%PDF-1.3
%
2 0 obj
<<
/Length 14441
>>
stream
BT
/TT2 1 Tf
14.3462 0 0 14.3462 178.8 689.22 Tm
0 g
/GS1 gs
0 Tc
0 Tw
[(An)-259.3(In)]TJ
/TT3 1 Tf
2.4829 0 TD
()Tj
/TT2 1 Tf
0.5562 0 TD
[(ationary)-250.9(Fixed)-250.9(P)16.7(oint)-250.9(in)-259.3(XQuery)]TJ
/TT5 1 Tf
11.9552 0 0 11.9552 56.04 651.54 Tm
[(Loredana)-261(Af)10(anasie)20.1(v)]TJ
/F1 1 Tf
8.2307 0.3614 TD
()Tj
/TT5 1 Tf
2.4692 -0.3614 TD
[(T)80.3(orsten)-240.9(Grust)]TJ
/F1 1 Tf
5.621 0.3614 TD
()Tj
/TT5 1 Tf
2.4692 -0.3614 TD
[(Maarten)-250.9(Marx)]TJ
/F1 1 Tf
5.9221 0.3614 TD
()Tj
/TT5 1 Tf
2.4692 -0.3614 TD
[(Jan)-250.9(Rittinger)]TJ
/F1 1 Tf
5.3199 0.3614 TD
()Tj
/TT5 1 Tf
2.4692 -0.3614 TD
[(Jens)-240.9(T)70.3(eubner)]TJ
/F1 1 Tf
5.4002 0.3614 TD
()Tj
-33.0334 -1.596 TD
()Tj
/TT5 1 Tf
0.7026 -0.3714 TD
[(ISLA,)-250.9(Uni)20.1(v)10(ersity)-230.9(of)-250.9(Amsterdam,)-230.9(Amsterdam,)-240.9(The)-250.9(Netherlands)]TJ
/F1 1 Tf
1.4053 -0.803 TD
()Tj
/TT5 1 Tf
0.7127 -0.3614 TD
[(T)70.3(echnische)-240.9(Uni)20.1(v)10(ersit)-60.2()]TJ
8.4172 0 TD
[(at)-230.9(M)-80.3()]TJ
1.8435 0 TD
[(unchen,)-240.9(Munich,)-240.9(German)10(y)]TJ
-19.2643 -1.2446 TD
(E-mail:)Tj
/F2 1 Tf
3.2399 0 TD
-0.0027 Tc
[({lafanasi,)-40.2(marx}@science.u)-10.1(va.n)-10.1(l)]TJ
/TT5 1 Tf
15.4173 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.8221 0 TD
-0.0027 Tc
[({grust,)-40.2(rittinge,)-40.2(teubner)-10.1(j}@i)-10.1(n.tu)-10.1(m.d)-10.1(e)]TJ
/TT2 1 Tf
-13.1056 -3.0213 TD
0 Tc
(Abstract)Tj
/TT7 1 Tf
9.9626 0 0 9.9626 62.04 542.8201 Tm
[(W)96.4(e)-313.2(intr)48.2(oduce)-289.1(a)-301.1(contr)48.2(olled)-277(form)-313.2(of)-289.1(r)36.1(ecur)12(sion)-301.1(in)-301.1(XQuery)60.2(,)]TJ
/TT5 1 Tf
-1.1925 -1.2045 TD
(in)Tj
/TT8 1 Tf
0.7778 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
(ationary)Tj
/TT8 1 Tf
3.6979 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(x)12(e)0(d)-433.6(points)]TJ
/TT7 1 Tf
4.3102 0 TD
[(,)-481.8(familiar)-445.7(in)-445.7(the)-445.7(conte)24.1(xt)-433.6(of)-445.7(r)36.1(ela-)]TJ
-9.8983 -1.1925 TD
[(tional)-265(databases.)-409.5(This)-289.1(imposes)-289.1(r)36.1(estrictions)-289.1(on)-277(the)-277(e)24.1(xpr)36.1(ess-)]TJ
0 -1.2045 TD
[(ible)-301.1(types)-301.1(of)-313.2(r)36.1(ecur)12(sion,)-313.2(b)24.1(u)0(t)-301.1(w)0(e)-313.2(show)-301.1(that)-301.1(in)]TJ
/TT9 1 Tf
17.5662 0 TD
()Tj
/TT7 1 Tf
0.5 0 TD
(ationary)Tj
/TT9 1 Tf
3.6777 0 TD
()Tj
/TT7 1 Tf
0.5 0 TD
(xed)Tj
-22.244 -1.1925 TD
[(points)-409.5(ne)12(vertheless)-421.6(ar)36.1(e)-421.6(suf)]TJ
/TT9 1 Tf
11.0797 0 TD
()Tj
/TT7 1 Tf
0.5 0 TD
[(ciently)-409.5(ver)12(satile)-433.6(to)-421.6(captur)36.1(e)-409.5(a)]TJ
-11.5797 -1.2045 TD
[(wide)-216.8(r)12(ang)12(e)-204.8(o)0(f)-228.9(inter)36.1(esting)-204.8(use)-228.9(cases,)-216.8(including)-204.8(the)-216.8(semantics)]TJ
T*
[(of)-240.9(Re)36.1(gular)-228.9(XP)84.3(ath)-240.9(and)-228.9(its)-252.9(cor)36.1(e)-240.9(t)0(r)12(ansitive)-240.9(closur)36.1(e)-252.9(construct.)]TJ
1.1925 -1.2647 TD
[(While)-252.9(the)-252.9(optimization)-240.9(of)-252.9(g)12(ener)12(al)-240.9(user)24.1(-de)]TJ
/TT9 1 Tf
16.5787 0 TD
()Tj
/TT7 1 Tf
0.5 0 TD
[(ned)-228.9(r)36.1(ecur)12(sive)]TJ
-18.2711 -1.2045 TD
[(functions)-252.9(in)-277(XQuery)-277(appear)12(s)-265(elusive)12(,)-289.1(w)0(e)-277(will)-289.1(describe)-277(how)]TJ
0 -1.1925 TD
(in)Tj
/TT9 1 Tf
0.7778 0 TD
()Tj
/TT7 1 Tf
0.5 0 TD
(ationary)Tj
/TT9 1 Tf
3.7259 0 TD
()Tj
/TT7 1 Tf
0.5 0 TD
[(xed)-361.3(points)-361.3(can)-361.4(be)-373.4(ef)]TJ
/TT9 1 Tf
8.3873 0 TD
()Tj
/TT7 1 Tf
0.5 0 TD
[(ciently)-349.3(e)12(valuated,)-373.4(pr)48.2(o-)]TJ
-14.3911 -1.2045 TD
[(vided)-313.2(that)-325.2(the)-325.2(r)36.1(ecur)12(sive)-337.3(XQuery)-325.2(e)24.1(xpr)36.1(essions)-325.2(e)24.1(xhibit)-337.3(a)]TJ
/TT5 1 Tf
22.1419 0 TD
(dis-)Tj
-22.1419 -1.2045 TD
[(trib)24.1(uti)24.1(vity)]TJ
/TT7 1 Tf
4.2289 0 TD
[(pr)48.2(operty)60.2(.)-445.7(W)96.4(e)-313.2(show)-289.1(how)-289.1(distrib)24.1(utivity)-301.1(can)-289.1(be)-289.1(as-)]TJ
-4.2289 -1.1925 TD
[(sessed)-409.5(both,)-433.6(syntactically)-409.5(and)-397.5(alg)12(ebr)12(aically)60.2(,)-421.6(and)-397.5(pr)48.2(o)12(vide)]TJ
0 -1.2045 TD
[(e)24.1(xperimental)-192.7(e)12(vidence)-180.7(that)-204.8(XQuery)-192.7(pr)48.2(ocessor)12(s)-216.8(can)-192.7(substan-)]TJ
T*
[(tially)-240.9(bene)]TJ
/TT9 1 Tf
4.1838 0 TD
()Tj
/TT7 1 Tf
0.5 0 TD
[(t)-228.9(during)-228.9(in)]TJ
/TT9 1 Tf
4.1804 0 TD
()Tj
/TT7 1 Tf
0.5 0 TD
(ationary)Tj
/TT9 1 Tf
3.6175 0 TD
()Tj
/TT7 1 Tf
0.5 0 TD
[(xed)-228.9(point)-228.9(e)12(valuation.)]TJ
/TT2 1 Tf
11.9552 0 0 11.9552 50.16 336.78 Tm
[(1)10(.)-250.9(Intr)20.1(oduction)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 62.04 308.82 Tm
[(The)-265(backbone)-228.9(of)-252.9(the)-265(XML)-265(data)-252.9(model,)-252.9(namely)]TJ
/TT7 1 Tf
19.0571 0 TD
[(or)36.1(der)36.1(ed,)]TJ
-20.2495 -1.2045 TD
[(unr)12(ank)12(ed)-180.7(tr)36.1(ees)-216.8(of)-204.8(nodes)]TJ
/TT5 1 Tf
9.3736 0 TD
[(,)-192.7(i)0(s)-216.8(inherently)-192.7(recursi)24.1(v)12(e)-180.7(and)-204.8(it)-204.8(is)-216.8(nat-)]TJ
-9.3736 -1.2045 TD
[(ural)-301.1(to)-301.1(equip)-289.1(the)-313.2(associated)-301.1(languages)-289.1(with)-301.1(constructs)-301.1(that)]TJ
0 -1.1925 TD
[(can)-385.4(query)-373.4(such)-385.4(recursi)24.1(v)12(e)-373.4(structures.)-734.7(T)84.3(o)-385.4(get)-385.4(from)-385.4(the)-385.4(re-)]TJ
0 -1.2045 TD
[(cursi)24.1(v)12(e)-361.4(ax)12(es)-385.4(in)-373.4(XP)12(ath,)]TJ
/TT7 1 Tf
9.6739 0 TD
-0.012 Tc
[(e.)-12(g.)]TJ
/TT5 1 Tf
1.4198 0 TD
0 Tc
(,)Tj
/F3 1 Tf
0.6475 0 TD
0.005 Tc
(ancestor)Tj
/TT5 1 Tf
4.5892 0 TD
0 Tc
(and)Tj
/F3 1 Tf
1.8172 0 TD
0.005 Tc
(descendant)Tj
/TT5 1 Tf
5.2999 0 TD
0 Tc
(,)Tj
-23.4475 -1.1925 TD
[(to)-277(XQuery)60.2(s)-277([)0(7)12(])-289.1(recursi)24.1(v)12(e)-265(user)24.1(-de)]TJ
/TT8 1 Tf
13.4703 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(ned)-265(functions,)-277(language)]TJ
-14.0264 -1.2045 TD
[(designers)-349.3(took)-361.4(a)-373.4(giant)-361.4(leap,)-397.5(ho)24.1(we)24.1(v)12(e)0(r)60.2(.)-662.5(User)24.1(-de)]TJ
/TT8 1 Tf
19.1323 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(ned)-349.3(func-)]TJ
-19.6885 -1.2045 TD
[(tions)-228.9(in)-240.9(XQuery)-228.9(admit)]TJ
/TT7 1 Tf
9.1487 0 TD
[(arbitr)12(ary)]TJ
/TT5 1 Tf
3.8958 0 TD
[(types)-228.9(of)-240.9(recursiona)-216.8(con-)]TJ
-13.0445 -1.1925 TD
[(struct)-337.3(that)-337.3(lar)12(gely)-325.2(e)24.1(v)24.1(ades)-325.2(optimization)-325.2(approaches)-313.2(be)12(yond)]TJ
0 -1.2045 TD
[(procedural)-325.2(impro)12(v)12(ements)-325.2(lik)12(e)-373.4(tail-recursion)-337.3(elimination)]TJ
T*
[(or)-240.9(unfolding.)]TJ
1.1925 -1.2647 TD
[(This)-397.5(paper)-373.4(embarks)-373.4(on)-373.4(a)-397.5(journe)12(y)-361.3(that)-385.4(e)12(xplores)-373.4(a)-397.5(con-)]TJ
-1.1925 -1.2045 TD
[(trolled)-313.2(form)-301.1(of)-325.2(recursion)-301.1(in)-325.2(XQuery)60.2(,)-313.2(the)]TJ
/TT7 1 Tf
16.7226 0 TD
(in)Tj
/TT9 1 Tf
0.7778 0 TD
()Tj
/TT7 1 Tf
0.5 0 TD
(ationary)Tj
/TT9 1 Tf
3.6898 0 TD
()Tj
/TT7 1 Tf
0.5 0 TD
(xed)Tj
-22.1903 -1.1925 TD
[(point)-313.2(\(IFP\))]TJ
/TT5 1 Tf
4.5895 0 TD
[(,)-313.2(f)12(amiliar)-313.2(in)-325.2(the)-337.3(conte)12(xt)-301.1(of)-325.2(relational)-313.2(databases)]TJ
-4.5895 -1.2045 TD
[([1)12(].)-289.1(While)-228.9(this)-216.8(imposes)-216.8(restrictions)-216.8(on)-204.8(the)-216.8(e)12(xpressible)-204.8(types)]TJ
0 -1.1925 TD
[(of)-180.7(recursion,)-192.7(IFP)-192.7(embraces)-180.7(a)-204.8(f)12(amily)-180.7(of)-192.7(widespread)-180.7(use)-192.7(cases)]TJ
0 -1.2045 TD
[(of)-204.8(recursion)-192.7(in)-216.8(XQuery)60.2(,)-204.8(including)-192.7(man)12(y)-192.7(forms)-204.8(of)-216.8(horizontal)]TJ
T*
