U
    L?h0                     @   s   d Z ddlmZmZmZ ddlmZmZ ddlm	Z	m
Z
mZmZmZmZ ddlmZ ddlmZmZmZmZ ddlmZmZmZmZmZmZ G dd	 d	ZG d
d dZG dd dZdddZdd Z G dd dZ!G dd dZ"dS )a  
The classes used here are for the internal use of assumptions system
only and should not be used anywhere else as these do not possess the
signatures common to SymPy objects. For general use of logic constructs
please refer to sympy.logic classes And, Or, Not, etc.
    )combinationsproductzip_longest)AppliedPredicate	Predicate)EqNeGtLtGeLe)S)OrAndNotXnor)
EquivalentITEImpliesNandNorXorc                       sZ   e Zd ZdZd fdd	Zedd Zdd Zd	d
 Zdd Z	e	Z
dd Zdd Z  ZS )Literala{  
    The smallest element of a CNF object.

    Parameters
    ==========

    lit : Boolean expression

    is_Not : bool

    Examples
    ========

    >>> from sympy import Q
    >>> from sympy.assumptions.cnf import Literal
    >>> from sympy.abc import x
    >>> Literal(Q.even(x))
    Literal(Q.even(x), False)
    >>> Literal(~Q.even(x))
    Literal(Q.even(x), True)
    Fc                    sT   t |tr|jd }d}nt |tttfr8|r4| S |S t | }||_||_	|S )Nr   T)

isinstancer   argsANDORr   super__new__litis_Not)clsr   r    obj	__class__ G/var/www/html/venv/lib/python3.8/site-packages/sympy/assumptions/cnf.pyr   &   s    

zLiteral.__new__c                 C   s   | j S Nr   selfr%   r%   r&   arg1   s    zLiteral.argc                 C   s2   t | jr| |}n| j|}t| || jS r'   )callabler   applytyper    )r*   exprr   r%   r%   r&   rcall5   s    
zLiteral.rcallc                 C   s   | j  }t| j|S r'   )r    r   r   )r*   r    r%   r%   r&   
__invert__<   s    zLiteral.__invert__c                 C   s   d t| j| j| jS )Nz
{}({}, {}))formatr.   __name__r   r    r)   r%   r%   r&   __str__@   s    zLiteral.__str__c                 C   s   | j |j ko| j|jkS r'   )r+   r    r*   otherr%   r%   r&   __eq__E   s    zLiteral.__eq__c                 C   s   t t| j| j| jf}|S r'   )hashr.   r3   r+   r    )r*   hr%   r%   r&   __hash__H   s    zLiteral.__hash__)F)r3   
__module____qualname____doc__r   propertyr+   r0   r1   r4   __repr__r7   r:   __classcell__r%   r%   r#   r&   r      s   
r   c                   @   sP   e Zd ZdZdd Zedd Zdd Zdd	 Zd
d Z	dd Z
dd ZeZdS )r   z+
    A low-level implementation for Or
    c                 G   s
   || _ d S r'   _argsr*   r   r%   r%   r&   __init__Q   s    zOR.__init__c                 C   s   t | jtdS N)keysortedrB   strr)   r%   r%   r&   r   T   s    zOR.argsc                    s   t |  fdd| jD  S )Nc                    s   g | ]}|  qS r%   r0   .0r+   r/   r%   r&   
<listcomp>Y   s   zOR.rcall.<locals>.<listcomp>r.   rB   r*   r/   r%   rM   r&   r0   X   s    zOR.rcallc                 C   s   t dd | jD  S )Nc                 S   s   g | ]
}| qS r%   r%   rK   r%   r%   r&   rN   ^   s     z!OR.__invert__.<locals>.<listcomp>)r   rB   r)   r%   r%   r&   r1   ]   s    zOR.__invert__c                 C   s   t t| jft| j S r'   r8   r.   r3   tupler   r)   r%   r%   r&   r:   `   s    zOR.__hash__c                 C   s   | j |j kS r'   r   r5   r%   r%   r&   r7   c   s    z	OR.__eq__c                 C   s"   dd dd | jD  d }|S )N( | c                 S   s   g | ]}t |qS r%   rI   rK   r%   r%   r&   rN   g   s     zOR.__str__.<locals>.<listcomp>)joinr   r*   sr%   r%   r&   r4   f   s    z
OR.__str__N)r3   r;   r<   r=   rD   r>   r   r0   r1   r:   r7   r4   r?   r%   r%   r%   r&   r   M   s   
r   c                   @   sP   e Zd ZdZdd Zdd Zedd Zdd	 Zd
d Z	dd Z
dd ZeZdS )r   z,
    A low-level implementation for And
    c                 G   s
   || _ d S r'   rA   rC   r%   r%   r&   rD   q   s    zAND.__init__c                 C   s   t dd | jD  S )Nc                 S   s   g | ]
}| qS r%   r%   rK   r%   r%   r&   rN   u   s     z"AND.__invert__.<locals>.<listcomp>)r   rB   r)   r%   r%   r&   r1   t   s    zAND.__invert__c                 C   s   t | jtdS rE   rG   r)   r%   r%   r&   r   w   s    zAND.argsc                    s   t |  fdd| jD  S )Nc                    s   g | ]}|  qS r%   rJ   rK   rM   r%   r&   rN   |   s   zAND.rcall.<locals>.<listcomp>rO   rP   r%   rM   r&   r0   {   s    z	AND.rcallc                 C   s   t t| jft| j S r'   rQ   r)   r%   r%   r&   r:      s    zAND.__hash__c                 C   s   | j |j kS r'   rS   r5   r%   r%   r&   r7      s    z
AND.__eq__c                 C   s"   dd dd | jD  d }|S )NrT    & c                 S   s   g | ]}t |qS r%   rV   rK   r%   r%   r&   rN      s     zAND.__str__.<locals>.<listcomp>rW   rX   rZ   r%   r%   r&   r4      s    zAND.__str__N)r3   r;   r<   r=   rD   r1   r>   r   r0   r:   r7   r4   r?   r%   r%   r%   r&   r   m   s   
r   Nc                    sn  ddl m}  dkri  t|jt|jt|jt|j	t
|jt|ji}t| |krb|t|  }|| j } t| tr| jd }t| }| S t| trt fddt| D  S t| trt fddt| D  S t| trt fdd| jD  }| S t| tr$t fdd| jD  }| S t| trg }tdt| jd	 d
D ]>}t| j|D ]* fdd| jD }	|t|	  qZqJt| S t| trg }tdt| jd	 d
D ]>}t| j|D ]* fdd| jD }	|t|	  qȐqt|  S t| t r<t| jd  t| jd	   }
}t|
 |S t| t!rg }t"| j| jd	d | jd dD ]0\}}t| }t| }|t| | qlt| S t| t#rt| jd  }
t| jd	  }t| jd
  }tt|
 |t|
|S t| t$r:| j%| j& }} '|d}|dk	r:t|j(|  S t| t)rf '| d}|dk	rft| S t*| S )a  
    Generates the Negation Normal Form of any boolean expression in terms
    of AND, OR, and Literal objects.

