def test_normal_form():
n = Ty('n')
w1, w2 = Word('a', n), Word('b', n)
diagram = w1 @ w2 >>\
Id(n) @ Cap(n, n.r) @ Id(n) >> Id(n @ n) @ Cup(n.r, n)
expected_result = w1 @ w2
assert expected_result == normal_form(diagram)
with raises(ValueError) as err:
normal_form(w2 >> w1 @ Id(n))
def generate(self,
start,
max_sentences,
max_depth,
max_iter=100,
remove_duplicates=False,
not_twice=[]):
"""
Generate sentences from a context-free grammar.
Assumes the only terminal symbol is Ty().
Parameters
----------
start : type
root of the generated trees.
max_sentences : int
maximum number of sentences to generate.
max_depth : int
maximum depth of the trees.
max_iter : int
maximum number of iterations, set to 100 by default.
remove_duplicates : bool
if set to True only distinct syntax trees will be generated.
not_twice : list
list of productions that you don't want appearing twice
in a sentence, set to the empty list by default
"""
prods, cache = list(self.productions), set()
n, i = 0, 0
while (not max_sentences or n < max_sentences) and i < max_iter:
i += 1
sentence = Id(start)
depth = 0
while depth < max_depth:
recall = depth
if sentence.dom == Ty():
if remove_duplicates and sentence in cache:
break
yield sentence
if remove_duplicates:
cache.add(sentence)
n += 1
break
tag = sentence.dom[0]
random.shuffle(prods)
for prod in prods:
if prod in not_twice and prod in sentence.boxes:
continue
if Ty(tag) == prod.cod:
sentence = sentence << prod @ Id(sentence.dom[1:])
depth += 1
break
if recall == depth: # in this case, no production was found
break
def normal_form(diagram, normalizer=None, **params):
"""
Applies normal form to a pregroup diagram of the form
`word @ ... @ word >> cups` by normalising the words and the sentences
seperately before combining them, so it can be drawn using `grammar.draw`.
"""
words, is_pregroup = Id(Ty()), True
for _, box, right in diagram.layers:
if isinstance(box, Word):
if right: # word boxes should be tensored left to right.
is_pregroup = False
break
words = words @ box
else:
break
wires = diagram[len(words):]
is_pregroup = is_pregroup and all(
isinstance(box, Cup) or isinstance(box, Swap) or isinstance(box, Cap)
for box in wires.boxes)
if not is_pregroup:
raise ValueError(messages.expected_pregroup())
norm = lambda d: monoidal.Diagram.normal_form(
d, normalizer=normalizer or Diagram.normalize, **params)
return norm(words) >> norm(wires)
def generate(self,
start,
max_sentences,
max_depth,
max_iter=100,
remove_duplicates=False):
"""
Generate sentences from a context-free grammar.
Assumes the only terminal symbol is Ty().
Parameters
----------
start : type
root of the generated trees.
max_sentences : int
maximum number of sentences to generate.
max_depth : int
maximum depth of the trees.
max_iter : int
maximum number of iterations, set to 100 by default.
remove_duplicates : bool
if set to True only distinct syntax trees will be generated.
"""
prods, cache = list(self.productions), set()
n, iter = 0, 0
while n < max_sentences and (iter < max_iter):
iter += 1
sentence = Id(start)
depth = 0
while depth < max_depth:
if sentence.dom == Ty():
if remove_duplicates and sentence in cache:
break
yield sentence
if remove_duplicates:
cache.add(sentence)
n += 1
break
tag = sentence.dom[0]
random.shuffle(prods)
for prod in prods:
if Ty(tag) == prod.cod:
sentence = sentence << prod @ Id(sentence.dom[1:])
depth += 1
break
def draw(diagram, **params):
"""
Draws a pregroup diagram, i.e. of shape :code:`word @ ... @ word >> cups`.
Parameters
----------
width : float, optional
Width of the word triangles, default is :code:`2.0`.
space : float, optional
Space between word triangles, default is :code:`0.5`.
textpad : pair of floats, optional
Padding between text and wires, default is :code:`(0.1, 0.2)`.
draw_type_labels : bool, optional
Whether to draw type labels, default is :code:`True`.
aspect : string, optional
Aspect ratio, one of :code:`['equal', 'auto']`.
margins : tuple, optional
Margins, default is :code:`(0.05, 0.05)`.
fontsize : int, optional
Font size for the words, default is :code:`12`.
fontsize_types : int, optional
Font size for the types, default is :code:`12`.
figsize : tuple, optional
Figure size.
path : str, optional
Where to save the image, if :code:`None` we call :code:`plt.show()`.
pretty_types : bool, optional
Whether to draw type labels with superscript, default is :code:`False`.
triangles : bool, optional
Whether to draw words as triangular states, default is :code:`False`.