[(or)-301.1(v)12(ertical)-301.1(structural)-289.1(recursion)-289.1(and)-301.1(the)-313.2(perv)24.1(asi)24.1(v)12(e)]TJ
/TT7 1 Tf
19.8367 0 TD
[(tr)12(ansitive)]TJ
-19.8367 -1.1925 TD
[(closur)36.1(e)]TJ
/TT5 1 Tf
3.2088 0 TD
[(problem)-277(\(IFP)-301.1(captures)]TJ
/TT7 1 Tf
9.3096 0 TD
[(Re)36.1(gular)-289.1(XP)84.3(ath)]TJ
/TT5 1 Tf
6.1789 0 TD
[([21)12(],)-313.2(in)-301.1(par)24.1(-)]TJ
-18.6974 -1.2045 TD
(ticular\).)Tj
/F4 1 Tf
8.9664 0 0 8.9664 342.24 571.14 Tm
-0.003 Tc
[()]TJ
0 -1.0974 TD
[()]TJ
T*
[()]TJ
T*
[()]TJ
T*
[()]TJ
/TT11 1 Tf
9.9626 0 0 9.9626 325.68 509.82 Tm
0 Tc
[(Figure)-277(1.)-277(Curriculum)-277(data)-277(\(simpli)]TJ
/TT12 1 Tf
15.6106 0 TD
()Tj
/TT11 1 Tf
0.6108 0 TD
[(ed)-265(DTD\).)]TJ
/TT2 1 Tf
-17.9077 -3.3726 TD
[(Example)-240.9(1.1)]TJ
/TT5 1 Tf
5.7626 0 TD
[(The)-313.2(DTD)-337.3(of)-325.2(Figure)-313.2(1)-325.2(\(tak)12(en)-325.2(from)-313.2([23)12.1(]\))-325.2(de-)]TJ
-5.7626 -1.2045 TD
[(scribes)-337.3(recursi)24.1(v)12(e)-325.2(curriculum)-325.2(data,)-361.3(including)-325.2(courses,)-349.3(their)]TJ
T*
[(lists)-445.7(of)-433.6(prerequisite)-421.6(courses,)-469.8(the)-433.6(prerequisites)-421.6(of)-433.6(the)-433.6(lat-)]TJ
0 -1.1925 TD
[(ter)36.1(,)-493.8(and)-433.6(so)-445.7(on.)-903.4(The)-445.7(XQuery)-433.6(program)-421.6(of)-433.6(Figure)-445.7(2)-445.7(uses)]TJ
0 -1.2045 TD
(the)Tj
/F3 1 Tf
1.5589 0 TD
0.005 Tc
(course)Tj
/TT5 1 Tf
3.481 0 TD
0 Tc
[(element)-337.3(node)-313.2(with)-337.3(code)]TJ
/F3 1 Tf
10.0873 0 TD
0.005 Tc
("c1")Tj
/TT5 1 Tf
2.4452 0 TD
0 Tc
[(to)-337.3(seed)-337.3(a)-337.3(com-)]TJ
-17.5725 -1.1925 TD
[(putation)-325.2(that)-349.3(recursi)24.1(v)12(ely)]TJ
/TT8 1 Tf
10.1828 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(nds)-349.3(all)-361.4(prerequisite)-325.2(courses,)-361.3(di-)]TJ
-10.739 -1.2045 TD
[(rect)-325.2(or)-325.2(indirect,)-325.2(of)-325.2(course)]TJ
/F3 1 Tf
10.6926 0 TD
0.005 Tc
("c1")Tj
/TT5 1 Tf
2.1199 0 TD
0 Tc
[(.)-542(F)12.1(or)-313.2(a)-337.3(g)0(i)24.1(v)12(en)-313.2(sequence)]TJ
/F3 1 Tf
9.7278 0 TD
0.005 Tc
($x)Tj
/TT5 1 Tf
-22.5404 -1.2045 TD
0 Tc
(of)Tj
/F3 1 Tf
1.1944 0 TD
0.005 Tc
(course)Tj
/TT5 1 Tf
3.5172 0 TD
0 Tc
[(nodes,)-373.4(function)]TJ
/F3 1 Tf
6.6262 0 TD
0.005 Tc
(fix\()Tj
/F1 1 Tf
2.1199 0 TD
0 Tc
()Tj
/F3 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.8793 0 TD
[(calls)-373.4(out)-349.3(to)]TJ
/F3 1 Tf
4.9722 0 TD
0.005 Tc
(rec\()Tj
/F1 1 Tf
2.1199 0 TD
0 Tc
()Tj
/F3 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.8793 0 TD
(to)Tj
/TT8 1 Tf
-22.8625 -1.1925 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(nd)-277(their)-289.1(prerequisites.)-409.5(While)-289.1(ne)24.1(w)-289.1(nodes)-277(are)-277(encountered,)]TJ
/F3 1 Tf
-0.5561 -1.2045 TD
0.005 Tc
(fix\()Tj
/F1 1 Tf
2.1199 0 TD
0 Tc
()Tj
/F3 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.8311 0 TD
[(calls)-337.3(itself)-337.3(with)-325.2(the)-325.2(accumulated)]TJ
/F3 1 Tf
13.5224 0 TD
0.005 Tc
(course)Tj
/TT5 1 Tf
3.481 0 TD
0 Tc
[(node)-313.2(se-)]TJ
-20.2315 -1.2045 TD
[(quence.)-277(\(This)-240.9(is)-265(not)-228.9(e)12(xpressible)-228.9(in)-252.9(XP)12(ath)-240.9(2.0.\))]TJ
/F5 1 Tf
22.8414 0 TD
()Tj
/TT5 1 Tf
-22.8414 -2.2283 TD
[(Note)-397.5(that)]TJ
/F3 1 Tf
4.2383 0 TD
0.005 Tc
(fix\()Tj
/F1 1 Tf
2.1199 0 TD
0 Tc
()Tj
/F3 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.9034 0 TD
[(implements)-385.4(a)-397.5(generic)]TJ
/TT8 1 Tf
9.2206 0 TD
()Tj
/TT5 1 Tf
0.5561 0 TD
[(x)12(e)0(d)-385.4(point)-385.4(com-)]TJ
-17.3155 -1.2045 TD
[(putation:)-457.7(only)-325.2(the)-325.2(initialization)-325.2(\()]TJ
/F3 1 Tf
13.3753 0 TD
0.005 Tc
[(let)-505.9($seed)-505.9(:=)]TJ
/F1 1 Tf
6.8175 0 TD
0.1679 Tc
()Tj
/TT5 1 Tf
1.337 0 TD
0 Tc
[(\))-337.3(and)]TJ
-21.5298 -1.1925 TD
(the)Tj
/TT7 1 Tf
1.5108 0 TD
[(payload)-277(function)]TJ
/F3 1 Tf
7.0531 0 TD
0.005 Tc
(rec\()Tj
/F1 1 Tf
2.1199 0 TD
0 Tc
()Tj
/F3 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.8191 0 TD
[(are)-289.1(speci)]TJ
/TT8 1 Tf
3.5645 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(c)-301.1(t)0(o)-301.1(the)-289.1(curriculum)]TJ
-15.9005 -1.2045 TD
[(problem.)-252.9(This)-192.7(moti)24.1(v)24.1(ates)-168.6(the)-192.7(introduction)-144.5(of)-192.7(a)-180.7(syntactic)-180.7(form)]TJ
T*
[(that)-337.3(can)-325.2(succinctly)-325.2(accommodate)-313.2(this)-337.3(pattern)-325.2(of)-325.2(computa-)]TJ
0 -1.1925 TD
[(tion)-240.9(\(Section)-228.9(2\).)]TJ
1.1925 -1.2888 TD
[(Most)-481.8(importantly)60.2(,)-493.8(h)0(o)24.1(w)0(e)24.1(v)12(er)36.1(,)-481.8(such)-469.8(computation)-445.7(in)-469.8(IFP)]TJ
-1.1925 -1.1925 TD
[(form)-433.6(is)-469.8(susceptible)-445.7(to)-457.7(systematic)-457.7(optimization,)-481.8(pro)12(vided)]TJ
0 -1.2045 TD
[(that)-325.2(the)-325.2(payload)-313.2(\(or)]TJ
/TT7 1 Tf
8.3415 0 TD
(body)Tj
/TT5 1 Tf
1.9439 0 TD
[(\))-301.1(o)0(f)-325.2(the)-337.3(recursion)-301.1(e)12(xhibits)-325.2(a)-325.2(spe-)]TJ
-10.2854 -1.1925 TD
(ci)Tj
/TT8 1 Tf
0.7217 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
(c)Tj
/TT7 1 Tf
0.6968 0 TD
[(distrib)24.1(utivity)]TJ
/TT5 1 Tf
5.3277 0 TD
[(property)60.2(.)]TJ
-6.1098 -1.2888 TD
[(Unlik)12(e)-337.3(the)-337.3(general)-325.2(user)24.1(-de)]TJ
/TT8 1 Tf
10.7922 0 TD
()Tj
/TT5 1 Tf
0.5561 0 TD
[(ned)-313.2(XQuery)-325.2(functions,)-337.3(this)]TJ
-12.5408 -1.1925 TD
[(account)-313.2(of)-313.2(recursion)-313.2(puts)-325.2(the)-325.2(query)-313.2(processor)-313.2(into)-313.2(control)]TJ
0 -1.2045 TD
[(in)-228.9(that)-228.9(it)-228.9(can)-228.9(decide)-216.8(whether)-204.8(the)-228.9(optimization)-204.8(may)-228.9(be)-216.8(safely)]TJ
0 -1.1925 TD
[(applied.)-819.1(Distrib)24.1(uti)24.1(vity)-409.5(may)-409.5(be)-421.6(assessed)-433.6(on)-409.5(a)-433.6(syntactical)]TJ
0 -1.2045 TD
[(le)24.1(v)12(ela)-313.2(non-in)36.1(v)24.1(asi)24.1(v)12(e)-289.1(approach)-289.1(that)-325.2(can)-325.2(easily)-325.2(be)-325.2(realized)]TJ
T*
[(on)-277(top)-277(of)-277(e)12(xisting)-265(XQuery)-277(processors)-265(\(Section)-277(3\).)-409.5(Further)36.1(,)]TJ
0 -1.1925 TD
[(though,)-204.8(if)-240.9(we)-228.9(adopt)-216.8(a)-240.9(relational)-216.8(vie)24.1(w)-240.9(o)0(f)-216.8(the)-240.9(XQuery)-216.8(seman-)]TJ
0 -1.2045 TD
[(tics)-252.9(\(as)-252.9(in)-252.9([15)12(]\),)-240.9(the)-252.9(seemingly)-228.9(XQuery-speci)]TJ
/TT8 1 Tf
17.9919 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(c)-228.9(distrib)24.1(uti)24.1(v-)]TJ
-18.5481 -1.2045 TD
[(ity)-277(notion)-265(turns)-277(out)-277(to)-277(be)-277(ele)12(gantly)-252.9(and)-277(uniformly)-252.9(tractable)]TJ
0 -1.1925 TD
[(on)-240.9(the)-240.9(f)12(amiliar)-240.9(algebraic)-228.9(le)24.1(v)12(e)0(l)-228.9(\(Section)-240.9(4\).)]TJ
1.1925 -1.2768 TD
[(Compliance)-469.8(with)-481.8(the)-481.8(restriction)-469.8(that)-481.8(IFP)-481.8(imposes)-481.8(on)]TJ
-1.1925 -1.2045 TD
[(query)-228.9(formulation)-228.9(is)-265(re)24.1(w)12(arded)-228.9(by)-240.9(signi)]TJ
/TT8 1 Tf
15.4859 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(cant)-252.9(query)-228.9(runtime)]TJ
-17.4272 -2.9992 TD
(1)Tj
ET
endstream
endobj
3 0 obj
<<
/ProcSet [/PDF /Text ]
/Font <<
/F1 4 0 R
/F2 5 0 R
/F3 6 0 R
/F4 7 0 R
/F5 8 0 R
/TT2 9 0 R
/TT3 10 0 R
/TT5 11 0 R
/TT7 12 0 R
/TT8 13 0 R
/TT9 14 0 R
/TT11 15 0 R
/TT12 16 0 R
>>
/ExtGState <<
/GS1 17 0 R
>>
>>
endobj
20 0 obj
<<
/Length 23058
>>
stream
0 G
0 J 0 j 0.398 w 10 M [2.989 1.993 ]0 d
/GS1 gs
1 i
74.695 674.585 m
74.695 613.64 l
250.446 613.64 l
250.446 674.585 l
h
250.446 613.64 m
S
BT
/TT5 1 Tf
6.9738 0 0 6.9738 63 706.14 Tm
0 g
0 Tc
0 Tw
(1)Tj
/F4 1 Tf
8.9664 0 0 8.9664 78.4869 706.14 Tm
-0.003 Tc
