pipeline/nltk/test/drt.doctest

.. Copyright (C) 2001-2023 NLTK Project
.. For license information, see LICENSE.TXT

================================
 Discourse Representation Theory
================================

    >>> from nltk.sem import logic
    >>> from nltk.inference import TableauProver

Overview
========

A DRS can be created with the ``DRS()`` constructor. This takes two arguments: a list of
discourse referents and list of conditions. .

    >>> from nltk.sem.drt import *
    >>> dexpr = DrtExpression.fromstring
    >>> man_x = dexpr('man(x)')
    >>> walk_x = dexpr('walk(x)')
    >>> x = dexpr('x')
    >>> print(DRS([x], [man_x, walk_x]))
    ([x],[man(x), walk(x)])

The ``parse()`` method can also be applied directly to DRS
expressions, which allows them to be specified more
easily.

    >>> drs1 = dexpr('([x],[man(x),walk(x)])')
    >>> print(drs1)
    ([x],[man(x), walk(x)])

DRSs can be *merged* using the ``+`` operator.

    >>> drs2 = dexpr('([y],[woman(y),stop(y)])')
    >>> drs3 = drs1 + drs2
    >>> print(drs3)
    (([x],[man(x), walk(x)]) + ([y],[woman(y), stop(y)]))
    >>> print(drs3.simplify())
    ([x,y],[man(x), walk(x), woman(y), stop(y)])

We can embed DRSs as components of an ``implies`` condition.

    >>> s = '([], [(%s -> %s)])' % (drs1, drs2)
    >>> print(dexpr(s))
    ([],[(([x],[man(x), walk(x)]) -> ([y],[woman(y), stop(y)]))])



The ``fol()`` method converts DRSs into FOL formulae.



    >>> print(dexpr(r'([x],[man(x), walks(x)])').fol())

    exists x.(man(x) & walks(x))

    >>> print(dexpr(r'([],[(([x],[man(x)]) -> ([],[walks(x)]))])').fol())

    all x.(man(x) -> walks(x))



In order to visualize a DRS, the ``pretty_format()`` method can be used.



    >>> print(drs3.pretty_format())

      _________     __________

     | x       |   | y        |

    (|---------| + |----------|)

     | man(x)  |   | woman(y) |

     | walk(x) |   | stop(y)  |

     |_________|   |__________|





Parse to semantics

------------------



..

    >>> logic._counter._value = 0



DRSs can be used for building compositional semantics in a feature

based grammar. To specify that we want to use DRSs, the appropriate

logic parser needs be passed as a parameter to ``load_earley()``



    >>> from nltk.parse import load_parser

    >>> from nltk.sem.drt import DrtParser

    >>> parser = load_parser('grammars/book_grammars/drt.fcfg', trace=0, logic_parser=DrtParser())

    >>> for tree in parser.parse('a dog barks'.split()):

    ...     print(tree.label()['SEM'].simplify())

    ...

    ([x],[dog(x), bark(x)])



Alternatively, a ``FeatStructReader`` can be passed with the ``logic_parser`` set on it



    >>> from nltk.featstruct import FeatStructReader

    >>> from nltk.grammar import FeatStructNonterminal

    >>> parser = load_parser('grammars/book_grammars/drt.fcfg', trace=0, fstruct_reader=FeatStructReader(fdict_class=FeatStructNonterminal, logic_parser=DrtParser()))

    >>> for tree in parser.parse('every girl chases a dog'.split()):

    ...     print(tree.label()['SEM'].simplify().normalize())

    ...

    ([],[(([z1],[girl(z1)]) -> ([z2],[dog(z2), chase(z1,z2)]))])







Unit Tests

==========



Parser

------



    >>> print(dexpr(r'([x,y],[sees(x,y)])'))

    ([x,y],[sees(x,y)])

    >>> print(dexpr(r'([x],[man(x), walks(x)])'))

    ([x],[man(x), walks(x)])

    >>> print(dexpr(r'\x.([],[man(x), walks(x)])'))

    \x.([],[man(x), walks(x)])

    >>> print(dexpr(r'\x.\y.([],[sees(x,y)])'))

    \x y.([],[sees(x,y)])



    >>> print(dexpr(r'([x,y],[(x = y)])'))

    ([x,y],[(x = y)])

    >>> print(dexpr(r'([x,y],[(x != y)])'))

    ([x,y],[-(x = y)])



    >>> print(dexpr(r'\x.([],[walks(x)])(john)'))

    (\x.([],[walks(x)]))(john)