    Examples
    ========

    >>> from sympy import Q, Eq
    >>> from sympy.assumptions.cnf import to_NNF
    >>> from sympy.abc import x, y
    >>> expr = Q.even(x) & ~Q.positive(x)
    >>> to_NNF(expr)
    (Literal(Q.even(x), False) & Literal(Q.positive(x), True))

    Supported boolean objects are converted to corresponding predicates.

    >>> to_NNF(Eq(x, y))
    Literal(Q.eq(x, y), False)

    If ``composite_map`` argument is given, ``to_NNF`` decomposes the
    specified predicate into a combination of primitive predicates.

    >>> cmap = {Q.nonpositive: Q.negative | Q.zero}
    >>> to_NNF(Q.nonpositive, cmap)
    (Literal(Q.negative, False) | Literal(Q.zero, False))
    >>> to_NNF(Q.nonpositive(x), cmap)
    (Literal(Q.negative(x), False) | Literal(Q.zero(x), False))
    r   )QNc                    s   g | ]}t | qS r%   to_NNFrL   xcomposite_mapr%   r&   rN      s     zto_NNF.<locals>.<listcomp>c                    s   g | ]}t | qS r%   r^   r`   rb   r%   r&   rN      s     c                    s   g | ]}t | qS r%   r^   r`   rb   r%   r&   rN      s     c                    s   g | ]}t | qS r%   r^   r`   rb   r%   r&   rN      s           c                    s*   g | ]"}|krt |  nt | qS r%   r^   rL   r[   rc   negr%   r&   rN      s   c                    s*   g | ]"}|krt |  nt | qS r%   r^   rf   rg   r%   r&   rN      s   )	fillvalue)+Zsympy.assumptions.askr]   r   eqr   ner	   gtr
   ltr   ger   ler.   r   r   r   r_   r   r   Z	make_argsr   r   r   r   r   rangelenr   appendr   r   r   r   r   r   function	argumentsgetr0   r   r   )r/   rc   r]   Zbinrelpredspredr+   tmpcnfsiclauseLRabMr   Znewpredr%   rg   r&   r_      s    (







