def cups(left, right):
if not isinstance(left, Dim):
raise TypeError(messages.type_err(Dim, left))
if not isinstance(right, Dim):
raise TypeError(messages.type_err(Dim, right))
if left.r != right:
raise AxiomError(messages.are_not_adjoints(left, right))
return Tensor(left @ right, Dim(1), Id(left).array)
def __init__(self, x, y):
if not isinstance(x, Ty):
raise TypeError(messages.type_err(Ty, x))
if not isinstance(y, Ty):
raise TypeError(messages.type_err(Ty, y))
if x != y.r and x.r != y:
raise AxiomError(messages.are_not_adjoints(x, y))
if len(x) != 1 or len(y) != 1:
raise ValueError(messages.cap_vs_caps(x, y))
if x.r == y:
raise NotImplementedError(messages.pivotal_not_implemented())
super().__init__('CAP', Ty(), x @ y)
def __init__(self, left, right):
if not isinstance(left, Ty):
raise TypeError(messages.type_err(Ty, left))
if not isinstance(right, Ty):
raise TypeError(messages.type_err(Ty, right))
if len(left) != 1 or len(right) != 1:
raise ValueError(messages.cap_vs_caps(left, right))
if left != right.r and left.r != right:
raise AxiomError(messages.are_not_adjoints(left, right))
self.left, self.right = left, right
super().__init__("Cap({}, {})".format(left, right), Ty(), left @ right)
self.draw_as_wires = True
def __init__(self, left, right):
if not isinstance(left, Ty):
raise TypeError(messages.type_err(Ty, left))
if not isinstance(right, Ty):
raise TypeError(messages.type_err(Ty, right))
if len(left) != 1 or len(right) != 1:
raise ValueError(messages.cup_vs_cups(left, right))
if left.r != right and left != right.r:
raise AxiomError(messages.are_not_adjoints(left, right))
if left == right.r:
raise AxiomError(messages.wrong_adjunction(left, right, cup=True))
self.left, self.right, self.draw_as_wire = left, right, True
super().__init__("Cup({}, {})".format(left, right), left @ right, Ty())
def __init__(self, left, right):
if not isinstance(left, Ty):
raise TypeError(messages.type_err(Ty, left))
if not isinstance(right, Ty):
raise TypeError(messages.type_err(Ty, right))
if len(left) != 1 or len(right) != 1:
raise ValueError(messages.cap_vs_caps(left, right))
if left != right.r and left.r != right:
raise AxiomError(messages.are_not_adjoints(left, right))
monoidal.BinaryBoxConstructor.__init__(self, left, right)
Box.__init__(
self, "Cap({}, {})".format(left, right), Ty(), left @ right)
self.draw_as_wires = True
def cups(left, right, ar_factory=Diagram, cup_factory=Cup, reverse=False):
""" Constructs a diagram of nested cups. """
for typ in left, right:
if not isinstance(typ, Ty):
raise TypeError(messages.type_err(Ty, typ))
if left.r != right and right.r != left:
raise AxiomError(messages.are_not_adjoints(left, right))
result = ar_factory.id(left @ right)
for i in range(len(left)):
j = len(left) - i - 1
cup = cup_factory(left[j:j + 1], right[i:i + 1])
layer = ar_factory.id(left[:j]) @ cup @ ar_factory.id(right[i + 1:])
result = result << layer if reverse else result >> layer
return result
def ba(left, right):
""" Backward application. """
if right.left != left:
raise AxiomError(messages.are_not_adjoints(left, right))
return BA(right)
def fa(left, right):
""" Forward application. """
if left.right != right:
raise AxiomError(messages.are_not_adjoints(left, right))
return FA(left)