Raises
------
ValueError
Whenever the input is not a pregroup diagram.
"""
from discopy.rigid import Swap
if not isinstance(diagram, Diagram):
raise TypeError(messages.type_err(Diagram, diagram))
words, is_pregroup = Id(Ty()), True
for _, box, right in diagram.layers:
if isinstance(box, Word):
if right: # word boxes should be tensored left to right.
is_pregroup = False
break
words = words @ box
else:
break
cups = diagram[len(words):].foliation().boxes\
if len(words) < len(diagram) else []
is_pregroup = is_pregroup and words and all(
isinstance(box, Cup) or isinstance(box, Swap) for s in cups
for box in s.boxes)
if not is_pregroup:
raise ValueError(messages.expected_pregroup())
drawing.pregroup_draw(words, cups, **params)
def eager_parse(*words, target=Ty('s')):
"""
Tries to parse a given list of words in an eager fashion.
"""
result = fold(lambda x, y: x @ y, words)
scan = result.cod
while True:
fail = True
for i in range(len(scan) - 1):
if scan[i:i + 1].r != scan[i + 1:i + 2]:
continue
cup = Cup(scan[i:i + 1], scan[i + 1:i + 2])
result = result >> Id(scan[:i]) @ cup @ Id(scan[i + 2:])
scan, fail = result.cod, False
break
if result.cod == target:
return result
if fail:
raise NotImplementedError
def test_pregroup_draw_errors():
n = Ty('n')
with raises(TypeError):
draw(0)
with raises(ValueError) as err:
draw(Cap(n, n.l))
with raises(ValueError) as err:
draw(Cup(n, n.r))
with raises(ValueError) as err:
draw(Word('Alice', n) >> Word('Alice', n) @ Id(n))
assert str(err.value) is messages.expected_pregroup()
def test_CFG():
s, n, v, vp = Ty('S'), Ty('N'), Ty('V'), Ty('VP')
R0, R1 = Box('R0', vp @ n, s), Box('R1', n @ v, vp)
Jane, loves, Bob = Word('Jane', n), Word('loves', v), Word('Bob', n)
cfg = CFG(R0, R1, Jane, loves, Bob)
assert Jane in cfg.productions
assert "CFG(Box('R0', Ty('VP', 'N'), Ty('S'))" in repr(cfg)
assert not list(CFG().generate(start=s, max_sentences=1, max_depth=1))
sentence, *_ = cfg.generate(
start=s, max_sentences=1, max_depth=10, not_twice=[Jane, Bob], seed=42)
assert sentence\
== (Jane @ loves @ Bob).normal_form(left=True) >> R1 @ Id(n) >> R0
def test_brute_force():
s, n = Ty('s'), Ty('n')
Alice = Word('Alice', n)
loves = Word('loves', n.r @ s @ n.l)
Bob = Word('Bob', n)
grammar = Cup(n, n.r) @ Id(s) @ Cup(n.l, n)
gen = brute_force(Alice, loves, Bob)
assert next(gen) == Alice @ loves @ Alice >> grammar
assert next(gen) == Alice @ loves @ Bob >> grammar
assert next(gen) == Bob @ loves @ Alice >> grammar
assert next(gen) == Bob @ loves @ Bob >> grammar
gen = brute_force(Alice, loves, Bob, target=n)
assert next(gen) == Word('Alice', Ty('n'))
assert next(gen) == Word('Bob', Ty('n'))
def test_eager_parse():
s, n = Ty('s'), Ty('n')
Alice = Word('Alice', n)
loves = Word('loves', n.r @ s @ n.l)
Bob = Word('Bob', n)
grammar = Cup(n, n.r) @ Id(s) @ Cup(n.l, n)
assert eager_parse(Alice, loves, Bob) == grammar << Alice @ loves @ Bob
who = Word('who', n.r @ n @ s.l @ n)
assert eager_parse(Bob, who, loves, Alice, target=n).offsets ==\
[0, 1, 5, 8, 0, 2, 1, 1]
with raises(NotImplementedError):
eager_parse(Alice, Bob, loves)
with raises(NotImplementedError):
eager_parse(Alice, loves, Bob, who, loves, Alice)
def test_from_tree():
s, n = Ty('s'), Ty('n')
Alice, Bob = Word('Alice', n), Word('Bob', n)
loves = Word('loves', n.r @ s @ n.l)
sentence = Alice @ loves @ Bob >> Cup(n, n.r) @ Id(s) @ Cup(n.l, n)
sentence == from_tree(sentence.to_tree())
