Functor

class discopy.traced.Functor(ob_map=None, ar_map=None, dom=None, cod=None, colour_map=None)

Bases: discopy.monoidal.Functor

A traced functor is a monoidal functor that preserves traces.

Parameters:

• ob_map (Mapping[monoidal.Ty, monoidal.Ty]) – Map from monoidal.Ty to cod.ob.

• ar_map (Mapping[Box, Diagram]) – Map from Box to cod.

• cod (Category) – The codomain, Diagram by default.

Example

Let’s compute the golden ratio by applying a (hacky) traced functor.

>>> from math import sqrt
>>> from discopy import python
>>> x = Ty('$\\mathbb{R}$')
>>> f = Box('$\\lambda x . (x, 1 + 1 / x)$', x, x @ x)
>>> g = Box('$\\frac{1 + \\sqrt{5}}{2}$', Ty(), x)
>>> F = Functor(
...     ob_map={x: (float, )},
...     ar_map={
...         f: lambda x=1.: (x, 1 + 1. / x),
...         g: lambda: (1 + sqrt(5)) / 2},
...     cod=python.Function)
>>> with python.Function.no_type_checking:
...     assert F(f.trace())() == F(g)()

>>> from discopy.monoidal import Equation
>>> Equation(f.trace(), g).draw(path="docs/_static/traced/golden.svg")

dom

alias of Diagram

cod

alias of Diagram