    >>> print(dexpr(r'\R.\x.([],[big(x,R)])(\y.([],[mouse(y)]))'))

    (\R x.([],[big(x,R)]))(\y.([],[mouse(y)]))



    >>> print(dexpr(r'(([x],[walks(x)]) + ([y],[runs(y)]))'))

    (([x],[walks(x)]) + ([y],[runs(y)]))

    >>> print(dexpr(r'(([x,y],[walks(x), jumps(y)]) + (([z],[twos(z)]) + ([w],[runs(w)])))'))

    (([x,y],[walks(x), jumps(y)]) + ([z],[twos(z)]) + ([w],[runs(w)]))

    >>> print(dexpr(r'((([],[walks(x)]) + ([],[twos(x)])) + ([],[runs(x)]))'))

    (([],[walks(x)]) + ([],[twos(x)]) + ([],[runs(x)]))

    >>> print(dexpr(r'((([],[walks(x)]) + ([],[runs(x)])) + (([],[threes(x)]) + ([],[fours(x)])))'))

    (([],[walks(x)]) + ([],[runs(x)]) + ([],[threes(x)]) + ([],[fours(x)]))



    >>> print(dexpr(r'(([],[walks(x)]) -> ([],[runs(x)]))'))

    (([],[walks(x)]) -> ([],[runs(x)]))



    >>> print(dexpr(r'([x],[PRO(x), sees(John,x)])'))

    ([x],[PRO(x), sees(John,x)])

    >>> print(dexpr(r'([x],[man(x), -([],[walks(x)])])'))

    ([x],[man(x), -([],[walks(x)])])

    >>> print(dexpr(r'([],[(([x],[man(x)]) -> ([],[walks(x)]))])'))

    ([],[(([x],[man(x)]) -> ([],[walks(x)]))])



    >>> print(dexpr(r'DRS([x],[walk(x)])'))

    ([x],[walk(x)])

    >>> print(dexpr(r'DRS([x][walk(x)])'))

    ([x],[walk(x)])

    >>> print(dexpr(r'([x][walk(x)])'))

    ([x],[walk(x)])



``simplify()``

--------------



    >>> print(dexpr(r'\x.([],[man(x), walks(x)])(john)').simplify())

    ([],[man(john), walks(john)])

    >>> print(dexpr(r'\x.\y.([z],[dog(z),sees(x,y)])(john)(mary)').simplify())

    ([z],[dog(z), sees(john,mary)])

    >>> print(dexpr(r'\R x.([],[big(x,R)])(\y.([],[mouse(y)]))').simplify())

    \x.([],[big(x,\y.([],[mouse(y)]))])



    >>> print(dexpr(r'(([x],[walks(x)]) + ([y],[runs(y)]))').simplify())

    ([x,y],[walks(x), runs(y)])

    >>> print(dexpr(r'(([x,y],[walks(x), jumps(y)]) + (([z],[twos(z)]) + ([w],[runs(w)])))').simplify())

    ([w,x,y,z],[walks(x), jumps(y), twos(z), runs(w)])

    >>> print(dexpr(r'((([],[walks(x)]) + ([],[runs(x)]) + ([],[threes(x)]) + ([],[fours(x)])))').simplify())

    ([],[walks(x), runs(x), threes(x), fours(x)])

    >>> dexpr(r'([x],[man(x)])+([x],[walks(x)])').simplify() == \

    ... dexpr(r'([x,z1],[man(x), walks(z1)])')

    True

    >>> dexpr(r'([y],[boy(y), (([x],[dog(x)]) -> ([],[chase(x,y)]))])+([x],[run(x)])').simplify() == \

    ... dexpr(r'([y,z1],[boy(y), (([x],[dog(x)]) -> ([],[chase(x,y)])), run(z1)])')

    True



    >>> dexpr(r'\Q.(([x],[john(x),walks(x)]) + Q)(([x],[PRO(x),leaves(x)]))').simplify() == \

    ... dexpr(r'([x,z1],[john(x), walks(x), PRO(z1), leaves(z1)])')

    True



    >>> logic._counter._value = 0

    >>> print(dexpr('([],[(([x],[dog(x)]) -> ([e,y],[boy(y), chase(e), subj(e,x), obj(e,y)]))])+([e,x],[PRO(x), run(e), subj(e,x)])').simplify().normalize().normalize())

    ([e02,z5],[(([z3],[dog(z3)]) -> ([e01,z4],[boy(z4), chase(e01), subj(e01,z3), obj(e01,z4)])), PRO(z5), run(e02), subj(e02,z5)])



