621 lines
19 KiB
Python
621 lines
19 KiB
Python
# Natural Language Toolkit: Classifier Interface
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#
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# Author: Ewan Klein <ewan@inf.ed.ac.uk>
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# Dan Garrette <dhgarrette@gmail.com>
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#
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# URL: <http://nltk.org/>
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# For license information, see LICENSE.TXT
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"""
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Interfaces and base classes for theorem provers and model builders.
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``Prover`` is a standard interface for a theorem prover which tries to prove a goal from a
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list of assumptions.
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``ModelBuilder`` is a standard interface for a model builder. Given just a set of assumptions.
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the model builder tries to build a model for the assumptions. Given a set of assumptions and a
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goal *G*, the model builder tries to find a counter-model, in the sense of a model that will satisfy
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the assumptions plus the negation of *G*.
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"""
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from __future__ import print_function
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from abc import ABCMeta, abstractmethod
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import threading
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import time
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from six import add_metaclass
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@add_metaclass(ABCMeta)
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class Prover(object):
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"""
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Interface for trying to prove a goal from assumptions. Both the goal and
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the assumptions are constrained to be formulas of ``logic.Expression``.
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"""
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def prove(self, goal=None, assumptions=None, verbose=False):
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"""
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:return: Whether the proof was successful or not.
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:rtype: bool
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"""
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return self._prove(goal, assumptions, verbose)[0]
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@abstractmethod
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def _prove(self, goal=None, assumptions=None, verbose=False):
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"""
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:return: Whether the proof was successful or not, along with the proof
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:rtype: tuple: (bool, str)
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"""
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@add_metaclass(ABCMeta)
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class ModelBuilder(object):
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"""
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Interface for trying to build a model of set of formulas.
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Open formulas are assumed to be universally quantified.
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Both the goal and the assumptions are constrained to be formulas
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of ``logic.Expression``.
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"""
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def build_model(self, goal=None, assumptions=None, verbose=False):
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"""
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Perform the actual model building.
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:return: Whether a model was generated
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:rtype: bool
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"""
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return self._build_model(goal, assumptions, verbose)[0]
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@abstractmethod
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def _build_model(self, goal=None, assumptions=None, verbose=False):
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"""
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Perform the actual model building.
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:return: Whether a model was generated, and the model itself
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:rtype: tuple(bool, sem.Valuation)
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"""
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@add_metaclass(ABCMeta)
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class TheoremToolCommand(object):
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"""
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This class holds a goal and a list of assumptions to be used in proving
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or model building.
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"""
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@abstractmethod
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def add_assumptions(self, new_assumptions):
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"""
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Add new assumptions to the assumption list.
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:param new_assumptions: new assumptions
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:type new_assumptions: list(sem.Expression)
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"""
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@abstractmethod
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def retract_assumptions(self, retracted, debug=False):
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"""
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Retract assumptions from the assumption list.
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:param debug: If True, give warning when ``retracted`` is not present on
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assumptions list.
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:type debug: bool
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:param retracted: assumptions to be retracted
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:type retracted: list(sem.Expression)
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"""
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@abstractmethod
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def assumptions(self):
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"""
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List the current assumptions.
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:return: list of ``Expression``
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"""
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@abstractmethod
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def goal(self):
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"""
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Return the goal
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:return: ``Expression``
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"""
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@abstractmethod
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def print_assumptions(self):
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"""
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Print the list of the current assumptions.
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"""
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class ProverCommand(TheoremToolCommand):
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"""
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This class holds a ``Prover``, a goal, and a list of assumptions. When
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prove() is called, the ``Prover`` is executed with the goal and assumptions.
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"""
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@abstractmethod
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def prove(self, verbose=False):
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"""
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Perform the actual proof.
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"""
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@abstractmethod
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def proof(self, simplify=True):
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"""
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Return the proof string
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:param simplify: bool simplify the proof?
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:return: str
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"""
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@abstractmethod
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def get_prover(self):
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"""
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Return the prover object
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:return: ``Prover``
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"""
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class ModelBuilderCommand(TheoremToolCommand):
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"""
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This class holds a ``ModelBuilder``, a goal, and a list of assumptions.
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When build_model() is called, the ``ModelBuilder`` is executed with the goal
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and assumptions.
