a
    khS                     @   sv   d Z ddlmZ ddlmZmZ ddlmZ ddlm	Z	 ddl
mZ ddd	Zd
d ZG dd dZG dd dZdS )zImplementation of DPLL algorithm

Features:
  - Clause learning
  - Watch literal scheme
  - VSIDS heuristic

References:
  - https://en.wikipedia.org/wiki/DPLL_algorithm
    )defaultdict)heappushheappop)ordered)
EncodedCNF)	LRASolverFc                 C   s   t | tst }||  |} dh| jv r@|r<dd dD S dS |rTt| \}}nd}g }t| j| | jt | j	|d}|
 }|rt|S z
t|W S  ty   Y dS 0 dS )a  
    Check satisfiability of a propositional sentence.
    It returns a model rather than True when it succeeds.
    Returns a generator of all models if all_models is True.

    Examples
    ========

    >>> from sympy.abc import A, B
    >>> from sympy.logic.algorithms.dpll2 import dpll_satisfiable
    >>> dpll_satisfiable(A & ~B)
    {A: True, B: False}
    >>> dpll_satisfiable(A & ~A)
    False

    r   c                 s   s   | ]
}|V  qd S N ).0fr	   r	   J/var/www/auris/lib/python3.9/site-packages/sympy/logic/algorithms/dpll2.py	<genexpr>.       z#dpll_satisfiable.<locals>.<genexpr>)FFN)
lra_theory)
isinstancer   Zadd_propdatar   Zfrom_encoded_cnf	SATSolver	variablessetsymbols_find_model_all_modelsnextStopIteration)exprZ
all_modelsZuse_lra_theoryexprslraZimmediate_conflictsZsolvermodelsr	   r	   r   dpll_satisfiable   s(    


r   c                 c   s:   d}zt | V  d}qW n ty4   |s0dV  Y n0 d S )NFT)r   r   )r   Zsatisfiabler	   r	   r   r   G   s    

r   c                   @   s   e Zd ZdZd0d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dd Zdd Zd d! Zd"d# Zd$d% Zd&d' Zd(d) Zd*d+ Zd,d- Zd.d/ ZdS )1r   z
    Class for representing a SAT solver capable of
     finding a model to a boolean theory in conjunctive
     normal form.
    Nvsidsnone  c	           	      C   s  || _ || _d| _g | _g | _|| _|d u r<tt|| _n|| _| 	| | 
| d|kr|   | j| _| j| _| j| _| j| _ntd|kr| j| _| j| _| j| j n"d|krdd | _dd | _nttdg| _|| j_d| _d| _ t!| j"| _#|| _$d S )	NFr   simpler    c                 S   s   d S r   r	   )xr	   r	   r   <lambda>~   r   z$SATSolver.__init__.<locals>.<lambda>c                   S   s   d S r   r	   r	   r	   r	   r   r$      r   r   )%var_settings	heuristicis_unsatisfied_unit_prop_queueupdate_functionsINTERVALlistr   r   _initialize_variables_initialize_clauses_vsids_init_vsids_calculateheur_calculate_vsids_lit_assignedheur_lit_assigned_vsids_lit_unsetheur_lit_unset_vsids_clause_addedheur_clause_addedNotImplementedError_simple_add_learned_clauseadd_learned_clause_simple_compute_conflictcompute_conflictappend_simple_clean_clausesLevellevels_current_levelZvarsettingsnum_decisionsnum_learned_clauseslenclausesZoriginal_num_clausesr   )	selfrD   r   r%   r   r&   Zclause_learningr*   r   r	   r	   r   __init__Y   s@    



zSATSolver.__init__c                 C   s,   t t| _t t| _dgt|d  | _dS )z+Set up the variable data structures needed.F   N)r   r   	sentinelsintoccurrence_countrC   variable_set)rE   r   r	   r	   r   r,      s    

zSATSolver._initialize_variablesc                 C   s   dd |D | _ t| j D ]j\}}dt|kr@| j|d  q| j|d  | | j|d  | |D ]}| j|  d7  < qlqdS )a<  Set up the clause data structures needed.

        For each clause, the following changes are made:
        - Unit clauses are queued for propagation right away.
        - Non-unit clauses have their first and last literals set as sentinels.
        - The number of clauses a literal appears in is computed.
        c                 S   s   g | ]}t |qS r	   )r+   )r
   clauser	   r	   r   
<listcomp>   r   z1SATSolver._initialize_clauses.<locals>.<listcomp>rG   r   N)rD   	enumeraterC   r(   r<   rH   addrJ   )rE   rD   irL   litr	   r	   r   r-      s    zSATSolver._initialize_clausesc                 #   s  d}   jrdS jj dkr8jD ]
}|  q,|rLd}jj}n& } jd7  _d|krbjrj	D ]}j
|  durx qqxj  j  nd  du s d r؇fddj	D V  n4 d  t fddjj	D s  qjjr"  qtjdkr6dS jj }  jt|d	d
 d	}qjt| |    jrd_jjr  dtjkrdS q  jj }  jt|d	d
 d	}qdS )an  
        Main DPLL loop. Returns a generator of models.

