updates
This commit is contained in:
Iliyan Angelov
@@ -0,0 +1,507 @@
|
||||
# Natural Language Toolkit: Interface to the Prover9 Theorem Prover
|
||||
#
|
||||
# Copyright (C) 2001-2025 NLTK Project
|
||||
# Author: Dan Garrette <dhgarrette@gmail.com>
|
||||
# Ewan Klein <ewan@inf.ed.ac.uk>
|
||||
#
|
||||
# URL: <https://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.inference.api import BaseProverCommand, Prover
|
||||
from nltk.sem.logic import (
|
||||
AllExpression,
|
||||
AndExpression,
|
||||
EqualityExpression,
|
||||
ExistsExpression,
|
||||
Expression,
|
||||
IffExpression,
|
||||
ImpExpression,
|
||||
NegatedExpression,
|
||||
OrExpression,
|
||||
)
|
||||
|
||||
#
|
||||
# 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:
|
||||
"""
|
||||
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:
|
||||
"""
|
||||
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=["PROVER9"],
|
||||
url="https://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=["PROVER9"],
|
||||
url="https://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
|
||||
try:
|
||||
input_str = input_str.encode("utf8")
|
||||
except AttributeError:
|
||||
pass
|
||||
p = subprocess.Popen(
|
||||
cmd, stdout=subprocess.PIPE, stderr=subprocess.STDOUT, stdin=subprocess.PIPE
|
||||
)
|
||||
(stdout, stderr) = p.communicate(input=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.decode("utf-8"), 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 = Expression.fromstring("(walk(j) & sing(j))")
|
||||
g = Expression.fromstring("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 = Expression.fromstring(t)
|
||||
print(convert_to_prover9(e))
|
||||
|
||||
|
||||
def test_prove(arguments):
|
||||
"""
|
||||
Try some proofs and exhibit the results.
|
||||
"""
|
||||
for goal, assumptions in arguments:
|
||||
g = Expression.fromstring(goal)
|
||||
alist = [Expression.fromstring(a) for a in assumptions]
|
||||
p = Prover9Command(g, assumptions=alist).prove()
|
||||
for a in alist:
|
||||
print(" %s" % a)
|
||||
print(f"|- {g}: {p}\n")
|
||||
|
||||
|
||||
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()
|
||||
Reference in New Issue
Block a user