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"""
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@abstractmethod
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def build_model(self, verbose=False):
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"""
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Perform the actual model building.
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:return: A model if one is generated; None otherwise.
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:rtype: sem.Valuation
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"""
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@abstractmethod
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def model(self, format=None):
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"""
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Return a string representation of the model
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:param simplify: bool simplify the proof?
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:return: str
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"""
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@abstractmethod
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def get_model_builder(self):
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"""
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Return the model builder object
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:return: ``ModelBuilder``
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"""
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class BaseTheoremToolCommand(TheoremToolCommand):
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"""
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This class holds a goal and a list of assumptions to be used in proving
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or model building.
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"""
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def __init__(self, goal=None, assumptions=None):
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"""
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:param goal: Input expression to prove
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:type goal: sem.Expression
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:param assumptions: Input expressions to use as assumptions in
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the proof.
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:type assumptions: list(sem.Expression)
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"""
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self._goal = goal
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if not assumptions:
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self._assumptions = []
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else:
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self._assumptions = list(assumptions)
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self._result = None
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"""A holder for the result, to prevent unnecessary re-proving"""
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def add_assumptions(self, new_assumptions):
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"""
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Add new assumptions to the assumption list.
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:param new_assumptions: new assumptions
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:type new_assumptions: list(sem.Expression)
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"""
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self._assumptions.extend(new_assumptions)
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self._result = None
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def retract_assumptions(self, retracted, debug=False):
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"""
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Retract assumptions from the assumption list.
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:param debug: If True, give warning when ``retracted`` is not present on
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assumptions list.
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:type debug: bool
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:param retracted: assumptions to be retracted
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:type retracted: list(sem.Expression)
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"""
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retracted = set(retracted)
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result_list = list(filter(lambda a: a not in retracted, self._assumptions))
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if debug and result_list == self._assumptions:
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print(Warning("Assumptions list has not been changed:"))
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self.print_assumptions()
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self._assumptions = result_list
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self._result = None
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def assumptions(self):
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"""
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List the current assumptions.
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:return: list of ``Expression``
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"""
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return self._assumptions
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def goal(self):
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"""
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Return the goal
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:return: ``Expression``
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"""
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return self._goal
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def print_assumptions(self):
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"""
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Print the list of the current assumptions.
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"""
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for a in self.assumptions():
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print(a)
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class BaseProverCommand(BaseTheoremToolCommand, ProverCommand):
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"""
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This class holds a ``Prover``, a goal, and a list of assumptions. When
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prove() is called, the ``Prover`` is executed with the goal and assumptions.
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"""
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def __init__(self, prover, goal=None, assumptions=None):
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"""
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:param prover: The theorem tool to execute with the assumptions
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:type prover: Prover
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:see: ``BaseTheoremToolCommand``
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"""
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self._prover = prover
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"""The theorem tool to execute with the assumptions"""
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BaseTheoremToolCommand.__init__(self, goal, assumptions)
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self._proof = None
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def prove(self, verbose=False):
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"""
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Perform the actual proof. Store the result to prevent unnecessary
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re-proving.
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"""
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if self._result is None:
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self._result, self._proof = self._prover._prove(
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self.goal(), self.assumptions(), verbose
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)
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return self._result
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def proof(self, simplify=True):
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"""
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Return the proof string
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:param simplify: bool simplify the proof?
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:return: str
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"""
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if self._result is None:
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raise LookupError("You have to call prove() first to get a proof!")
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else:
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return self.decorate_proof(self._proof, simplify)
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def decorate_proof(self, proof_string, simplify=True):
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"""
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Modify and return the proof string
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:param proof_string: str the proof to decorate
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:param simplify: bool simplify the proof?
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:return: str
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"""
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return proof_string
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def get_prover(self):
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return self._prover
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class BaseModelBuilderCommand(BaseTheoremToolCommand, ModelBuilderCommand):
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"""
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This class holds a ``ModelBuilder``, a goal, and a list of assumptions. When
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build_model() is called, the ``ModelBuilder`` is executed with the goal and
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assumptions.
