drawing

The category of labeled progressive plane graphs.

This was first defined in Joyal and Street [JS88].

Summary

Point	A point is a pair of floats for the x and y coordinates.
PlaneGraph	A plane graph is a graph with a mapping from nodes to points.
Drawing	A drawing is a plane graph with designated input and output types.

Axioms

• Associativity and unit

>>> from discopy.monoidal import Ty, Box
>>> from discopy.monoidal import Equation

>>> x, y, z, w = map(Ty, "xyzw")
>>> f = Box('f', x, y).to_drawing()
>>> g = Box('g', y, z).to_drawing()
>>> h = Box('h', z, w).to_drawing()

>>> assert (f >> g) >> h == f >> (g >> h)
>>> assert (f @ g) @ h == f @ (g @ h)

>>> assert f >> Drawing.id(f.cod) == f == Drawing.id(f.dom) >> f
>>> assert f @ Drawing.id() == f == Drawing.id() @ f

• Interchanger

>>> f0, f1 = (Box(f'f{i}', f'x{i}', f'y{i}').to_drawing() for i in (0, 1))
>>> g0, g1 = (Box(f'g{i}', f'y{i}', f'z{i}').to_drawing() for i in (0, 1))

>>> Equation(f0 @ f1 >> g0 @ g1, (f0 >> g0) @ (f1 >> g1)).draw(
...     doctest="docs/_static/drawing/interchanger-1.svg")

>>> Equation(f @ g.dom >> f.cod @ g, f @ g, f.dom @ g >> f @ g.cod).draw(
...     doctest="docs/_static/drawing/interchanger-2.svg")

Gallery

The drawing parameters below are exercised by the documentation itself.

>>> from discopy import monoidal
>>> Ty, Box, Id = monoidal.Ty, monoidal.Box, monoidal.Diagram.id
>>> x = Ty('x')

Boxes and wires reserve enough horizontal space for their labels:

>>> (Box('f', x, x @ x)
...  >> Box('a_box_with_a_very_long_name', x @ x, x)
...  >> Box('g', x, x)).draw(
...      aspect='equal', doctest="docs/_static/drawing/long-box-name.svg")
>>> (Box('$\\Lambda$', x, x, min_width=3) @ Box('f', x, x)).draw(
...     aspect='equal', doctest="docs/_static/drawing/box-min-width.svg")
>>> long_type = Ty('a_long_type_name')
>>> long_type.inside[0].min_right_margin = 1.5
>>> Id(x @ long_type @ x).draw(aspect='equal',
...     doctest="docs/_static/drawing/wire-min-right-margin.svg")
>>> custom = Ty('custom_margin_wire')
>>> custom.inside[0].right_margin = 3
>>> Id(x @ custom @ x).draw(
...     aspect='equal', doctest="docs/_static/drawing/wire-custom-margin.svg")
>>> Box('f', x, x @ Ty('a_long_output_type')).draw(
...     aspect='equal', doctest="docs/_static/drawing/wire-auto-margin.svg")
>>> (Box('$\\int_a^b f(x)\\,dx = \\sqrt{2}$', x, x)
...  @ Box('f', x, x)).draw(
...      aspect='equal', doctest="docs/_static/drawing/long-latex-name.svg")

Bubbles, grammatical diagrams and quantum circuits use the same backend:

>>> (x @ Box('s', Ty(), Ty())).bubble().draw(
...     wire_labels=False,
...     doctest="docs/_static/drawing/bubble-straight-wire.svg")
>>> from discopy.compact import (
...     Cap, Ty as RTy, Box as RBox, Id as RId)
>>> n, s = map(RTy, 'ns')
>>> who = (Cap(n.r, n) >> RId(n.r) @ RBox('copy', n, n @ n)
...        >> RId(n.r @ n) @ Cap(s, s.l) @ RId(n)
...        >> RId(n.r) @ RBox('update', n @ s, s) @ RId(s.l @ n))
>>> who.draw(aspect='equal', doctest="docs/_static/drawing/who-ansatz.svg")
>>> from discopy.grammar.categorial import Eval, Ty as CTy, Word
>>> s, n = map(CTy, 'sn')
>>> sentence = (Word('Alice', n) @ Word('loves', (n >> s) << n)
...             @ Word('Bob', n) >> n @ Eval((n >> s) << n) >> Eval(n >> s))
>>> sentence.draw(
...     aspect='equal', doctest="docs/_static/drawing/categorial-grammar.svg")
>>> from discopy.quantum.zx import Z, X, Id as ZId, SWAP
>>> bialgebra = (Z(1, 2) @ Z(1, 2) >> ZId(1) @ SWAP @ ZId(1)
...              >> X(2, 1) @ X(2, 1))
>>> (bialgebra + bialgebra).draw(
...     aspect='equal', doctest="docs/_static/drawing/bialgebra.svg")
>>> from discopy.quantum import qubit, H, sqrt, Bra, Ket, CX
>>> bell = sqrt(2) >> Ket(0, 0) >> H @ qubit >> CX >> Bra(0) @ qubit
>>> bell.draw(aspect='equal', doctest="docs/_static/drawing/bell-state.svg")
>>> from discopy.quantum import Controlled, CZ
>>> circuit = (Controlled(CX.l, distance=3)
...            >> Controlled(Controlled(CZ.l, distance=2), distance=-1))
>>> circuit.draw(
...     wire_labels=False, doctest="docs/_static/drawing/long-controlled.svg")

A controlled gate over distinct wires, e.g. a classically-controlled gate, picks the x-coordinate of its control from the wire it sits on:

>>> bit, qubit = Ty("bit"), Ty("qubit")
>>> gate = Box("F", qubit, qubit)
>>> controlled = Box(
...     "CF", bit @ qubit, bit @ qubit,
...     draw_as_controlled=True, controlled=gate, distance=1)
>>> left_controlled = Box(
...     "FC", qubit @ bit, qubit @ bit,
...     draw_as_controlled=True, controlled=gate, distance=-1)
>>> (controlled @ left_controlled).draw(
...     doctest="docs/_static/drawing/controlled-classical.svg")

Coloured regions are also checked as part of the gallery:

>>> Colour, Wire = monoidal.Colour, monoidal.Wire
>>> ol, o1, o2, o_r, o3, o4 = map(
...     Colour, ("red", "orange", "gold", "green", "blue", "purple"))
>>> il, i1, i_r, i2 = map(
...     Colour, ("cyan", "magenta", "brown", "pink"))
>>> outer_dom = Ty(
...     Wire("d", ol, o1), Wire("c", o1, o2), Wire("c", o2, o_r))
>>> outer_cod = Ty(
...     Wire("b", ol, o3), Wire("a", o3, o4), Wire("a", o4, o_r))
>>> inner_dom = Ty(Wire("a", il, i1), Wire("b", i1, i_r))
>>> inner_cod = Ty(Wire("c", il, i2), Wire("d", i2, i_r))
>>> Box("f", inner_dom, inner_cod).bubble(
...     dom=outer_dom, cod=outer_cod, name="g").draw(wire_labels=False,
...         doctest="docs/_static/drawing/coloured-bubble.svg")