[(declare)-548.7(function)-548.7(rec)-174(\($cs\))-548.7(as)-521.9(node\(\)*)]TJ
/TT5 1 Tf
6.9738 0 0 6.9738 63 696.1801 Tm
0 Tc
(2)Tj
/F4 1 Tf
8.9664 0 0 8.9664 78.4869 696.1801 Tm
-0.003 Tc
[({)-521.9($cs/id)-200.7(\(./prerequisites/pre_code\))]TJ
/TT5 1 Tf
6.9738 0 0 6.9738 63 686.34 Tm
0 Tc
(3)Tj
/F4 1 Tf
8.9664 0 0 8.9664 78.4869 686.34 Tm
-0.003 Tc
(};)Tj
/TT5 1 Tf
6.9738 0 0 6.9738 63 676.5 Tm
0 Tc
(4)Tj
0 -1.411 TD
(5)Tj
/F4 1 Tf
8.9664 0 0 8.9664 78.4869 666.66 Tm
-0.003 Tc
[(declare)-548.7(function)-548.7(fix)-174(\($x\))-548.7(as)-521.9(node\(\)*)]TJ
/TT5 1 Tf
6.9738 0 0 6.9738 63 656.8201 Tm
0 Tc
(6)Tj
/F4 1 Tf
8.9664 0 0 8.9664 78.4869 656.8201 Tm
-0.003 Tc
[({)-521.9(let)-535.3($res)-535.3(:=)-535.3(rec)-187.3(\($x\))]TJ
/TT5 1 Tf
6.9738 0 0 6.9738 63 646.86 Tm
0 Tc
(7)Tj
/F4 1 Tf
8.9664 0 0 8.9664 87.8469 646.86 Tm
-0.003 Tc
[(return)-548.7(if)-535.3(\(empty)-187.3(\($x)-535.3(except)-535.3($res\)\))]TJ
/TT5 1 Tf
6.9738 0 0 6.9738 63 637.02 Tm
0 Tc
(8)Tj
/F4 1 Tf
8.9664 0 0 8.9664 120.8469 637.02 Tm
-0.003 Tc
[(then)-535.3($res)]TJ
/TT5 1 Tf
6.9738 0 0 6.9738 63 627.1801 Tm
0 Tc
(9)Tj
/F4 1 Tf
8.9664 0 0 8.9664 120.8469 627.1801 Tm
-0.003 Tc
[(else)-535.3(fix)-187.3(\($res)-535.3(union)-535.3($x\))]TJ
/TT5 1 Tf
6.9738 0 0 6.9738 59.52 617.34 Tm
0 Tc
(10)Tj
/F4 1 Tf
8.9664 0 0 8.9664 78.4939 617.34 Tm
-0.003 Tc
(};)Tj
/TT5 1 Tf
6.9738 0 0 6.9738 59.52 607.5 Tm
0 Tc
(11)Tj
0 -1.4282 TD
(12)Tj
/F4 1 Tf
8.9664 0 0 8.9664 78.4939 597.54 Tm
-0.003 Tc
[(let)-535.3($seed)-535.3(:=)-535.3(doc)-187.3(\("curriculum.xml"\))]TJ
/TT5 1 Tf
6.9738 0 0 6.9738 59.52 587.7001 Tm
0 Tc
(13)Tj
/F4 1 Tf
8.9664 0 0 8.9664 182.0539 587.7001 Tm
-0.003 Tc
(/course[@code="c1"])Tj
/TT5 1 Tf
6.9738 0 0 6.9738 59.52 577.86 Tm
0 Tc
(14)Tj
/F4 1 Tf
8.9664 0 0 8.9664 78.4939 577.86 Tm
-0.003 Tc
[(return)-535.3(fix)-187.3(\(rec)-187.3(\($seed\)\))]TJ
/TT11 1 Tf
9.9626 0 0 9.9626 62.04 551.9401 Tm
0 Tc
[(Figure)-481.8(2.)-493.8(Prerequisites)-493.8(f)24.1(o)0(r)-481.8(the)-481.8(cour)12(se)]TJ
/F3 1 Tf
19.2171 0 TD
0.005 Tc
("c1")Tj
/TT11 1 Tf
-19.2171 -1.1925 TD
0 Tc
(\()Tj
ET
67.32 539.22 m
67.32 547.724 l
87.163 547.724 l
87.163 539.22 l
h
87.163 547.724 m
S
BT
9.9626 0 0 9.9626 90 540.0601 Tm
[(marks)-289.1(the)]TJ
/TT12 1 Tf
5.0129 0 TD
()Tj
/TT11 1 Tf
0.6108 0 TD
[(x)12(e)0(d)-277(point)-265(computation\).)]TJ
/TT5 1 Tf
-9.6227 -4.3121 TD
[(sa)24.1(vings)-325.2(that)-337.3(the)-337.3(IFP-inherent)-325.2(optimization)-313.2(hook)-313.2(can)-337.3(of)24.1(fer)60.2(.)]TJ
0 -1.1925 TD
[(W)84.3(e)-373.4(document)-349.3(the)-361.4(ef)24.1(fect)-361.4(for)-361.4(the)-373.4(XQuery)-349.3(processors)]TJ
/TT7 1 Tf
21.4406 0 TD
(Mon-)Tj
-21.4406 -1.2045 TD
(etDB/XQuery)Tj
/TT5 1 Tf
5.7194 0 TD
[([8)12(])-301.1(and)]TJ
/TT7 1 Tf
3.176 0 TD
(Saxon)Tj
/TT5 1 Tf
2.7209 0 TD
[([20)12(])-289.1(i)0(n)-289.1(Section)-289.1(5.)-445.7(This)-289.1(is)-301.1(pri-)]TJ
-11.6163 -1.1925 TD
[(marily)-204.8(due)-216.8(to)-216.8(a)-228.9(substantial)-216.8(reduction)-204.8(of)-216.8(the)-216.8(number)-192.7(of)-216.8(items)]TJ
0 -1.2045 TD
[(that)-252.9(are)-252.9(fed)-240.9(into)-252.9(the)-252.9(recursion)60.2(s)-240.9(payload)-240.9(function)-228.9(\(the)-252.9(na)24.1()]TJ
/TT8 1 Tf
22.3657 0 TD
()Tj
/TT5 1 Tf
0.2778 0 TD
-0.012 Tc
(ve)Tj
-22.6435 -1.2045 TD
0 Tc
[(implementation)-373.4(of)-397.5(Example)-385.4(1.1)-385.4(feeds)-397.5(already)-385.4(disco)12(v)12(ered)]TJ
/F3 1 Tf
0 -1.1924 TD
0.005 Tc
(course)Tj
/TT5 1 Tf
3.3967 0 TD
0 Tc
[(element)-228.9(nodes)-240.9(back)-228.9(into)]TJ
/F3 1 Tf
9.8809 0 TD
0.005 Tc
(rec\()Tj
/F1 1 Tf
2.1199 0 TD
0 Tc
()Tj
/F3 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.53 0 TD
(\).)Tj
-15.0122 -1.2527 TD
[(In)-349.3(Section)-349.3(6,)-373.4(we)-361.4(stop)-349.3(by)-349.3(related)-337.3(w)12(ork)-349.3(on)-349.3(recursion)-325.2(on)]TJ
-1.1925 -1.1925 TD
[(the)-289.1(XQuery)-289.1(as)-301.1(well)-313.2(as)-301.1(the)-301.1(relational)-277(side)-301.1(of)-301.1(the)-301.1(fence,)-289.1(and)]TJ
/TT8 1 Tf
0 -1.2045 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(nally)-240.9(wrap-up)-216.8(in)-240.9(Section)-240.9(7.)]TJ
/TT2 1 Tf
11.9552 0 0 11.9552 50.16 363.78 Tm
[(2)10(.)-250.9(An)-250.9(In)]TJ
/TT3 1 Tf
3.4655 0 TD
()Tj
/TT2 1 Tf
0.5562 0 TD
[(ationary)-261(Fixed)-250.9(P)20.1(oint)-240.9(in)-250.9(XQuery)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 62.04 336.54 Tm
[(The)-385.4(subsequent)-361.4(discussion)-385.4(will)-397.5(re)24.1(v)24.1(olv)12(e)-361.3(around)-361.3(the)-385.4(re-)]TJ
-1.1925 -1.1925 TD
[(cursion)-301.1(pattern)-313.2(embodied)-301.1(by)-313.2(function)]TJ
/F3 1 Tf
15.5258 0 TD
0.005 Tc
(fix\()Tj
/F1 1 Tf
2.1199 0 TD
0 Tc
()Tj
/F3 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.8311 0 TD
[(of)-313.2(Figure)-313.2(2,)]TJ
-18.7539 -1.2045 TD
[(kno)24.1(wn)-361.4(as)-385.4(the)]TJ
/TT7 1 Tf
5.885 0 TD
(in)Tj
/TT9 1 Tf
0.7778 0 TD
()Tj
/TT7 1 Tf
0.5 0 TD
(ationary)Tj
/TT9 1 Tf
3.75 0 TD
()Tj
/TT7 1 Tf
0.5 0 TD
[(xed)-373.4(point)-373.4(\(IFP\))]TJ
/TT5 1 Tf
6.7842 0 TD
[([1)12(].)-722.7(W)84.3(e)-397.5(will)]TJ
-18.1971 -1.2045 TD
[(introduce)-421.6(a)-457.7(n)0(e)24.1(w)-457.7(syntactic)-445.7(form)-433.6(to)-457.7(introduce)-433.6(IFP)-457.7(on)-445.7(the)]TJ
0 -1.1925 TD
[(XQuery)-373.4(language)-361.4(le)24.1(v)12(e)0(l)-385.4(and)-385.4(then)-385.4(e)12(xplore)-361.3(its)-409.5(semantics)-385.4(in)]TJ
0 -1.2045 TD
[(the)-240.9(XQuery)-228.9(conte)12(xt,)-228.9(application,)-216.8(and)-240.9(optimization.)]TJ
1.1925 -1.2406 TD
[(In)-397.5(the)-409.5(follo)24.1(wing,)-409.5(we)-409.5(re)12(gard)-373.4(an)-397.5(XQuery)-397.5(e)12(xpression)]TJ
/F6 1 Tf
21.4746 0 TD
(e)Tj
/F7 1 Tf
6.9738 0 0 6.9738 281.88 262.98 Tm
(1)Tj
/TT5 1 Tf
9.9626 0 0 9.9626 50.16 252.42 Tm
[(containing)-240.9(a)-277(free)-265(v)24.1(ariable)]TJ
/F3 1 Tf
10.4507 0 TD
0.005 Tc
($x)Tj
/TT5 1 Tf
1.325 0 TD
0 Tc
[(as)-277(a)-277(function)-240.9(of)]TJ
/F3 1 Tf
6.5023 0 TD
0.005 Tc
($x)Tj
/TT5 1 Tf
1.06 0 TD
0 Tc
[(.)-373.4(W)84.3(e)-289.1(write)]TJ
/F6 1 Tf
-19.338 -1.2045 TD
(e)Tj
/F7 1 Tf
6.9738 0 0 6.9738 54.84 238.98 Tm
(1)Tj
/F8 1 Tf
9.9626 0 0 9.9626 59.28 240.42 Tm
(\()Tj
/F6 1 Tf
0.3854 0 TD
(e)Tj
/F7 1 Tf
6.9738 0 0 6.9738 67.8 238.98 Tm
(2)Tj
/F8 1 Tf
9.9626 0 0 9.9626 72.24 240.42 Tm
(\))Tj
/TT5 1 Tf
0.6745 0 TD
[(to)-289.1(denote)]TJ
/F6 1 Tf
4.0095 0 TD
(e)Tj
/F7 1 Tf
6.9738 0 0 6.9738 123.84 238.98 Tm
(1)Tj
/F8 1 Tf
9.9626 0 0 9.9626 128.28 240.42 Tm
([)Tj
/F6 1 Tf
0.277 0.2048 TD
(e)Tj
/F7 1 Tf
6.9738 0 0 6.9738 135.72 241.02 Tm
(2)Tj
/F6 1 Tf
9.9626 0 0 9.9626 139.08 240.42 Tm
(/)Tj
/F3 1 Tf
0.4457 0 TD
0.005 Tc
($x)Tj
/F8 1 Tf
1.0479 0 TD
0 Tc
(])Tj
/TT5 1 Tf
0.277 0 TD
(,)Tj
/TT7 1 Tf
0.5511 0 TD
[(i.e)12(.)]TJ
/TT5 1 Tf
1.2096 0 TD
[(,)-289.1(the)-289.1(consistent)-289.1(replacement)]TJ
-12.4567 -1.1925 TD
[(of)-337.3(all)-349.3(free)-349.3(occurrences)-313.2(of)]TJ
/F3 1 Tf
10.692 0 TD
0.005 Tc
($x)Tj
/TT5 1 Tf
1.3972 0 TD
0 Tc
(in)Tj
/F6 1 Tf
1.1271 0 TD
(e)Tj
/F7 1 Tf
6.9738 0 0 6.9738 187.2 227.1 Tm
(1)Tj
/TT5 1 Tf
9.9626 0 0 9.9626 195.12 228.54 Tm
(by)Tj
/F6 1 Tf
1.3373 0 TD
(e)Tj
/F7 1 Tf
6.9738 0 0 6.9738 213.24 227.1 Tm
(2)Tj
/TT5 1 Tf
9.9626 0 0 9.9626 217.68 228.54 Tm
[(.)-614.3(Function)]TJ
/F9 1 Tf
4.7572 0 TD
-0.0055 Tc
(fv)Tj
/F8 1 Tf
0.8673 0 TD
0 Tc
(\()Tj
/F6 1 Tf
0.3854 0 TD
(e)Tj
/F8 1 Tf
0.4698 0 TD
(\))Tj
/TT5 1 Tf
-23.2945 -1.2045 TD
[(returns)-252.9(the)-252.9(set)-277(of)-252.9(free)-265(v)24.1(ariables)-252.9(of)-252.9(e)12(xpression)]TJ
/F6 1 Tf
18.2389 0 TD
(e)Tj
/TT5 1 Tf
0.4698 0 TD
[(.)-349.3(W)84.3(e)-277(further)]TJ
-18.7086 -1.2045 TD
(introduce)Tj
/TT7 1 Tf
