Diagram

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

Bases: Diagram

A pregroup diagram is a rigid diagram with Word boxes.

Parameters:

• inside (tuple[frobenius.Layer, ...]) – The layers of the diagram.

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

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

Note

In order to define more general DisCoCat diagrams, pregroup diagrams subclass frobenius rather than rigid. Have fun with swaps and spiders!

Example

>>> s, n = Ty('s'), Ty('n')
>>> Alice, Bob = Word('Alice', n), Word('Bob', n)
>>> loves = Word('loves', n.r @ s @ n.l)
>>> grammar = Cup(n, n.r) @ Id(s) @ Cup(n.l, n)
>>> sentence = grammar << Alice @ loves @ Bob
>>> print(sentence[:4])
Alice >> n @ loves >> n @ n.r @ s @ n.l @ Bob >> Cup(n, n.r) @ s @ n.l @ n
>>> from discopy import tensor
>>> ob = {s: 1, n: 2}
>>> ar = {Alice: [1, 0], loves: [0, 1, 1, 0], Bob: [0, 1]}
>>> F = tensor.Functor(ob, ar, dom=Category(), dtype=bool)
>>> assert F(sentence)

ty_factory

alias of Ty

normal_form(**params)

Applies normal form to a pregroup diagram of the form word @ ... @ word >> wires by normalising words and wires seperately before combining them, so it can be drawn with draw().

classmethod cups(left, right)

Construct a diagram of nested cups for types left and right.

Parameters:

• left (Ty) – The type left of the cup.

• right (Ty) – Its right adjoint.

Return type:

Diagram

Example

>>> a, b = Ty('a'), Ty('b')
>>> Diagram.cups(a.l @ b, b.r @ a).draw(figsize=(3, 1),\
... margins=(0.3, 0.05), path='docs/_static/rigid/cups.png')

classmethod caps(left, right)

Construct a diagram of nested caps for types left and right.

Parameters:

• left (Ty) – The type left of the cap.

• right (Ty) – Its left adjoint.

Return type:

Diagram

Example

>>> a, b = Ty('a'), Ty('b')
>>> Diagram.caps(a.r @ b, b.l @ a).draw(figsize=(3, 1),\
... margins=(0.3, 0.05), path='docs/_static/rigid/caps.png')

braid_factory

alias of Swap

cap_factory

alias of Cap

cup_factory

alias of Cup

factory

alias of Diagram

spider_factory

alias of Spider