jqdZddlZddlZddlmZddlmZddlmZm Z ddl m Z ddl m Z mZmZmZmZmZmZmZmZmZmZGdd eZGd d e ZGd d eZGddeZGddeZ d(dZ d(dZ d)dZ!dZ"dZ#dZ$dZ%GddZ&d(dZ'dZ(GddeZ)Gdd eZ*Gd!d"Z+d#Z,d$Z-d%Z.d&Z/e0d'kr e/dSdS)*z; Module for a resolution-based First Order theorem prover. N) defaultdict)reduce)BaseProverCommandProver) skolemize) AndExpressionApplicationExpressionEqualityExpression ExpressionIndividualVariableExpressionNegatedExpression OrExpressionVariableVariableExpression is_indvarunique_variableceZdZdS)ProverParseErrorN)__name__ __module__ __qualname__|/home/lighthouse/badge-speaker-benchmark/.benchmark-venv-community/lib/python3.11/site-packages/nltk/inference/resolution.pyrr#sDrrc(eZdZdZdZdZddZdZdS) ResolutionProverANSWERT<NFc|sg}d} g}|r#|t| |D]$}|t|%||\}}|r'tt|nY#t $rL}|jr't| drd}g}n|rt|n|Yd}~nd}~wwxYw||fS)z :param goal: Input expression to prove :type goal: sem.Expression :param assumptions: Input expressions to use as assumptions in the proof :type assumptions: list(sem.Expression) Nz maximum recursion depth exceededF) extendclausify_attempt_proofprintResolutionProverCommand_decorate_clauses RuntimeError _assume_falsestr startswith)selfgoal assumptionsverboseresultclausesaes r_provezResolutionProver._prove3s. K G 0x///  , ,x{{++++"11'::OFG J-??HHIII   ! c!ff&7&72'' !HHHHG   sBB C."AC))C.cNtt}|jrtj|jznd}d}|t |krT||s ||r||ddz}n|dz}|t |kr||kr|r||s|tj|krdgfS||| |||||}n#t$rdgfcYSwxYw|rA|D];}|dz|dzf|_ ||t |sd|fcS##dl22 #g,,1:**,,# 8a q(AAAA#g,,&&Avv!vGAJ,C,C,E,Ev#/DN4D4Dx4O4O%*2;.a***/)0)9)9'!*x)9)X)XJJ,///%*2;.../&"-7;; 67!eQU^ 2 'y 9 9 9'*9~~!;,0'?$:$:$:!; "A!FA7#g,,&&8 FAK#g,,Lws7#DD,+D,)NNF)rrr ANSWER_KEYr'r8r2r"rrrrr'sIJMG!!!!B2 2 2 2 2 rrc<eZdZddZddZddZedZdS) r$Nc|t|tsJnt}tj||||d|_dS)z :param goal: Input expression to prove :type goal: sem.Expression :param assumptions: Input expressions to use as assumptions in the proof. :type assumptions: list(sem.Expression) N) isinstancerr__init___clauses)r*r+r,provers rrJz ResolutionProverCommand.__init__sQ  f&677 7 7 7 7%''F"4{CCC rFc|jn|j|||\|_}||_t ||_|jS)zh Perform the actual proof. Store the result to prevent unnecessary re-proving. ) _result_proverr2r+r,rKr$r%_proof)r*r-r/s rprovezResolutionProverCommand.provesk < $(L$7$7 T--//%% !DL'$DM1CCGLLDK|rc||t}tttj}|jD]}t|dkrlt|dtrQ|dj |kr@t|dj ts | |dj |S)Nr5r)rQsetrrrrFrKr;rIr functionargumentr add)r*r-answers answer_exclauses r find_answersz$ResolutionProverCommand.find_answerss 7%%&x0@0K'L'LMM m 0 0FF q  vay*?@@!1I&)33"6!9#57STT4 F1I.///rc ^d}|s|Std|D}ttt|}tt|D]}d}d}||rd}||jrt||j}d|tt||z dzz|z}d|tt|dzz zt|dzz}|d|d||d|d|d z }|S) z, Decorate the proof output. c3NK|] }tt|V!dSN)r;r().0rYs r z.s0DD&SV--DDDDDDrA Tautology r5[z]  )maxr;r(ranger<r@)r/outmax_clause_len max_seq_lenrBparentstautseqs rr%z)ResolutionProverCommand._decorate_clausessH  JDDGDDDDD#c'll++,, s7||$$ > >AGDqz&&(( #"qz" 3gaj122^c#gaj//.B.BBQFG'QGs3q1u::67#a!e**DC =s==gaj==7==T=== =CC r)NNN)F)rrrrJrQrZ staticmethodr%rrrr$r$sk        \rr$c`eZdZdZ ddZdZdZdZdZd Z d Z d Z d Z d Z dZdZdS)ClausecXt||d|_d|_dSr^)r7rJ _is_tautologyr@)r*datas rrJzClause.