        Variables are chosen successively, and assigned to be either
        True or False. If a solution is not found with this setting,
        the opposite is chosen and the search continues. The solver
        halts when every variable has a setting.

        Examples
        ========

        >>> from sympy.logic.algorithms.dpll2 import SATSolver
        >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2},
        ... {3, -2}], {1, 2, 3}, set())
        >>> list(l._find_model())
        [{1: True, 2: False, 3: False}, {1: True, 2: True, 3: True}]

        >>> from sympy.abc import A, B, C
        >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2},
        ... {3, -2}], {1, 2, 3}, set(), [A, B, C])
        >>> list(l._find_model())
        [{A: True, B: False, C: False}, {A: True, B: True, C: True}]

        FNr   rG   c                    s$   i | ]} j t|d   |dkqS )rG   r   )r   absr
   rR   rE   r	   r   
<dictcomp>   s   z)SATSolver._find_model.<locals>.<dictcomp>c                 3   s   | ]}|  d  v V  qdS )rG   Nr	   rT   )resr	   r   r      r   z(SATSolver._find_model.<locals>.<genexpr>T)flipped)	_simplifyr'   rA   r*   r)   r@   decisionr0   r   r%   Z
assert_litcheckZreset_boundsr8   any_undorX   rC   r?   r<   r>   _assign_literalr9   r;   )rE   Zflip_varfuncrR   Zenc_varZflip_litr	   )rW   rE   r   r      sf    











zSATSolver._find_modelc                 C   s
   | j d S )a  The current decision level data structure

        Examples
        ========

        >>> from sympy.logic.algorithms.dpll2 import SATSolver
        >>> l = SATSolver([{1}, {2}], {1, 2}, set())
        >>> next(l._find_model())
        {1: True, 2: True}
        >>> l._current_level.decision
        0
        >>> l._current_level.flipped
        False
        >>> l._current_level.var_settings
        {1, 2}

        rN   r?   rU   r	   r	   r   r@   "  s    zSATSolver._current_levelc                 C   s$   | j | D ]}|| jv r
 dS q
dS )a  Check if a clause is satisfied by the current variable setting.

        Examples
        ========

        >>> from sympy.logic.algorithms.dpll2 import SATSolver
        >>> l = SATSolver([{1}, {-1}], {1}, set())
        >>> try:
        ...     next(l._find_model())
        ... except StopIteration:
        ...     pass
        >>> l._clause_sat(0)
        False
        >>> l._clause_sat(1)
        True

        TF)rD   r%   rE   clsrR   r	   r	   r   _clause_sat7  s    
zSATSolver._clause_satc                 C   s   || j | v S )a  Check if a literal is a sentinel of a given clause.

        Examples
        ========

        >>> from sympy.logic.algorithms.dpll2 import SATSolver
        >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2},
        ... {3, -2}], {1, 2, 3}, set())
        >>> next(l._find_model())
        {1: True, 2: False, 3: False}
        >>> l._is_sentinel(2, 3)
        True
        >>> l._is_sentinel(-3, 1)
        False

        )rH   )rE   rR   rb   r	   r	   r   _is_sentinelN  s    zSATSolver._is_sentinelc                 C   s   | j | | jj | d| jt|< | | t| j|  }|D ]}| |sFd}| j	| D ]X}|| krb| 
||r|}qb| jt| sb| j|  | | j| | d} qqb|rF| j| qFdS )a  Make a literal assignment.

        The literal assignment must be recorded as part of the current
        decision level. Additionally, if the literal is marked as a
        sentinel of any clause, then a new sentinel must be chosen. If
        this is not possible, then unit propagation is triggered and
        another literal is added to the queue to be set in the future.

        Examples
        ========

        >>> from sympy.logic.algorithms.dpll2 import SATSolver
        >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2},
        ... {3, -2}], {1, 2, 3}, set())
        >>> next(l._find_model())
        {1: True, 2: False, 3: False}
        >>> l.var_settings
        {-3, -2, 1}

        >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2},
        ... {3, -2}], {1, 2, 3}, set())
        >>> l._assign_literal(-1)
        >>> try:
        ...     next(l._find_model())
        ... except StopIteration:
        ...     pass
        >>> l.var_settings
        {-1}

        TN)r%   rP   r@   rK   rS   r2   r+   rH   rc   rD   rd   remover(   r<   )rE   rR   Zsentinel_listrb   Zother_sentinelZnewlitr	   r	   r   r^   a  s&    


zSATSolver._assign_literalc                 C   s@   | j jD ](}| j| | | d| jt|< q| j  dS )ag  
        _undo the changes of the most recent decision level.

