Diagram

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

Bases: discopy.symmetric.Diagram

A Markov diagram is a symmetric diagram with Copy boxes.

Parameters:

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

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

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

Note

We can create arbitrary Markov diagrams with the standard notation for Python functions.

>>> x = Ty('x')
>>> f = Box('f', x, x)

>>> copy_then_apply = Diagram.from_callable(x, x @ x)(
...     lambda x: (f(x), f(x)))

>>> @Diagram.from_callable(x, x @ x)
... def apply_then_copy(x):
...     y = f(x)
...     return x, x

>>> from discopy.drawing import Equation
>>> Equation(copy_then_apply, apply_then_copy, symbol="$\\neq$").draw(
...     path="docs/_static/markov/copy_and_apply.png")

classmethod copy(x, n=2)

Make n copies of a given type x.

Parameters:

• x (Ty) – The type to copy.

• n – The number of copies.

Return type:

Diagram

classmethod merge(x, n=2)

Merge n copies of a given type x.

Parameters:

• x (Ty) – The type to copy.

• n – The number of copies.

Return type:

Diagram

classmethod discard(x, n=2)

The discard of an atomic type x.

Parameters:

x (Ty) – The type to discard.

Return type:

Diagram

braid_factory

alias of Swap

copy_factory

alias of Copy

discard_factory

alias of Discard

factory

alias of Diagram

merge_factory

alias of Merge

sum_factory

alias of Sum

trace_factory

alias of Trace