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# Natural Language Toolkit: Interface to the Prover9 Theorem Prover
#
# Copyright (C) 2001-2012 NLTK Project
# Author: Dan Garrette <dhgarrette@gmail.com>
# Ewan Klein <ewan@inf.ed.ac.uk>
#
# URL: <http://www.nltk.org/>
# For license information, see LICENSE.TXT
"""
A theorem prover that makes use of the external 'Prover9' package.
"""
import os
import subprocess
import nltk
from nltk.sem.logic import LogicParser, ExistsExpression, AllExpression, \
NegatedExpression, AndExpression, IffExpression, OrExpression, \
EqualityExpression, ImpExpression
from api import BaseProverCommand, Prover
#
# Following is not yet used. Return code for 2 actually realized as 512.
#
p9_return_codes = {
0: True,
1: "(FATAL)", #A fatal error occurred (user's syntax error).
2: False, # (SOS_EMPTY) Prover9 ran out of things to do
# (sos list exhausted).
3: "(MAX_MEGS)", # The max_megs (memory limit) parameter was exceeded.
4: "(MAX_SECONDS)", # The max_seconds parameter was exceeded.
5: "(MAX_GIVEN)", # The max_given parameter was exceeded.
6: "(MAX_KEPT)", # The max_kept parameter was exceeded.
7: "(ACTION)", # A Prover9 action terminated the search.
101: "(SIGSEGV)", # Prover9 crashed, most probably due to a bug.
}
class Prover9CommandParent(object):
"""
A common base class used by both ``Prover9Command`` and ``MaceCommand``,
which is responsible for maintaining a goal and a set of assumptions,
and generating prover9-style input files from them.
"""
def print_assumptions(self, output_format='nltk'):
"""
Print the list of the current assumptions.
"""
if output_format.lower() == 'nltk':
for a in self.assumptions():
print a
elif output_format.lower() == 'prover9':
for a in convert_to_prover9(self.assumptions()):
print a
else:
raise NameError("Unrecognized value for 'output_format': %s" %
output_format)
class Prover9Command(Prover9CommandParent, BaseProverCommand):
"""
A ``ProverCommand`` specific to the ``Prover9`` prover. It contains
the a print_assumptions() method that is used to print the list
of assumptions in multiple formats.
"""
def __init__(self, goal=None, assumptions=None, timeout=60, prover=None):
"""
:param goal: Input expression to prove
:type goal: sem.Expression
:param assumptions: Input expressions to use as assumptions in
the proof.
:type assumptions: list(sem.Expression)
:param timeout: number of seconds before timeout; set to 0 for
no timeout.
:type timeout: int
:param prover: a prover. If not set, one will be created.
:type prover: Prover9
"""
if not assumptions:
assumptions = []
if prover is not None:
assert isinstance(prover, Prover9)
else:
prover = Prover9(timeout)
BaseProverCommand.__init__(self, prover, goal, assumptions)
def decorate_proof(self, proof_string, simplify=True):
"""
:see BaseProverCommand.decorate_proof()
"""
if simplify:
return self._prover._call_prooftrans(proof_string, ['striplabels'])[0].rstrip()
else:
return proof_string.rstrip()
class Prover9Parent(object):
"""
A common class extended by both ``Prover9`` and ``Mace <mace.Mace>``.
It contains the functionality required to convert NLTK-style
expressions into Prover9-style expressions.
"""
_binary_location = None
def config_prover9(self, binary_location, verbose=False):
if binary_location is None:
self._binary_location = None
self._prover9_bin = None
else:
name = 'prover9'
self._prover9_bin = nltk.internals.find_binary(
name,
path_to_bin=binary_location,
env_vars=['PROVER9HOME'],
url='http://www.cs.unm.edu/~mccune/prover9/',
binary_names=[name, name + '.exe'],
verbose=verbose)
self._binary_location = self._prover9_bin.rsplit(os.path.sep, 1)
def prover9_input(self, goal, assumptions):
"""
:return: The input string that should be provided to the
prover9 binary. This string is formed based on the goal,
assumptions, and timeout value of this object.
"""
s = ''
if assumptions:
s += 'formulas(assumptions).\n'
for p9_assumption in convert_to_prover9(assumptions):
s += ' %s.\n' % p9_assumption
s += 'end_of_list.\n\n'
if goal:
s += 'formulas(goals).\n'
s += ' %s.\n' % convert_to_prover9(goal)
s += 'end_of_list.\n\n'
return s
def binary_locations(self):
"""
A list of directories that should be searched for the prover9
executables. This list is used by ``config_prover9`` when searching
for the prover9 executables.
