dhKc@sOdZddkZddkZddklZddklZeZdefdYZ dZ dZ d Z d efd YZ eed Zed ZdefdYZdefdYZdefdYZdefdYZdefdYZdefdYZdeefdYZeZeZeZeZdZdefdYZdefd YZd!efd"YZ d#efd$YZ!ed%Z"d&efd'YZ#d(e#fd)YZ$d*e$fd+YZ%d,e$fd-YZ&d.e&fd/YZ'd0e&fd1YZ(d2e'fd3YZ)d4e&fd5YZ*d6Z+d7e$fd8YZ,d9e,fd:YZ-d;e,fd<YZ.d=e.fd>YZ/d?e.fd@YZ0dAe$fdBYZ1dCe$fdDYZ2dEe2fdFYZ3dGe3fdHYZ4dIe3fdJYZ5dKe3fdLYZ6dMe3fdNYZ7dOe2fdPYZ8dQefdRYZ9dSefdTYZ:dUefdVYZ;dWe;fdXYZ<dYZ=dZZ>d[Z?d\Z@d]ZAeBd^jo e@ndS(_sW A version of first order predicate logic, built on top of the typed lambda calculus. iN(t defaultdict(tCountertTokenscBsZeZdZdZdZdddgZdddgZdddgZdddgZd Z d Z d Z d d d gZ dddgZ dddgZdddgZdddgZdddgZdddgZe eeeZeeZeee e e gZeeeeeee Zeeeee eeee eeeeegZRS(iiis\tsometexiststallt.t t(t)t,tnott-tandt&tort|timpliess->tiffs<->t=s!=(t__name__t __module__tOLD_NLTKtNLTKtPROVER9tLAMBDAtEXISTStALLtDOTtOPENtCLOSEtCOMMAtNOTtANDtORtIMPtIFFtEQtNEQtBINOPStQUANTStPUNCTtTOKENStSYMBOLS(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRs. cCs}dddddg}xat|titititititititititigD]}d|GHqfWdS(s Boolean operators tnegationt conjunctiont disjunctiont implicationt equivalences%-15s %sN(tzipRR RR!R"R#R$(tnamestpair((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyt boolean_ops>s   cCsMddg}x:t|titititigD]}d|GHq6WdS(s Equality predicates tequalityt inequalitys%-15s %sN(R1RR%RR&(R2R3((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pytequality_predsJs  cCs]dddg}xGt|titititititigD]}d|GHqFWdS(s Binding operators t existentialt universaltlambdas%-15s %sN(R1RRRRR(R2R3((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyt binding_opsSs  tVariablecBsPeZdZdZdZdZdZdZdZdZ RS(cCs+t|tptd|||_dS(s7 @param name: the name of the variable s%s is not a stringN(t isinstancetstrtAssertionErrortname(tselfR@((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyt__init___scCs t|to|i|ijS(N(R=R<R@(RAtother((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyt__eq__fscCs ||j S(N((RARC((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyt__neq__iscCs/tt|t|pt|i|iS(N(tcmpttypeR@(RARC((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyt__cmp__lscCs|i||S(N(tget(RAtbindings((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pytsubstitute_bindingsoscCs t|iS(N(thashR@(RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyt__hash__rscCs|iS(N(R@(RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyt__str__uscCsd|idS(Ns Variable('s')(R@(RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyt__repr__xs( RRRBRDRERHRKRMRNRO(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR<^s       cCs|tj oct|io d}qvt|io d}qvt|io d}qvtp tdnd}t|tt i }x;|tj o-||jo t|tt i }qW|S(s Return a new, unique variable. param pattern: C{Variable} that is being replaced. The new variable must be the same type. param term: a C{set} of C{Variable}s that should not be returned from this function. return: C{Variable} tztFte0s!Cannot generate a unique constant( tNonet is_indvarR@t is_funcvart is_eventvartFalseR?R<R>t_counterRI(tpatterntignoretprefixtv((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pytunique_variable|s    !cCsTttdti}|o-x*t|D]}|t|}q0Wn|S(sX Return a skolem function over the variables in univ_scope param univ_scope sF%s(tVariableExpressionR<RXRItlist(t univ_scopetskolemR\((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pytskolem_functions  tTypecBseZdZdZRS(cCs t|S(N(R>(RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyROscCstt|S(N(RLR>(RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRMs(RRRORM(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRcs t ComplexTypecBs>eZdZdZdZdZdZdZRS(cCsRt|tptd|t|tptd|||_||_dS(Ns%s is not a Type(R=RcR?tfirsttsecond(RAReRf((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRBs cCs3t|to#|i|ijo|i|ijS(N(R=RdReRf(RARC((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRDscCsKt|to-|ii|io|ii|iSn |tjSdS(N(R=RdRetmatchesRftANY_TYPE(RARC((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRgscCs|tjo|Sn{t|toQ|ii|i}|ii|i}|o|ot||SqdSn|tjo|SndSdS(N(RhR=RdRetresolveRfRS(RARCtfts((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRis  cCs3|tjottSnd|i|ifSdS(Ns<%s,%s>(RhR>ReRf(RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRNs cCs?