``fol()``

-----------



    >>> print(dexpr(r'([x,y],[sees(x,y)])').fol())

    exists x y.sees(x,y)

    >>> print(dexpr(r'([x],[man(x), walks(x)])').fol())

    exists x.(man(x) & walks(x))

    >>> print(dexpr(r'\x.([],[man(x), walks(x)])').fol())

    \x.(man(x) & walks(x))

    >>> print(dexpr(r'\x y.([],[sees(x,y)])').fol())

    \x y.sees(x,y)



    >>> print(dexpr(r'\x.([],[walks(x)])(john)').fol())

    \x.walks(x)(john)

    >>> print(dexpr(r'\R x.([],[big(x,R)])(\y.([],[mouse(y)]))').fol())

    (\R x.big(x,R))(\y.mouse(y))



    >>> print(dexpr(r'(([x],[walks(x)]) + ([y],[runs(y)]))').fol())

    (exists x.walks(x) & exists y.runs(y))



    >>> print(dexpr(r'(([],[walks(x)]) -> ([],[runs(x)]))').fol())

    (walks(x) -> runs(x))



    >>> print(dexpr(r'([x],[PRO(x), sees(John,x)])').fol())

    exists x.(PRO(x) & sees(John,x))

    >>> print(dexpr(r'([x],[man(x), -([],[walks(x)])])').fol())

    exists x.(man(x) & -walks(x))

    >>> print(dexpr(r'([],[(([x],[man(x)]) -> ([],[walks(x)]))])').fol())

    all x.(man(x) -> walks(x))



    >>> print(dexpr(r'([x],[man(x) | walks(x)])').fol())

    exists x.(man(x) | walks(x))

    >>> print(dexpr(r'P(x) + ([x],[walks(x)])').fol())

    (P(x) & exists x.walks(x))



``resolve_anaphora()``

----------------------



    >>> from nltk.sem.drt import AnaphoraResolutionException



    >>> print(resolve_anaphora(dexpr(r'([x,y,z],[dog(x), cat(y), walks(z), PRO(z)])')))

    ([x,y,z],[dog(x), cat(y), walks(z), (z = [x,y])])

    >>> print(resolve_anaphora(dexpr(r'([],[(([x],[dog(x)]) -> ([y],[walks(y), PRO(y)]))])')))

    ([],[(([x],[dog(x)]) -> ([y],[walks(y), (y = x)]))])

    >>> print(resolve_anaphora(dexpr(r'(([x,y],[]) + ([],[PRO(x)]))')).simplify())

    ([x,y],[(x = y)])

    >>> try: print(resolve_anaphora(dexpr(r'([x],[walks(x), PRO(x)])')))

    ... except AnaphoraResolutionException as e: print(e)

    Variable 'x' does not resolve to anything.

    >>> print(resolve_anaphora(dexpr('([e01,z6,z7],[boy(z6), PRO(z7), run(e01), subj(e01,z7)])')))

    ([e01,z6,z7],[boy(z6), (z7 = z6), run(e01), subj(e01,z7)])



``equiv()``:

----------------



    >>> a = dexpr(r'([x],[man(x), walks(x)])')

    >>> b = dexpr(r'([x],[walks(x), man(x)])')

    >>> print(a.equiv(b, TableauProver()))

    True





``replace()``:

--------------



    >>> a = dexpr(r'a')

    >>> w = dexpr(r'w')

    >>> x = dexpr(r'x')

    >>> y = dexpr(r'y')

    >>> z = dexpr(r'z')





replace bound

-------------



    >>> print(dexpr(r'([x],[give(x,y,z)])').replace(x.variable, a, False))

    ([x],[give(x,y,z)])

    >>> print(dexpr(r'([x],[give(x,y,z)])').replace(x.variable, a, True))

    ([a],[give(a,y,z)])



replace unbound

---------------



    >>> print(dexpr(r'([x],[give(x,y,z)])').replace(y.variable, a, False))

    ([x],[give(x,a,z)])

    >>> print(dexpr(r'([x],[give(x,y,z)])').replace(y.variable, a, True))

    ([x],[give(x,a,z)])



replace unbound with bound

--------------------------



    >>> dexpr(r'([x],[give(x,y,z)])').replace(y.variable, x, False) == \

    ... dexpr('([z1],[give(z1,x,z)])')

    True

    >>> dexpr(r'([x],[give(x,y,z)])').replace(y.variable, x, True) == \

    ... dexpr('([z1],[give(z1,x,z)])')