"""
return ['/usr/local/bin/prover9',
'/usr/local/bin/prover9/bin',
'/usr/local/bin',
'/usr/bin',
'/usr/local/prover9',
'/usr/local/share/prover9']
def _find_binary(self, name, verbose=False):
binary_locations = self.binary_locations()
if self._binary_location is not None:
binary_locations += [self._binary_location]
return nltk.internals.find_binary(name,
searchpath=binary_locations,
env_vars=['PROVER9HOME'],
url='http://www.cs.unm.edu/~mccune/prover9/',
binary_names=[name, name + '.exe'],
verbose=verbose)
def _call(self, input_str, binary, args=[], verbose=False):
"""
Call the binary with the given input.
:param input_str: A string whose contents are used as stdin.
:param binary: The location of the binary to call
:param args: A list of command-line arguments.
:return: A tuple (stdout, returncode)
:see: ``config_prover9``
"""
if verbose:
print 'Calling:', binary
print 'Args:', args
print 'Input:\n', input_str, '\n'
# Call prover9 via a subprocess
cmd = [binary] + args
p = subprocess.Popen(cmd, stdout=subprocess.PIPE,
stderr=subprocess.STDOUT,
stdin=subprocess.PIPE)
(stdout, stderr) = p.communicate(input_str)
if verbose:
print 'Return code:', p.returncode
if stdout: print 'stdout:\n', stdout, '\n'
if stderr: print 'stderr:\n', stderr, '\n'
return (stdout, p.returncode)
def convert_to_prover9(input):
"""
Convert a ``logic.Expression`` to Prover9 format.
"""
if isinstance(input, list):
result = []
for s in input:
try:
result.append(_convert_to_prover9(s.simplify()))
except:
print 'input %s cannot be converted to Prover9 input syntax' % input
raise
return result
else:
try:
return _convert_to_prover9(input.simplify())
except:
print 'input %s cannot be converted to Prover9 input syntax' % input
raise
def _convert_to_prover9(expression):
"""
Convert ``logic.Expression`` to Prover9 formatted string.
"""
if isinstance(expression, ExistsExpression):
return 'exists ' + str(expression.variable) + ' ' + _convert_to_prover9(expression.term)
elif isinstance(expression, AllExpression):
return 'all ' + str(expression.variable) + ' ' + _convert_to_prover9(expression.term)
elif isinstance(expression, NegatedExpression):
return '-(' + _convert_to_prover9(expression.term) + ')'
elif isinstance(expression, AndExpression):
return '(' + _convert_to_prover9(expression.first) + ' & ' + \
_convert_to_prover9(expression.second) + ')'
elif isinstance(expression, OrExpression):
return '(' + _convert_to_prover9(expression.first) + ' | ' + \
_convert_to_prover9(expression.second) + ')'
elif isinstance(expression, ImpExpression):
return '(' + _convert_to_prover9(expression.first) + ' -> ' + \
_convert_to_prover9(expression.second) + ')'
elif isinstance(expression, IffExpression):
return '(' + _convert_to_prover9(expression.first) + ' <-> ' + \
_convert_to_prover9(expression.second) + ')'
elif isinstance(expression, EqualityExpression):
return '(' + _convert_to_prover9(expression.first) + ' = ' + \
_convert_to_prover9(expression.second) + ')'
else:
return str(expression)
class Prover9(Prover9Parent, Prover):
_prover9_bin = None
_prooftrans_bin = None
def __init__(self, timeout=60):
self._timeout = timeout
"""The timeout value for prover9. If a proof can not be found
in this amount of time, then prover9 will return false.
(Use 0 for no timeout.)"""
def _prove(self, goal=None, assumptions=None, verbose=False):
"""
Use Prover9 to prove a theorem.
:return: A pair whose first element is a boolean indicating if the
proof was successful (i.e. returns value of 0) and whose second element
is the output of the prover.
"""
if not assumptions:
assumptions = []
stdout, returncode = self._call_prover9(self.prover9_input(goal, assumptions),
verbose=verbose)
return (returncode == 0, stdout)
def prover9_input(self, goal, assumptions):
"""
:see: Prover9Parent.prover9_input
"""
s = 'clear(auto_denials).\n' #only one proof required
return s + Prover9Parent.prover9_input(self, goal, assumptions)
def _call_prover9(self, input_str, args=[], verbose=False):
"""
Call the ``prover9`` binary with the given input.
:param input_str: A string whose contents are used as stdin.
:param args: A list of command-line arguments.