|tjotiSn!d|ii|iifSdS(Ns (%s -> %s)(RhR>ReRf(RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR>s (RRRBRDRgRiRNR>(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRds      t BasicTypecBs#eZdZdZdZRS(cCs&t|tot|t|jS(N(R=RlR>(RARC((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRDscCs|tjp ||jS(N(Rh(RARC((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRgscCs |i|o|SndSdS(N(RgRS(RARC((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRis(RRRDRgRi(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRls  t EntityTypecBseZdZdZRS(cCsdS(Nte((RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRNscCsdS(NtIND((RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR>s(RRRNR>(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRms tTruthValueTypecBseZdZdZRS(cCsdS(Ntt((RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRNscCsdS(NtBOOL((RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR>s(RRRNR>(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRps t EventTypecBseZdZdZRS(cCsdS(NR\((RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRNscCsdS(NtEVENT((RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR>s(RRRNR>(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRss tAnyTypecBs\eZdZedZedZdZdZdZdZ dZ RS(cCsdS(N((RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRBscCs|S(((RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pytscCs|S(((RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRvscCst|tp |i|S(N(R=RuRD(RARC((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRDscCstS(N(tTrue(RARC((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRgscCs|S(N((RARC((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRiscCsdS(Nt?((RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRN scCsdS(NtANY((RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR> s( RRRBtpropertyReRfRDRgRiRNR>(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRus     c Cst|tpt|idd}|ddjo|ddjptd}xt|D]y\}}|djo|d7}qe|djo"|d8}|djptqe|djo|djoPqqeqeWtt|d|!t||dd!Snr|dttjotSnS|dttjotSn4|dtt jot Snt d |ddS( NRtitiR sUnexpected character: '%s'.( R=R>R?treplacet enumerateRdt parse_typet ENTITY_TYPEt TRUTH_TYPERhtParseException(t type_stringt paren_counttitchar((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRs0       t TypeExceptioncBseZdZRS(cCsti||dS(N(t ExceptionRB(RAtmsg((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRB3s(RRRB(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR2st"InconsistentTypeHierarchyExceptioncBseZedZRS(cCs9|od||f}n d|}ti||dS(NsLThe variable '%s' was found in multiple places with different types in '%s'.sDThe variable '%s' was found in multiple places with different types.(RRB(RAtvariablet expressionR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRB7s (RRRSRB(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR6stTypeResolutionExceptioncBseZdZRS(cCs$ti|d||i|fdS(Ns9The type of '%s', '%s', cannot be resolved with type '%s'(RRBRG(RARt other_type((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRBAs (RRRB(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR@stIllegalTypeExceptioncBseZdZRS(cCs*ti|d|ii|||fdS(Ns9Cannot set type of %s '%s' to '%s'; must match type '%s'.(RRBt __class__R(RARRt allowed_type((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRBGs  (RRRB(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRFscCsFx|D]}|i|}qWx|d D]}|i|q+W|S(s Ensure correct typing across a collection of C{Expression}s. @param expressions: a collection of expressions @param signature: C{dict} that maps variable names to types (or string representations of types) i(t typecheck(t expressionst signatureR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRNs tSubstituteBindingsIcBs eZdZdZdZRS(sT An interface for classes that can perform substitutions for variables. cCs tdS(s @return: The object that is obtained by replacing each variable bound by C{bindings} with its values. Aliases are already resolved. (maybe?) @rtype: (any) N(tNotImplementedError(RARJ((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRKcscCs tdS(sB @return: A list of all variables in this object. N(R(RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyt variablesls(RRt__doc__RKR(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR^s t ExpressioncBseZdZdZdZdZdZdZdZdZ dZ d Z d Z e d Zd Zd Ze dZdZee dZedZdZdZdZdZdZedZdZdZRS(s<This is the base abstract object for all logical expressionscGs0|i|}x|D]}||}qW|S(N(tapplyto(RARCt additionaltaccumta((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyt__call__vs cCs+t|tptd|t||S(Ns%s is not an Expression(R=RR?tApplicationExpression(RARC((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR|scCs t|S(N(tNegatedExpression(RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyt__neg__scCs| S(sYIf this is a negated expression, remove the negation. Otherwise add a negation.((RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pytnegatescCs+t|tptd|t||S(Ns%s is not an Expression(R=RR?t AndExpression(RARC((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyt__and__scCs+t|tptd|t||S(Ns%s is not an Expression(R=RR?t OrExpression(RARC((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyt__or__scCs+t|tptd|t||S(Ns%s is not an Expression(R=RR?t ImpExpression(RARC((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyt__gt__scCs+t|tptd|t||S(Ns%s is not an Expression(R=RR?t IffExpression(RARC((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyt__lt__scCs tdS(N(R(RARC((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRDscCs ||j S(N((RARC((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyREscCspt|tptd||tjoddkl}|}nt|i|i}|i|S(s Pass the expression (self <-> other) to the theorem prover. If the prover says it is valid, then the self and other are equal. @param other: an C{Expression} to check equality against @param prover: a C{nltk.inference.api.Prover} s%s is not an Expressioni(tProver9( R=RR?RStnltk.inferenceRRtsimplifytprove(RARCtproverRtbicond((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyt tp_equalss   cCstt|S(N(RLtrepr(RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRMscCs|}x|iD]}||jov||}t|tot|}n(t|tptd|fn|i|}|i||}qqW|iS(Ns@Can not substitute a non-expression value into an expression: %r( RR=R<R^Rt ValueErrorRKR~R(RARJtexprtvartval((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRKs   c Cstt}|opxm|iD][\}}tt|}t|to ||_nt||_||i |q Wn|i d|t g}|iD] \}}|||difq~S(s Infer and check types. Raise exceptions if necessary. @param signature: C{dict} that maps variable names to types (or string representations of types) @return: the signature, plus any additional type mappings Ri( RR_t iteritemsR^R<R=RcRGRtappendt _set_typetdict(RARtsigtkeyRtvarExt_[1]tvars((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRs   cCs tdS(s Find the type of the given variable as it is used in this expression. For example, finding the type of "P" in "P(x) & Q(x,y)" yields "" @param variable: C{Variable} N(R(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pytfindtypescCs tdS(s& Set the type of this expression to be the given type. Raise type exceptions where applicable. @param other_type: C{Type} to set @param signature: C{dict>} store all variable expressions with a given name N(R(RARR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRscspttptdttptdfd}ifd|tS(s% Replace every instance of 'variable' with 'expression' @param variable: C{Variable} The variable to replace @param expression: C{Expression} The expression with which to replace it @param replace_bound: C{boolean} Should bound variables be replaced? s%s is not a Variables%s is not an ExpressioncsSt|djoi|Sn,t|djoi||dSndS(Nii(tlenR(RR(RA(s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyt combinatorscs|iS((R~(Rn(RRt replace_bound(s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRvs(R=R<R?Rtvisittset(RARRRR((RRARRs$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR~s csfd|}xttt|D]`\}}t|iod|d}nd|d}|i||it|t}q4W|S(s&Rename auto-generated unique variablescs~t|toKtid|iptid|iot|gSqztgSn d}|i|tSdS(Ns^z\d+$s^e0\d+$cWstti|S((treducetoperatortor_(tparts((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRvs(R=R<tretmatchR@RR(RnR(Rj(s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRjs , se0%sisz%s( RtsortedR_RVR@R~tmake_VariableExpressionR<Rw(RAtresultRR\tnewVar((Rjs$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyt normalizes   cCs tdS(s Recursively visit sub expressions @param function: C{Function} to call on each sub expression @param combinator: C{Function} to combine the results of the function calls @return: result of combination N(R(RAtfunctionRtdefault((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRscCsd|ii|fS(Ns<%s %s>(RR(RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyROscCs |iS(N(R>(RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRNscCs|iddtS(s Return a set of all the variables that are available to be replaced. This includes free (non-bound) variables as well as predicates. @return: C{set} of C{Variable}s cSs*t|tot|gp |iS((R=R<RR(Rn((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRv'scWstti|S((RRR(R((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRv)s(RR(RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR!s