    True



replace unbound with unbound

----------------------------



    >>> print(dexpr(r'([x],[give(x,y,z)])').replace(y.variable, z, False))

    ([x],[give(x,z,z)])

    >>> print(dexpr(r'([x],[give(x,y,z)])').replace(y.variable, z, True))

    ([x],[give(x,z,z)])





replace unbound

---------------



    >>> print(dexpr(r'([x],[P(x,y,z)])+([y],[Q(x,y,z)])').replace(z.variable, a, False))

    (([x],[P(x,y,a)]) + ([y],[Q(x,y,a)]))

    >>> print(dexpr(r'([x],[P(x,y,z)])+([y],[Q(x,y,z)])').replace(z.variable, a, True))

    (([x],[P(x,y,a)]) + ([y],[Q(x,y,a)]))



replace bound

-------------



    >>> print(dexpr(r'([x],[P(x,y,z)])+([y],[Q(x,y,z)])').replace(x.variable, a, False))

    (([x],[P(x,y,z)]) + ([y],[Q(x,y,z)]))

    >>> print(dexpr(r'([x],[P(x,y,z)])+([y],[Q(x,y,z)])').replace(x.variable, a, True))

    (([a],[P(a,y,z)]) + ([y],[Q(a,y,z)]))



replace unbound with unbound

----------------------------



    >>> print(dexpr(r'([x],[P(x,y,z)])+([y],[Q(x,y,z)])').replace(z.variable, a, False))

    (([x],[P(x,y,a)]) + ([y],[Q(x,y,a)]))

    >>> print(dexpr(r'([x],[P(x,y,z)])+([y],[Q(x,y,z)])').replace(z.variable, a, True))

    (([x],[P(x,y,a)]) + ([y],[Q(x,y,a)]))



replace unbound with bound on same side

---------------------------------------



    >>> dexpr(r'([x],[P(x,y,z)])+([y],[Q(x,y,w)])').replace(z.variable, x, False) == \

    ... dexpr(r'(([z1],[P(z1,y,x)]) + ([y],[Q(z1,y,w)]))')

    True

    >>> dexpr(r'([x],[P(x,y,z)])+([y],[Q(x,y,w)])').replace(z.variable, x, True) == \

    ... dexpr(r'(([z1],[P(z1,y,x)]) + ([y],[Q(z1,y,w)]))')

    True



replace unbound with bound on other side

----------------------------------------



    >>> dexpr(r'([x],[P(x,y,z)])+([y],[Q(x,y,w)])').replace(w.variable, x, False) == \

    ... dexpr(r'(([z1],[P(z1,y,z)]) + ([y],[Q(z1,y,x)]))')

    True

    >>> dexpr(r'([x],[P(x,y,z)])+([y],[Q(x,y,w)])').replace(w.variable, x, True) == \

    ... dexpr(r'(([z1],[P(z1,y,z)]) + ([y],[Q(z1,y,x)]))')

    True



replace unbound with double bound

---------------------------------



    >>> dexpr(r'([x],[P(x,y,z)])+([x],[Q(x,y,w)])').replace(z.variable, x, False) == \

    ... dexpr(r'(([z1],[P(z1,y,x)]) + ([z1],[Q(z1,y,w)]))')

    True

    >>> dexpr(r'([x],[P(x,y,z)])+([x],[Q(x,y,w)])').replace(z.variable, x, True) == \

    ... dexpr(r'(([z1],[P(z1,y,x)]) + ([z1],[Q(z1,y,w)]))')

    True





regression tests

----------------



    >>> d = dexpr('([x],[A(c), ([y],[B(x,y,z,a)])->([z],[C(x,y,z,a)])])')

    >>> print(d)

    ([x],[A(c), (([y],[B(x,y,z,a)]) -> ([z],[C(x,y,z,a)]))])

    >>> print(d.pretty_format())

     ____________________________________

    | x                                  |

    |------------------------------------|

    | A(c)                               |

    |   ____________      ____________   |

    |  | y          |    | z          |  |

    | (|------------| -> |------------|) |

    |  | B(x,y,z,a) |    | C(x,y,z,a) |  |

    |  |____________|    |____________|  |

    |____________________________________|

    >>> print(str(d))

    ([x],[A(c), (([y],[B(x,y,z,a)]) -> ([z],[C(x,y,z,a)]))])

    >>> print(d.fol())

    exists x.(A(c) & all y.(B(x,y,z,a) -> exists z.C(x,y,z,a)))