"(




r_   c                 C   sp   t | ttfs,t }|t| f t|S t | trLtjdd | jD  S t | trltj	dd | jD  S dS )z
    Distributes AND over OR in the NNF expression.
    Returns the result( Conjunctive Normal Form of expression)
    as a CNF object.
    c                 S   s   g | ]}t |qS r%   distribute_AND_over_ORrK   r%   r%   r&   rN     s   z*distribute_AND_over_OR.<locals>.<listcomp>c                 S   s   g | ]}t |qS r%   r   rK   r%   r%   r&   rN   
  s   N)
r   r   r   setadd	frozensetCNFall_orrB   all_and)r/   rw   r%   r%   r&   r      s    



r   c                   @   s   e Zd ZdZd%ddZdd Zdd Zd	d
 Zdd Zdd Z	e
dd Zdd Zdd Zdd Zdd Zdd Zdd Ze
dd Ze
dd  Ze
d!d" Ze
d#d$ ZdS )&r   a  
    Class to represent CNF of a Boolean expression.
    Consists of set of clauses, which themselves are stored as
    frozenset of Literal objects.

    Examples
    ========

    >>> from sympy import Q
    >>> from sympy.assumptions.cnf import CNF
    >>> from sympy.abc import x
    >>> cnf = CNF.from_prop(Q.real(x) & ~Q.zero(x))
    >>> cnf.clauses
    {frozenset({Literal(Q.zero(x), True)}),
    frozenset({Literal(Q.negative(x), False),
    Literal(Q.positive(x), False), Literal(Q.zero(x), False)})}
    Nc                 C   s   |s
t  }|| _d S r'   r   clausesr*   r   r%   r%   r&   rD      s    zCNF.__init__c                 C   s   t |j}| | d S r'   )r   to_CNFr   add_clauses)r*   propr   r%   r%   r&   r   %  s    zCNF.addc                 C   s   d dd | jD }|S )Nr\   c                 S   s(   g | ] }d d dd |D  d qS )rT   rU   c                 S   s   g | ]}t |qS r%   rV   )rL   r   r%   r%   r&   rN   +  s     z*CNF.__str__.<locals>.<listcomp>.<listcomp>rW   )rY   rL   rz   r%   r%   r&   rN   +  s   zCNF.__str__.<locals>.<listcomp>)rY   r   rZ   r%   r%   r&   r4   )  s    zCNF.__str__c                 C   s   |D ]}|  | q| S r'   r   )r*   propspr%   r%   r&   extend0  s    z
CNF.extendc                 C   s   t t| jS r'   )r   r   r   r)   r%   r%   r&   copy5  s    zCNF.copyc                 C   s   |  j |O  _ d S r'   )r   r   r%   r%   r&   r   8  s    zCNF.add_clausesc                 C   s   |  }| | |S r'   r   )r!   r   resr%   r%   r&   	from_prop;  s    
zCNF.from_propc                 C   s   |  |j | S r'   )r   r   r5   r%   r%   r&   __iand__A  s    zCNF.__iand__c                 C   s(   t  }| jD ]}|dd |D O }q|S )Nc                 S   s   h | ]
}|j qS r%   r(   rK   r%   r%   r&   	<setcomp>H  s     z%CNF.all_predicates.<locals>.<setcomp>r   )r*   Z
predicatescr%   r%   r&   all_predicatesE  s    
zCNF.all_predicatesc                 C   sF   t  }t| j|jD ](\}}t |}|| |t| qt|S r'   )r   r   r   updater   r   r   )r*   cnfr   r}   r~   rw   r%   r%   r&   _orK  s    
zCNF._orc                 C   s   | j |j }t|S r'   )r   unionr   r*   r   r   r%   r%   r&   _andS  s    zCNF._andc                 C   sV   t | j}dd |d D }t|}|d d D ] }dd |D }|t|}q0|S )Nc                 S   s   h | ]}t | fqS r%   r   r`   r%   r%   r&   r   Y  s     zCNF._not.<locals>.<setcomp>c                 S   s   h | ]}t | fqS r%   r   r`   r%   r%   r&   r   ]  s     )listr   r   r   )r*   ZclssZllrestr   r%   r%   r&   _notW  s    
zCNF._notc                    s@   g }| j D ]$} fdd|D }|t|  q
t|  t S )Nc                    s   g | ]}|  qS r%   rJ   rK   rM   r%   r&   rN   d  s     zCNF.rcall.<locals>.<listcomp>)r   rr   r   r   r   )r*   r/   Zclause_listrz   Zlitsr%   rM   r&   r0   a  s    
z	CNF.rcallc                 G   s,   |d   }|dd  D ]}||}q|S Nr   rd   )r   r   r!   rx   r~   r   r%   r%   r&   r   i  s    z
CNF.all_orc                 G   s,   |d   }|dd  D ]}||}q|S r   )r   r   r   r%   r%   r&   r   p  s    zCNF.all_andc                 C   s$   ddl m} t|| }t|}|S )Nr   )get_composite_predicates)Zsympy.assumptions.factsr   r_   r   )r!   r/   r   r%   r%   r&   r   w  s    z
CNF.to_CNFc                    s    dd  t  fdd|jD  S )zm
        Converts CNF object to SymPy's boolean expression
        retaining the form of expression.
        c                 S   s   | j rt| jS | jS r'   )r    r   r   )r+   r%   r%   r&   remove_literal  s    z&CNF.CNF_to_cnf.<locals>.remove_literalc                 3   s$   | ]}t  fd d|D  V  qdS )c                 3   s   | ]} |V  qd S r'   r%   rK   r   r%   r&   	<genexpr>  s     z+CNF.CNF_to_cnf.<locals>.<genexpr>.<genexpr>N)r   r   r   r%   r&   r     s     z!CNF.CNF_to_cnf.<locals>.<genexpr>)r   r   )r!   r   r%   r   r&   
CNF_to_cnf~  s    zCNF.CNF_to_cnf)N)r3   r;   r<   r=   rD   r   r4   r   r   r   classmethodr   r   r   r   r   r   r0   r   r   r   r   r%   r%   r%   r&   r     s.   