__init__s) dD!!!! rNFc |t}|ggf}|ggf}t|trt|}t |||||t ||}g}t |D]R\} } | |vrIt |D]9\} } | | kr.| |vr*| | r|| :Sg} tt|D]!} | |vr| || "| S)a Attempt to unify this Clause with the other, returning a list of resulting, unified, Clauses. :param other: ``Clause`` with which to unify :param bindings: ``BindingDict`` containing bindings that should be used during the unification :param used: tuple of two lists of atoms. The first lists the atoms from 'self' that were successfully unified with atoms from 'other'. The second lists the atoms from 'other' that were successfully unified with atoms from 'self'. :param skipped: tuple of two ``Clause`` objects. The first is a list of all the atoms from the 'self' Clause that have not been unified with anything on the path. The second is same thing for the 'other' Clause. :param debug: bool indicating whether debug statements should print :return: list containing all the resulting ``Clause`` objects that could be obtained by unification ) BindingDictrIbool DebugObject_iterate_first_complete_unify_path enumeratesubsumesr=rgr;)r*otherbindingsusedskippeddebugr6rDsubsumedrBc1rCc2r.s rr>z Clause.unifys6*  "}}H <8D ?2hG eT " " '&&E# %42Fx  z** + +EAr  &z22++EArAvv!8"3"3 B"3 ***s:'' - -A   jm,,, rc|D] }||vrdS dS)z Return True iff every term in 'self' is a term in 'other'. :param other: ``Clause`` :return: bool FTr)r*r|r0s r isSubsetOfzClause.isSubsetOfs-  A~~uutrc Zg}|D]H}t|tr||j2|| It |}t }ggf}ggf}t d}tt|||||t|dkS)z Return True iff 'self' subsumes 'other', this is, if there is a substitution such that every term in 'self' can be unified with a term in 'other'. :param other: ``Clause`` :return: bool Fr) rIr r=termrprurwr;rx_subsumes_finalize) r*r| negatedotheratomnegatedotherClauser}r~rrs rr{zClause.subsumess  + +D$ 122 +##DI....##TE****#L11==Bxr(E"" &&    rcTtt|||Sr^)rpr7 __getslice__)r*startends rrzClause.__getslice__9s"d''eS99:::rc:tfd|DS)Ncg|]}|v| Srr)r_r0r|s r z"Clause.__sub__..=s999Q!5..q...rrpr*r|s `r__sub__zClause.__sub__<s&9999$999:::rcRtt||Sr^)rpr7__add__rs rrzClause.__add__?sdll4//000rc|j|jSt|D]\}}t|tst |dz }||krh||}t|t r|j|kr d|_dSn*t|t r||jkr d|_dS|dz}||khd|_dS)z Self is a tautology if it contains ground terms P and -P. The ground term, P, must be an exact match, ie, not using unification. Nr5TF)rrrzrIr r;r r)r*rBr0rCbs rr<zClause.is_tautologyBs   )% %dOO  DAqa!344 IIM!eeQA!!%677(6Q;;15D.#'44'$A'899(;;15D.#'44FA!ee#urcJttjd|DS)Nc3hK|]-}||zV.dSr^)free constants)r_rs rr`zClause.free..