    >>> print(d.replace(Variable('a'), DrtVariableExpression(Variable('r'))))

    ([x],[A(c), (([y],[B(x,y,z,r)]) -> ([z],[C(x,y,z,r)]))])

    >>> print(d.replace(Variable('x'), DrtVariableExpression(Variable('r'))))

    ([x],[A(c), (([y],[B(x,y,z,a)]) -> ([z],[C(x,y,z,a)]))])

    >>> print(d.replace(Variable('y'), DrtVariableExpression(Variable('r'))))

    ([x],[A(c), (([y],[B(x,y,z,a)]) -> ([z],[C(x,y,z,a)]))])

    >>> print(d.replace(Variable('z'), DrtVariableExpression(Variable('r'))))

    ([x],[A(c), (([y],[B(x,y,r,a)]) -> ([z],[C(x,y,z,a)]))])

    >>> print(d.replace(Variable('x'), DrtVariableExpression(Variable('r')), True))

    ([r],[A(c), (([y],[B(r,y,z,a)]) -> ([z],[C(r,y,z,a)]))])

    >>> print(d.replace(Variable('y'), DrtVariableExpression(Variable('r')), True))

    ([x],[A(c), (([r],[B(x,r,z,a)]) -> ([z],[C(x,r,z,a)]))])

    >>> print(d.replace(Variable('z'), DrtVariableExpression(Variable('r')), True))

    ([x],[A(c), (([y],[B(x,y,r,a)]) -> ([r],[C(x,y,r,a)]))])

    >>> print(d == dexpr('([l],[A(c), ([m],[B(l,m,z,a)])->([n],[C(l,m,n,a)])])'))

    True

    >>> d = dexpr('([],[([x,y],[B(x,y,h), ([a,b],[dee(x,a,g)])])->([z,w],[cee(x,y,f), ([c,d],[E(x,c,d,e)])])])')

    >>> sorted(d.free())

    [Variable('B'), Variable('E'), Variable('e'), Variable('f'), Variable('g'), Variable('h')]

    >>> sorted(d.variables())

    [Variable('B'), Variable('E'), Variable('e'), Variable('f'), Variable('g'), Variable('h')]

    >>> sorted(d.get_refs(True))

    [Variable('a'), Variable('b'), Variable('c'), Variable('d'), Variable('w'), Variable('x'), Variable('y'), Variable('z')]

    >>> sorted(d.conds[0].get_refs(False))

    [Variable('x'), Variable('y')]

    >>> print(dexpr('([x,y],[A(x,y), (x=y), ([],[B(x,y)])->([],[C(x,y)]), ([x,y],[D(x,y)])->([],[E(x,y)]), ([],[F(x,y)])->([x,y],[G(x,y)])])').eliminate_equality())

    ([x],[A(x,x), (([],[B(x,x)]) -> ([],[C(x,x)])), (([x,y],[D(x,y)]) -> ([],[E(x,y)])), (([],[F(x,x)]) -> ([x,y],[G(x,y)]))])

    >>> print(dexpr('([x,y],[A(x,y), (x=y)]) -> ([],[B(x,y)])').eliminate_equality())

    (([x],[A(x,x)]) -> ([],[B(x,x)]))

    >>> print(dexpr('([x,y],[A(x,y)]) -> ([],[B(x,y), (x=y)])').eliminate_equality())

    (([x,y],[A(x,y)]) -> ([],[B(x,x)]))

    >>> print(dexpr('([x,y],[A(x,y), (x=y), ([],[B(x,y)])])').eliminate_equality())

    ([x],[A(x,x), ([],[B(x,x)])])

    >>> print(dexpr('([x,y],[A(x,y), ([],[B(x,y), (x=y)])])').eliminate_equality())

    ([x,y],[A(x,y), ([],[B(x,x)])])

    >>> print(dexpr('([z8 z9 z10],[A(z8), z8=z10, z9=z10, B(z9), C(z10), D(z10)])').eliminate_equality())

    ([z9],[A(z9), B(z9), C(z9), D(z9)])



    >>> print(dexpr('([x,y],[A(x,y), (x=y), ([],[B(x,y)]), ([x,y],[C(x,y)])])').eliminate_equality())

    ([x],[A(x,x), ([],[B(x,x)]), ([x,y],[C(x,y)])])

    >>> print(dexpr('([x,y],[A(x,y)]) + ([],[B(x,y), (x=y)]) + ([],[C(x,y)])').eliminate_equality())

