U Zʹj-@sdZddlmZddlmZddlmZmZddlm Z m Z ddl m Z m Z ddlmZddlmZdd lmZdd lmZmZdd lmZd e d efd dZddZdddZddZdddZd efddZdS)zJ Module to evaluate the proposition with assumptions using SAT algorithm. )S)Symbol) NumberKind UndefinedKind)get_all_known_matrix_factsget_all_known_number_facts)global_assumptionsAppliedPredicate)class_fact_registry)oo) satisfiable)CNF EncodedCNF) MatrixKindTc Csjt|}t|}t|}t}|r4||}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 Z from_propextendget_all_relevant_facts add_from_cnfcheck_satisfiability) proposition assumptionscontextrrpropsZ_propsZ context_cnfsatrW/var/www/html/bwave/python/venv/lib/python3.8/site-packages/sympy/assumptions/satask.pysatasks2      rcCsl|}|}||||t|}t|}|r@|r@dS|rL|sLdS|sX|rXdS|sh|shtddS)NTFzInconsistent assumptions)copyrr ValueError)propZ_propZfactbaseZsat_trueZ sat_falseZ can_be_trueZ can_be_falserrrrUs  rNc st||}t}|r&||O}|r6||O}|tjtjh}d}|tkrt}|D]"}t|}|@tkr^||O}q^|}|OqJ|fdd|DO}t} |D](} t| tr| 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).0lZreq_keysrr sz#extract_predargs..) r!all_predicatesr"rtruefalse isinstancer argumentsadd) rrrkeysZlkeysZtmp_keystmpr$Zsymsexprskeyrr%rextract_predargsms0       r1cCs8t|tr.t}|D]}|t|O}q|S|tS)z Find every :obj:`~.Symbol` in *pred*. Parameters ========== pred : sympy.assumptions.cnf.CNF, or any Expr. )r*r r"r'r!Zatomsr)predsymbolsarrrr!s  r!cCsn|s t}t}|D]L}t|D]>}t|}||}|D]}t|tr@|t|jO}q@q q|||fS)a2 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 containing 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"r Zto_CNFZ_andr'r*r r+)r/relevant_factsZnewexprsexprZfactZnewfactr0rrrget_relevant_clsfactssF     r7csPd}t}t}|dkr$t|||}||O}t||\}}|d7}||krLqT|sqTq|r>> 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 rcss|]}|jttkVqdSN)kindrrr#r6rrr Rsz)get_all_relevant_facts..css"|]}|jtkp|jtkVqdSr9)r:rrr;rrrr<UscSs|dkr||S||SdS)Nrr)Zlitdeltarrrtranslate_literal[sz1get_all_relevant_facts..translate_literalcsfdd|DS)Ncs g|]}fdd|DqS)csh|]}|qSrr)r#ir=r>rrr&bszLget_all_relevant_facts..translate_data...r)r#Zclauser@rr bszBget_all_relevant_facts..translate_data..r)datar=)r>)r=rtranslate_dataasz.get_all_relevant_facts..translate_datacsg|] }|qSrr)r#r2)r6rrrAgsz*get_all_relevant_facts..)r r"r1r7anyZ add_clausesrrrZfrom_cnflenr3 enumeraterBdictlistzipranger)rrrrrr?r5Z all_exprsr/Zknown_facts_CNFZ kf_encodedrCrBr3Zn_litencodingctxr)r6r>rr sB4         r)NN)N)__doc__Zsympy.core.singletonrZsympy.core.symbolrZsympy.core.kindrrZsympy.assumptions.ask_generatedrrZsympy.assumptions.assumerr Zsympy.assumptions.sathandlersr Z sympy.corer Zsympy.logic.inferencer Zsympy.assumptions.cnfr rZsympy.matrices.kindrrrr1r!r7rrrrrs*       D 9 V