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"""
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def __init__(self, modelbuilder, goal=None, assumptions=None):
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"""
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:param modelbuilder: The theorem tool to execute with the assumptions
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:type modelbuilder: ModelBuilder
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:see: ``BaseTheoremToolCommand``
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"""
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self._modelbuilder = modelbuilder
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"""The theorem tool to execute with the assumptions"""
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BaseTheoremToolCommand.__init__(self, goal, assumptions)
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self._model = None
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def build_model(self, verbose=False):
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"""
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Attempt to build a model. Store the result to prevent unnecessary
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re-building.
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"""
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if self._result is None:
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self._result, self._model = self._modelbuilder._build_model(
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self.goal(), self.assumptions(), verbose
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)
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return self._result
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def model(self, format=None):
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"""
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Return a string representation of the model
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:param simplify: bool simplify the proof?
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:return: str
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"""
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if self._result is None:
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raise LookupError('You have to call build_model() first to ' 'get a model!')
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else:
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return self._decorate_model(self._model, format)
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def _decorate_model(self, valuation_str, format=None):
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"""
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:param valuation_str: str with the model builder's output
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:param format: str indicating the format for displaying
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:return: str
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"""
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return valuation_str
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def get_model_builder(self):
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return self._modelbuilder
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class TheoremToolCommandDecorator(TheoremToolCommand):
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"""
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A base decorator for the ``ProverCommandDecorator`` and
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``ModelBuilderCommandDecorator`` classes from which decorators can extend.
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"""
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def __init__(self, command):
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"""
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:param command: ``TheoremToolCommand`` to decorate
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"""
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self._command = command
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# The decorator has its own versions of 'result' different from the
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# underlying command
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self._result = None
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def assumptions(self):
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return self._command.assumptions()
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def goal(self):
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return self._command.goal()
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def add_assumptions(self, new_assumptions):
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self._command.add_assumptions(new_assumptions)
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self._result = None
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def retract_assumptions(self, retracted, debug=False):
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self._command.retract_assumptions(retracted, debug)
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self._result = None
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def print_assumptions(self):
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self._command.print_assumptions()
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class ProverCommandDecorator(TheoremToolCommandDecorator, ProverCommand):
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"""
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A base decorator for the ``ProverCommand`` class from which other
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prover command decorators can extend.
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"""
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def __init__(self, proverCommand):
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"""
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:param proverCommand: ``ProverCommand`` to decorate
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"""
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TheoremToolCommandDecorator.__init__(self, proverCommand)
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# The decorator has its own versions of 'result' and 'proof'
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# because they may be different from the underlying command
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self._proof = None
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def prove(self, verbose=False):
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if self._result is None:
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prover = self.get_prover()
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self._result, self._proof = prover._prove(
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self.goal(), self.assumptions(), verbose
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)
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return self._result
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def proof(self, simplify=True):
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"""
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Return the proof string
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:param simplify: bool simplify the proof?
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:return: str
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"""
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if self._result is None:
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raise LookupError("You have to call prove() first to get a proof!")
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else:
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return self.decorate_proof(self._proof, simplify)
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def decorate_proof(self, proof_string, simplify=True):
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"""
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Modify and return the proof string
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:param proof_string: str the proof to decorate
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:param simplify: bool simplify the proof?
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:return: str
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"""
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return self._command.decorate_proof(proof_string, simplify)
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def get_prover(self):
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return self._command.get_prover()
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class ModelBuilderCommandDecorator(TheoremToolCommandDecorator, ModelBuilderCommand):
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"""
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A base decorator for the ``ModelBuilderCommand`` class from which other
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prover command decorators can extend.
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"""
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def __init__(self, modelBuilderCommand):
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"""
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:param modelBuilderCommand: ``ModelBuilderCommand`` to decorate
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"""
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TheoremToolCommandDecorator.__init__(self, modelBuilderCommand)
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# The decorator has its own versions of 'result' and 'valuation'
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# because they may be different from the underlying command
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self._model = None
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def build_model(self, verbose=False):
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"""
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Attempt to build a model. Store the result to prevent unnecessary
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re-building.
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"""
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if self._result is None:
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modelbuilder = self.get_model_builder()
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self._result, self._model = modelbuilder._build_model(
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self.goal(), self.assumptions(), verbose
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)
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return self._result
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def model(self, format=None):
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"""
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Return a string representation of the model
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:param simplify: bool simplify the proof?
