Functor

class discopy.traced.Functor(ob=None, ar=None, dom=None, cod=None)

Bases: discopy.monoidal.Functor

A traced functor is a monoidal functor that preserves traces.

Parameters:

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

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

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

• dom (T) –

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={x: (float, )},
...     ar={f: lambda x=1.: (x, 1 + 1. / x), g: lambda: (1 + sqrt(5)) / 2},
...     cod=Category(python.Ty, python.Function))
>>> with python.Function.no_type_checking:
...     assert F(f.trace())() == F(g)()

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