r   c                   @   sb   e Zd ZdZdddZdd Zedd Zed	d
 Zdd Z	dd Z
dd Zdd Zdd ZdS )
EncodedCNFz0
    Class for encoding the CNF expression.
    Nc                 C   s.   |s|sg }i }|| _ || _t| | _d S r'   )dataencodingr   keys_symbols)r*   r   r   r%   r%   r&   rD     s    zEncodedCNF.__init__c                    sN   t |  _t j}tt jtd|d  _ fdd|jD  _	d S )Nrd   c                    s   g | ]}  |qS r%   encoder   r)   r%   r&   rN     s     z'EncodedCNF.from_cnf.<locals>.<listcomp>)
r   r   r   rq   dictziprp   r   r   r   )r*   r   nr%   r)   r&   from_cnf  s    
zEncodedCNF.from_cnfc                 C   s   | j S r'   )r   r)   r%   r%   r&   symbols  s    zEncodedCNF.symbolsc                 C   s   t dt| jd S Nrd   )rp   rq   r   r)   r%   r%   r&   	variables  s    zEncodedCNF.variablesc                 C   s    dd | j D }t|t| jS )Nc                 S   s   g | ]}t |qS r%   )r   r   r%   r%   r&   rN     s     z#EncodedCNF.copy.<locals>.<listcomp>)r   r   r   r   )r*   Znew_datar%   r%   r&   r     s    zEncodedCNF.copyc                 C   s   t |}| | d S r'   )r   r   add_from_cnf)r*   r   r   r%   r%   r&   add_prop  s    
zEncodedCNF.add_propc                    s&    fdd|j D }  j|7  _d S )Nc                    s   g | ]}  |qS r%   r   r   r)   r%   r&   rN     s     z+EncodedCNF.add_from_cnf.<locals>.<listcomp>)r   r   r   r%   r)   r&   r     s    zEncodedCNF.add_from_cnfc                 C   sX   |j }| j|d }|d krDt| j}| j| |d  }| j|< |jrP| S |S d S r   )r   r   ru   rq   r   rr   r    )r*   r+   literalvaluer   r%   r%   r&   
encode_arg  s    
zEncodedCNF.encode_argc                    s    fdd|D S )Nc                    s&   h | ]}|j tjks |nd qS )r   )r   r   falser   rK   r)   r%   r&   r     s     z$EncodedCNF.encode.<locals>.<setcomp>r%   )r*   rz   r%   r)   r&   r     s    zEncodedCNF.encode)NN)r3   r;   r<   r=   rD   r   r>   r   r   r   r   r   r   r   r%   r%   r%   r&   r     s   


r   )N)#r=   	itertoolsr   r   r   Zsympy.assumptions.assumer   r   Zsympy.core.relationalr   r   r	   r
   r   r   Zsympy.core.singletonr   Zsympy.logic.boolalgr   r   r   r   r   r   r   r   r   r   r   r   r   r_   r   r   r   r%   r%   r%   r&   <module>   s     >  
m|