o *ήc,@sdZddlmZddlmZddlmZddlmZm Z ddl m Z ddl m Z ddlmZdd lmZmZd ed e fd d Zd dZdddZddZdddZd e fddZdS)zJ Module to evaluate the proposition with assumptions using SAT algorithm. )S)Symbol)get_all_known_facts)global_assumptionsAppliedPredicate)class_fact_registry)oo) satisfiable)CNF EncodedCNFTc Csjt|}t|}t|}t}|r||}t|||||d}|||r/||t|||S)a Function to evaluate the proposition with assumptions using SAT algorithm. This function extracts every fact relevant to the expressions composing proposition and assumptions. For example, if a predicate containing ``Abs(x)`` is proposed, then ``Q.zero(Abs(x)) | Q.positive(Abs(x))`` will be found and passed to SAT solver because ``Q.nonnegative`` is registered as a fact for ``Abs``. Proposition is evaluated to ``True`` or ``False`` if the truth value can be determined. If not, ``None`` is returned. Parameters ========== proposition : Any boolean expression. Proposition which will be evaluated to boolean value. assumptions : Any boolean expression, optional. Local assumptions to evaluate the *proposition*. context : AssumptionsContext, optional. Default assumptions to evaluate the *proposition*. By default, this is ``sympy.assumptions.global_assumptions`` variable. use_known_facts : bool, optional. If ``True``, facts from ``sympy.assumptions.ask_generated`` module are passed to SAT solver as well. iterations : int, optional. Number of times that relevant facts are recursively extracted. Default is infinite times until no new fact is found. Returns ======= ``True``, ``False``, or ``None`` Examples ======== >>> from sympy import Abs, Q >>> from sympy.assumptions.satask import satask >>> from sympy.abc import x >>> satask(Q.zero(Abs(x)), Q.zero(x)) True )use_known_facts iterations)r from_propextendget_all_relevant_facts add_from_cnfcheck_satisfiability) proposition assumptionscontextr r props_props context_cnfsatr?/tmp/pip-target-vg8gfxp4/lib/python/sympy/assumptions/satask.pysatasks 2      rcCsp|}|}||||t|}t|}|r |r dS|r&|s&dS|s,|r,dS|s4|s6tddSdS)NTFzInconsistent assumptions)copyrr ValueError)prop_propfactbasesat_true sat_false can_be_true can_be_falserrrrSs  rNc st||}t}|r||O}|r||O}|tjtjh}d}|tkrNt}|D]}t|}|@tkr@||O}q/|}|O|tks*|fdd|DO}t} |D]} t| trm| t| jO} q^| | q^| S)a Extract every expression in the argument of predicates from *proposition*, *assumptions* and *context*. Parameters ========== proposition : sympy.assumptions.cnf.CNF assumptions : sympy.assumptions.cnf.CNF, optional. context : sympy.assumptions.cnf.CNF, optional. CNF generated from assumptions context. Examples ======== >>> from sympy import Q, Abs >>> from sympy.assumptions.cnf import CNF >>> from sympy.assumptions.satask import extract_predargs >>> from sympy.abc import x, y >>> props = CNF.from_prop(Q.zero(Abs(x*y))) >>> assump = CNF.from_prop(Q.zero(x) & Q.zero(y)) >>> extract_predargs(props, assump) {x, y, Abs(x*y)} Ncs"h|] }t|@tkr|qSr) find_symbolsset).0lreq_keysrr s"z#extract_predargs..) r&all_predicatesr'rtruefalse isinstancer argumentsadd) rrrkeyslkeystmp_keystmpr)symsexprskeyrr*rextract_predargsks4      r:cCs8t|trt}|D]}|t|O}q |S|tS)z Find every :obj:`~.Symbol` in *pred*. Parameters ========== pred : sympy.assumptions.cnf.CNF, or any Expr. )r0r r'r-r&atomsr)predsymbolsarrrr&s   r&cCsn|st}t}|D]&}t|D]}t|}||}|D]}t|tr.