4.0414 0 TD
(set-equality)Tj
/TT5 1 Tf
4.9541 0 TD
(\()Tj
/F10 1 Tf
6.9738 0 0 6.9738 145.56 210.3 Tm
(s)Tj
/F8 1 Tf
9.9626 0 0 9.9626 143.64 204.54 Tm
(=)Tj
/TT5 1 Tf
0.7709 0 TD
[(\),)-301.1(a)-301.1(relax)12(ed)-289.1(notion)-277(of)-289.1(equality)-289.1(for)]TJ
-10.1539 -1.1925 TD
[(XQuery)-228.9(item)-252.9(sequences)-240.9(that)-252.9(disre)12(gards)-228.9(duplicate)-228.9(items)-252.9(and)]TJ
0 -1.2045 TD
[(order)36.1(,)]TJ
/TT7 1 Tf
2.5405 0 TD
-0.012 Tc
[(e.)-12(g.)]TJ
/TT5 1 Tf
1.4198 0 TD
0 Tc
(,)Tj
/F3 1 Tf
0.4789 0 TD
0.005 Tc
(\(1,"a"\))Tj
/F10 1 Tf
6.9738 0 0 6.9738 135.6 186.3 Tm
0 Tc
(s)Tj
/F8 1 Tf
9.9626 0 0 9.9626 133.56 180.66 Tm
(=)Tj
/F3 1 Tf
0.9997 0 TD
0.005 Tc
(\("a",1,1\))Tj
/TT5 1 Tf
4.7337 0 TD
0 Tc
(.)Tj
-12.9123 -1.2406 TD
[(T)84.3(o)-204.8(streamline)-204.8(the)-204.8(discussion,)-204.8(in)-204.8(the)-204.8(follo)24.1(wing)-192.7(we)-204.8(assume)]TJ
-1.1925 -1.2045 TD
[(computations)-252.9(o)12(v)12(e)0(r)-277(sequences)-277(of)-277(type)]TJ
/F3 1 Tf
15.1225 0 TD
0.005 Tc
(node\(\)*)Tj
/TT5 1 Tf
3.9629 0 TD
0 Tc
[(as)-301.1(trees)-289.1(are)]TJ
/TT7 1 Tf
-19.0853 -1.1925 TD
(the)Tj
/TT5 1 Tf
1.5108 0 TD
[(recursi)24.1(v)12(e)-277(data)-301.1(structure)-289.1(in)-289.1(the)-301.1(XQuery)-289.1(Data)-301.1(Model.)-445.7(In)]TJ
-1.5108 -1.2045 TD
[(this)-240.9(case,)-252.9(with)]TJ
/F6 1 Tf
5.9281 0 TD
(X)Tj
/F7 1 Tf
6.9738 0 0 6.9738 117.6 130.98 Tm
(1)Tj
/TT5 1 Tf
9.9626 0 0 9.9626 122.04 132.42 Tm
(,)Tj
/F6 1 Tf
0.5029 0 TD
(X)Tj
/F7 1 Tf
6.9738 0 0 6.9738 135.36 130.98 Tm
(2)Tj
/TT5 1 Tf
9.9626 0 0 9.9626 142.2 132.42 Tm
[(of)-240.9(type)]TJ
/F3 1 Tf
3.0365 0 TD
0.005 Tc
(node\(\)*)Tj
/TT5 1 Tf
3.7099 0 TD
0.2168 Tc
[(,w)216.8(e)-24.1(h)216.8(a)240.9(v)228.8(e)]TJ
6.9738 0 0 6.9738 246.96 136.02 Tm
0 Tc
(1)Tj
/F6 1 Tf
9.9626 0 0 9.9626 66.6 109.62 Tm
(X)Tj
/F7 1 Tf
6.9738 0 0 6.9738 74.88 108.18 Tm
(1)Tj
/F10 1 Tf
1.2389 1.0152 TD
(s)Tj
/F8 1 Tf
9.9626 0 0 9.9626 81.6 109.62 Tm
(=)Tj
/F6 1 Tf
0.9997 0 TD
(X)Tj
/F7 1 Tf
6.9738 0 0 6.9738 99.84 108.18 Tm
(2)Tj
/F1 1 Tf
9.9626 0 0 9.9626 117 109.62 Tm
()Tj
/F3 1 Tf
2.2765 0 TD
0.005 Tc
(fs:ddo\()Tj
/F6 1 Tf
3.7099 0 TD
0 Tc
(X)Tj
/F7 1 Tf
6.9738 0 0 6.9738 184.92 108.18 Tm
(1)Tj
/F3 1 Tf
9.9626 0 0 9.9626 189 109.62 Tm
(\))Tj
/F8 1 Tf
0.807 0 TD
(=)Tj
/F3 1 Tf
1.0479 0 TD
0.005 Tc
(fs:ddo\()Tj
/F6 1 Tf
3.7099 0 TD
0 Tc
(X)Tj
/F7 1 Tf
6.9738 0 0 6.9738 252.72 108.18 Tm
(2)Tj
/F3 1 Tf
9.9626 0 0 9.9626 256.92 109.62 Tm
(\))Tj
/F6 1 Tf
1.0238 0 TD
(.)Tj
ET
q
94.56 0 0 -0.48 50.148 100.368 cm
/Im1 Do
Q
BT
/TT5 1 Tf
5.9776 0 0 5.9776 60.96 93.18 Tm
(1)Tj
7.9701 0 0 7.9701 64.44 90.42 Tm
[(Here)-602.2(and)-587.2(in)-587.2(the)-602.2(follo)30.1(wing,)]TJ
/F11 1 Tf
12.5663 0 TD
-0.0043 Tc
(fs:ddo\()Tj
/F12 1 Tf
3.689 0 TD
0 Tc
()Tj
/F11 1 Tf
0.3011 0 TD
(\))Tj
/TT5 1 Tf
1.1293 0 TD
[(abbre)30.1(viates)-632.4(the)-602.2(function)]TJ
/F11 1 Tf
-19.4773 -1.1894 TD
-0.0043 Tc
(fs:distinct-doc-order\()Tj
/F12 1 Tf
11.594 0 TD
0 Tc
()Tj
/F11 1 Tf
0.3011 0 TD
(\))Tj
/TT5 1 Tf
0.8582 0 TD
[(of)-256(the)-271(XQuery)-271(F)15.1(ormal)-256(Semantics)-286.1([9].)]TJ
9.9626 0 0 9.9626 308.88 709.98 Tm
[(An)-240.9(e)12(xtension)-228.9(to)-252.9(general)-228.9(sequences)-240.9(of)-240.9(type)]TJ
/F3 1 Tf
17.0455 0 TD
0.005 Tc
(item\(\)*)Tj
/TT5 1 Tf
3.9267 0 TD
0 Tc
[(is)-265(pos-)]TJ
-20.9722 -1.2045 TD
[(sible)-277(and)-277(entails)-277(the)-277(replacement)-252.9(of)-277(XQuery)60.2(s)-265(node)-265(set)-289.1(op-)]TJ
0 -1.1925 TD
[(erations)-228.9(\()]TJ
/F3 1 Tf
3.7274 0 TD
0.005 Tc
(union)Tj
/TT5 1 Tf
2.6499 0 TD
0 Tc
(,)Tj
/F3 1 Tf
0.4789 0 TD
0.005 Tc
(except)Tj
/TT5 1 Tf
3.1799 0 TD
0 Tc
[(\))-204.8(with)-252.9(appropriate)-216.8(v)24.1(ariants.)]TJ
/TT2 1 Tf
-10.0361 -2.3006 TD
(De)Tj
/TT3 1 Tf
1.166 0 TD
()Tj
/TT2 1 Tf
0.5562 0 TD
[(nition)-240.9(2.1)]TJ
/TT14 1 Tf
4.4737 0 TD
(\(In)Tj
/TT15 1 Tf
1.2783 0 TD
()Tj
/TT14 1 Tf
0.5562 0 TD
[(ationary)-505.9(F)36.1(i)0(x)12(e)0(d)-505.9(P)60.2(oint\))]TJ
/TT5 1 Tf
9.8105 0 TD
(Let)Tj
/F6 1 Tf
1.8384 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 510.12 661.7401 Tm
-0.0454 Tc
[(s)-41.5(eed)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 530.76 663.1801 Tm
0 Tc
(and)Tj
/F6 1 Tf
-22.2712 -1.2045 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 313.56 649.7401 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 324.6 651.1801 Tm
0 Tc
(\()Tj
/F3 1 Tf
0.3854 0 TD
0.005 Tc
($x)Tj
/F8 1 Tf
1.0479 0 TD
0 Tc
(\))Tj
/TT5 1 Tf
0.6745 0 TD
[(be)-265(XQuery)-265(e)12(xpressions)-252.9(of)-265(type)]TJ
/F3 1 Tf
12.6866 0 TD
0.005 Tc
(node\(\)*)Tj
/TT5 1 Tf
3.7099 0 TD
0 Tc
[(.)-361.4(The)]TJ
/TT7 1 Tf
2.431 0 TD
(in-)Tj
/TT9 1 Tf
-22.5133 -1.2045 TD
()Tj
/TT7 1 Tf
0.5 0 TD
(ationary)Tj
/TT9 1 Tf
3.7018 0 TD
()Tj
/TT7 1 Tf
0.5 0 TD
[(xed)-337.3(point)-325.2(\(IFP\))-337.3(of)]TJ
/F6 1 Tf
7.7789 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 438.72 637.7401 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 449.76 639.1801 Tm
0 Tc
(\()Tj
/F3 1 Tf
0.3854 0 TD
0.005 Tc
($x)Tj
/F8 1 Tf
1.06 0 TD
0 Tc
(\))Tj
/TT7 1 Tf
0.7347 0 TD
[(seeded)-325.2(by)]TJ
/F6 1 Tf
4.3391 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 519.6 637.7401 Tm
-0.0454 Tc
[(s)-41.5(eed)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 538.44 639.1801 Tm
0 Tc
(is)Tj
-23.0421 -1.1925 TD
[(an)-228.9(XQuery)-228.9(e)12(xpression)-216.8(represented)-216.8(by)-228.9(the)-240.9(follo)24.1(wing)-216.8(syntac-)]TJ
0 -1.2045 TD
[(tic)-252.9(form:)]TJ
/F3 1 Tf
1.0841 -2.2404 TD
0.005 Tc
[(with)-505.9($x)-505.9(seeded)-493.8(by)]TJ
/F6 1 Tf
9.4434 0 TD
0 Tc
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 418.44 591.54 Tm
-0.0454 Tc
[(s)-41.5(eed)]TJ
/F3 1 Tf
9.9626 0 0 9.9626 439.2 592.98 Tm
0.005 Tc
(recurse)Tj
/F6 1 Tf
4.1917 0 TD
0 Tc
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 485.64 591.54 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 496.8 592.98 Tm
0 Tc
(\()Tj
/F3 1 Tf
0.3854 0 TD
0.005 Tc
($x)Tj
/F8 1 Tf
1.0479 0 TD
0 Tc
(\))Tj
/F6 1 Tf
0.8913 0 TD
(.)Tj
/TT5 1 Tf
1.3611 0 TD
(\(1\))Tj
-22.5483 -2.2404 TD
[(The)-421.6(payload)-421.6(e)12(xpression)]TJ
/F6 1 Tf
10.2377 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 416.16 569.22 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 431.52 570.66 Tm
0 Tc
[(is)-445.7(called)-433.6(the)]TJ
/TT7 1 Tf
5.5767 0 TD
(body)Tj
/TT5 1 Tf
1.9438 0 TD
(,)Tj
/F6 1 Tf
0.7198 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 518.64 569.22 Tm
-0.0454 Tc
[(s)-41.5(eed)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 538.44 570.66 Tm
0 Tc
(is)Tj
-23.0421 -1.1925 TD
[(called)-325.2(the)]TJ
/TT7 1 Tf
4.2593 0 TD
(seed)Tj
/TT5 1 Tf
1.7769 0 TD
[(,)-349.3(and)]TJ
/F3 1 Tf
2.3563 0 TD
0.005 Tc
($x)Tj
/TT5 1 Tf
1.3852 0 TD
0 Tc
[(is)-337.3(called)-325.2(the)]TJ
/TT7 1 Tf
5.2636 0 TD
[(r)36.1(ecur)12(sion)-325.2(variable)]TJ
/TT5 1 Tf
7.7557 0 TD
(of)Tj
-22.797 -1.2045 TD
[(the)-240.9(in)]TJ
/TT8 1 Tf
2.2404 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
(ationary)Tj
/TT8 1 Tf
3.5052 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(x)12(e)0(d)-228.9(point)-240.9(operator)60.2(.)]TJ
-5.6655 -1.2165 TD
[(The)-385.4(semantics)-385.4(of)-385.4(the)-385.4(IFP)-385.4(of)]TJ
/F6 1 Tf
12.1437 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 446.88 533.22 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 457.92 534.66 Tm
0 Tc
(\()Tj
/F3 1 Tf
0.3854 0 TD
0.005 Tc
($x)Tj
/F8 1 Tf
1.06 0 TD
0 Tc
(\))Tj
/TT5 1 Tf
0.7829 0 TD
[(seeded)-373.4(by)]TJ
/F6 1 Tf
4.4795 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 529.68 533.22 Tm
-0.0454 Tc