        Examples
        ========

        >>> from sympy.logic.algorithms.dpll2 import SATSolver
        >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2},
        ... {3, -2}], {1, 2, 3}, set())
        >>> next(l._find_model())
        {1: True, 2: False, 3: False}
        >>> level = l._current_level
        >>> level.decision, level.var_settings, level.flipped
        (-3, {-3, -2}, False)
        >>> l._undo()
        >>> level = l._current_level
        >>> level.decision, level.var_settings, level.flipped
        (0, {1}, False)

        FN)r@   r%   re   r4   rK   rS   r?   poprE   rR   r	   r	   r   r]     s
    
zSATSolver._undoc                 C   s*   d}|r&d}||   O }||  O }qdS )ad  Iterate over the various forms of propagation to simplify the theory.

        Examples
        ========

        >>> from sympy.logic.algorithms.dpll2 import SATSolver
        >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2},
        ... {3, -2}], {1, 2, 3}, set())
        >>> l.variable_set
        [False, False, False, False]
        >>> l.sentinels
        {-3: {0, 2}, -2: {3, 4}, 2: {0, 3}, 3: {2, 4}}

        >>> l._simplify()

        >>> l.variable_set
        [False, True, False, False]
        >>> l.sentinels
        {-3: {0, 2}, -2: {3, 4}, -1: set(), 2: {0, 3},
        ...3: {2, 4}}

        TFN)
_unit_prop_pure_literal)rE   changedr	   r	   r   rY     s
    zSATSolver._simplifyc                 C   sJ   t | jdk}| jrF| j }| | jv r:d| _g | _dS | | q|S )z/Perform unit propagation on the current theory.r   TF)rC   r(   rf   r%   r'   r^   )rE   resultZnext_litr	   r	   r   rh     s    
zSATSolver._unit_propc                 C   s   dS )z2Look for pure literals and assign them when found.Fr	   rU   r	   r	   r   ri     s    zSATSolver._pure_literalc                 C   s   g | _ i | _tdt| jD ]d}t| j|  | j|< t| j|   | j| < t| j | j| |f t| j | j|  | f qdS )z>Initialize the data structures needed for the VSIDS heuristic.rG   N)lit_heap
lit_scoresrangerC   rK   floatrJ   r   )rE   varr	   r	   r   r.     s    zSATSolver._vsids_initc                 C   s&   | j  D ]}| j |  d  < q
dS )a  Decay the VSIDS scores for every literal.

        Examples
        ========

        >>> from sympy.logic.algorithms.dpll2 import SATSolver
        >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2},
        ... {3, -2}], {1, 2, 3}, set())

        >>> l.lit_scores
        {-3: -2.0, -2: -2.0, -1: 0.0, 1: 0.0, 2: -2.0, 3: -2.0}

        >>> l._vsids_decay()

        >>> l.lit_scores
        {-3: -1.0, -2: -1.0, -1: 0.0, 1: 0.0, 2: -1.0, 3: -1.0}

        g       @N)rm   keysrg   r	   r	   r   _vsids_decay  s    zSATSolver._vsids_decayc                 C   sV   t | jdkrdS | jt| jd d  rHt| j t | jdkrdS qt| jd S )a  
            VSIDS Heuristic Calculation

        Examples
        ========

        >>> from sympy.logic.algorithms.dpll2 import SATSolver
        >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2},
        ... {3, -2}], {1, 2, 3}, set())

        >>> l.lit_heap
        [(-2.0, -3), (-2.0, 2), (-2.0, -2), (0.0, 1), (-2.0, 3), (0.0, -1)]

        >>> l._vsids_calculate()
        -3

        >>> l.lit_heap
        [(-2.0, -2), (-2.0, 2), (0.0, -1), (0.0, 1), (-2.0, 3)]

        r   rG   )rC   rl   rK   rS   r   rU   r	   r	   r   r/     s    
zSATSolver._vsids_calculatec                 C   s   dS )z;Handle the assignment of a literal for the VSIDS heuristic.Nr	   rg   r	   r	   r   r1   3  s    zSATSolver._vsids_lit_assignedc                 C   s<   t |}t| j| j| |f t| j| j|  | f dS )a  Handle the unsetting of a literal for the VSIDS heuristic.