:return: A tuple (stdout, returncode)
:see: ``config_prover9``
"""
if self._prover9_bin is None:
self._prover9_bin = self._find_binary('prover9', verbose)
updated_input_str = ''
if self._timeout > 0:
updated_input_str += 'assign(max_seconds, %d).\n\n' % self._timeout
updated_input_str += input_str
stdout, returncode = self._call(updated_input_str, self._prover9_bin, args, verbose)
if returncode not in [0,2]:
errormsgprefix = '%%ERROR:'
if errormsgprefix in stdout:
msgstart = stdout.index(errormsgprefix)
errormsg = stdout[msgstart:].strip()
else:
errormsg = None
if returncode in [3,4,5,6]:
raise Prover9LimitExceededException(returncode, errormsg)
else:
raise Prover9FatalException(returncode, errormsg)
return stdout, returncode
def _call_prooftrans(self, input_str, args=[], verbose=False):
"""
Call the ``prooftrans`` binary with the given input.
:param input_str: A string whose contents are used as stdin.
:param args: A list of command-line arguments.
:return: A tuple (stdout, returncode)
:see: ``config_prover9``
"""
if self._prooftrans_bin is None:
self._prooftrans_bin = self._find_binary('prooftrans', verbose)
return self._call(input_str, self._prooftrans_bin, args, verbose)
class Prover9Exception(Exception):
def __init__(self, returncode, message):
msg = p9_return_codes[returncode]
if message:
msg += '\n%s' % message
Exception.__init__(self, msg)
class Prover9FatalException(Prover9Exception):
pass
class Prover9LimitExceededException(Prover9Exception):
pass
######################################################################
#{ Tests and Demos
######################################################################
def test_config():
a = LogicParser().parse('(walk(j) & sing(j))')
g = LogicParser().parse('walk(j)')
p = Prover9Command(g, assumptions=[a])
p._executable_path = None
p.prover9_search=[]
p.prove()
#config_prover9('/usr/local/bin')
print p.prove()
print p.proof()
def test_convert_to_prover9(expr):
"""
Test that parsing works OK.
"""
for t in expr:
e = LogicParser().parse(t)
print convert_to_prover9(e)
def test_prove(arguments):
"""
Try some proofs and exhibit the results.
"""
for (goal, assumptions) in arguments:
g = LogicParser().parse(goal)
alist = [LogicParser().parse(a) for a in assumptions]
p = Prover9Command(g, assumptions=alist).prove()
for a in alist:
print ' %s' % a
print '|- %s: %s\n' % (g, p)
arguments = [
('(man(x) <-> (not (not man(x))))', []),
('(not (man(x) & (not man(x))))', []),
('(man(x) | (not man(x)))', []),
('(man(x) & (not man(x)))', []),
('(man(x) -> man(x))', []),
('(not (man(x) & (not man(x))))', []),
('(man(x) | (not man(x)))', []),
('(man(x) -> man(x))', []),
('(man(x) <-> man(x))', []),
('(not (man(x) <-> (not man(x))))', []),
('mortal(Socrates)', ['all x.(man(x) -> mortal(x))', 'man(Socrates)']),
('((all x.(man(x) -> walks(x)) & man(Socrates)) -> some y.walks(y))', []),
('(all x.man(x) -> all x.man(x))', []),
('some x.all y.sees(x,y)', []),
('some e3.(walk(e3) & subj(e3, mary))',
['some e1.(see(e1) & subj(e1, john) & some e2.(pred(e1, e2) & walk(e2) & subj(e2, mary)))']),
('some x e1.(see(e1) & subj(e1, x) & some e2.(pred(e1, e2) & walk(e2) & subj(e2, mary)))',
['some e1.(see(e1) & subj(e1, john) & some e2.(pred(e1, e2) & walk(e2) & subj(e2, mary)))'])
]
expressions = [r'some x y.sees(x,y)',
r'some x.(man(x) & walks(x))',
r'\x.(man(x) & walks(x))',
r'\x y.sees(x,y)',
r'walks(john)',
r'\x.big(x, \y.mouse(y))',
r'(walks(x) & (runs(x) & (threes(x) & fours(x))))',
r'(walks(x) -> runs(x))',
r'some x.(PRO(x) & sees(John, x))',
r'some x.(man(x) & (not walks(x)))',
r'all x.(man(x) -> walks(x))']
def spacer(num=45):
print '-' * num
def demo():
print "Testing configuration"
spacer()
test_config()
print
print "Testing conversion to Prover9 format"
spacer()
test_convert_to_prover9(expressions)
print
print "Testing proofs"
spacer()
test_prove(arguments)
if __name__ == '__main__':
demo()
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