[(s)-41.5(eed)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 308.88 522.66 Tm
0 Tc
[(is)-349.3(the)-325.2(sequence)-325.2(of)-337.3(nodes)]TJ
/F9 1 Tf
10.3815 0 TD
-0.0483 Tc
[(re)-46(s)]TJ
/F10 1 Tf
6.9738 0 0 6.9738 425.88 521.22 Tm
0 Tc
(k)Tj
/TT5 1 Tf
9.9626 0 0 9.9626 430.8 522.66 Tm
[(,)-361.4(i)0(f)-337.3(i)0(t)-349.3(e)12(xists,)-361.3(obtained)-313.2(in)-337.3(the)]TJ
-12.2377 -1.2045 TD
[(follo)24.1(wing)-216.8(manner:)]TJ
/F9 1 Tf
2.3367 -2.1922 TD
-0.0483 Tc
[(re)-46(s)]TJ
/F7 1 Tf
6.9738 0 0 6.9738 345.36 487.38 Tm
0 Tc
(0)Tj
/F1 1 Tf
9.9626 0 0 9.9626 368.76 488.82 Tm
()Tj
/F6 1 Tf
1.9995 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 393.36 487.38 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 404.4 488.82 Tm
0 Tc
(\()Tj
/F6 1 Tf
0.3854 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 412.92 487.38 Tm
-0.0454 Tc
[(s)-41.5(eed)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 428.4 488.82 Tm
0 Tc
(\))Tj
/F9 1 Tf
-9.6601 -1.2045 TD
-0.0483 Tc
[(re)-46(s)]TJ
/F10 1 Tf
6.9738 0 0 6.9738 345.36 475.38 Tm
0 Tc
(i)Tj
/F7 1 Tf
0.3958 0 TD
0.0007 Tc
(+1)Tj
/F1 1 Tf
9.9626 0 0 9.9626 368.76 476.82 Tm
0 Tc
()Tj
/F6 1 Tf
1.9995 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 393.36 475.38 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 404.4 476.82 Tm
0 Tc
(\()Tj
/F9 1 Tf
0.3854 0 TD
-0.0483 Tc
[(re)-46(s)]TJ
/F10 1 Tf
6.9738 0 0 6.9738 421.44 475.38 Tm
0 Tc
(i)Tj
/F8 1 Tf
9.9626 0 0 9.9626 424.8 476.82 Tm
(\))Tj
/F3 1 Tf
0.6143 0 TD
0.005 Tc
(union)Tj
/F9 1 Tf
2.8427 0 TD
-0.0483 Tc
[(re)-46(s)]TJ
/F10 1 Tf
6.9738 0 0 6.9738 472.44 475.38 Tm
0 Tc
(i)Tj
/F6 1 Tf
9.9626 0 0 9.9626 485.64 476.82 Tm
1.1676 Tc
(,i)Tj
/F5 1 Tf
2.0718 0 TD
0 Tc
()Tj
/F8 1 Tf
1.0479 0 TD
(0)Tj
/TT5 1 Tf
-20.862 -2.1922 TD
(where)Tj
/F6 1 Tf
2.8042 0 TD
(k)Tj
/F5 1 Tf
1.072 0 TD
()Tj
/F8 1 Tf
1.3009 0 TD
(1)Tj
/TT5 1 Tf
0.8793 0 TD
[(is)-385.4(the)-373.4(minimum)-361.4(number)-349.3(for)-361.4(which)]TJ
/F9 1 Tf
14.6466 0 TD
-0.0483 Tc
[(re)-46(s)]TJ
/F10 1 Tf
6.9738 0 0 6.9738 529.32 453.54 Tm
0 Tc
(k)Tj
1.4454 1.0152 TD
(s)Tj
/F8 1 Tf
9.9626 0 0 9.9626 537.36 454.98 Tm
(=)Tj
/F9 1 Tf
-22.9337 -1.1925 TD
-0.0483 Tc
[(re)-46(s)]TJ
/F10 1 Tf
6.9738 0 0 6.9738 322.08 441.66 Tm
0 Tc
(k)Tj
/F14 1 Tf
0.6195 0 TD
()Tj
/F7 1 Tf
0.8949 0 TD
(1)Tj
/TT5 1 Tf
9.9626 0 0 9.9626 337.08 443.1 Tm
[(.)-481.8(Otherwise,)-313.2(the)-301.1(IFP)-301.1(of)]TJ
/F6 1 Tf
9.8082 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 439.8 441.66 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 450.84 443.1 Tm
0 Tc
(\()Tj
/F3 1 Tf
0.3854 0 TD
0.005 Tc
($x)Tj
/F8 1 Tf
1.0479 0 TD
0 Tc
(\))Tj
/TT5 1 Tf
0.6986 0 TD
[(seeded)-289.1(by)]TJ
/F6 1 Tf
4.3109 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 519.96 441.66 Tm
-0.0454 Tc
[(s)-41.5(eed)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 538.44 443.1 Tm
0 Tc
(is)Tj
/TT7 1 Tf
-23.0421 -1.2045 TD
(unde)Tj
/TT9 1 Tf
1.9438 0 TD
()Tj
/TT7 1 Tf
0.5 0 TD
(ned)Tj
/TT5 1 Tf
1.4438 0 TD
(.)Tj
/F5 1 Tf
19.0041 0 TD
()Tj
/TT5 1 Tf
-22.8918 -2.2765 TD
[(Note)-252.9(that)-265(if)-252.9(e)12(xpression)]TJ
/F6 1 Tf
9.3308 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 406.92 406.98 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 420.6 408.42 Tm
0 Tc
(does)Tj
/TT7 1 Tf
2.086 0 TD
(not)Tj
/TT5 1 Tf
1.5428 0 TD
[(in)36.1(v)24.1(o)0(k)12(e)-240.9(node)-252.9(construc-)]TJ
-14.8427 -1.2045 TD
[(tors)-204.8(\()]TJ
/TT7 1 Tf
2.0378 0 TD
-0.012 Tc
[(e.)-12(g.)]TJ
/TT5 1 Tf
1.4198 0 TD
0 Tc
(,)Tj
/F3 1 Tf
0.4307 0 TD
0.005 Tc
[(element)-144.5({)]TJ
/F1 1 Tf
4.3844 0 TD
0 Tc
()Tj
/F3 1 Tf
0.277 0 TD
0.1736 Tc
(}{)Tj
/F1 1 Tf
1.2286 0 TD
0 Tc
()Tj
/F3 1 Tf
0.277 0 TD
(})Tj
/TT5 1 Tf
0.7227 0 TD
(or)Tj
/F3 1 Tf
1.0378 0 TD
0.005 Tc
[(text)-156.6({)]TJ
/F1 1 Tf
2.8065 0 TD
0 Tc
()Tj
/F3 1 Tf
0.277 0 TD
(})Tj
/TT5 1 Tf
0.53 0 TD
[(\),)-192.7(such)-204.8(that)-204.8(the)-204.8(query)]TJ
-15.4293 -1.2045 TD
[(operates)-277(o)12(v)12(e)0(r)-277(a)]TJ
/TT8 1 Tf
6.3833 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(nite)-301.1(domain)-277(of)-289.1(nodes,)-289.1(IFP)-301.1(will)-301.1(al)12(w)12(ays)-301.1(be)]TJ
-6.9395 -1.1925 TD
(de)Tj
/TT8 1 Tf
0.9438 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(ned.)-457.7(Otherwise,)-301.1(the)-301.1(in)36.1(v)24.1(ocation)-277(of)-301.1(node)-289.1(constructors)-277(in)]TJ
-1.5 -1.2045 TD
[(the)-240.9(recursion)-228.9(body)-228.9(might)-240.9(yield)-240.9(an)-240.9(in)]TJ
/TT8 1 Tf
14.4184 0 TD
()Tj
/TT5 1 Tf
0.5561 0 TD
[(nite)-240.9(node)-240.9(domain)-228.9(and)]TJ
-14.9745 -1.2045 TD
[(IFP)-252.9(might)-228.9(be)-240.9(unde)]TJ
/TT8 1 Tf
7.3892 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
(ned.)Tj
/TT2 1 Tf
-7.9454 -2.3006 TD
[(Example)-240.9(2.2)]TJ
/TT5 1 Tf
5.7626 0 TD
[(In)-252.9(terms)-265(of)-265(the)-265(ne)24.1(w)]TJ
/F3 1 Tf
8.0642 0 TD
0.005 Tc
(with)Tj
/F1 1 Tf
2.2645 0 TD
0.1679 Tc
()Tj
/F3 1 Tf
1.337 0 TD
0.005 Tc
[(seeded)-493.8(by)]TJ
/F1 1 Tf
4.8903 0 TD
0.1679 Tc
()Tj
/F3 1 Tf
-22.3186 -1.1925 TD
0.005 Tc
(recurse)Tj
/TT5 1 Tf
3.9388 0 TD
0 Tc
[(syntactic)-265(form,)-240.9(we)-277(can)-252.9(no)24.1(w)-252.9(e)12(xpress)-252.9(the)-265(transiti)24.1(v)12(e)]TJ
-3.9388 -1.2045 TD
[(closure)-240.9(query)-240.9(from)-252.9(Example)-240.9(1.1)-240.9(in)-265(a)-265(quite)-252.9(concise)-240.9(and)-252.9(ele-)]TJ
0 -1.1925 TD
[(gant)-228.9(f)12(ashion:)]TJ
/F3 1 Tf
0.5902 -2.0597 TD
0.005 Tc
[(with)-505.9($x)-505.9(seeded)-493.8(by)-517.9(doc)-156.6(\("curriculum.xml")12.1(\))]TJ
10.4912 -1.1925 TD
[(/course[@code="c1)12.1("])]TJ
-10.4912 -1.2045 TD
[(recurse)-481.8($x/id)-156.6(\(./prerequisites)12.1(/p)12.1(re_)12.1(co)12.1(de)12.1(\))]TJ
/TT5 1 Tf
21.2353 1.1804 TD
0 Tc
(\(Q1\))Tj
/F5 1 Tf
1.1081 -3.0956 TD
()Tj
/TT5 1 Tf
-22.9337 -2.6017 TD
[(Ob)12(viously)60.2(,)-228.9(the)-265(ne)24.1(w)-252.9(form)]TJ
/F3 1 Tf
10.1519 0 TD
0.005 Tc
(with)Tj
/F1 1 Tf
2.2645 0 TD
0.1679 Tc
()Tj
/F3 1 Tf
1.337 0 TD
0.005 Tc
[(seeded)-493.8(by)]TJ
/F1 1 Tf
4.8903 0 TD
0.1679 Tc
()Tj
/F3 1 Tf
1.325 0 TD
0.005 Tc
(recurse)Tj
/TT5 1 Tf
-19.9687 -1.1925 TD
0 Tc
[(is)-614.3(mere)-590.2(syntactic)-590.2(sugar)-590.2(as)-602.3(it)-614.3(can)-602.2(be)-590.2(equi)24.1(v)24.1(alently)-578.2(e)12(x)0(-)]TJ
0 -1.2045 TD
[(pressed)-481.8(via)-481.8(the)-481.8(recursi)24.1(v)12(e)-469.8(user)24.1(-de)]TJ
/TT8 1 Tf
13.9047 0 TD
()Tj
/TT5 1 Tf
0.5561 0 TD
[(ned)-457.7(function)-469.8(template)]TJ
/F3 1 Tf
-14.4609 -1.2045 TD
0.005 Tc
(fix\()Tj
/F1 1 Tf
2.1199 0 TD
0 Tc
()Tj
/F3 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.9275 0 TD
[(\(sho)24.1(wn)-409.5(in)]TJ
ET
387.6 163.74 m
387.6 172.244 l
407.443 172.244 l
407.443 163.74 l
h
407.443 172.244 m
S
BT
9.9626 0 0 9.9626 411.96 164.58 Tm
[(in)-421.6(Figure)-409.5(2\).)-843.2(Since)-421.6(the)-421.6(syntac-)]TJ
-10.3467 -1.1925 TD
[(tic)-505.9(form)-505.9(is)-517.9(a)-505.9(second-order)-469.8(construct)-493.8(taking)-493.8(an)-505.9(XQuery)]TJ
0 -1.2045 TD
[(v)24.1(ariable)-313.2(name)-313.2(and)-313.2(tw)12(o)-325.2(XQuery)-313.2(e)12(xpressions)-313.2(as)-325.2(ar)12(guments,)]TJ
0 -1.1925 TD
(function)Tj
/F3 1 Tf
3.8143 0 TD
0.005 Tc
(fix\()Tj
/F1 1 Tf
2.1199 0 TD
0 Tc
()Tj
/F3 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
1.0118 0 TD
[(has)-505.9(to)-505.9(be)-505.9(interpreted)-481.8(as)-517.9(a)-505.9(template)-493.9(in)]TJ
-7.2231 -1.2045 TD
[(which)-505.9(the)-505.9(recursion)-493.8(body)]TJ
/F3 1 Tf
11.3857 0 TD
0.005 Tc
(rec\()Tj
/F1 1 Tf
2.1199 0 TD
0 Tc
()Tj
/F3 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
1.0238 0 TD
