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Filename : prover9.py
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# Natural Language Toolkit: Interface to the Prover9 Theorem Prover
#
# Copyright (C) 2001-2020 NLTK Project
# Author: Dan Garrette <dhgarrette@gmail.com>
#         Ewan Klein <ewan@inf.ed.ac.uk>
#
# URL: <http://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 (
    Expression,
    ExistsExpression,
    AllExpression,
    NegatedExpression,
    AndExpression,
    IffExpression,
    OrExpression,
    EqualityExpression,
    ImpExpression,
)
from nltk.inference.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=["PROVER9"],
                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=["PROVER9"],
            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
        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("|- %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()