cs"|ifddtS(s Return a set of all the free (non-bound) variables in self. Variables serving as predicates are not included. @param indvar_only: C{boolean} only return individual variables? @return: C{set} of C{Variable}s cs-t|tot|gp |iS((R=R<Rtfree(Rn(t indvar_only(s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRv2scWstti|S((RRR(R((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRv4s(RR(RAR((Rs$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR+scs(fd}id|tS(sD @return: beta-converted version of this expression csSt|djoi|Sn,t|djoi||dSndS(Nii(RR(RR(RA(s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR:scSs!t|to|p |iS((R=R<R(Rn((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRv@s(RR(RAR((RAs$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR6s cCs t|S(N(R^(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRCs( RRRRRRRRRRRRDRERSRRMRKRRRhRRWR~RRRORNRRwRRR(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRss4                    RcBseZdZdZdZedZdZeeZ e e dZ dZ dZdZeid Zd Zed d d ZRS(so This class is used to represent two related types of logical expressions. The first is a Predicate Expression, such as "P(x,y)". A predicate expression is comprised of a C{FunctionVariableExpression} or C{ConstantExpression} as the predicate and a list of Expressions as the arguments. The second is a an application of one expression to another, such as "(\x.dog(x))(fido)". The reason Predicate Expressions are treated as Application Expressions is that the Variable Expression predicate of the expression may be replaced with another Expression, such as a LambdaExpression, which would mean that the Predicate should be thought of as being applied to the arguments. The LogicParser will always curry arguments in a application expression. So, "\x y.see(x,y)(john,mary)" will be represented internally as "((\x y.(see(x))(y))(john))(mary)". This simplifies the internals since there will always be exactly one argument in an application. The str() method will usually print the curried forms of application expressions. The one exception is when the the application expression is really a predicate expression (ie, underlying function is an C{AbstractVariableExpression}). This means that the example from above will be returned as "(\x y.see(x,y)(john))(mary)". cCsRt|tptd|t|tptd|||_||_dS(s @param function: C{Expression}, for the function expression @param argument: C{Expression}, for the argument s%s is not an ExpressionN(R=RR?Rtargument(RARR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRBcs cCsb|ii}|ii}t|to |ii|i|iSn|i||SdS(N( RRRR=tLambdaExpressionttermR~RR(RARR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRms  cCsKt|ito|ii|Sn!|ii||ii|BSdS(s@see: Expression.free()N(R=RtAbstractVariableExpressionRR(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRuscCs/t|iito|iiiSntSdS(N(R=RRGRdRfRh(RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyt _get_type}scCst|tpt|djott}n|iit|y&|i it |ii ||WnOt j oC}t d|i |i i |i|ii |i i ifnXdS(s@see Expression._set_type()sqThe function '%s' is of type '%s' and cannot be applied to '%s' of type '%s'. Its argument must match type '%s'.N(R=RcR?RSRR_RRRhRRdRGRRRe(RARRRn((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRs &c Cst|tptd||i\}}t|tp|i}|ig}ng}|g|D]}||i|qk~}g}x]|D]U}|tjoB|o*x4|D]} |i | oPqqWq|i |qqWt |djot |dSntSdS(s@see Expression.findtype()s%s is not a VariableiiN( R=R<R?tuncurryRRRRRhRgRRR_( RARRtargsRtargtfoundtuniqueRjtu((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRs& 1  cCs|||i||iS(s@see: Expression.visit()(RR(RARRR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRscCs3t|to#|i|ijo|i|ijS(N(R=RRR(RARC((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRDsc Cs@|i\}}t|to7dig}|D]}||i|q3~}n|i}|ii|}|i|}t}t|toXt|i t o$t|i itp t }qq t|i t p t }q nt|t o t }n|ot i|t i}n|t i|t iS(NR (RR=RtjoinR>RRRWRRRRwtBooleanExpressionRRR( RAtsyntaxRRRRtarg_strt function_strtparenthesize_function((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR>s&7    cCsS|i}|ig}x1t|to |id|i|i}qW||fS(sp Uncurry this application expression return: A tuple (base-function, arg-list) i(RRR=Rtinsert(RARR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRs   cCs|idS(i(R(RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRvstdocsuncurried arg-list(RRRRBRRwRRRzRGRhRSRRRRDRRR>RR(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRGs        RcBseeZdZdZdZedZeedZ dZ dZ dZ e idZRS( sDThis class represents a variable to be used as a predicate or entitycCs+t|tptd|||_dS(s@ @param variable: C{Variable}, for the variable s%s is not a VariableN(R=R<R?R(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRBscCs|S(N((RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRscCs\t|tptd|t|tptd||i|jo|Sn|SdS(s@see: Expression.replace()s%s is not an Variables%s is not an ExpressionN(R=R<R?RR(RARRR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR~s cCst|tpt|djott}n|}xA||iiD]/}|ii |}|pt |qKqKW||iii |x!