[s9$W$W$diikkDNN4D4D&D$W$W$W$W$W$Wr)roperatoror_r*s rrz Clause.freeZs$hl$W$WRV$W$W$WXXXrc>tfd|DS)z Replace every instance of variable with expression across every atom in the clause :param variable: ``Variable`` :param expression: ``Expression`` c<g|]}|Sr)replace)r_r expressionvariables rrz"Clause.replace..es'KKKdt||Hj99KKKrr)r*rrs ``rrzClause.replace]s,KKKKKdKKKLLLrc:tfd|DS)z Replace every binding :param bindings: A list of tuples mapping Variable Expressions to the Expressions to which they are bound. :return: ``Clause`` c:g|]}|Sr)substitute_bindings)r_rr}s rrz.Clause.substitute_bindings..os'KKKdt//99KKKrr)r*r}s `rrzClause.substitute_bindingsgs(KKKKdKKKLLLrcLddd|DzdzS)N{, c3 K|] }d|zV dS)%sNr)r_items rr`z!Clause.__str__..rs&<rr{rrrr<rrrrrrrrrprps TX////b   $ $ $ L;;;;;;1110YYYMMMMMMCCCrrpceZdZdZdS)r?aRaised inside a single ``Clause.unify`` when its ``deadline`` passes. Unifying two clauses that share many same-predicate literals explores an exponential number of literal pairings inside one ``unify`` call, which the saturation loop's between-call ``TIMEOUT`` cannot interrupt. Checking the deadline inside the recursion (and aborting via this exception) makes the time bound effective (CWE-407/CWE-400). N)rrr__doc__rrrr?r?xsrr?c |tj|krt|d|d|d|t |rt |s|||||||St |||||||dz|}|d|dgz|df} |t |dd|||| ||dz|z } t|d|d||\} } } |dd|dz| dz} |dd|dz| dz}|t | || | ggf||dz|z }n#t$rYnwxYw|S)zF This method facilitates movement through the terms of 'self' Nunify(,) r5r) r9r:r?liner;_iterate_secondrx _unify_termsBindingException)firstsecondr}r~rfinalize_methodrr6r. newskipped newbindingsnewusedunusednewfirst newseconds rrxrxs  0 08 ; ; JJ44444(44555 u::+S[[+ufhguMMM! 68T7OUQYPX   ajE!H:-wqz: . !""I      AI     +7a&)Xt,, (K& QRRy71:-q 9Hqrr WQZ/&);I nR    FF     D  sA8D>> E  E c h|tj|krt|d|d|d|t |rt |s|||||||S|d|d|dgzf}t ||dd|||||dz|} t |d|d||\} } } |dd|dz| dz} |dd|dz| dz}| t | || | ggf||dz|z } n#t$rYnwxYw| S)zG This method facilitates movement through the terms of 'other' Nrrrrr5)r9r:r?rr;rrr)rrr}r~rrrr6rr.rrrrrs rrrs  0 08 ; ; JJ44444(44555 u::&S[[&ufhguMMMaj'!*q {":;   122J     AI     +7a&)Xt,, (K& QRRy71:-q 9Hqrr WQZ/&);I oR    FF     D  s)A8D"" D/.D/clt|tsJt|tsJ|t}|ggf}t|trIt|tr4t |j||}|d|gz|d|gzf}ggf}nt|trHt|tr3t ||j|}|d|gz|d|gzf}ggf}nt|tr;t|jj |j fg}|d|gz|df}g|gf}nat|tr;t|jj |j fg}|d|d|gzf}|ggf}nt||f|||fS)a This method attempts to unify two terms. Two expressions are unifiable if there exists a substitution function S such that S(a) == S(-b). :param a: ``Expression`` :param b: ``Expression`` :param bindings: ``BindingDict`` a starting set of bindings with which the unification must be consistent :return: ``BindingDict`` A dictionary of the bindings required to unify :raise ``BindingException``: If the terms cannot be unified Nrr5) rIr rur r most_general_unificationrr rrrr)r0rr}r~rrrs rrrs a $ $$$$ a $ $$$$== |Bx!