[(needs)-505.9(to)-517.9(be)-505.9(instanti-)]TJ
-14.8065 -1.2045 TD
[(ated)-252.9(\(XQuery)-240.9(1.0)-252.9(does)-252.9(not)-252.9(support)-240.9(higher)24.1(-order)-216.8(functions\).)]TJ
0 -1.1925 TD
[(Gi)24.1(v)12(e)0(n)-349.3(this,)-385.4(Expression)-349.3(\(1\))-349.3(is)-373.4(equi)24.1(v)24.1(alent)-337.3(to)-361.3(the)-361.4(e)12(xpression)]TJ
/F3 1 Tf
0 -1.2045 TD
0.005 Tc
[(let)-505.9($x)-517.9(:=)]TJ
/F6 1 Tf
5.2517 0 TD
0 Tc
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 365.88 79.5 Tm
-0.0454 Tc
[(s)-41.5(eed)]TJ
/F3 1 Tf
9.9626 0 0 9.9626 386.52 80.94 Tm
0.005 Tc
[(return)-493.8(fix)-168.6(\(rec)-156.6(\($x\)\))]TJ
/TT5 1 Tf
10.3227 0 TD
0 Tc
(.)Tj
-19.501 -2.9992 TD
(2)Tj
ET
endstream
endobj
21 0 obj
<<
/ProcSet [/PDF /Text /ImageB ]
/Font <<
/F1 4 0 R
/F3 6 0 R
/F4 7 0 R
/F5 8 0 R
/F6 22 0 R
/F7 23 0 R
/F8 24 0 R
/F9 25 0 R
/F10 26 0 R
/F11 27 0 R
/F12 28 0 R
/F13 29 0 R
/F14 30 0 R
/TT2 9 0 R
/TT3 10 0 R
/TT5 11 0 R
/TT7 12 0 R
/TT8 13 0 R
/TT9 14 0 R
/TT11 15 0 R
/TT12 16 0 R
/TT14 31 0 R
/TT15 32 0 R
>>
/XObject <<
/Im1 33 0 R
>>
/ExtGState <<
/GS1 17 0 R
>>
>>
endobj
35 0 obj
<<
/Length 19626
>>
stream
BT
/TT2 1 Tf
9.9626 0 0 9.9626 50.16 709.98 Tm
0 g
/GS1 gs
0 Tc
0 Tw
[(Using)-192.7(IFP)-204.8(to)-192.7(Compute)-192.7(T)72.3(ransiti)12(v)12(e)-204.8(Closur)12(e.)]TJ
/TT5 1 Tf
18.6721 0 TD
[(Much)-180.7(lik)12(e)-204.8(i)0(n)]TJ
-18.6721 -1.2045 TD
[(the)-301.1(relational)-301.1(conte)12(xt,)]TJ
/TT7 1 Tf
9.0822 0 TD
[(tr)12(ansitive)-313.2(closur)36.1(e)]TJ
/TT5 1 Tf
7.2873 0 TD
[(is)-325.2(an)-301.1(archetype)-289.1(of)]TJ
-16.3696 -1.1925 TD
[(recursi)24.1(v)12(e)-216.8(computation)-216.8(o)12(v)12(e)0(r)-228.9(XML)-252.9(instances.)-301.1(Re)12(gular)-228.9(XP)12(ath)]TJ
0 -1.2045 TD
[([21)24.1(],)-216.8(for)-204.8(e)12(xample,)-192.7(de)]TJ
/TT8 1 Tf
8.2412 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(nes)-204.8(the)-216.8(transiti)24.1(v)12(e)-192.7(closure)-204.8(of)-204.8(XP)12(ath)-204.8(lo-)]TJ
-8.7974 -1.2045 TD
[(cation)-265(steps)-277(to)-289.1(obtain)-265(po)24.1(werful)-252.9(primiti)24.1(v)12(e)0(s)-265(that)-265(e)12(xpress)-277(hor)24.1(-)]TJ
0 -1.1925 TD
[(izontal)-313.2(and)-325.2(v)12(ertical)-313.2(structural)-325.2(recursion.)-530(W)84.3(e)-337.3(can)-325.2(naturally)]TJ
0 -1.2045 TD
[(e)12(xtend)-409.5(this)-445.7(de)]TJ
/TT8 1 Tf
5.8973 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(nition)-421.6(to)-433.6(an)12(y)-433.6(XQuery)-421.6(e)12(xpression)-421.6(of)-421.6(type)]TJ
/F3 1 Tf
-6.4535 -1.1924 TD
0.005 Tc
(node\(\)*)Tj
/TT5 1 Tf
3.7099 0 TD
0 Tc
(.)Tj
/TT2 1 Tf
-3.7099 -1.9995 TD
(De)Tj
/TT3 1 Tf
1.166 0 TD
()Tj
/TT2 1 Tf
0.5562 0 TD
[(nition)-240.9(2.3)]TJ
/TT14 1 Tf
4.4737 0 TD
[(\(T)36.1(ransitiv)12(e)-252.9(Closure\))]TJ
/TT5 1 Tf
8.5134 0 TD
(Let)Tj
/F6 1 Tf
1.5855 0 TD
(e)Tj
/TT5 1 Tf
0.7227 0 TD
[(be)-252.9(an)-252.9(e)12(xpression)]TJ
-17.0174 -1.1925 TD
[(of)-240.9(type)]TJ
/F3 1 Tf
3.0244 0 TD
0.005 Tc
(node\(\)*)Tj
/TT5 1 Tf
3.7099 0 TD
0 Tc
[(.)-277(The)]TJ
/TT7 1 Tf
2.3226 0 TD
[(tr)12(ansitive)-240.9(closur)36.1(e)]TJ
/F6 1 Tf
7.1548 0 TD
(e)Tj
/F11 1 Tf
6.9738 0 0 6.9738 216.84 598.14 Tm
(+)Tj
/TT7 1 Tf
9.9626 0 0 9.9626 223.44 594.54 Tm
(of)Tj
/F6 1 Tf
1.1753 0 TD
(e)Tj
/TT5 1 Tf
0.7107 0 TD
(is)Tj
/F6 1 Tf
-15.4366 -2.1922 TD
(e)Tj
/F3 1 Tf
0.7107 0 TD
0.005 Tc
(union)Tj
/F6 1 Tf
2.8788 0 TD
0 Tc
(e)Tj
/F3 1 Tf
0.4698 0 TD
(/)Tj
/F6 1 Tf
0.5179 0 TD
(e)Tj
/F3 1 Tf
0.7227 0 TD
0.005 Tc
(union)Tj
/F6 1 Tf
2.8667 0 TD
0 Tc
(e)Tj
/F3 1 Tf
0.4698 0 TD
(/)Tj
/F6 1 Tf
0.53 0 TD
(e)Tj
/F3 1 Tf
0.4698 0 TD
(/)Tj
/F6 1 Tf
0.5179 0 TD
(e)Tj
/F3 1 Tf
0.7107 0 TD
0.005 Tc
(union)Tj
/F1 1 Tf
3.0474 0 TD
0.1679 Tc
()Tj
/F6 1 Tf
1.8309 0 TD
0 Tc
(,)Tj
/TT5 1 Tf
2.9631 0 TD
(\(2\))Tj
-22.5484 -2.1922 TD
[(if)-385.4(the)-385.4(resulting)-361.4(node)-373.4(sequence)-373.4(is)]TJ
/TT8 1 Tf
13.8839 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(nite.)-722.7(Otherwise,)]TJ
/F6 1 Tf
7.2416 0 TD
(e)Tj
/F11 1 Tf
6.9738 0 0 6.9738 271.68 554.46 Tm
(+)Tj
/TT5 1 Tf
9.9626 0 0 9.9626 279.72 550.86 Tm
(is)Tj
/TT7 1 Tf
-23.0421 -1.2045 TD
(unde)Tj
/TT9 1 Tf
1.9438 0 TD
()Tj
/TT7 1 Tf
0.5 0 TD
(ned)Tj
/TT5 1 Tf
1.4438 0 TD
(.)Tj
/F5 1 Tf
19.0041 0 TD
()Tj
/TT5 1 Tf
-22.8918 -1.9874 TD
[(Gi)24.1(v)12(e)0(n)-180.7(simple)-204.8(restrictions)-192.7(on)]TJ
/F6 1 Tf
11.2885 0 TD
(e)Tj
/TT5 1 Tf
0.4698 0 TD
[(,)-204.8(see)-204.8(Section)-192.7(3.1,)-192.7(with)-204.8(the)-192.7(ne)24.1(w)]TJ
-11.7582 -1.2045 TD
[(IFP)-240.9(form)]TJ
/F6 1 Tf
3.8589 0 TD
(e)Tj
/F11 1 Tf
6.9738 0 0 6.9738 93.48 510.66 Tm
(+)Tj
/TT5 1 Tf
9.9626 0 0 9.9626 100.2 507.06 Tm
[(is)-252.9(\()]TJ
/F3 1 Tf
1.586 0 TD
(.)Tj
/TT5 1 Tf
0.53 0 TD
[()-289.1(denotes)-240.9(the)-240.9(conte)12(xt)-228.9(node\):)]TJ
/F3 1 Tf
-4.0431 -2.1801 TD
0.005 Tc
[(with)-505.9($x)-505.9(seeded)-505.9(by)-505.9(.)-517.9(recurse)-493.8($x/)]TJ
/F6 1 Tf
16.285 0 TD
0.4859 Tc
(e.)Tj
/TT2 1 Tf
-19.3806 -2.6619 TD
0 Tc
[(IFP)-409.5(in)-421.6(SQL:1999.)]TJ
/TT5 1 Tf
8.8235 0 TD
[(IFP)-421.6(has)-409.5(found)-385.4(its)-421.6(w)12(a)0(y)-421.6(into)-397.5(SQL)-421.6(in)]TJ
-8.8235 -1.2045 TD
[(terms)-433.6(of)-433.6(the)]TJ
/F3 1 Tf
5.5772 0 TD
0.005 Tc
[(WITH)-505.9(RECURSIVE)]TJ
/TT5 1 Tf
7.7812 0 TD
0 Tc
[(clause)-445.7(introduced)-397.5(by)-433.6(the)]TJ
-13.3584 -1.2045 TD
[(ANSI/ISO)-204.8(SQL:1999)-192.7(standard)-192.7([22)12(].)-289.1(T)84.3(o)-216.8(e)12(x)12(emplify)60.2(,)-180.7(consider)]TJ
0 -1.1925 TD
[(the)-301.1(table)]TJ
/F3 1 Tf
3.7793 0 TD
(C)Tj
/F8 1 Tf
0.53 0 TD
(\()Tj
/F3 1 Tf
0.3854 0 TD
0.005 Tc
(course)Tj
/F6 1 Tf
3.1558 0 TD
0 Tc
(,)Tj
/F3 1 Tf
0.4457 0 TD
0.005 Tc
(prerequisite)Tj
/F8 1 Tf
6.2996 0 TD
0 Tc
(\))Tj
/TT5 1 Tf
0.6986 0 TD
[(as)-325.2(a)-313.2(relational)-301.1(repre-)]TJ
-15.2945 -1.2045 TD
[(sentation)-252.9(of)-265(the)-265(curriculum)-240.9(XML)-277(data)-265(\(Figure)-252.9(1\).)-373.4(The)-265(pre-)]TJ
0 -1.1925 TD
(requisites)Tj
/F3 1 Tf
4.1577 0 TD
(P)Tj
/F8 1 Tf
0.53 0 TD
(\()Tj
/F3 1 Tf
0.3854 0 TD
0.005 Tc
(course_code)Tj
/F8 1 Tf
5.7696 0 TD
0 Tc
(\))Tj
/TT5 1 Tf
0.7347 0 TD
[(of)-325.2(the)-337.3(course)-313.2(with)-337.3(code)]TJ
/F3 1 Tf
9.9682 0 TD
0.005 Tc
(c1)Tj
/TT5 1 Tf
-21.5457 -1.2045 TD
0 Tc
[(then)-228.9(are:)]TJ
/F3 1 Tf
0.807 -2.0236 TD
0.005 Tc
[(WITH)-493.8(RECURSIVE)-481.8(P\(course_code\))-457.7(AS)]TJ
0.9997 -1.3009 TD
[(\(SELECT)-481.8(prerequisite)]TJ
0.5179 -1.2045 TD
[(FROM)-1553.8(C)]TJ
T*
[(WHERE)-1023.8(course)-493.8(=)-530(c1\))]TJ
/F15 1 Tf
17.923 3.3124 TD
0 Tc
()Tj
0 -0.9034 TD
()Tj
0 -1.7947 TD
()Tj
/TT5 1 Tf
7.9701 0 0 7.9701 262.44 342.54 Tm
(seed)Tj
/F3 1 Tf
9.9626 0 0 9.9626 63.12 317.82 Tm
0.005 Tc
[(UNION)-505.9(ALL)]TJ
0.5059 -1.2888 TD
[(\(SELECT)-481.8(C.prerequisite)]TJ
0.5179 -1.2045 TD
[(FROM)-1553.8(P,)-517.9(C)]TJ
T*
[(WHERE)-1023.8(P.course_code)-457.7(=)-530(C.course\))]TJ
/F15 1 Tf
17.923 3.3003 TD
0 Tc
()Tj
0 -0.8913 TD
()Tj
0 -1.8068 TD
()Tj
/TT5 1 Tf
7.9701 0 0 7.9701 262.44 293.46 Tm
(body)Tj
/F3 1 Tf
9.9626 0 0 9.9626 58.2 268.86 Tm
0.005 Tc
[(SELECT)-493.8(DISTINCT)-481.8(*)-517.9(FROM)-505.9(P;)]TJ
/TT5 1 Tf
-0.807 -2.1681 TD
0 Tc
[(Analogous)-361.4(to)-373.4(the)-385.4(XQuery)-373.4(v)24.1(ariant,)-397.5(table)]TJ
/F3 1 Tf
16.7638 0 TD
(P)Tj
/TT5 1 Tf
0.9154 0 TD
[(is)-397.5(seeded)-373.4(with)]TJ
-17.6792 -1.2045 TD
[(the)-265(direct)-252.9(prerequisites)-252.9(of)-265(course)]TJ
/F3 1 Tf
13.3391 0 TD
0.005 Tc
(c1)Tj
/TT5 1 Tf
2.3729 0 TD
0 Tc
[(before)-252.9(the)-265(join)-265(with)]TJ
-15.712 -1.1925 TD
(table)Tj
/F3 1 Tf
2.1602 0 TD
(C)Tj
/TT5 1 Tf
0.7588 0 TD
