Ty

class discopy.closed.Ty(*inside, dom=None, cod=None, _scan=True, **kwargs)

Bases: discopy.biclosed.Ty

A closed type is a biclosed type in a symmetric category where left and right exponentials coincide, i.e. X << Y == X ** Y == Y >> X.

Applying a closed type to a function yields an Term e.g.

>>> X, Y = Ty("X"), Ty("Y")
>>> t = X(lambda x: (X >> Y)(lambda f: f(x)))
>>> t.draw(
...     doctest='docs/_static/closed/diagram.svg',
...     aspect="auto", figsize=(8, 8), margins=(0.2, 0))

Parameters:

• inside (str | cat.Ob)

• dom (C0)

• cod (C0)

• _scan (bool)

product(*others)

The Product of a type with a tuple of others.

Parameters:

others (Ty)

Return type:

Ty

property is_product

Whether the type is a Product object.

Example

>>> x, y = Ty('x'), Ty('y')
>>> assert (x * y).is_product and (x * y @ Ty()).is_product

property factors

The factors of a product type, assumes self.is_product.

classmethod from_biclosed(old)

Translate a biclosed type into a closed type, collapsing left and right exponentials into a single exponential.

Parameters:

old (Ty) – The biclosed type to translate.

Return type:

Ty

Example

>>> x, y = biclosed.Ty("x"), biclosed.Ty("y")
>>> assert Ty.from_biclosed(x << y) == Ty.from_biclosed(y >> x)

abstraction_factory

alias of Abstraction

application_factory

alias of Application

constant_factory

alias of Constant

exp_factory

alias of Exp

factory

alias of Ty

over_factory

alias of Exp

product_factory

alias of Product

under_factory

alias of Exp

variable_factory

alias of Variable