&'''Jq:O,P,P'.qvq(CC 7aS=$q'QC-0b A, - -'*Q@Q2R2R'.q!&(CC 7aS=$q'QC-0b A) * * '!AG$4ah#?"@AA 7aS=$q'*qc A) * *'!AG$4ah#?"@AA 7DGqcM*#r1v&&&  ''rc|ds|drRt|d|dz|z|z}|d|z||gS|dgS)Nrr5z -> New Clause: %sz -> End)rprr)rrr}r~rrrEs rryrys Aw$q'71: 2U:VCDD  (94555--h7788 : rcTt|dst|sdgSgS)NrT)r;)rrr}r~rrs rrr&s/ wqz??3u:: v  rc*g}tt|D]s}|D]G}t|jr1t t }|||}H||t|S)zC Skolemize, clausify, and standardize the variables apart. ) _clausifyrrrnamerrrr=)r clause_listrYrnewvars rr!r!2sKIj1122##KKMM 6 6D## 6+O,=,=>>f556"""" rct|tr)t|jt|jzSt|t rdt|j}t|j}t |dksJt |dksJ|d|dzgSt|trt|ggSt|trt|ggSt|trVt|j trt|ggSt|j trt|ggSt)z; :param expression: a skolemized expression in CNF r5r) rIrrrrrr;r rpr r rr)rrrs rrr@sd*m,,*)**Yz7H-I-III J - -***++:,--5zzQ6{{aa6!9$%% J 2 3 3* |$$%% J 5 6 6* |$$%% J 1 2 2* jo'< = = *J<(() )  ); < < *J<(() )   rc@eZdZd dZdZdZdZdZdZdZ d Z dS) ruNc6i|_|r |D] \}}|||< dSdS)z :param binding_list: list of (``AbstractVariableExpression``, ``AtomicExpression``) to initialize the dictionary Nd)r* binding_listvrs rrJzBindingDict.__init__YsE  $  1Q    rct|tsJt|tsJ ||}n#t$rd}YnwxYw|r||kr ||j|<dSt|t r[ ||j}n#t$rd}YnwxYwt|}|r||kr||j|j<dStd|ztd|z)a A binding is consistent with the dict if its variable is not already bound, OR if its variable is already bound to its argument. :param variable: ``Variable`` The variable to bind :param binding: ``Expression`` The atomic to which 'variable' should be bound :raise BindingException: If the variable cannot be bound in this dictionary Nz*Variable %s already bound to another value) rIrr KeyErrorrr rrr)r*rbindingexistingbinding2s r __setitem__zBindingDict.__setitem__csA(H-----':..... H~HH   HHH  7h..&DF8    != > >   01    *(33H x833+3w'(((&CxP#?8L s!9 AA5 B BBct|tsJ|j|}|r% |j|}n#t$r|cYSwxYw|#dSdS)zD Return the expression to which 'variable' is bound N)rIrrr)r*r intermediates r __getitem__zBindingDict.__getitem__s(H-----vh'  $ $#vl3  $ $ $#### $ $ $ $ $ $s 6 AAc||jvSr^r)r*rs r __contains__zBindingDict.__contains__stv~rc t}|jD]}|j|||<|jD]}|j|||<|S#t$r}td|d|d|d}~wwxYw)a :param other: ``BindingDict`` The dict with which to combine self :return: ``BindingDict`` A new dict containing all the elements of both parameters :raise BindingException: If the parameter dictionaries are not consistent with each other z3Attempting to add two contradicting BindingDicts: 'z' and ''N)rurr)r*r|combinedrr1s rrzBindingDict.__add__s "}}HV ( ("fQi W ) )#gaj O   ""15uuu>  sAA A,A''A,c*t|jSr^)r;rrs r__len__zBindingDict.__len__s46{{rcdfdtjD}d|zdzS)Nrc3<K|]}|dj|VdS): Nr)r_rr*s rr`z&BindingDict.__str__..s7PPQ00TVAY00PPPPPPrrr)rsortedrkeys)r*data_strs` rrzBindingDict.__str__sJ99PPPP&:O:OPPPPPX~##rc d|zSrrrs rrzBindingDict.