||iiD]}||_qWdS(s@see Expression._set_type()N( R=RcR?RSRR_RR@RGRiRR(RARRt resolutionR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRs cCsAt|tptd||i|jo |iSntSdS(s@see Expression.findtype()s%s is not a VariableN(R=R<R?RRGRh(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR s cCs|||iS(s@see: Expression.visit()(R(RARRR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRscCs t|to|i|ijS(sTAllow equality between instances of C{AbstractVariableExpression} subtypes.(R=RR(RARC((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRDscCs t|iS(N(R>R(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR>s(RRRRBRRWR~RhRSRRRRDRRR>(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRs      tIndividualVariableExpressioncBs/eZdZeedZedeZRS(sThis class represents variables that take the form of a single lowercase character (other than 'e') followed by zero or more digits.cCsut|tpt|djott}n|itpt||tn||i i i |dS(s@see Expression._set_type()N( R=RcR?RSRR_RgRRRR@R(RARR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR$s  cCstS((R(RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRv0s(RRRRhRSRRzRG(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR!s tFunctionVariableExpressioncBs eZdZeZedZRS(swThis class represents variables that take the form of a single uppercase character followed by zero or more digits.cCs&|pt|igSntSdS(s@see: Expression.free()N(RR(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR7s(RRRRhRGRwR(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR2stEventVariableExpressioncBseZdZeZRS(s{This class represents variables that take the form of a single lowercase 'e' character followed by zero or more digits.(RRRt EVENT_TYPERG(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR>stConstantExpressioncBs/eZdZeZeedZedZ RS(stThis class represents variables that do not take the form of a single character followed by zero or more digits.cCst|tpt|djott}n|tjo t}n-|}|itjo|i |i}nxA||i i D]/}|ii |}|pt |qqW||i i i |x!||i i D]}||_qWdS(s@see Expression._set_type()N(R=RcR?RSRR_RhRRGRiRR@RR(RARRRR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRHs"   cCs&|pt|igSntSdS(s@see: Expression.free()N(RR(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR`s( RRRRRGRhRSRRwR(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRCscCst|tptd|t|iot|SnGt|iot|Sn)t|iot |Sn t |SdS(s This is a factory method that instantiates and returns a subtype of C{AbstractVariableExpression} appropriate for the given variable. s%s is not a VariableN( R=R<R?RTR@RRURRVRR(R((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR^hstVariableBinderExpressioncBs\eZdZdZedZdZdZedZ dZ dZ dZ RS( sThis an abstract class for any Expression that binds a variable in an Expression. This includes LambdaExpressions and Quantified ExpressionscCsRt|tptd|t|tptd|||_||_dS(sq @param variable: C{Variable}, for the variable @param term: C{Expression}, for the term s%s is not a Variables%s is not an ExpressionN(R=R<R?RRR(RARR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRB{s cCst|tptd|t|tptd||i|joV|oGt|tptd||i|i|ii||t Sq|Sn[|i|i jo|i t d|i}n|i|i|ii|||SdS(s@see: Expression.replace()s%s is not a Variables%s is not an Expressions&%s is not a AbstractVariableExpressionRYN( R=R<R?RRRRRR~RwRt alpha_convertR](RARRR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR~s   cCsIt|tptd||i||ii|it|tS(sRename all occurrences of the variable introduced by this variable binder in the expression to @C{newvar}. @param newvar: C{Variable}, for the new variable s%s is not a Variable( R=R<R?RRR~RR^Rw(RAtnewvar((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRs   cCs|iit|igS(s@see: Expression.variables()(RRRR(RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRscCs |ii|t|igS(s@see: Expression.free()(RRRR(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRscCsJt|tptd|||ijotSn|ii|SdS(s@see Expression.findtype()s%s