    ([x],[A(x,x), B(x,x), C(x,x)])

    >>> print(dexpr('([x,y],[B(x,y)])+([x,y],[C(x,y)])').replace(Variable('y'), DrtVariableExpression(Variable('x'))))

    (([x,y],[B(x,y)]) + ([x,y],[C(x,y)]))

    >>> print(dexpr('(([x,y],[B(x,y)])+([],[C(x,y)]))+([],[D(x,y)])').replace(Variable('y'), DrtVariableExpression(Variable('x'))))

    (([x,y],[B(x,y)]) + ([],[C(x,y)]) + ([],[D(x,y)]))

    >>> print(dexpr('(([],[B(x,y)])+([],[C(x,y)]))+([],[D(x,y)])').replace(Variable('y'), DrtVariableExpression(Variable('x'))))

    (([],[B(x,x)]) + ([],[C(x,x)]) + ([],[D(x,x)]))

    >>> print(dexpr('(([],[B(x,y), ([x,y],[A(x,y)])])+([],[C(x,y)]))+([],[D(x,y)])').replace(Variable('y'), DrtVariableExpression(Variable('x'))).normalize())

    (([],[B(z3,z1), ([z2,z3],[A(z3,z2)])]) + ([],[C(z3,z1)]) + ([],[D(z3,z1)]))





Parse errors

============



    >>> def parse_error(drtstring):

    ...     try: dexpr(drtstring)

    ...     except logic.LogicalExpressionException as e: print(e)



    >>> parse_error(r'')

    End of input found.  Expression expected.

    <BLANKLINE>

    ^

    >>> parse_error(r'(')

    End of input found.  Expression expected.

    (

     ^

    >>> parse_error(r'()')

    Unexpected token: ')'.  Expression expected.

    ()

     ^

    >>> parse_error(r'([')

    End of input found.  Expected token ']'.

    ([

      ^

    >>> parse_error(r'([,')

    ',' is an illegal variable name.  Constants may not be quantified.

    ([,

      ^

    >>> parse_error(r'([x,')

    End of input found.  Variable expected.

    ([x,

        ^

    >>> parse_error(r'([]')

    End of input found.  Expected token '['.

    ([]

       ^

    >>> parse_error(r'([][')

    End of input found.  Expected token ']'.

    ([][

        ^

    >>> parse_error(r'([][,')

    Unexpected token: ','.  Expression expected.

    ([][,

        ^

    >>> parse_error(r'([][]')

    End of input found.  Expected token ')'.

    ([][]

         ^

    >>> parse_error(r'([x][man(x)]) |')

    End of input found.  Expression expected.

    ([x][man(x)]) |

                   ^



Pretty Printing

===============



    >>> dexpr(r"([],[])").pretty_print()

     __

    |  |

    |--|

    |__|



    >>> dexpr(r"([],[([x],[big(x), dog(x)]) -> ([],[bark(x)]) -([x],[walk(x)])])").pretty_print()

     _____________________________

    |                             |

    |-----------------------------|

    |   ________      _________   |

    |  | x      |    |         |  |

    | (|--------| -> |---------|) |

    |  | big(x) |    | bark(x) |  |

    |  | dog(x) |    |_________|  |

    |  |________|                 |

    |      _________              |

    |     | x       |             |

    | __  |---------|             |

    |   | | walk(x) |             |

    |     |_________|             |

    |_____________________________|



    >>> dexpr(r"([x,y],[x=y]) + ([z],[dog(z), walk(z)])").pretty_print()

      _________     _________

     | x y     |   | z       |

    (|---------| + |---------|)

     | (x = y) |   | dog(z)  |

     |_________|   | walk(z) |

                   |_________|



    >>> dexpr(r"([],[([x],[]) | ([y],[]) | ([z],[dog(z), walk(z)])])").pretty_print()

     _______________________________

    |                               |

    |-------------------------------|

    |   ___     ___     _________   |

    |  | x |   | y |   | z       |  |

    | (|---| | |---| | |---------|) |

    |  |___|   |___|   | dog(z)  |  |

    |                  | walk(z) |  |

    |                  |_________|  |

    |_______________________________|



    >>> dexpr(r"\P.\Q.(([x],[]) + P(x) + Q(x))(\x.([],[dog(x)]))").pretty_print()

              ___                        ________

     \       | x |                 \    |        |

     /\ P Q.(|---| + P(x) + Q(x))( /\ x.|--------|)

             |___|                      | dog(x) |

                                        |________|