o
    8Va!                     @   s   d Z ddlmZmZmZmZ ddlmZ ddlm	Z	 ddl
mZ dd Zdd
dZdd ZdddZdddZG dd dZG dd deZdS )z Inference in propositional logic    )AndNot	conjunctsto_cnf)ordered)sympify)import_modulec              	   C   sV   | du s| du r
| S z| j r| W S | jrt| jd W S t ttfy*   tdw )z
    The symbol in this literal (without the negation).

    Examples
    ========

    >>> from sympy.abc import A
    >>> from sympy.logic.inference import literal_symbol
    >>> literal_symbol(A)
    A
    >>> literal_symbol(~A)
    A

    TFr   z#Argument must be a boolean literal.)Z	is_SymbolZis_Notliteral_symbolargs
ValueErrorAttributeError)literal r   7/usr/lib/python3/dist-packages/sympy/logic/inference.pyr	   	   s   r	   NFc           	      C   s   |du s|dkrt d}|durd}n
|dkrtdd}|dkr+t d}|du r+d}|dkr9dd	lm} || S |dkrHdd	lm} || |S |dkrWdd
lm} || |S |dkrgddlm} || ||S t	)a  
    Check satisfiability of a propositional sentence.
    Returns a model when it succeeds.
    Returns {true: true} for trivially true expressions.

    On setting all_models to True, if given expr is satisfiable then
    returns a generator of models. However, if expr is unsatisfiable
    then returns a generator containing the single element False.

    Examples
    ========

    >>> from sympy.abc import A, B
    >>> from sympy.logic.inference import satisfiable
    >>> satisfiable(A & ~B)
    {A: True, B: False}
    >>> satisfiable(A & ~A)
    False
    >>> satisfiable(True)
    {True: True}
    >>> next(satisfiable(A & ~A, all_models=True))
    False
    >>> models = satisfiable((A >> B) & B, all_models=True)
    >>> next(models)
    {A: False, B: True}
    >>> next(models)
    {A: True, B: True}
    >>> def use_models(models):
    ...     for model in models:
    ...         if model:
    ...             # Do something with the model.
    ...             print(model)
    ...         else:
    ...             # Given expr is unsatisfiable.
    ...             print("UNSAT")
    >>> use_models(satisfiable(A >> ~A, all_models=True))
    {A: False}
    >>> use_models(satisfiable(A ^ A, all_models=True))
    UNSAT

    Npycosatzpycosat module is not presentZdpll2Z	minisat22pysatZdpllr   )dpll_satisfiable)pycosat_satisfiable)minisat22_satisfiable)
r   ImportErrorZsympy.logic.algorithms.dpllr   Zsympy.logic.algorithms.dpll2Z&sympy.logic.algorithms.pycosat_wrapperr   Z(sympy.logic.algorithms.minisat22_wrapperr   NotImplementedError)	expr	algorithmZ
all_modelsZminimalr   r   r   r   r   r   r   r   satisfiable&   s0   *

r   c                 C   s   t t|  S )ax  
    Check validity of a propositional sentence.
    A valid propositional sentence is True under every assignment.

    Examples
    ========

    >>> from sympy.abc import A, B
    >>> from sympy.logic.inference import valid
    >>> valid(A | ~A)
    True
    >>> valid(A | B)
    False

    References
    ==========

    .. [1] https://en.wikipedia.org/wiki/Validity

    )r   r   r   r   r   r   valido   s   r   c                    s   ddl m ddlm  d fdd| v r| S t| } | s+td|  |s/i }fdd	| D }| |}|v rGt|S |red
d	 |	 D }t
||r_t|r]dS dS t|sedS dS )a+  
    Returns whether the given assignment is a model or not.

    If the assignment does not specify the value for every proposition,
    this may return None to indicate 'not obvious'.

    Parameters
    ==========

    model : dict, optional, default: {}
        Mapping of symbols to boolean values to indicate assignment.
    deep: boolean, optional, default: False
        Gives the value of the expression under partial assignments
        correctly. May still return None to indicate 'not obvious'.


