Diagram

class discopy.pivotal.Diagram(inside, dom, cod, _scan=True)

Bases: discopy.rigid.Diagram, discopy.traced.Diagram

A pivotal diagram is a rigid diagram and a traced diagram with pivotal types as domain and codomain.

Parameters

• inside (Layer) – The layers of the diagram.

• dom (Ty) – The domain of the diagram, i.e. its input.

• cod (Ty) – The codomain of the diagram, i.e. its output.

ty_factory

alias of Ty

dagger()

The dagger of a pivotal diagram is its vertical reflection.

Example

>>> x, y, z = map(Ty, "xyz")
>>> f = Box('f', x @ y, z).curry()

>>> from discopy.drawing import Equation
>>> Equation(f, f.dagger(), symbol="$\\mapsto$").draw(
...     figsize=(6, 3), asymmetry=.1,
...     path="docs/_static/pivotal/dagger.png")

conjugate()

The horizontal reflection of a diagram, defined as the dagger of the rotation.

Equivalently, it is the rotation of the dagger.

Example

>>> x, y, z = map(Ty, "xyz")
>>> x, y, z = map(Ty, "xyz")
>>> f = Box('f', x @ y, z).curry()
>>> assert f.conjugate() == f[::-1].rotate() == f.rotate()[::-1]

>>> from discopy.drawing import Equation
>>> Equation(f, f.conjugate(), symbol="$\\mapsto$").draw(
...     figsize=(6, 3), path="docs/_static/pivotal/conjugate.png")

classmethod trace_factory(diagram, left=False)

The trace of a pivotal diagram is its pre- and post-composition with cups and caps to form a feedback loop.

Parameters

left – Whether to trace the wire on the left or right.

Example

>>> from discopy.drawing import Equation as Eq
>>> x = Ty('x')
>>> f = Box('f', x @ x, x @ x)
>>> LHS, RHS = f.trace(left=True), f.trace(left=False)
>>> Eq(Eq(LHS, f, symbol="$\\mapsfrom$"),
...     RHS, symbol="$\\mapsto$").draw(
...         path="docs/_static/pivotal/trace.png")

cap_factory

alias of Cap

cup_factory

alias of Cup

factory

alias of Diagram