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_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 point(seq: Sequent, name: Union[str, List[str]]) -> Sequent:
"""
The :math:`\\textbf{OptSet${}^?$}` :math:`\\texttt{point}` rule.
* If argument ``name`` is a ``str``, creates a new point with that name
(this is just the :math:`\\texttt{point}`);
* if it is a list of ``str``, then creates as many points.
"""
if isinstance(name, list):
res = seq
for n in name:
res = point(res, n)
return res
elif isinstance(name, str):
if seq.pastingDiagram is not None:
raise DerivationError("point rule",
"Sequent cannot have a pasting diagram")
var = Variable(name, UnnamedOpetope.Point())
if var in seq.context:
raise DerivationError(
"point rule",
"Point shaped variable {name} is already typed in context "
"{ctx}",
name=name,
ctx=str(seq.context))
res = deepcopy(seq)
res.context = res.context + Typing(var,
Type(PastingDiagram.point(), None))
return res
else:
raise DerivationError(
"point rule",
"Argument name is expected to be a str or list of str")
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___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 target(self, name: str) -> str:
"""
Returns the target of the variable whose name is ``name``.
"""
res = self[name].type.target
if self[name].type.source.shape == \
UnnamedOpetope.Point().eval().source:
raise DerivationError(
"Context, target of variable",
"Variable {var} is a point, and do not have a target",
var=name)
elif res is None:
raise RuntimeError(
"[Context, target of variable] Variable {var} "
"is not a point, but has no target. In valid "
"derivations, this should not happen".format(var=name))
return res.name
def __init__(self, source: PastingDiagram,
target: Optional[Variable]) -> None:
if target is None:
if source.shape != UnnamedOpetope.Point().eval().source:
raise DerivationError(
"Type, creation",
"Source pasting diagram is not a point, but target is "
"unspecified")
elif source.shapeTarget() != target.shape:
raise DerivationError(
"Type, creation",
"Target variable {var} has shape {shape}, should have "
"{should}",
var=str(target),
shape=target.shape,
should=source.shapeTarget())
self.source = source
self.target = target
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 point():
"""
Creates the trivial pasting diagram with shape the point
"""
return PastingDiagram.nonDegeneratePastingDiagram(
UnnamedOpetope.Point(), {})