jupytersketcher/Lib/site-packages/nltk/inference/mace.py

# Natural Language Toolkit: Interface to the Mace4 Model Builder
#
# Author: Dan Garrette <dhgarrette@gmail.com>
#         Ewan Klein <ewan@inf.ed.ac.uk>

# URL: <http://nltk.org/>
# For license information, see LICENSE.TXT

"""
A model builder that makes use of the external 'Mace4' package.
"""

import os
import tempfile

from nltk.sem.logic import is_indvar
from nltk.sem import Valuation, Expression

from nltk.inference.api import ModelBuilder, BaseModelBuilderCommand
from nltk.inference.prover9 import Prover9CommandParent, Prover9Parent


class MaceCommand(Prover9CommandParent, BaseModelBuilderCommand):
    """
    A ``MaceCommand`` specific to the ``Mace`` model builder.  It contains
    a print_assumptions() method that is used to print the list
    of assumptions in multiple formats.
    """

    _interpformat_bin = None

    def __init__(self, goal=None, assumptions=None, max_models=500, model_builder=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 max_models: The maximum number of models that Mace will try before
            simply returning false. (Use 0 for no maximum.)
        :type max_models: int
        """
        if model_builder is not None:
            assert isinstance(model_builder, Mace)
        else:
            model_builder = Mace(max_models)

        BaseModelBuilderCommand.__init__(self, model_builder, goal, assumptions)

    @property
    def valuation(mbc):
        return mbc.model("valuation")

    def _convert2val(self, valuation_str):
        """
        Transform the output file into an NLTK-style Valuation.

        :return: A model if one is generated; None otherwise.
        :rtype: sem.Valuation
        """
        valuation_standard_format = self._transform_output(valuation_str, "standard")

        val = []
        for line in valuation_standard_format.splitlines(False):
            l = line.strip()

            if l.startswith("interpretation"):
                # find the number of entities in the model
                num_entities = int(l[l.index("(") + 1 : l.index(",")].strip())

            elif l.startswith("function") and l.find("_") == -1:
                # replace the integer identifier with a corresponding alphabetic character
                name = l[l.index("(") + 1 : l.index(",")].strip()
                if is_indvar(name):
                    name = name.upper()
                value = int(l[l.index("[") + 1 : l.index("]")].strip())
                val.append((name, MaceCommand._make_model_var(value)))

            elif l.startswith("relation"):
                l = l[l.index("(") + 1 :]
                if "(" in l:
                    # relation is not nullary
                    name = l[: l.index("(")].strip()
                    values = [
                        int(v.strip())
                        for v in l[l.index("[") + 1 : l.index("]")].split(",")
                    ]
                    val.append(
                        (name, MaceCommand._make_relation_set(num_entities, values))
                    )
                else:
                    # relation is nullary
                    name = l[: l.index(",")].strip()
                    value = int(l[l.index("[") + 1 : l.index("]")].strip())
                    val.append((name, value == 1))

        return Valuation(val)

    @staticmethod
    def _make_relation_set(num_entities, values):
        """
        Convert a Mace4-style relation table into a dictionary.

        :param num_entities: the number of entities in the model; determines the row length in the table.
        :type num_entities: int
        :param values: a list of 1's and 0's that represent whether a relation holds in a Mace4 model.
        :type values: list of int
        """
        r = set()
        for position in [pos for (pos, v) in enumerate(values) if v == 1]:
            r.add(
                tuple(MaceCommand._make_relation_tuple(position, values, num_entities))
            )
        return r

    @staticmethod
    def _make_relation_tuple(position, values, num_entities):
        if len(values) == 1:
            return []
        else:
            sublist_size = len(values) // num_entities
            sublist_start = position // sublist_size
            sublist_position = int(position % sublist_size)

            sublist = values[
                sublist_start * sublist_size : (sublist_start + 1) * sublist_size
            ]
            return [
                MaceCommand._make_model_var(sublist_start)
            ] + MaceCommand._make_relation_tuple(
                sublist_position, sublist, num_entities
            )

    @staticmethod
    def _make_model_var(value):
        """
        Pick an alphabetic character as identifier for an entity in the model.

        :param value: where to index into the list of characters
        :type value: int
        """
        letter = [
            "a",
            "b",
            "c",
            "d",
            "e",
            "f",
            "g",
            "h",
            "i",
            "j",
            "k",
            "l",
            "m",
            "n",
            "o",
            "p",
            "q",
            "r",
            "s",
            "t",
            "u",
            "v",
            "w",
            "x",
            "y",
            "z",
        ][value]
        num = value // 26
        return letter + str(num) if num > 0 else letter

    def _decorate_model(self, valuation_str, format):
        """
        Print out a Mace4 model using any Mace4 ``interpformat`` format.
        See http://www.cs.unm.edu/~mccune/mace4/manual/ for details.

        :param valuation_str: str with the model builder's output
        :param format: str indicating the format for displaying
        models. Defaults to 'standard' format.
        :return: str
        """
        if not format:
            return valuation_str
        elif format == "valuation":
            return self._convert2val(valuation_str)
        else:
            return self._transform_output(valuation_str, format)

    def _transform_output(self, valuation_str, format):
        """
        Transform the output file into any Mace4 ``interpformat`` format.