is not a VariableN(R=R<R?RRhRR(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRscCs|||i||iS(s@see: Expression.visit()(RR(RARRR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRscCst||ipt||ioY|i|ijo|i|ijSqt|i}|i|ii|i|jSntSdS(sDefines equality modulo alphabetic variance. If we are comparing \x.M and \y.N, then check equality of M and N[x/y].N(R=RRRR^R~RW(RARCtvarex((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRDs#( RRRRBRWR~RRRwRRRRD(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRxs     RcBs5eZedZeedZeidZ RS(cCs"t|ii|i|iiS((RdRRRRG(RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRvscCstt|tpt|djott}n|ii|i||i i |pt ||ndS(s@see Expression._set_type()N( R=RcR?RSRR_RRRfRGRiR(RARR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRs  cCs|ig}|i}|tijo8x5|i|ijo|i|i|i}q(Wnti|did|Dti||i |S(NRcssx|]}t|VqWdS(N(R>(t.0R\((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pys s( RRRRRRRRRR>(RARRR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR>s  ( RRRzRGRhRSRRRR>(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRs tQuantifiedExpressioncBs5eZedZeedZeidZ RS(cCstS((R(RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRvscCsqt|tpt|djott}n|itpt||tn|i i t|dS(s@see Expression._set_type()N( R=RcR?RSRR_RgRRRR(RARR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRs  cCs|ig}|i}|tijo8x5|i|ijo|i|i|i}q(Wn|i|ddid|Dti||i |S(NRcssx|]}t|VqWdS(N(R>(RR\((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pys s( RRRRRRt getQuantifierRRR>(RARRR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR>s  ( RRRzRGRhRSRRRR>(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRs tExistsExpressioncBseZeidZRS(cCs ti|S(N(RR(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRs(RRRRR(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRst AllExpressioncBseZeidZRS(cCs ti|S(N(RR(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRs(RRRRR(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRsRcBsbeZdZedZeedZdZdZ dZ dZ e i dZRS(cCs+t|tptd|||_dS(Ns%s is not an Expression(R=RR?R(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRBscCstS((R(RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRv scCsqt|tpt|djott}n|itpt||tn|i i t|dS(s@see Expression._set_type()N( R=RcR?RSRR_RgRRRR(RARR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRs  cCs.t|tptd||ii|S(Ns%s is not a Variable(R=R<R?RR(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRscCs|||iS(s@see: Expression.visit()(R(RARRR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRscCs|iS(s@see: Expression.negate()(R(RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR!scCs t|to|i|ijS(N(R=RR(RARC((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRD%scCs\|tijo-ti|ti|ii|tiSnti||ii|SdS(N(RRR RRR>R(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR>(s! (RRRBRzRGRhRSRRRRRDRRR>(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRs     tBinaryExpressioncBsJeZdZedZdZdZdZei dZ RS(cCsRt|tptd|t|tptd|||_||_dS(Ns%s is not an Expression(R=RR?ReRf(RAReRf((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRB1s cCstS((R(RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRv7scCst|tptd||ii|}|ii|}||jp |tjo|Sn|tjo|SntSdS(s@see Expression.findtype()s%s is not a VariableN(R=R<R?ReRRfRh(RARRjRk((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR9s cCs|||i||iS(s@see: Expression.visit()(ReRf(RARRR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyREscCsIt||ipt||io#|i|ijo|i|ijS(N(R=RReRf(RARC((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRDIscCsCti|ii|d|i|d|ii|tiS(NR(RRReR>tgetOpRfR(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR>Ns( RRRBRzRGRRRDRRR>(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR0s    RcBseZeedZRS(cCst|tpt|djott}n|itpt||tn|i i t||i i t|dS(s@see Expression._set_type()N( R=RcR?RSRR_RgRRReRRf(RARR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRTs (RRRhRSR(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRSsRcBseZdZeidZRS(s"This class represents conjunctionscCs ti|S(N(RR!