o 8Va}@sdZddlmZGdddZGdddZGdddZdd d Zd d ZddZddZ ddZ ddZ ddZ ddZ ddZd S)aG Generic Unification algorithm for expression trees with lists of children This implementation is a direct translation of Artificial Intelligence: A Modern Approach by Stuart Russel and Peter Norvig Second edition, section 9.2, page 276 It is modified in the following ways: 1. We allow associative and commutative Compound expressions. This results in combinatorial blowup. 2. We explore the tree lazily. 3. We provide generic interfaces to symbolic algebra libraries in Python. A more traditional version can be found here http://aima.cs.berkeley.edu/python/logic.html )kbinsc@0eZdZdZddZddZddZdd Zd S) Compoundzr A little class to represent an interior node in the tree This is analogous to SymPy.Basic for non-Atoms cC||_||_dSN)opargs)selfrrr 2/usr/lib/python3/dist-packages/sympy/unify/core.py__init__ zCompound.__init__cC(t|t|ko|j|jko|j|jkSr)typerrr otherr r r __eq__s zCompound.__eq__cCtt||j|jfSr)hashrrrr r r r __hash__"zCompound.__hash__cCs dt|jdtt|jfS)Nz%s[%s]z, )strrjoinmaprrr r r __str__%s zCompound.__str__N__name__ __module__ __qualname____doc__r rrrr r r r rs  rc@r) Variablez A Wild token cCs ||_dSr)arg)r r"r r r r *s zVariable.__init__cCst|t|ko |j|jkSr)rr"rr r r r-szVariable.__eq__cCstt||jfSr)rrr"rr r r r0szVariable.__hash__cCdt|jS)Nz Variable(%s)rr"rr r r r3zVariable.__str__Nrr r r r r!(s  r!c@r) CondVariablez A wild token that matches conditionally. arg - a wild token. valid - an additional constraining function on a match. cCrr)r"valid)r r"r'r r r r <r zCondVariable.__init__cCrr)rr"r'rr r r r@s   zCondVariable.__eq__cCrr)rrr"r'rr r r rErzCondVariable.__hash__cCr#)NzCondVariable(%s)r$rr r r rHr%zCondVariable.__str__Nrr r r r r&6s  r&Nc +sN|pi}||kr|VdSt|ttfr$t|||fi|EdHdSt|ttfr:t|||fi|EdHdSt|trt|tr|ddd}|ddd}t|j|j|fi|D]w}||r||rt|j t|j krx||fn||f\||r||rt j j d}nt j j d}|D]#\}} fd d |D} fd d | D} t| | |fi|EdHqq`t|j t|j krt|j |j |fi|EdHq`dSt |rt |r!t|t|kr#t|d kr|VdSt|d |d |fi|D]} t|d d|d d| fi|EdHqdSdSdSdS)a  Unify two expressions. Parameters ========== x, y - expression trees containing leaves, Compounds and Variables. s - a mapping of variables to subtrees. Returns ======= lazy sequence of mappings {Variable: subtree} Examples ======== >>> from sympy.unify.core import unify, Compound, Variable >>> expr = Compound("Add", ("x", "y")) >>> pattern = Compound("Add", ("x", Variable("a"))) >>> next(unify(expr, pattern, {})) {Variable(a): 'y'} Nis_commutativecSdSNFr xr r r kzunify..is_associativecSr)r*r r+r r r r-lr. commutative associativecg|] }ttj|qSr unpackrr.0r")ar r uzunify..cr2r r3r5)br r r8vr9r) isinstancer!r& unify_varrgetunifyrlenrallcombinationsis_args) r,ysfnsr(r/ZsopZcombsZaaargsZbbargsZaaZbbZsheadr )r7r:r r?KsB ( &   . r?cks||vrt||||fi|EdHdSt||rdSt|tr0||r0t|||VdSt|tr>t|||VdSdSr)r? occur_checkr<r&r'assocr!)varr,rDrEr r r r=s"  r=csH|krdSt|trt|jSt|r"tfdd|Dr"dSdS)z# var occurs in subtree owned by x? Tc3s|]}t|VqdSr)rF)r6ZxirHr r szoccur_check..F)r<rrFrrBany)rHr,r rIr rFs  rFcCs|}|||<|S)z- Return copy of d with key associated to val )copy)dkeyvalr r r rGsrGcCst|tttfvS)z Is x a traditional iterable? )rtuplelistsetr+r r r rBsrBcCs&t|trt|jdkr|jdS|S)Nr;r)r<rr@rr+r r r r4s r4ccs|dkrd}|dkr d}t|t|kr||fn||f\}}tttt|t||dD]%}||krDtdd|Dt||fVq.t||tdd|DfVq.dS) a Restructure A and B to have the same number of elements. Parameters ========== ordered must be either 'commutative' or 'associative'. A and B can be rearranged so that the larger of the two lists is reorganized into smaller sublists. Examples ======== >>> from sympy.unify.core import allcombinations >>> for x in allcombinations((1, 2, 3), (5, 6), 'associative'): print(x) (((1,), (2, 3)), ((5,), (6,))) (((1, 2), (3,)), ((5,), (6,))) >>> for x in allcombinations((1, 2, 3), (5, 6), 'commutative'): print(x) (((1,), (2, 3)), ((5,), (6,))) (((1, 2), (3,)), ((5,), (6,))) (((1,), (3, 2)), ((5,), (6,))) (((1, 3), (2,)), ((5,), (6,))) (((2,), (1, 3)), ((5,), (6,))) (((2, 1), (3,)), ((5,), (6,))) (((2,), (3, 1)), ((5,), (6,))) (((2, 3), (1,)), ((5,), (6,))) (((3,), (1, 2)), ((5,), (6,))) (((3, 1), (2,)), ((5,), (6,))) (((3,), (2, 1)), ((5,), (6,))) (((3, 2), (1,)), ((5,), (6,))) r0 r1N)orderedcs|]}|fVqdSrr )r6r7r r r rJz"allcombinations..csrUrr )r6r:r r r rJrV)r@rrQrangerP partition)ABrTZsmbgpartr r r rAs#$"  rActfdd|DS)z Partition a tuple/list into pieces defined by indices. Examples ======== >>> from sympy.unify.core import partition >>> partition((10, 20, 30, 40), [[0, 1, 2], [3]]) ((10, 20, 30), (40,)) csg|]}t|qSr )index)r6inditr r r8szpartition..r)rar\r r`r rX rXcr])z Fancy indexing into an indexable iterable (tuple, list). Examples ======== >>> from sympy.unify.core import index >>> index([10, 20, 30], (1, 2, 0)) [20, 30, 10] csg|]}|qSr r )r6ir`r r r8szindex..rb)rar_r r`r r^rcr^r)r Zsympy.utilities.iterablesrrr!r&r?r=rFrGrBr4rArXr^r r r r s  7  .