        :param format: Output format for displaying models.
        :type format: str
        """
        if format in [
            "standard",
            "standard2",
            "portable",
            "tabular",
            "raw",
            "cooked",
            "xml",
            "tex",
        ]:
            return self._call_interpformat(valuation_str, [format])[0]
        else:
            raise LookupError("The specified format does not exist")

    def _call_interpformat(self, input_str, args=[], verbose=False):
        """
        Call the ``interpformat`` 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._interpformat_bin is None:
            self._interpformat_bin = self._modelbuilder._find_binary(
                "interpformat", verbose
            )

        return self._modelbuilder._call(
            input_str, self._interpformat_bin, args, verbose
        )


class Mace(Prover9Parent, ModelBuilder):
    _mace4_bin = None

    def __init__(self, end_size=500):
        self._end_size = end_size
        """The maximum model size that Mace will try before
           simply returning false. (Use -1 for no maximum.)"""

    def _build_model(self, goal=None, assumptions=None, verbose=False):
        """
        Use Mace4 to build a first order model.

        :return: ``True`` if a model was found (i.e. Mace returns value of 0),
        else ``False``
        """
        if not assumptions:
            assumptions = []

        stdout, returncode = self._call_mace4(
            self.prover9_input(goal, assumptions), verbose=verbose
        )
        return (returncode == 0, stdout)

    def _call_mace4(self, input_str, args=[], verbose=False):
        """
        Call the ``mace4`` 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._mace4_bin is None:
            self._mace4_bin = self._find_binary("mace4", verbose)

        updated_input_str = ""
        if self._end_size > 0:
            updated_input_str += "assign(end_size, %d).\n\n" % self._end_size
        updated_input_str += input_str

        return self._call(updated_input_str, self._mace4_bin, args, verbose)


def spacer(num=30):
    print("-" * num)


def decode_result(found):
    """
    Decode the result of model_found()

    :param found: The output of model_found()
    :type found: bool
    """
    return {True: "Countermodel found", False: "No countermodel found", None: "None"}[
        found
    ]


def test_model_found(arguments):
    """
    Try some proofs and exhibit the results.
    """
    for (goal, assumptions) in arguments:
        g = Expression.fromstring(goal)
        alist = [lp.parse(a) for a in assumptions]
        m = MaceCommand(g, assumptions=alist, max_models=50)
        found = m.build_model()
        for a in alist:
            print("   %s" % a)
        print("|- %s: %s\n" % (g, decode_result(found)))


def test_build_model(arguments):
    """
    Try to build a ``nltk.sem.Valuation``.
    """
    g = Expression.fromstring("all x.man(x)")
    alist = [
        Expression.fromstring(a)
        for a in [
            "man(John)",
            "man(Socrates)",
            "man(Bill)",
            "some x.(-(x = John) & man(x) & sees(John,x))",
            "some x.(-(x = Bill) & man(x))",
            "all x.some y.(man(x) -> gives(Socrates,x,y))",
        ]
    ]

    m = MaceCommand(g, assumptions=alist)
    m.build_model()
    spacer()
    print("Assumptions and Goal")
    spacer()
    for a in alist:
        print("   %s" % a)
    print("|- %s: %s\n" % (g, decode_result(m.build_model())))
    spacer()
    # print(m.model('standard'))
    # print(m.model('cooked'))
    print("Valuation")
    spacer()
    print(m.valuation, "\n")


def test_transform_output(argument_pair):
    """
    Transform the model into various Mace4 ``interpformat`` formats.
    """
    g = Expression.fromstring(argument_pair[0])
    alist = [lp.parse(a) for a in argument_pair[1]]
    m = MaceCommand(g, assumptions=alist)
    m.build_model()
    for a in alist:
        print("   %s" % a)
    print("|- %s: %s\n" % (g, m.build_model()))
    for format in ["standard", "portable", "xml", "cooked"]:
        spacer()
        print("Using '%s' format" % format)
        spacer()
        print(m.model(format=format))


def test_make_relation_set():
    print(
        MaceCommand._make_relation_set(num_entities=3, values=[1, 0, 1])
        == set([("c",), ("a",)])
    )
    print(
        MaceCommand._make_relation_set(
            num_entities=3, values=[0, 0, 0, 0, 0, 0, 1, 0, 0]
        )
        == set([("c", "a")])
    )
    print(
        MaceCommand._make_relation_set(num_entities=2, values=[0, 0, 1, 0, 0, 0, 1, 0])
        == set([("a", "b", "a"), ("b", "b", "a")])
    )


arguments = [
    ("mortal(Socrates)", ["all x.(man(x) -> mortal(x))", "man(Socrates)"]),
    ("(not mortal(Socrates))", ["all x.(man(x) -> mortal(x))", "man(Socrates)"]),
]


def demo():
    test_model_found(arguments)
    test_build_model(arguments)
    test_transform_output(arguments[1])


if __name__ == "__main__":
    demo()