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:return: str
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"""
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if self._result is None:
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raise LookupError('You have to call build_model() first to ' 'get a model!')
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else:
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return self._decorate_model(self._model, format)
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def _decorate_model(self, valuation_str, format=None):
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"""
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Modify and return the proof string
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:param valuation_str: str with the model builder's output
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:param format: str indicating the format for displaying
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:return: str
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"""
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return self._command._decorate_model(valuation_str, format)
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def get_model_builder(self):
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return self._command.get_prover()
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class ParallelProverBuilder(Prover, ModelBuilder):
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"""
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This class stores both a prover and a model builder and when either
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prove() or build_model() is called, then both theorem tools are run in
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parallel. Whichever finishes first, the prover or the model builder, is the
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result that will be used.
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"""
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def __init__(self, prover, modelbuilder):
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self._prover = prover
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self._modelbuilder = modelbuilder
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def _prove(self, goal=None, assumptions=None, verbose=False):
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return self._run(goal, assumptions, verbose), ''
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def _build_model(self, goal=None, assumptions=None, verbose=False):
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return not self._run(goal, assumptions, verbose), ''
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def _run(self, goal, assumptions, verbose):
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# Set up two thread, Prover and ModelBuilder to run in parallel
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tp_thread = TheoremToolThread(
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lambda: self._prover.prove(goal, assumptions, verbose), verbose, 'TP'
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)
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mb_thread = TheoremToolThread(
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lambda: self._modelbuilder.build_model(goal, assumptions, verbose),
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verbose,
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'MB',
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)
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tp_thread.start()
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mb_thread.start()
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while tp_thread.isAlive() and mb_thread.isAlive():
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# wait until either the prover or the model builder is done
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pass
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if tp_thread.result is not None:
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return tp_thread.result
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elif mb_thread.result is not None:
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return not mb_thread.result
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else:
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return None
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class ParallelProverBuilderCommand(BaseProverCommand, BaseModelBuilderCommand):
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"""
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This command stores both a prover and a model builder and when either
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prove() or build_model() is called, then both theorem tools are run in
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parallel. Whichever finishes first, the prover or the model builder, is the
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result that will be used.
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Because the theorem prover result is the opposite of the model builder
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result, we will treat self._result as meaning "proof found/no model found".
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"""
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def __init__(self, prover, modelbuilder, goal=None, assumptions=None):
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BaseProverCommand.__init__(self, prover, goal, assumptions)
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BaseModelBuilderCommand.__init__(self, modelbuilder, goal, assumptions)
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def prove(self, verbose=False):
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return self._run(verbose)
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def build_model(self, verbose=False):
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return not self._run(verbose)
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def _run(self, verbose):
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# Set up two thread, Prover and ModelBuilder to run in parallel
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tp_thread = TheoremToolThread(
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lambda: BaseProverCommand.prove(self, verbose), verbose, 'TP'
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)
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mb_thread = TheoremToolThread(
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lambda: BaseModelBuilderCommand.build_model(self, verbose), verbose, 'MB'
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)
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tp_thread.start()
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mb_thread.start()
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while tp_thread.isAlive() and mb_thread.isAlive():
|
|
# wait until either the prover or the model builder is done
|
|
pass
|
|
|
|
if tp_thread.result is not None:
|
|
self._result = tp_thread.result
|
|
elif mb_thread.result is not None:
|
|
self._result = not mb_thread.result
|
|
return self._result
|
|
|
|
|
|
class TheoremToolThread(threading.Thread):
|
|
def __init__(self, command, verbose, name=None):
|
|
threading.Thread.__init__(self)
|
|
self._command = command
|
|
self._result = None
|
|
self._verbose = verbose
|
|
self._name = name
|
|
|
|
def run(self):
|
|
try:
|
|
self._result = self._command()
|
|
if self._verbose:
|
|
print(
|
|
'Thread %s finished with result %s at %s'
|
|
% (self._name, self._result, time.localtime(time.time()))
|
|
)
|
|
except Exception as e:
|
|
print(e)
|
|
print('Thread %s completed abnormally' % (self._name))
|
|
|
|
@property
|
|
def result(self):
|
|
return self._result
|