o o h#@sdZddlmZddlmZmZmZmZmZm Z m Z ddl m Z ddl mZmZddZdd Zd d Zifd d ZddZddZddZddZddZddZdS)a&Implementation of DPLL algorithm Further improvements: eliminate calls to pl_true, implement branching rules, efficient unit propagation. References: - https://en.wikipedia.org/wiki/DPLL_algorithm - https://www.researchgate.net/publication/242384772_Implementations_of_the_DPLL_Algorithm )default_sort_key)OrNot conjuncts disjunctsto_cnf to_int_repr_find_predicates)CNF)pl_trueliteral_symbolcCst|ts tt|}n|j}d|vrdStt|td}tt dt |d}t ||}t ||i}|s7|Si}|D]}| ||d||iq;|S)a> Check satisfiability of a propositional sentence. It returns a model rather than True when it succeeds >>> from sympy.abc import A, B >>> from sympy.logic.algorithms.dpll import dpll_satisfiable >>> dpll_satisfiable(A & ~B) {A: True, B: False} >>> dpll_satisfiable(A & ~A) False F)key) isinstancer rrclausessortedr rsetrangelenr dpll_int_reprupdate)exprrsymbolssymbols_int_reprclauses_int_reprresultoutputr ro/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/sympy/logic/algorithms/dpll.pydpll_satisfiables   rc CsHt||\}}|r(|||i|||s|}t||}t||\}}|s t||\}}|rP|||i|||sB|}t||}t||\}}|s1g}|D]}t||}|durbdS|durk||qT|sp|S|st|S|}|}||di||di|dd} t t||||pt t|t || |S)z Compute satisfiability in a partial model. Clauses is an array of conjuncts. >>> from sympy.abc import A, B, D >>> from sympy.logic.algorithms.dpll import dpll >>> dpll([A, B, D], [A, B], {D: False}) False FTN) find_unit_clauserremoveunit_propagatefind_pure_symbolr appendpopcopydpllr rrmodelPvalueunknown_clausescval model_copy symbols_copyrrrr'1sL        r'c Cs:t||\}}|r(|||i|||s| }t||}t||\}}|s t||\}}|rP|||i|||sB| }t||}t||\}}|s1g}|D]}t||}|durbdS|durk||qT|sp|S|}|}||di||di|} t t||||pt t|| | |S)z Compute satisfiability in a partial model. Arguments are expected to be in integer representation >>> from sympy.logic.algorithms.dpll import dpll_int_repr >>> dpll_int_repr([{1}, {2}, {3}], {1, 2}, {3: False}) False FT) find_unit_clause_int_reprrr!unit_propagate_int_reprfind_pure_symbol_int_reprpl_true_int_reprr$r%r&rr(rrrrbsH       rcCsZd}|D]&}|dkr|| }|dur| }n||}|dur$dS|dur*d}q|S)af Lightweight version of pl_true. Argument clause represents the set of args of an Or clause. This is used inside dpll_int_repr, it is not meant to be used directly. >>> from sympy.logic.algorithms.dpll import pl_true_int_repr >>> pl_true_int_repr({1, 2}, {1: False}) >>> pl_true_int_repr({1, 2}, {1: False, 2: False}) False FrNT)get)clauser)rlitprrrr4s   r4csvg}|D]4}|jtkr||q|jD]}|kr,|tfdd|jDn |kr2nq||q|S)a Returns an equivalent set of clauses If a set of clauses contains the unit clause l, the other clauses are simplified by the application of the two following rules: 1. every clause containing l is removed 2. in every clause that contains ~l this literal is deleted Arguments are expected to be in CNF. >>> from sympy.abc import A, B, D >>> from sympy.logic.algorithms.dpll import unit_propagate >>> unit_propagate([A | B, D | ~B, B], B) [D, B] csg|] }|kr|qSrr).0xsymbolrr sz"unit_propagate..)funcrr$args)rr<rr-argrr;rr"s     r"cs hfdd|DS)z Same as unit_propagate, but arguments are expected to be in integer representation >>> from sympy.logic.algorithms.dpll import unit_propagate_int_repr >>> unit_propagate_int_repr([{1, 2}, {3, -2}, {2}], 2) [{3}] csg|] }|vr|qSrr)r9r6negatedsrrr=sz+unit_propagate_int_repr..r)rrCrrArr2s r2cCs`|D]+}d\}}|D]}|s|t|vrd}|s"t|t|vr"d}q ||kr-||fSqdS)a# Find a symbol and its value if it appears only as a positive literal (or only as a negative) in clauses. >>> from sympy.abc import A, B, D >>> from sympy.logic.algorithms.dpll import find_pure_symbol >>> find_pure_symbol([A, B, D], [A|~B,~B|~D,D|A]) (A, True) )FFTNN)rr)rr,sym found_pos found_negr-rrrr#s  r#cCsptj|}||}|dd|D}|D] }| |vr$|dfSq|D]}| |vr5| dfSq'dS)a Same as find_pure_symbol, but arguments are expected to be in integer representation >>> from sympy.logic.algorithms.dpll import find_pure_symbol_int_repr >>> find_pure_symbol_int_repr({1,2,3}, ... [{1, -2}, {-2, -3}, {3, 1}]) (1, True) cSsg|]}| qSrr)r9rCrrrr=z-find_pure_symbol_int_repr..TFrD)runion intersection)rr, all_symbolsrFrGr8rrrr3s    r3cCs^|D]*}d}t|D]}t|}||vr!|d7}|t|t }}q |dkr,||fSqdS)a A unit clause has only 1 variable that is not bound in the model. >>> from sympy.abc import A, B, D >>> from sympy.logic.algorithms.dpll import find_unit_clause >>> find_unit_clause([A | B | D, B | ~D, A | ~B], {A:True}) (B, False) rrrD)rr rr)rr)r6num_not_in_modelliteralrEr*r+rrrr s   r cCsbt|dd|DB}|D]!}||}t|dkr.|}|dkr(| dfS|dfSq dS)a Same as find_unit_clause, but arguments are expected to be in integer representation. >>> from sympy.logic.algorithms.dpll import find_unit_clause_int_repr >>> find_unit_clause_int_repr([{1, 2, 3}, ... {2, -3}, {1, -2}], {1: True}) (2, False) cSsh|]}| qSrr)r9rErrr +rHz,find_unit_clause_int_repr..rrFTrD)rrr%)rr)boundr6unboundr8rrrr1 s   r1N)__doc__sympy.core.sortingrsympy.logic.boolalgrrrrrrr sympy.assumptions.cnfr sympy.logic.inferencer r rr'rr4r"r2r#r3r r1rrrrs $ 1 0!