(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRbs(RRRRRR(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR`sRcBseZdZeidZRS(s"This class represents disjunctionscCs ti|S(N(RR"(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRgs(RRRRRR(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyResRcBseZdZeidZRS(s"This class represents implicationscCs ti|S(N(RR#(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRls(RRRRRR(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRjsRcBseZdZeidZRS(s$This class represents biconditionalscCs ti|S(N(RR$(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRqs(RRRRRR(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRostEqualityExpressioncBs,eZdZeedZeidZRS(s:This class represents equality expressions like "(x = y)".cCst|tpt|djott}n|itpt||tn|i i t ||i i t |dS(s@see Expression._set_type()N( R=RcR?RSRR_RgRRReRRRf(RARR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRws cCs ti|S(N(RR%(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRs( RRRRhRSRRRR(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRus t LogicParsercBs(eZdZedZedZdZdZdZ dZ edZ dZ e d Zd Zd Zd Zd ZdZdZdZdZdZdZdZdZdZdZdZdZdZdZ dZ!dZ"dZ#RS(s$A lambda calculus expression parser.cCs?t|tptd|_g|_||_g|_dS(sj @param type_check: C{boolean} should type checking be performed? to their types. iN(R=tboolR?t _currentIndext_buffert type_checkt quote_chars(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRBs    cCsod|_|i||_|i}|idot|idn|io|i|n|S(s Parse the expression. @param data: C{str} for the input to be parsed @param signature: C{dict} that maps variable names to type strings @returns: a parsed Expression i( RtprocessRtparse_ExpressiontinRangetUnexpectedTokenExceptionttokenRR(RAtdataRR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pytparses   c Cs}g}t|i}d}x@|o8|i|\}}|o||7}q!n|}|d}d}xT||joF||7}||}t|t|jo|t|}qnPqnWti|jo?|o|i|d}n|i||t|}q!|ddjo"|o|i|d}qRn||d7}|d}q!W|o|i|n|S(sSplit the data into tokensR{is i(t StringTrietget_all_symbolstprocess_quoted_tokenRtLEAFR( RARtoutt tokenTrieRt quoted_tokentsttctsymbol((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRs@         c Cspd}|d}d}xI|iD]>\}}}}||jo|o||7}nd}x|||jo|||jo\|o|||7}n|d7}t||jotd|n|||7}n|||7}|d7}t||jotd|q]q]W|o|||7}n|d7}|ptdnPq q W|||fS(NR{iis:End of input reached. Escape character [%s] found at end.s%End of input reached. Expected: [%s]sEmpty quoted token found(RRR( RARRRRtstarttendtescapet incl_quotes((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR s<       cCstiS(s#This method exists to be overridden(RR+(RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR scCs|i|t|ijS(s6Return TRUE if the given location is within the buffer(RRR(RAtlocation((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRscCsoyL|djo#|i|i}|id7_n|i|i|}|SWntj otdnXdS(sGet the next waiting token. If a location is given, then return the token at currentIndex+location without advancing currentIndex; setting it gives lookahead/lookback capability.isMore tokens expected.N(RSRRt IndexErrorR(RARttok((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRs cCs |tijS(N(RR*(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyt isvariablescCs_|i}|i|}|pt|n|o"|i|}|i|}n|S(sAParse the next complete expression from the stream and return it.(RthandleRtattempt_ApplicationExpressiontattempt_BooleanExpression(RAtallow_adjunctsRR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRs cCs|i|o|i|Sn|tijo|iSnd|tijo|i|SnC|tijo|i|Sn"|ti jo|i |SndS(shThis method is intended to be overridden for logics that use different operators or expressionsN( Rthandle_variableRR thandle_negationRt handle_lambdaR(t handle_quantRt handle_open(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR&scCs|i|itS(N(tmake_NegatedExpressionRRW(RA((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR8scCs t|S(N(R(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR#;scCs|i|}|ido|idtijot|totd|n|i|i||i }x@|idti jo&|i|i||i }qW|i |iti n|i |S(NisW'%s' is an illegal predicate name. Individual variables may not be used as predicates.(RRRRRR=RRtmake_ApplicationExpressionRRt assertTokenRtattempt_EqualityExpression(RARR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR>s)    cCs4ttt|totd|ndS(NsC'%s' is an illegal variable name. Constants may not be abstracted.(R=R^R<RR(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pytensure_abstractableUscCs|i|idt|ig}xM|i|ido3|i|id|it|iq.W|i|iti|it }x$|o|i |i |}qW|S(Ni( R'RR<RRR%RRRRWtmake_LambdaExpressiontpop(RARRR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR Zs cCs|i|}|ig}x1|i|ido|i|iq!W|i|iti|it}xf|o^|i }|i |}t |t ot d|n|i|t||}q}W|S(NisN'%s' is an illegal variable name. Constant expressions may not be quantified.