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 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
def test_toDict(self):
for i in range(5):
seq = UnnamedOpetope.OpetopicInteger(i).eval()
self.assertEqual(
seq,
UnnamedOpetope.ProofTree(seq.source.toDict()).eval())
