ó ¡¼™\c@ sÖdZddlmZmZddlmZddlmZdefd„ƒYZ defd„ƒYZ d efd „ƒYZ dd „Z d „Zd „Zd„Zd„Zd„Zd„Zd„Zd„ZdS(sG 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 iÿÿÿÿ(tprint_functiontdivision(trange(tkbinstCompoundcB s2eZdZd„Zd„Zd„Zd„ZRS(sr A little class to represent an interior node in the tree This is analogous to SymPy.Basic for non-Atoms cC s||_||_dS(N(toptargs(tselfRR((s/lib/python2.7/site-packages/sympy/unify/core.pyt__init__s cC s:t|ƒt|ƒko9|j|jko9|j|jkS(N(ttypeRR(Rtother((s/lib/python2.7/site-packages/sympy/unify/core.pyt__eq__!s*cC stt|ƒ|j|jfƒS(N(thashR RR(R((s/lib/python2.7/site-packages/sympy/unify/core.pyt__hash__%scC s,dt|jƒdjtt|jƒƒfS(Ns%s[%s]s, (tstrRtjointmapR(R((s/lib/python2.7/site-packages/sympy/unify/core.pyt__str__(s(t__name__t __module__t__doc__RR R R(((s/lib/python2.7/site-packages/sympy/unify/core.pyRs    tVariablecB s2eZdZd„Zd„Zd„Zd„ZRS(s A Wild token cC s ||_dS(N(targ(RR((s/lib/python2.7/site-packages/sympy/unify/core.pyR-scC s(t|ƒt|ƒko'|j|jkS(N(R R(RR ((s/lib/python2.7/site-packages/sympy/unify/core.pyR 0scC stt|ƒ|jfƒS(N(R R R(R((s/lib/python2.7/site-packages/sympy/unify/core.pyR 3scC sdt|jƒS(Ns Variable(%s)(RR(R((s/lib/python2.7/site-packages/sympy/unify/core.pyR6s(RRRRR R R(((s/lib/python2.7/site-packages/sympy/unify/core.pyR+s    t CondVariablecB s2eZdZd„Zd„Zd„Zd„ZRS(s‚ A wild token that matches conditionally arg - a wild token valid - an additional constraining function on a match cC s||_||_dS(N(Rtvalid(RRR((s/lib/python2.7/site-packages/sympy/unify/core.pyR?s cC s:t|ƒt|ƒko9|j|jko9|j|jkS(N(R RR(RR ((s/lib/python2.7/site-packages/sympy/unify/core.pyR CscC stt|ƒ|j|jfƒS(N(R R RR(R((s/lib/python2.7/site-packages/sympy/unify/core.pyR HscC sdt|jƒS(NsCondVariable(%s)(RR(R((s/lib/python2.7/site-packages/sympy/unify/core.pyRKs(RRRRR R R(((s/lib/python2.7/site-packages/sympy/unify/core.pyR9s    ck s1|p i}||kr |Vn t|ttfƒr]xõt||||D] }|VqKWnÐt|ttfƒršx¸t||||D] }|VqˆWn“t|tƒr‹t|tƒr‹|jdd„ƒ}|jdd„ƒ}xHt|j|j||D]†}||ƒr8||ƒr8t|j ƒt|j ƒkrF||fn ||f\}} ||ƒr‹||ƒr‹t |j | j dƒ} nt |j | j dƒ} xÞ| D]‡\} } g| D]} t t|j| ƒƒ^q½}g| D]} t t| j| ƒƒ^qè}x"t||||D] }|Vq"WqªWqþt|j ƒt|j ƒkrþx+t|j |j ||D] }|VqrWqþqþWn¢t |ƒr-t |ƒr-t|ƒt|ƒkr-t|ƒdkrÕ|Vq-xUt|d|d||D]3}x*t|d|d||D] }|VqWqóWnd S( s 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'} tis_commutativecS stS(N(tFalse(tx((s/lib/python2.7/site-packages/sympy/unify/core.pytpttis_associativecS stS(N(R(R((s/lib/python2.7/site-packages/sympy/unify/core.pyRqRt commutativet associativeiiN( t isinstanceRRt unify_varRtgettunifyRtlenRtallcombinationstunpacktis_args(RtytstfnstmatchRRtsoptatbtcombstaaargstbbargsRtaatbbtshead((s/lib/python2.7/site-packages/sympy/unify/core.pyR$Ns@    "<++"0$$ck s£||kr8xt|||||D] }|Vq&Wngt||ƒrJnUt|tƒr||j|ƒr|t|||ƒVn#t|tƒrŸt|||ƒVndS(N(R$t occur_checkR!RRtassocR(tvarRR*R+R,((s/lib/python2.7/site-packages/sympy/unify/core.pyR"Šs   c sbˆ|krtSt|tƒr/tˆ|jƒSt|ƒr^t‡fd†|Dƒƒr^tSntS(s# var occurs in subtree owned by x? c3 s|]}tˆ|ƒVqdS(N(R6(t.0txi(R8(s/lib/python2.7/site-packages/sympy/unify/core.pys œs(tTrueR!RR6RR(tanyR(R8R((R8s/lib/python2.7/site-packages/sympy/unify/core.pyR6•s  cC s|jƒ}|||<|S(s- Return copy of d with key associated to val (tcopy(tdtkeytval((s/lib/python2.7/site-packages/sympy/unify/core.pyR7Ÿs  cC st|ƒtttfkS(s Is x a traditional iterable? (R ttupletlisttset(R((s/lib/python2.7/site-packages/sympy/unify/core.pyR(¥scC s7t|tƒr/t|jƒdkr/|jdS|SdS(Nii(R!RR%R(R((s/lib/python2.7/site-packages/sympy/unify/core.pyR'©s$ cc só|dkrd}n|dkr*d}nt|ƒt|ƒkrN||fn ||f\}}xŒtttt|ƒƒƒt|ƒd|ƒD]]}||krÇtd„|Dƒƒt||ƒfVqŽt||ƒtd„|DƒƒfVqŽWdS(sï Restructure A and B to have the same number of elements 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,))) Ri R torderedcs s|]}|fVqdS(N((R9R.((s/lib/python2.7/site-packages/sympy/unify/core.pys Öscs s|]}|fVqdS(N((R9R/((s/lib/python2.7/site-packages/sympy/unify/core.pys ØsN(tNoneR%RRBRRAt partition(tAtBRDtsmtbgtpart((s/lib/python2.7/site-packages/sympy/unify/core.pyR&¯s    64 'cC s,t|ƒg|D]}t||ƒ^qƒS(sÖ 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,)) (R tindex(titRKtind((s/lib/python2.7/site-packages/sympy/unify/core.pyRFÚs cC s't|ƒg|D]}||^qƒS(s¼ 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] (R (RMRNti((s/lib/python2.7/site-packages/sympy/unify/core.pyRLæs N(Rt __future__RRtsympy.core.compatibilityRtsympy.utilities.iterablesRtobjectRRRRER$R"R6R7R(R'R&RFRL(((s/lib/python2.7/site-packages/sympy/unify/core.pyts <    +