        Examples
        ========

        >>> from sympy.logic.algorithms.dpll2 import SATSolver
        >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2},
        ... {3, -2}], {1, 2, 3}, set())
        >>> l.lit_heap
        [(-2.0, -3), (-2.0, 2), (-2.0, -2), (0.0, 1), (-2.0, 3), (0.0, -1)]

        >>> l._vsids_lit_unset(2)

        >>> l.lit_heap
        [(-2.0, -3), (-2.0, -2), (-2.0, -2), (-2.0, 2), (-2.0, 3), (0.0, -1),
        ...(-2.0, 2), (0.0, 1)]

        N)rS   r   rl   rm   )rE   rR   rp   r	   r	   r   r3   7  s    zSATSolver._vsids_lit_unsetc                 C   s.   |  j d7  _ |D ]}| j|  d7  < qdS )aD  Handle the addition of a new clause for the VSIDS heuristic.

        Examples
        ========

        >>> from sympy.logic.algorithms.dpll2 import SATSolver
        >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2},
        ... {3, -2}], {1, 2, 3}, set())

        >>> l.num_learned_clauses
        0
        >>> l.lit_scores
        {-3: -2.0, -2: -2.0, -1: 0.0, 1: 0.0, 2: -2.0, 3: -2.0}

        >>> l._vsids_clause_added({2, -3})

        >>> l.num_learned_clauses
        1
        >>> l.lit_scores
        {-3: -1.0, -2: -2.0, -1: 0.0, 1: 0.0, 2: -1.0, 3: -2.0}

        rG   N)rB   rm   ra   r	   r	   r   r5   N  s    zSATSolver._vsids_clause_addedc                 C   sh   t | j}| j| |D ]}| j|  d7  < q| j|d  | | j|d  | | | dS )a  Add a new clause to the theory.

        Examples
        ========

        >>> from sympy.logic.algorithms.dpll2 import SATSolver
        >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2},
        ... {3, -2}], {1, 2, 3}, set())

        >>> l.num_learned_clauses
        0
        >>> l.clauses
        [[2, -3], [1], [3, -3], [2, -2], [3, -2]]
        >>> l.sentinels
        {-3: {0, 2}, -2: {3, 4}, 2: {0, 3}, 3: {2, 4}}

        >>> l._simple_add_learned_clause([3])

        >>> l.clauses
        [[2, -3], [1], [3, -3], [2, -2], [3, -2], [3]]
        >>> l.sentinels
        {-3: {0, 2}, -2: {3, 4}, 2: {0, 3}, 3: {2, 4, 5}}

        rG   r   rN   N)rC   rD   r<   rJ   rH   rP   r6   )rE   rb   Zcls_numrR   r	   r	   r   r8   l  s    
z$SATSolver._simple_add_learned_clausec                 C   s   dd | j dd D S )a   Build a clause representing the fact that at least one decision made
        so far is wrong.

        Examples
        ========

        >>> from sympy.logic.algorithms.dpll2 import SATSolver
        >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2},
        ... {3, -2}], {1, 2, 3}, set())
        >>> next(l._find_model())
        {1: True, 2: False, 3: False}
        >>> l._simple_compute_conflict()
        [3]

        c                 S   s   g | ]}|j  qS r	   )rZ   )r
   levelr	   r	   r   rM     r   z6SATSolver._simple_compute_conflict.<locals>.<listcomp>rG   Nr`   rU   r	   r	   r   r:     s    z"SATSolver._simple_compute_conflictc                 C   s   dS )zClean up learned clauses.Nr	   rU   r	   r	   r   r=     s    zSATSolver._simple_clean_clauses)Nr   r    r!   N)__name__
__module____qualname____doc__rF   r,   r-   r   propertyr@   rc   rd   r^   r]   rY   rh   ri   r.   rr   r/   r1   r3   r5   r8   r:   r=   r	   r	   r	   r   r   R   s4      
5w
7& $r   c                   @   s   e Zd ZdZdddZdS )r>   z
    Represents a single level in the DPLL algorithm, and contains
    enough information for a sound backtracking procedure.
    Fc                 C   s   || _ t | _|| _d S r   )rZ   r   r%   rX   )rE   rZ   rX   r	   r	   r   rF     s    zLevel.__init__N)F)rt   ru   rv   rw   rF   r	   r	   r	   r   r>     s   r>   N)FF)rw   collectionsr   heapqr   r   Zsympy.core.sortingr   Zsympy.assumptions.cnfr   Z!sympy.logic.algorithms.lra_theoryr   r   r   r   r>   r	   r	   r	   r   <module>   s   
2    Y