o
    *ήc]O                     @   sj   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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)
EncodedCNFFc                 C   s   t | tst }||  |} dh| jv r |rdd dD S dS t| j| jt | j}| }|r5t	|S zt
|W S  tyD   Y dS w )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   C/tmp/pip-target-vg8gfxp4/lib/python/sympy/logic/algorithms/dpll2.py	<genexpr>,   s    z#dpll_satisfiable.<locals>.<genexpr>FF)
isinstancer   add_propdata	SATSolver	variablessetsymbols_find_model_all_modelsnextStopIteration)expr
all_modelsexprssolvermodelsr   r   r   dpll_satisfiable   s"   


r   c                 c   s>    d}z		 t | V  d}q ty   |sdV  Y d S Y d S w )NFT)r   r   )r   satisfiabler   r   r   r   @   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$d% Zd&d' Zd(d) Zd*d+ Zd,d- Zd.d/ ZdS )1r   z
    Class for representing a SAT solver capable of
     finding a model to a boolean theory in conjunctive
     normal form.
    Nvsidsnone  c                 C   s  || _ || _d| _g | _g | _|| _|d u rtt|| _n|| _| 	| | 
| d|krD|   | j| _| j| _| j| _| j| _ntd|krZ| j| _| j| _| j| j nd|kridd | _dd | _nttdg| _|| j_d| _d| _ t!| j"| _#d S )	NFr    simpler!   c                 S      d S r   r   )xr   r   r   <lambda>v       z$SATSolver.__init__.<locals>.<lambda>c                   S   r$   r   r   r   r   r   r   r&   w   r'   r   )$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_levelvarsettingsnum_decisionsnum_learned_clauseslenclausesoriginal_num_clauses)selfrH   r   r(   r   r)   clause_learningr-   r   r   r   __init__R   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_countrG   variable_set)rJ   r   r   r   r   r/      s   

zSATSolver._initialize_variablesc                 C   s   dd |D | _ t| j D ]5\}}dt|kr | j|d  q| j|d  | | j|d  | |D ]}| j|  d7  < q6q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>       z1SATSolver._initialize_clauses.<locals>.<listcomp>rM   r   N)rH   	enumeraterG   r+   r?   rN   addrP   )rJ   rH   irR   litr   r   r   r0      s   zSATSolver._initialize_clausesc                 #   sj   d}     jrdS 	  j j dkr jD ]}|  q|r'd} jj}nM  }  jd7  _d|krl fdd jD V   jj	rM 
   jj	sEt jdkrVdS  jj } 
   jt|dd d}q jt|  |      jrd _ jj	r 
  dt jkrdS  jj	s     jj } 
   jt|dd d}q)	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}]

        FNTr   rM   c                    s$   i | ]} j t|d   |dkqS )rM   r   )r   abs)r	   rY   rJ   r   r   
<dictcomp>   s
    z)SATSolver._find_model.<locals>.<dictcomp>)flipped)	_simplifyr*   rE   r-   r,   rC   decisionr3   r(   r]   _undorG   rB   r?   rA   _assign_literalr<   r>   )rJ   flip_varfuncrY   flip_litr   r[   r   r      sX   





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}

        rU   rB   r[   r   r   r   rC     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)rH   r(   rJ   clsrY   r   r   r   _clause_sat  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

        )rN   )rJ   rY   rg   r   r   r   _is_sentinel1  s   zSATSolver._is_sentinelc                 C   s   | j | | jj | d| jt|< | | t| j|  }|D ]C}| |sfd}| j	| D ],}|| kr]| 
||rA|}q1| jt| s]| j|  | | j| | d} nq1|rf| j| q#d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(   rW   rC   rQ   rZ   r5   r.   rN   rh   rH   ri   remover+   r?   )rJ   rY   sentinel_listrg   other_sentinelnewlitr   r   r   ra   D  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)rC   r(   rj   r7   rQ   rZ   rB   poprJ   rY   r   r   r   r`   {  s
   
zSATSolver._undoc                 C   s0   d}|rd}||   O }||  O }|sdS 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)rJ   changedr   r   r   r^     s   zSATSolver._simplifyc                 C   sN   t | jdk}| jr%| j }| | jv rd| _g | _dS | | | js
|S )z/Perform unit propagation on the current theory.r   TF)rG   r+   rn   r(   r*   ra   )rJ   resultnext_litr   r   r   rp     s   

	zSATSolver._unit_propc                 C      dS )z2Look for pure literals and assign them when found.Fr   r[   r   r   r   rq        zSATSolver._pure_literalc                 C   s   g | _ i | _tdt| jD ]2}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.rM   N)lit_heap
lit_scoresrangerG   rQ   floatrP   r   )rJ   varr   r   r   r1     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)rx   keysro   r   r   r   _vsids_decay  s   zSATSolver._vsids_decayc                 C   sl   t | jdkr	dS | jt| jd d  r/t| j t | jdkr#dS | jt| jd d  s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   rM   )rG   rw   rQ   rZ   r   r[   r   r   r   r2     s   
zSATSolver._vsids_calculatec                 C   ru   )z;Handle the assignment of a literal for the VSIDS heuristic.Nr   ro   r   r   r   r4     rv   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)rZ   r   rw   rx   )rJ   rY   r{   r   r   r   r6     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}

        rM   N)rF   rx   rf   r   r   r   r8   1  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}}

        rM   r   rU   N)rG   rH   r?   rP   rN   rW   r9   )rJ   rg   cls_numrY   r   r   r   r;   O  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   )r_   )r	   levelr   r   r   rS     rT   z6SATSolver._simple_compute_conflict.<locals>.<listcomp>rM   Nre   r[   r   r   r   _simple_compute_conflicts  s   z"SATSolver._simple_compute_conflictc                 C   ru   )zClean up learned clauses.Nr   r[   r   r   r   _simple_clean_clauses  rv   zSATSolver._simple_clean_clauses)Nr    r!   r"   )__name__
__module____qualname____doc__rL   r/   r0   r   propertyrC   rh   ri   ra   r`   r^   rp   rq   r1   r}   r2   r4   r6   r8   r;   r   r   r   r   r   r   r   K   s6    
2d
7! $r   c                   @   s   e Zd ZdZdddZdS )rA   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   )r_   r   r(   r]   )rJ   r_   r]   r   r   r   rL     s   
zLevel.__init__Nr   )r   r   r   r   rL   r   r   r   r   rA     s    rA   Nr   )r   collectionsr   heapqr   r   sympy.core.sortingr   sympy.assumptions.cnfr   r   r   r   rA   r   r   r   r   <module>   s    
-    C