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")
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 tfill(seq: UnnamedOpetopicSet.Sequent, targetName: str,
fillerName: str) -> UnnamedOpetopicSet.Sequent:
"""
This function takes a :class:`opetopy.UnnamedOpetopicSet.Sequent`, (recall
that the context of a sequent derivable in :math:`\\textbf{OptSet${}^?$}`
is a finite opetopic set) typing a pasting diagram :math:`\\mathbf{P}`, and
solves the Kan filler problem by adding
* a new cell :math:`t` with name ``targetName``;
* a new cell :math:`\\alpha : \\mathbf{P} \\longrightarrow t` with name
``fillerName``.
"""
if seq.pastingDiagram is None:
raise DerivationError(
"Kan filling, target",
"Argument sequent expecting to type a pasting diagram")
# Source of alpha
P = seq.pastingDiagram
tPshapeProof = UnnamedOpetope.ProofTree(P.shapeTarget().toDict())
# Start deriving
res = deepcopy(seq)
res.pastingDiagram = None
# Derive t
if P.shape.dimension - 1 == 0:
# t is a point
res = UnnamedOpetopicSet.point(res, targetName)
else:
# Set u, target of t
if P.shape.isDegenerate:
u = P.degeneracyVariable()
else:
u = seq.context.target(
P.source(UnnamedOpetope.address([], P.shape.dimension - 1)))
# Derive Q, source of t
if P.shapeTarget().isDegenerate:
Q = UnnamedOpetopicSet.pastingDiagram(tPshapeProof,
seq.context.target(u))
else:
nodes = {} # type: Dict[UnnamedOpetope.Address, str]
if P.shape.isDegenerate:
nodes[UnnamedOpetope.address([], P.shape.dimension - 2)] = \
P.degeneracyVariable()
else:
readdress = P.shapeProof.eval().context
for l in P.shape.leafAddresses():
p, q = l.edgeDecomposition()
nodes[readdress(l)] = seq.context.source(P[p], q)
Q = UnnamedOpetopicSet.pastingDiagram(tPshapeProof, nodes)
if Q.shape.isDegenerate:
res = UnnamedOpetopicSet.degen(res, Q.degeneracyVariable())
else:
res = UnnamedOpetopicSet.graft(res, Q)
# Derive t, target of alpha
res = UnnamedOpetopicSet.shift(res, u, targetName)
# Derive P, source of alpha
if P.shape.isDegenerate:
res = UnnamedOpetopicSet.degen(res, u)
else:
res = UnnamedOpetopicSet.graft(res, P)
# Derive alpha
res = UnnamedOpetopicSet.shift(res, targetName, fillerName)
# Mark t as universal in the type of alpha
rawFillerType = res.context[fillerName].type
fillerType = Type(rawFillerType.source, rawFillerType.target)
fillerType.targetUniversal = True
res.context[fillerName].type = fillerType
# Done
return res