__repr__rrr^) rrrrJrrrrrrrrrrruruXs%%%N $ $ $&$$$rruc|t}||kr|St|trt|||St|trt|||St|trLt|tr7t |j|j|t |j|j|zSt||f)ah Find the most general unification of the two given expressions :param a: ``Expression`` :param b: ``Expression`` :param bindings: ``BindingDict`` a starting set of bindings with which the unification must be consistent :return: a list of bindings :raise BindingException: if the Expressions cannot be unified ) rurIr _mgu_varr rrTrUr)r0rr}s rrrs==Avv A3 4 4G1h''' A3 4 4G1h''' A, - -G*Q@U2V2VG' J H  $QZX F FG G Aq6 " ""rc|j||zvrt||ft |j|fg|zSr^)rrrrru)varrr}s rrrsZ |z((:+?+?+A+AAAAZ0111S\:67888CCrceZdZdZdS)rct|tr t|d|zdSt||dS)Nz'%s' cannot be bound to '%s')rItuple ExceptionrJ)r*args rrJzBindingException.__init__sR c5 ! ! *   t%Cc%I J J J J J   tS ) ) ) ) )rNrrrrJrrrrrs#*****rrceZdZdZdS)UnificationExceptioncJt|d|d|ddS)Nrz' cannot unify with ')rrJ)r*r0rs rrJzUnificationException.__init__s24!AQ!A!AQ!A!A!ABBBBBrNrrrrrrs(CCCCCrrc"eZdZddZdZdZdS)rwTrc"||_||_dSr^)enabledindent)r*rrs rrJzDebugObject.__init__s  rc<t|j|j|zSr^)rwrr)r*rBs rrzDebugObject.__add__s4<q999rcL|jrtd|jz|zdSdS)Nz )rr#r)r*rs rrzDebugObject.lines6 < / &4;&- . . . . . / /rN)Tr)rrrrJrrrrrrwrwsF::://///rrwc Jtdtdtdtdtdtdtdtdtdtdtdtdtd td tjd }tjd }tjd }t|d|d|dt |||gtjd}tjd}tjd}t|d|d|dt |||gtjd}tjd}t|d|dt ||gdS)Nman(x)z(man(x) -> man(x))z(man(x) -> --man(x))z-(man(x) and -man(x))z(man(x) or -man(x))z(man(x) iff man(x))z-(man(x) iff -man(x))z all x.man(x)z--all x.some y.F(x,y) & some x.all y.(-F(x,y))zsome x.all y.sees(x,y)zall x.(man(x) -> mortal(x))z man(Socrates)zmortal(Socrates)rz |- rzall x.(man(x) -> walks(x))z man(John)zsome y.walks(y)z5some e1.some e2.(believe(e1,john,e2) & walk(e2,mary))zsome e0.walk(e0,mary))resolution_testr fromstringr#rrQ)p1p2cps rtestResolutionProverr s*I)***+,,,,---*+++)***,---*+++)****+++,---N###CDDD,---  = > >B  / 0 0B122A R G G2 G G1 G G 0 2 2 8 8RH E E G GHHH  < = =B  | , ,B011A R G G2 G G1 G G 0 2 2 8 8RH E E G GHHHVWWA677A Q ; ;A ; ;)++11!aS99 ; ;<<<< Q(x)z-(P(x) <-> Q(x))z -(all x.P(x))z-(some x.P(x))z some x.P(x)zsome x.all y.P(x,y)zall y.some x.P(x,y)zall z.all y.some x.P(x,y,z)z1all x.(all y.P(x,y) -> -all y.(Q(x,y) -> R(x,y))))r rr#r!)lexprs r test_clausifyrs=  !E (55'' ( ())) (55/00 1 1222 (55/00 1 1222 (55899 : :;;; (55-.. / /000 (55677 8 8999 (55/00 1 1222 (55*++ , ,--- (55)) * *+++ (55+,, - -... (55)) * *+++ (55)** + +,,, (55'' ( ())) (55.// 0 0111 (55.// 0 0111 (55677 8 8999 (55LMM N NOOOOOrctttttjd}tt ||gdS)Nr)rr#r r rr$rQ)r s rdemor3sfOOO GGG GGGh''A !!aS ) ) / / 1 122222r__main__r^)NN)1rrr9 collectionsr functoolsrnltk.inference.apirrnltk.semrnltk.sem.logicrr r r r r rrrrrrrrr$r7rpr?rxrrryrr!rrurrrrrwr rrrrrrrrs ######88888888                               y   _ _ _ _ _ v_ _ _ DDDDDD/DDDNeeeeeTeeePINR5555rNR0000f+(+(+(+(\      0]]]]]]]]@####6DDD*****y***CCCCC9CCC / / / / / / / /===> PPP4333 zDFFFFFr