[(in)-228.9(the)-228.9(body)-216.8(is)-228.9(iterated)-228.9(to)-228.9(also)-228.9(add)-216.8(all)-240.9(indirect)-216.8(prereq-)]TJ
-2.919 -1.2045 TD
[(uisites)-252.9(until)]TJ
/F3 1 Tf
4.883 0 TD
(P)Tj
/TT5 1 Tf
0.7709 0 TD
[(does)-240.9(not)-240.9(gro)24.1(w)-228.9(further)60.2(.)]TJ
-4.4614 -1.2045 TD
[(The)-361.4(SQL:1999)-337.3(standard)-337.3(dictates)-361.4(quite)-349.3(rigid)-349.3(syntactical)]TJ
-1.1925 -1.1925 TD
[(restrictions)-409.5(for)-421.6(the)]TJ
/F3 1 Tf
8.0837 0 TD
0.005 Tc
[(WITH)-505.9(RECURSIVE)]TJ
/TT5 1 Tf
7.7812 0 TD
0 Tc
[(form)-421.6(\(the)-421.6(body)60.2(,)-445.7(i)0(n)]TJ
-15.8649 -1.2045 TD
[(particular)36.1(,)-397.5(must)-397.5(be)]TJ
/TT7 1 Tf
8.114 0 TD
(linear)Tj
/TT5 1 Tf
2.4128 0 TD
(:)Tj
/F3 1 Tf
0.8801 0 TD
(P)Tj
/TT5 1 Tf
0.9275 0 TD
[(may)-385.4(occur)-385.4(only)-373.4(once)-385.4(in)-397.5(its)]TJ
/F3 1 Tf
-12.3343 -1.2045 TD
0.005 Tc
(FROM)Tj
/TT5 1 Tf
2.3488 0 TD
0 Tc
[(clause\).)-289.1(W)84.3(e)-265(will)-252.9(return)-228.9(to)-240.9(this)-252.9(in)-240.9(Section)-240.9(3.2)-228.9(and)-240.9(6.)]TJ
/TT2 1 Tf
10.9589 0 0 10.9589 50.16 141.66 Tm
[(2.1)11(.)-240.9(Algorithms)-251.9(f)21.9(o)0(r)-240.9(IFP)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 62.04 116.82 Tm
[(The)-252.9(semantics)-265(of)-252.9(the)-265(in)]TJ
/TT8 1 Tf
9.3664 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
(ationary)Tj
/TT8 1 Tf
3.5052 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(x)12(e)0(d)-252.9(point)-252.9(in)-265(XQuery)60.2(,)]TJ
/TT7 1 Tf
-15.1764 -1.2045 TD
[(i.e)12(.)]TJ
/TT5 1 Tf
1.2096 0 TD
[(,)-313.2(the)-301.1(speci)]TJ
/TT8 1 Tf
4.1407 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(cation)-301.1(of)-301.1(the)-313.2(node)-289.1(sequence)]TJ
/F9 1 Tf
11.6 0 TD
-0.0483 Tc
[(re)-46(s)]TJ
/F10 1 Tf
6.9738 0 0 6.9738 238.68 103.38 Tm
0 Tc
(k)Tj
/TT5 1 Tf
9.9626 0 0 9.9626 246.72 104.82 Tm
[(of)-301.1(De)]TJ
/TT8 1 Tf
2.3001 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
(ni-)Tj
-22.586 -1.1925 TD
[(tion)-373.4(2.1,)-397.5(can)-373.4(be)-373.4(straightforw)12(ardly)-337.3(turned)-361.3(into)-373.4(an)-385.4(iterati)24.1(v)12(e)]TJ
0 -1.2045 TD
[(algorithm)-289.1(to)-325.2(compute)-301.1(IFP)108.4(.)-313.2(Figure)-313.2(3\(a\))-313.2(sho)24.1(ws)-313.2(the)-325.2(resulting)]TJ
/F16 1 Tf
8.9664 0 0 8.9664 309.96 708.1801 Tm
-0.0581 Tc
[(re)-54.3(s)]TJ
/F17 1 Tf
1.6462 0 TD
0 Tc
()Tj
/F18 1 Tf
1.3116 0 TD
(e)Tj
/F13 1 Tf
5.9776 0 0 5.9776 340.8 707.22 Tm
-0.0607 Tc
(rec)Tj
/F19 1 Tf
8.9664 0 0 8.9664 350.28 708.1801 Tm
0 Tc
(\()Tj
/F18 1 Tf
0.4015 0 TD
(e)Tj
/F13 1 Tf
5.9776 0 0 5.9776 358.2 707.1 Tm
-0.0626 Tc
[(s)-58.7(eed)]TJ
/F19 1 Tf
8.9664 0 0 8.9664 371.52 708.1801 Tm
0 Tc
(\))Tj
/TT5 1 Tf
0.4015 0 TD
(;)Tj
/TT2 1 Tf
-7.2672 -2.4358 TD
(do)Tj
ET
q
0.48 0 0 -19.32 314.988 682.9681 cm
/Im1 Do
Q
BT
/F16 1 Tf
8.9664 0 0 8.9664 325.32 665.9401 Tm
-0.0581 Tc
[(re)-54.3(s)]TJ
/F17 1 Tf
1.6328 0 TD
0 Tc
()Tj
/F18 1 Tf
1.325 0 TD
(e)Tj
/F13 1 Tf
5.9776 0 0 5.9776 356.16 664.98 Tm
-0.0607 Tc
(rec)Tj
/F19 1 Tf
8.9664 0 0 8.9664 365.64 665.9401 Tm
0 Tc
(\()Tj
/F16 1 Tf
0.4015 0 TD
-0.0581 Tc
[(re)-54.3(s)]TJ
/F19 1 Tf
1.3518 0 TD
0 Tc
(\))Tj
/F4 1 Tf
0.629 0 TD
-0.003 Tc
(union)Tj
/F16 1 Tf
2.8507 0 TD
-0.0581 Tc
[(re)-54.3(s)]TJ
/TT5 1 Tf
1.3518 0 TD
0 Tc
(;)Tj
/TT2 1 Tf
-12.7947 -1.0974 TD
(while)Tj
/F16 1 Tf
2.5187 0 TD
-0.0581 Tc
[(re)-54.3(s)]TJ
/TT5 1 Tf
1.606 0 TD
0 Tc
[(gro)26.8(ws;)]TJ
-1.8764 -1.606 TD
[(\(a\))-361.4(Algorithm)]TJ
/TT7 1 Tf
5.892 0 TD
[(Na)26.8()]TJ
/TT9 1 Tf
1.1654 0 TD
()Tj
/TT7 1 Tf
0.2778 0 TD
(ve)Tj
ET
q
0.48 0 0 -85.32 433.548 720.048 cm
/Im1 Do
Q
BT
/F16 1 Tf
8.9664 0 0 8.9664 441.84 708.1801 Tm
-0.0581 Tc
[(re)-54.3(s)]TJ
/F17 1 Tf
1.6462 0 TD
0 Tc
()Tj
/F18 1 Tf
1.3116 0 TD
(e)Tj
/F13 1 Tf
5.9776 0 0 5.9776 472.68 707.22 Tm
-0.0607 Tc
(rec)Tj
/F19 1 Tf
8.9664 0 0 8.9664 482.28 708.1801 Tm
0 Tc
(\()Tj
/F18 1 Tf
0.4015 0 TD
(e)Tj
/F13 1 Tf
5.9776 0 0 5.9776 490.2 707.1 Tm
-0.0626 Tc
[(s)-58.7(eed)]TJ
/F19 1 Tf
8.9664 0 0 8.9664 503.52 708.1801 Tm
0 Tc
(\))Tj
/TT5 1 Tf
0.4015 0 TD
(;)Tj
/F19 1 Tf
-7.2805 -1.2179 TD
()Tj
/F17 1 Tf
1.151 0 TD
()Tj
/F16 1 Tf
1.3116 0 TD
-0.0581 Tc
[(re)-54.3(s)]TJ
/TT5 1 Tf
1.3518 0 TD
0 Tc
(;)Tj
/TT2 1 Tf
-3.8144 -1.2179 TD
(do)Tj
ET
q
0.48 0 0 -18.96 446.868 683.0881 cm
/Im1 Do
Q
BT
/F19 1 Tf
8.9664 0 0 8.9664 457.2 676.26 Tm
()Tj
/F17 1 Tf
1.151 0 TD
()Tj
/F18 1 Tf
1.3116 0 TD
(e)Tj
/F13 1 Tf
5.9776 0 0 5.9776 483.6 675.3 Tm
-0.0607 Tc
(rec)Tj
/F19 1 Tf
8.9664 0 0 8.9664 493.08 676.26 Tm
0.001 Tc
(\(\))Tj
/F4 1 Tf
1.8871 0 TD
-0.003 Tc
(except)Tj
/F16 1 Tf
3.3861 0 TD
-0.0581 Tc
[(re)-54.3(s)]TJ
/TT5 1 Tf
1.3518 0 TD
0 Tc
(;)Tj
/F16 1 Tf
-10.6266 -1.2179 TD
-0.0581 Tc
[(re)-54.3(s)]TJ
/F17 1 Tf
1.6462 0 TD
0 Tc
()Tj
/F19 1 Tf
1.3116 0 TD
()Tj
/F4 1 Tf
1.0841 0 TD
-0.003 Tc
(union)Tj
/F16 1 Tf
2.8507 0 TD
-0.0581 Tc
[(re)-54.3(s)]TJ
/TT5 1 Tf
1.3518 0 TD
0 Tc
(;)Tj
/TT2 1 Tf
-9.9574 -0.9904 TD
(while)Tj
/F16 1 Tf
2.5187 0 TD
-0.0581 Tc
[(re)-54.3(s)]TJ
/TT5 1 Tf
1.606 0 TD
0 Tc
[(gro)26.8(ws;)]TJ
-1.7158 -1.606 TD
[(\(b\))-361.4(Algorithm)]TJ
/TT7 1 Tf
5.9615 0 TD
(Delta)Tj
/TT11 1 Tf
9.9626 0 0 9.9626 320.76 616.5 Tm
[(Figure)-469.8(3.)-457.7(Algorithms)-457.7(to)-445.7(e)12(v)24.1(aluate)-469.8(the)-457.7(IFP)-469.8(of)]TJ
/F6 1 Tf
0 -1.2045 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 325.44 603.0601 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT11 1 Tf
9.9626 0 0 9.9626 339.36 604.5 Tm
0 Tc
(given)Tj
/F6 1 Tf
2.8889 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 372.84 603.0601 Tm
-0.0454 Tc
[(s)-41.5(eed)]TJ
/TT11 1 Tf
9.9626 0 0 9.9626 388.32 604.5 Tm
0 Tc
[(.)-337.3(Result)-277(is)]TJ
/F9 1 Tf
5.0593 0 TD
-0.0483 Tc
[(re)-46(s)]TJ
/TT11 1 Tf
1.325 0 TD
0 Tc
(.)Tj
/F4 1 Tf
8.9664 0 0 8.9664 320.28 574.02 Tm
-0.003 Tc
[(declare)-548.7(function)-548.7(delta)-187.3(\($x,$res\))-548.7(as)-535.3(node\(\)*)]TJ
0 -1.0974 TD
[({)-535.3(let)-521.9($delta)-548.7(:=)-535.3(rec)-174(\($x\))-548.7(except)-535.3($res)]TJ
1.0573 -1.0974 TD
[(return)-535.3(if)-535.3(\(empty)-187.3(\($delta\)\))]TJ
3.667 -1.0974 TD
[(then)-535.3($res)]TJ
T*
[(else)-535.3(delta)-187.3(\($delta,$delta)-575.4(union)-535.3($res\))]TJ
-4.7243 -1.1108 TD
(};)Tj
/TT11 1 Tf
9.9626 0 0 9.9626 329.4 502.86 Tm
0 Tc
[(Figure)-277(4.)-277(An)-277(XQuer)-12(y)-277(f)24.1(orm)24.1(ulation)-277(of)-265(Delta.)]TJ
/TT5 1 Tf
-2.0597 -3.2401 TD
[(procedure,)-277(commonly)-277(referred)-277(to)-301.1(as)]TJ
/TT7 1 Tf
14.7447 0 TD
(Na)Tj
1.251 -0.012 TD
()Tj
/TT9 1 Tf
0.0241 0.012 TD
()Tj
/TT7 1 Tf
0.2778 0 TD
(ve)Tj
/TT5 1 Tf
1.1888 0 TD
[(in)-301.1(the)-301.1(literature)]TJ
-17.4865 -1.2045 TD
[([5)12(].)-517.9(In)-313.2(the)]TJ
/TT2 1 Tf
4.6029 0 TD
(do)Tj
/F1 1 Tf
1.2127 0 TD
0.1679 Tc
()Tj
/TT2 1 Tf
1.337 0 TD
0 Tc
(while)Tj
/TT5 1 Tf
2.603 0 TD
[(loop)-301.1(body)60.2(,)-313.2(the)-313.2(procedure)-289.1(calls)-313.2(out)]TJ
-9.7557 -1.1925 TD
[(to)-265(the)-265(recursion)60.2(s)-252.9(payload)-252.9(function)]TJ
/F6 1 Tf
14.157 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 455.52 445.26 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 466.68 446.7 Tm
0 Tc
(\()Tj
/F1 1 Tf
0.3854 0 TD
()Tj
/F8 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.6625 0 TD
[(to)-265(determine)-252.9(the)]TJ
-17.1641 -1.2045 TD
[(ne)12(xt)-204.8(portion)-192.7(of)-216.8(nodes)-204.8(that)-216.8(will)-228.9(augment)-204.8(the)-216.8(current)-192.7(interme-)]TJ
T*
[(diate)-349.3(result.)-614.3(Only)-349.3(if)]TJ
/F6 1 Tf
8.6881 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 400.44 421.26 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 411.6 422.7 Tm
