOpetopicSet.PastingDiagram.degeneratePastingDiagram(
UnnamedOpetope.OpetopicInteger(1), "d")
def setUp(self):
self.s = UnnamedOpetopicSet.PastingDiagram.nonDegeneratePastingDiagram(
UnnamedOpetope.OpetopicInteger(2), {
UnnamedOpetope.Address.epsilon(1): "a",
UnnamedOpetope.Address.epsilon(0).shift(): "b"
})
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_toDict(self):
for i in range(5):
seq = UnnamedOpetope.OpetopicInteger(i).eval()
self.assertEqual(
seq,
UnnamedOpetope.ProofTree(seq.source.toDict()).eval())