(t get_QuantifiedExpression_factoryRRRR%RRRRWR)RR=RRtmake_QuanifiedExpressionR<(RARtfactoryRRRR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR!is   cCsG|tijotSn,|tijotSn|i|tidS(s\This method serves as a hook for other logic parsers that have different quantifiersN(RRRRRR%R((RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR*~s cCs |||S(N((RAR,RR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR+scCs)|i}|i|iti|S(N(RR%RRR(RARR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR"s cCs|ido=|idtijo$|i|i||iSnW|idoF|idtijo-|i|i|i||iSn|S(sAttempt to make an equality expression. If the next token is an equality operator, then an EqualityExpression will be returned. Otherwise, the parameter will be returned.i(RRRR%tmake_EqualityExpressionRR&R#(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR&s)  )  cCs t||S(slThis method serves as a hook for other logic parsers that have different equality expression classes(R(RAReRf((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR-scCs^|idoJ|i|id}|o'|i|i|||iSqZn|S(sAttempt to make a boolean expression. If the next token is a boolean operator, then a BooleanExpression will be returned. Otherwise, the parameter will be returned.i(Rtget_BooleanExpression_factoryRtmake_BooleanExpressionR(RARR,((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRs  !cCsh|tijotSnM|tijotSn5|tijotSn|tijotSndSdS(sbThis method serves as a hook for other logic parsers that have different boolean operatorsN( RR!RR"RR#RR$RRS(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR.scCs |||S(N((RAR,ReRf((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR/scCs|ido|idtijot|t o/t|t otdt|dn|i|i ||i }x@|idti jo&|i|i ||i }qW|i |iti |i|Sn|SdS(sAttempt to make an application expression. The next tokens are a list of arguments in parens, then the argument expression is a function being applied to the arguments. Otherwise, return the argument expression.isThe function 'sV is not a Lambda Expression or an Application Expression, so it may not take argumentsN(RRRRR=RRRR>R$RRR%RR(RARR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRs)    cCs t||S(N(R(RARR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR$scCstt|S(N(R^R<(RAR@((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRscCs t||S(N(R(RARR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR(scCsXt|to$||jot||qTn!||jot||ndS(N(R=R_R(RARtexpected((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyR%s   cCsG|idod|id}nd}d|iid|dS(Nis Next token: sNo more tokensR|s: R}(RRRR(RAR((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyROs($RRRRWRBRSRRR R RRRRwRRRR#RR'R R!R*R+R"R&R-RR.R/RR$RR(R%RO(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRs>   ( !                       RcBs#eZdZedZdZRS(scCs=ti|t|o"x|D]}|i|qWndS(N(RRBRR(RAtstringststring((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRBs cCs;t|o||di|dnd|tiR?RR(R((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRTscCs.t|tptd|tid|S(s A function variable must be a single uppercase character followed by zero or more digits. @param expr: C{str} @return: C{boolean} True if expr is of the correct form s%s is not a strings ^[A-Z]\d*$(R=R>R?RR(R((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRUscCs.t|tptd|tid|S(s An event variable must be a single lowercase 'e' character followed by zero or more digits. @param expr: C{str} @return: C{boolean} True if expr is of the correct form s%s is not a strings^e\d*$(R=R>R?RR(R((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyRV)scCs5ti}dddGH|dGH|dGH|dGH|dGH|dGH|d GH|d GH|d GH|d GH|d GH|dGH|dGHdddGH|diGH|diGH|diGH|diGHdddGH|d}|GH|itd}|GH||jGHdS(NRis Test parsertjohnsman(x)s-man(x)s(man(x) & tall(x) & walks(x))sexists x.(man(x) & tall(x))s \x.man(x)s\x.man(x)(john)s\x y.sees(x,y)s\x y.sees(x,y)(a,b)s(\x.exists y.walks(x,y))(x)sexists x.(x = y)s\P Q.exists x.(P(x) & Q(x))s Test simplifys\x.\y.sees(x,y)(john)(mary)s\x.\y.sees(x,y)(john, mary)s,all x.(man(x) & (\x.exists y.walks(x,y))(x))s5(\P.\Q.exists x.(P(x) & Q(x)))(\x.dog(x))(\x.bark(x))s4Test alpha conversion and binder expression equalitys exists x.P(x)RPs====================s====================s====================s====================s====================s====================(RRRRR<(tpte1te2((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pytdemo5s2                 cCs |idt|iGHdS(Ns : (R>RG(tex((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pyt printtypeRst__main__(CRRRt nltk.compatRtnltk.internalsRRXtobjectRR4R7R;R<RSR]RbRcRdRlRmRpRsRuRRRRhRRRRRRRRRRRRRRRR^RRRRRRRRRRRRRRRRRRTRURVR8R:R(((s$/p/zhu/06/nlp/nltk/nltk/sem/logic.pys s~   (  .        < % R)# n