def tensor(self, *others):
"""
Returns the horizontal composition of 'self' with a diagram 'other'.
This method is called using the binary operator `@`:
>>> x, y, z, w = Ty('x'), Ty('y'), Ty('z'), Ty('w')
>>> f0, f1 = Box('f0', x, y), Box('f1', z, w)
>>> assert f0 @ f1 == f0.tensor(f1) == f0 @ Id(z) >> Id(y) @ f1
Parameters
----------
other : :class:`Diagram`
Returns
-------
diagram : :class:`Diagram`
the tensor of 'self' and 'other'.
"""
if not others:
return self
if len(others) > 1:
return self.tensor(others[0]).tensor(*others[1:])
other = others[0]
if not isinstance(other, Diagram):
raise TypeError(messages.type_err(Diagram, other))
dom, cod = self.dom @ other.dom, self.cod @ other.cod
boxes = self.boxes + other.boxes
offsets = self.offsets + [n + len(self.cod) for n in other.offsets]
layers = cat.Id(dom)
for left, box, right in self.layers:
layers = layers >> Layer(left, box, right @ other.dom)
for left, box, right in other.layers:
layers = layers >> Layer(self.cod @ left, box, right)
return Diagram(dom, cod, boxes, offsets, layers=layers)
def __init__(self, dom, cod, boxes, offsets, layers=None):
if not isinstance(dom, Ty):
raise TypeError(messages.type_err(Ty, dom))
if not isinstance(cod, Ty):
raise TypeError(messages.type_err(Ty, cod))
if len(boxes) != len(offsets):
raise ValueError(messages.boxes_and_offsets_must_have_same_len())
if layers is None:
layers = cat.Id(dom)
for box, off in zip(boxes, offsets):
if not isinstance(box, Diagram):
raise TypeError(messages.type_err(Diagram, box))
if not isinstance(off, int):
raise TypeError(messages.type_err(int, off))
left = layers.cod[:off] if layers else dom[:off]
right = layers.cod[off + len(box.dom):]\
if layers else dom[off + len(box.dom):]
layers = layers >> Layer(left, box, right)
layers = layers >> cat.Id(cod)
self._layers, self._offsets = layers, tuple(offsets)
super().__init__(dom, cod, boxes, _scan=False)
def tensor(self, other=None, *rest):
"""
Returns the horizontal composition of 'self' with a diagram 'other'.
This method is called using the binary operator `@`:
>>> x, y, z, w = Ty('x'), Ty('y'), Ty('z'), Ty('w')
>>> f0, f1 = Box('f0', x, y), Box('f1', z, w)
>>> assert f0 @ f1 == f0.tensor(f1) == f0 @ Id(z) >> Id(y) @ f1
>>> (f0 @ f1).draw(
... figsize=(2, 2),
... path='docs/_static/imgs/monoidal/tensor-example.png')
.. image:: ../_static/imgs/monoidal/tensor-example.png
:align: center
Parameters
----------
other : :class:`Diagram`
Returns
-------
diagram : :class:`Diagram`
the tensor of 'self' and 'other'.
"""
if other is None:
return self
if rest:
return self.tensor(other).tensor(*rest)
if isinstance(other, Sum):
return self.sum([self]).tensor(other)
if not isinstance(other, Diagram):
raise TypeError(messages.type_err(Diagram, other))
dom, cod = self.dom @ other.dom, self.cod @ other.cod
boxes = self.boxes + other.boxes
offsets = self.offsets + [n + len(self.cod) for n in other.offsets]
layers = cat.Id(dom)
for left, box, right in self.layers:
layers = layers >> Layer(left, box, right @ other.dom)
for left, box, right in other.layers:
layers = layers >> Layer(self.cod @ left, box, right)
return self.upgrade(Diagram(dom, cod, boxes, offsets, layers=layers))
def __init__(self, dom):
monoidal.Id.__init__(self, dom)
Diagram.__init__(self, dom, dom, [], [], layers=cat.Id(dom))
def __init__(self, t):
super().__init__(t, t, [], [], layers=cat.Id(t))
def __init__(self, dom=Dim()):
rigid.Id.__init__(self, dom)
Diagram.__init__(self, dom, dom, [], [], layers=cat.Id(dom))
def __init__(self, dom=Ty()):
cat.Id.__init__(self, dom)
Diagram.__init__(self, dom, dom, [], [], layers=cat.Id(dom))
def __init__(self, x):
super().__init__(x, x, [], [], layers=cat.Id(x))
def __str__(self):
return ("{} @ ".format(cat.Id(self._left)) if self._left else "")\
+ str(self._box)\
+ (" @ {}".format(cat.Id(self._right)) if self._right else "")