|t|jO}q qq |||fS)a1 Extract relevant facts from the items in *exprs*. Facts are defined in ``assumptions.sathandlers`` module. This function is recursively called by ``get_all_relevant_facts()``. Parameters ========== exprs : set Expressions whose relevant facts are searched. relevant_facts : sympy.assumptions.cnf.CNF, optional. Pre-discovered relevant facts. Returns ======= exprs : set Candidates for next relevant fact searching. relevant_facts : sympy.assumptions.cnf.CNF Updated relevant facts. Examples ======== Here, we will see how facts relevant to ``Abs(x*y)`` are recursively extracted. On the first run, set containing the expression is passed without pre-discovered relevant facts. The result is a set containig candidates for next run, and ``CNF()`` instance containing facts which are relevant to ``Abs`` and its argument. >>> from sympy import Abs >>> from sympy.assumptions.satask import get_relevant_clsfacts >>> from sympy.abc import x, y >>> exprs = {Abs(x*y)} >>> exprs, facts = get_relevant_clsfacts(exprs) >>> exprs {x*y} >>> facts.clauses #doctest: +SKIP {frozenset({Literal(Q.odd(Abs(x*y)), False), Literal(Q.odd(x*y), True)}), frozenset({Literal(Q.zero(Abs(x*y)), False), Literal(Q.zero(x*y), True)}), frozenset({Literal(Q.even(Abs(x*y)), False), Literal(Q.even(x*y), True)}), frozenset({Literal(Q.zero(Abs(x*y)), True), Literal(Q.zero(x*y), False)}), frozenset({Literal(Q.even(Abs(x*y)), False), Literal(Q.odd(Abs(x*y)), False), Literal(Q.odd(x*y), True)}), frozenset({Literal(Q.even(Abs(x*y)), False), Literal(Q.even(x*y), True), Literal(Q.odd(Abs(x*y)), False)}), frozenset({Literal(Q.positive(Abs(x*y)), False), Literal(Q.zero(Abs(x*y)), False)})} We pass the first run's results to the second run, and get the expressions for next run and updated facts. >>> exprs, facts = get_relevant_clsfacts(exprs, relevant_facts=facts) >>> exprs {x, y} On final run, no more candidate is returned thus we know that all relevant facts are successfully retrieved. >>> exprs, facts = get_relevant_clsfacts(exprs, relevant_facts=facts) >>> exprs set() ) r r'rto_CNF_andr-r0rr1)r8relevant_factsnewexprsexprfactnewfactr9rrrget_relevant_clsfactssF      rFcs d}t}t} |dkrt|||}||O}t||\}}|d7}||kr'n|s*nq |rt} | tt} | | ddfdd} g} g} t| j }t |D]\}| fdd | j D7} | | | j ||7} qUt t t| tdt| d}t| |}nt}|||S) al Extract all relevant facts from *proposition* and *assumptions*. This function extracts the facts by recursively calling ``get_relevant_clsfacts()``. Extracted facts are converted to ``EncodedCNF`` and returned. Parameters ========== proposition : sympy.assumptions.cnf.CNF CNF generated from proposition expression. assumptions : sympy.assumptions.cnf.CNF CNF generated from assumption expression. context : sympy.assumptions.cnf.CNF CNF generated from assumptions context. use_known_facts : bool, optional. If ``True``, facts from ``sympy.assumptions.ask_generated`` module are encoded as well. iterations : int, optional. Number of times that relevant facts are recursively extracted. Default is infinite times until no new fact is found. Returns ======= sympy.assumptions.cnf.EncodedCNF Examples ======== >>> from sympy import Q >>> from sympy.assumptions.cnf import CNF >>> from sympy.assumptions.satask import get_all_relevant_facts >>> from sympy.abc import x, y >>> props = CNF.from_prop(Q.nonzero(x*y)) >>> assump = CNF.from_prop(Q.nonzero(x)) >>> context = CNF.from_prop(Q.nonzero(y)) >>> get_all_relevant_facts(props, assump, context) #doctest: +SKIP rTcSs|dkr||S||S)Nrr)litdeltarrrtranslate_literalSsz1get_all_relevant_facts..translate_literalcsfdd|DS)Ncs g|] }fdd|DqS)csh|]}|qSrr)r(irIrJrrr,ZszLget_all_relevant_facts..translate_data...r)r(clauserLrr Zs zBget_all_relevant_facts..translate_data..r)datarI)rJ)rIrtranslate_dataYsz.get_all_relevant_facts..translate_datacsg|]}|qSrr)r(r<)rCrrrN_sz*get_all_relevant_facts..)r r'r:rF add_clausesrr from_cnflenr= enumeraterOdictlistzipranger)rrrr r rKrA all_exprsr8known_facts_CNF kf_encodedrPrOr=n_litencodingctxr)rCrJrr s@4         r)NN)N)__doc__sympy.core.singletonrsympy.core.symbolrsympy.assumptions.ask_generatedrsympy.assumptions.assumerrsympy.assumptions.sathandlersr sympy.corersympy.logic.inferencer sympy.assumptions.cnfr r rrr:r&rFrrrrrs$       D 9 V