Functor

class discopy.rigid.Functor(ob, ar, ob_factory=<class 'discopy.rigid.Ty'>, ar_factory=<class 'discopy.rigid.Diagram'>)

Bases: Functor

Implements rigid monoidal functors, i.e. preserving cups and caps.

>>> s, n = Ty('s'), Ty('n')
>>> Alice, Bob = Box("Alice", Ty(), n), Box("Bob", Ty(), n)
>>> loves = Box('loves', Ty(), n.r @ s @ n.l)
>>> love_box = Box('loves', n @ n, s)
>>> ob = {s: s, n: n}
>>> ar = {Alice: Alice, Bob: Bob}
>>> ar.update({loves: Cap(n.r, n) @ Cap(n, n.l)
...                   >> Id(n.r) @ love_box @ Id(n.l)})
>>> F = Functor(ob, ar)
>>> sentence = Alice @ loves @ Bob >> Cup(n, n.r) @ Id(s) @ Cup(n.l, n)
>>> assert F(sentence).normal_form() == Alice >> Id(n) @ Bob >> love_box
>>> from discopy import drawing
>>> drawing.equation(
...     sentence, F(sentence), symbol='$\\mapsto$', figsize=(5, 2),
...     path='docs/_static/imgs/rigid/functor-example.png')