    Examples
    ========

    >>> from sympy.abc import A, B
    >>> from sympy.logic.inference import pl_true
    >>> pl_true( A & B, {A: True, B: True})
    True
    >>> pl_true(A & B, {A: False})
    False
    >>> pl_true(A & B, {A: True})
    >>> pl_true(A & B, {A: True}, deep=True)
    >>> pl_true(A >> (B >> A))
    >>> pl_true(A >> (B >> A), deep=True)
    True
    >>> pl_true(A & ~A)
    >>> pl_true(A & ~A, deep=True)
    False
    >>> pl_true(A & B & (~A | ~B), {A: True})
    >>> pl_true(A & B & (~A | ~B), {A: True}, deep=True)
    False

    r   )Symbol)BooleanFunction)TFc                    s<   t | s	| v rdS t |  sdS tfdd| jD S )NTFc                 3   s    | ]} |V  qd S Nr   ).0arg)	_validater   r   	<genexpr>   s    z-pl_true.<locals>._validate.<locals>.<genexpr>)
isinstanceallr
   r   r   r   r!   booleanr   r   r!      s
   
zpl_true.<locals>._validatez$%s is not a valid boolean expressionc                    s   i | ]\}}| v r||qS r   r   )r   kv)r&   r   r   
<dictcomp>   s    zpl_true.<locals>.<dictcomp>c                 S   s   i | ]}|d qS )Tr   )r   r'   r   r   r   r)      s    TFN)Zsympy.core.symbolr   sympy.logic.boolalgr   r   r   itemsZsubsboolZatomspl_truer   r   )r   ZmodelZdeepresultr   r%   r   r-      s0   (

r-   c                 C   s.   |rt |}ng }|t|  tt|  S )a  
    Check whether the given expr_set entail an expr.
    If formula_set is empty then it returns the validity of expr.

    Examples
    ========

    >>> from sympy.abc import A, B, C
    >>> from sympy.logic.inference import entails
    >>> entails(A, [A >> B, B >> C])
    False
    >>> entails(C, [A >> B, B >> C, A])
    True
    >>> entails(A >> B)
    False
    >>> entails(A >> (B >> A))
    True

    References
    ==========

    .. [1] https://en.wikipedia.org/wiki/Logical_consequence

    )listappendr   r   r   )r   Zformula_setr   r   r   entails   s
   
r1   c                   @   s>   e Zd ZdZdddZdd Zdd Zd	d
 Zedd Z	dS )KBz"Base class for all knowledge basesNc                 C   s   t  | _|r| | d S d S r   )setclauses_tellselfsentencer   r   r   __init__   s   zKB.__init__c                 C      t r   r   r6   r   r   r   r5         zKB.tellc                 C   r:   r   r;   r7   Zqueryr   r   r   ask   r<   zKB.askc                 C   r:   r   r;   r6   r   r   r   retract   r<   z
KB.retractc                 C   s   t t| jS r   )r/   r   r4   )r7   r   r   r   clauses  s   z
KB.clausesr   )
__name__
__module____qualname____doc__r9   r5   r>   r?   propertyr@   r   r   r   r   r2      s    
r2   c                   @   s(   e Zd ZdZdd Zdd Zdd ZdS )	PropKBz=A KB for Propositional Logic.  Inefficient, with no indexing.c                 C   "   t t|D ]}| j| qdS )ai  Add the sentence's clauses to the KB

        Examples
        ========

        >>> from sympy.logic.inference import PropKB
        >>> from sympy.abc import x, y
        >>> l = PropKB()
        >>> l.clauses
        []

        >>> l.tell(x | y)
        >>> l.clauses
        [x | y]

        >>> l.tell(y)
        >>> l.clauses
        [y, x | y]

        N)r   r   r4   addr7   r8   cr   r   r   r5   	     zPropKB.tellc                 C   s   t || jS )a8  Checks if the query is true given the set of clauses.

        Examples
        ========

        >>> from sympy.logic.inference import PropKB
        >>> from sympy.abc import x, y
        >>> l = PropKB()
        >>> l.tell(x & ~y)
        >>> l.ask(x)
        True
        >>> l.ask(y)
        False

        )r1   r4   r=   r   r   r   r>   !  s   z
PropKB.askc                 C   rG   )am  Remove the sentence's clauses from the KB

        Examples
        ========

        >>> from sympy.logic.inference import PropKB
        >>> from sympy.abc import x, y
        >>> l = PropKB()
        >>> l.clauses
        []

        >>> l.tell(x | y)
        >>> l.clauses
        [x | y]

        >>> l.retract(x | y)
        >>> l.clauses
        []

        N)r   r   r4   discardrI   r   r   r   r?   3  rK   zPropKB.retractN)rA   rB   rC   rD   r5   r>   r?   r   r   r   r   rF     s
    rF   )NFF)NFr   )rD   r*   r   r   r   r   Zsympy.core.compatibilityr   Zsympy.core.sympifyr   Zsympy.external.importtoolsr   r	   r   r   r-   r1   r2   rF   r   r   r   r   <module>   s    
I

I!