0 Tc
(\()Tj
/F1 1 Tf
0.3854 0 TD
()Tj
/F8 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.7468 0 TD
[(cannot)-337.3(contrib)24.1(ute)-325.2(ne)24.1(w)-349.3(nodes,)]TJ
-11.7198 -1.1925 TD
[(the)-240.9(procedure)-216.8(returns)-228.9(the)-240.9(current)]TJ
/F9 1 Tf
13.2056 0 TD
-0.0483 Tc
[(re)-46(s)]TJ
/TT5 1 Tf
1.325 0 TD
0 Tc
(.)Tj
-13.3382 -1.2165 TD
(Since)Tj
/F9 1 Tf
2.4385 0 TD
-0.0483 Tc
[(re)-46(s)]TJ
/TT5 1 Tf
1.5418 0 TD
0 Tc
[(gro)24.1(ws,)-204.8(this)-228.9(feeds)-204.8(the)-216.8(same)-204.8(nodes)-204.8(o)12(v)12(e)0(r)-192.7(and)-216.8(o)12(v)12(e)0(r)]TJ
-5.1727 -1.1925 TD
[(again)-397.5(into)]TJ
/F6 1 Tf
4.5403 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 359.04 385.38 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 370.08 386.82 Tm
0 Tc
(\()Tj
/F1 1 Tf
0.3854 0 TD
()Tj
/F8 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.3854 0 TD
[(.)-843.1(Dependent)-385.4(on)-421.6(the)-409.5(nature)-409.5(of)-409.5(the)-421.6(pay-)]TJ
-7.1909 -1.2045 TD
(load,)Tj
/F6 1 Tf
2.2849 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 336.48 373.38 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 347.52 374.82 Tm
0 Tc
(\()Tj
/F1 1 Tf
0.3854 0 TD
()Tj
/F8 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.3854 0 TD
[()60.2(s)-325.2(answer)-313.2(might)-289.1(include)-301.1(nodes)-301.1(which)-301.1(we)-313.2(ha)24.1(v)12(e)]TJ
-4.9264 -1.1925 TD
[(seen)-252.9(before.)-313.2(Ultimately)60.2(,)]TJ
/TT7 1 Tf
9.8663 0 TD
(Na)Tj
1.1911 -0.0121 TD
()Tj
/TT9 1 Tf
0.0241 0.0121 TD
()Tj
/TT7 1 Tf
0.2778 0 TD
(ve)Tj
/TT5 1 Tf
1.1406 0 TD
[(risks)-252.9(to)-265(initiate)-252.9(a)-252.9(substantial)]TJ
-12.4999 -1.2045 TD
[(amount)-228.9(of)-240.9(redundant)-204.8(computation.)]TJ
0 -1.5177 TD
[(A)-578.2(n)0(o)24.1(w)-578.2(folklore)-554.1(v)24.1(ariation)-566.1(of)]TJ
/TT7 1 Tf
12.8036 0 TD
(Na)Tj
1.2168 -0.0121 TD
()Tj
/TT9 1 Tf
0.0241 0.0121 TD
()Tj
/TT7 1 Tf
0.2778 0 TD
(ve)Tj
/TT5 1 Tf
1.4659 0 TD
[(is)-590.2(the)]TJ
/TT7 1 Tf
3.057 0 TD
(Delta)Tj
/TT5 1 Tf
2.7998 0 TD
(algo-)Tj
-21.645 -1.2045 TD
[(rithm)-373.4([17)24.1(])-385.4(o)0(f)-373.4(Figure)-361.4(3\(b\).)-686.6(In)-373.4(this)-385.4(v)24.1(ariant,)-385.4(the)-385.4(payload)-349.3(is)]TJ
0 -1.1925 TD
[(in)36.1(v)24.1(o)0(k)12(e)0(d)-349.3(only)-361.3(for)-373.4(those)-373.4(nodes)-361.4(that)-373.4(ha)24.1(v)12(e)-373.4(not)-373.4(been)-361.3(encoun-)]TJ
0 -1.2045 TD
[(tered)-204.8(in)-204.8(earlier)-204.8(iterations:)-289.1(node)-192.7(sequence)]TJ
/F8 1 Tf
16.2258 0 TD
()Tj
/TT5 1 Tf
1.0479 0 TD
[(is)-228.9(the)-204.8(dif)24.1(ference)]TJ
-17.2737 -1.2045 TD
(between)Tj
/F6 1 Tf
3.5965 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 349.56 286.5 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 360.72 287.94 Tm
0 Tc
(\()Tj
/F1 1 Tf
0.3854 0 TD
()Tj
/F8 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.3854 0 TD
[()60.2(s)-301.1(last)-289.1(answer)-277(and)-277(the)-277(current)-265(result)]TJ
/F9 1 Tf
14.5768 0 TD
-0.0483 Tc
[(re)-46(s)]TJ
/TT5 1 Tf
1.3129 0 TD
0.4216 Tc
[(.I)421.6(n)]TJ
-22.1411 -1.1925 TD
0 Tc
(general,)Tj
/F6 1 Tf
3.4212 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 347.88 274.62 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 358.92 276.06 Tm
0 Tc
(\()Tj
/F1 1 Tf
0.3854 0 TD
()Tj
/F8 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.6384 0 TD
[(will)-252.9(thus)-240.9(process)-240.9(fe)24.1(wer)-240.9(nodes.)]TJ
/TT7 1 Tf
-5.1312 -1.2165 TD
(Delta)Tj
/TT5 1 Tf
2.5228 0 TD
[(introduces)-277(a)-289.1(signi)]TJ
/TT8 1 Tf
7.1203 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(cant)-289.1(potential)-277(for)-289.1(performance)]TJ
-11.3917 -1.1925 TD
[(impro)12(v)12(ement,)-614.3(especially)-566.1(for)-566.1(lar)12(ge)-566.1(node)-566.1(sequences)-566.1(and)]TJ
0 -1.2045 TD
[(computationally)-542(e)12(xpensi)24.1(v)12(e)-554.1(payloads)-554.1(\(Section)-566.1(5\).)-1288.8(Fig-)]TJ
T*
[(ure)-710.7(4)-722.7(sho)24.1(ws)-722.7(the)-722.7(corresponding)-686.6(XQuery)-710.7(user)24.1(-de)]TJ
/TT8 1 Tf
21.6116 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
(ned)Tj
-22.1677 -1.1925 TD
(function)Tj
/F3 1 Tf
3.8384 0 TD
0.005 Tc
(delta\()Tj
/F1 1 Tf
3.1799 0 TD
0 Tc
()Tj
/F3 1 Tf
0.277 0 TD
(,)Tj
/F1 1 Tf
0.53 0 TD
()Tj
/F3 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
1.0359 0 TD
[(which,)-590.2(for)-530(Example)-517.9(1.1)-530(and)-517.9(thus)]TJ
-9.1383 -1.2045 TD
[(Query)-409.5(Q1,)-457.7(can)-409.5(serv)12(e)-421.6(a)0(s)-421.6(a)-421.6(drop-in)-397.5(replacement)-397.5(for)-409.5(func-)]TJ
T*
(tion)Tj
/F3 1 Tf
1.8207 0 TD
0.005 Tc
(fix\()Tj
/F1 1 Tf
2.1199 0 TD
0 Tc
()Tj
/F3 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.53 0 TD
[(line)-252.9(14)-265(then)-265(needs)-265(to)-265(be)-277(replaced)-252.9(by)]TJ
/F3 1 Tf
15.7138 0 TD
0.005 Tc
(return)Tj
-20.4615 -1.1925 TD
[(delta)-144.5(\(rec)-156.6(\($seed\),\(\)\))]TJ
/TT5 1 Tf
10.9009 0 TD
0 Tc
(.)Tj
-10.9009 -1.5177 TD
[(Is)-216.8(this)-216.8(replacement)-192.7(of)]TJ
/F3 1 Tf
8.7169 0 TD
0.005 Tc
(fix\()Tj
/F1 1 Tf
2.1199 0 TD
0 Tc
()Tj
/F3 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.7347 0 TD
(by)Tj
/F3 1 Tf
1.2048 0 TD
0.005 Tc
(delta\()Tj
/F1 1 Tf
3.1799 0 TD
0 Tc
()Tj
/F3 1 Tf
0.277 0 TD
(,)Tj
/F1 1 Tf
0.53 0 TD
()Tj
/F3 1 Tf
0.277 0 TD
(\))Tj
/TT7 1 Tf
0.7107 0 TD
(always)Tj
/TT5 1 Tf
2.9946 0 TD
[(a)-216.8(v)24.1(alid)]TJ
-21.0226 -1.2045 TD
[(optimization?)-277(F)12(o)0(r)-240.9(XQuery)60.2(,)-228.9(the)-240.9(answer)-240.9(is)]TJ
/TT7 1 Tf
16.4889 0 TD
(no)Tj
/TT5 1 Tf
1 0 TD
(.)Tj
/TT2 1 Tf
-17.4889 -2.0356 TD
[(Example)-240.9(2.4)]TJ
/TT5 1 Tf
5.7626 0 TD
[(Consider)-228.9(the)-240.9(follo)24.1(wing)-228.9(e)12(xpression:)]TJ
/F3 1 Tf
-4.8231 -2.0356 TD
0.005 Tc
[(let)-505.9($seed)-505.9(:=)-505.9(\(,<)12.1(/c)12.1(>)12.1(b>)12.1(\))]TJ
0 -1.1925 TD
[(return)-493.8(with)-505.9($x)-517.9(seeded)-493.8(by)-505.9($seed)]TJ
3.6737 -1.2045 TD
[(recurse)-493.8(if)-505.9(\(count)-144.5(\($x/self::a\)\))]TJ
4.2037 -1.2045 TD
[(then)-493.8($x/*)-505.9(else)-505.9(\(\))]TJ
/TT5 1 Tf
13.0086 1.8549 TD
0 Tc
(\(Q2\))Tj
-23.2107 -4.4326 TD
(3)Tj
ET
endstream
endobj
36 0 obj
<<
/ProcSet [/PDF /Text /ImageB ]
/Font <<
/F1 4 0 R
/F3 6 0 R
/F4 7 0 R
/F5 8 0 R
/F6 22 0 R
/F8 24 0 R
/F9 25 0 R
/F10 26 0 R
/F11 27 0 R
/F13 29 0 R
/F15 37 0 R
/F16 38 0 R
/F17 39 0 R
/F18 40 0 R
/F19 41 0 R
/TT2 9 0 R
/TT3 10 0 R
/TT5 11 0 R
/TT7 12 0 R
/TT8 13 0 R
/TT9 14 0 R
/TT11 15 0 R
/TT14 31 0 R
>>
/XObject <<
/Im1 33 0 R
>>
/ExtGState <<
/GS1 17 0 R
>>
>>
endobj
43 0 obj
<<
/Length 25354
>>
stream
BT
/TT5 1 Tf
9.9626 0 0 9.9626 50.16 709.98 Tm
0 g
/GS1 gs
0 Tc
0 Tw
(Let)Tj
/F6 1 Tf
1.6216 0 TD
(a)Tj
/TT5 1 Tf
0.53 0 TD
(,)Tj
/F6 1 Tf
0.5511 0 TD
(b)Tj
/TT5 1 Tf
0.4336 0 TD
(,)Tj
/F6 1 Tf
0.5511 0 TD
(c)Tj
/TT5 1 Tf
0.4336 0 TD
[(,)-301.1(and)]TJ
/F6 1 Tf
2.272 0 TD
(d)Tj
/TT5 1 Tf
0.8191 0 TD
[(denote)-277(the)-289.1(tree)-289.1(fragments)-265(constructed)-265(by)]TJ
-7.2122 -1.2045 TD
[(the)-469.8(seed)60.2(s)-469.8(sube)12(xpressions)]TJ
/F3 1 Tf
11.0888 0 TD
0.005 Tc
()Tj
/TT5 1 Tf
2.1199 0 TD
0 Tc
(,)Tj
/F3 1 Tf
0.7559 0 TD
0.005 Tc
[()12.1(b>)]TJ
/TT5 1 Tf
9.5277 0 TD
0 Tc
(,)Tj
/F3 1 Tf
-23.4923 -1.1924 TD
0.005 Tc
()Tj
/TT5 1 Tf
5.8299 0 TD
0 Tc
[(,)-240.9(and)]TJ
/F3 1 Tf
2.2118 0 TD
0.005 Tc
()Tj
/TT5 1 Tf
2.1199 0 TD
0 Tc
[(,)-277(respecti)24.1(v)12(ely)60.2(.)-397.5(Thus,)]TJ
/F6 1 Tf
8.4363 0 TD
(b)Tj
/F3 1 Tf
0.4336 0 TD
0.005 Tc
[(/*)-168.6(is)]TJ
/F6 1 Tf
2.4452 0 TD
0 Tc
(c)Tj
/TT5 1 Tf
0.7227 0 TD
(and)Tj
/F6 1 Tf
-22.1993 -1.2045 TD
(c)Tj
/F3 1 Tf
0.4336 0 TD
0.005 Tc
[(/*)-156.6(is)]TJ
/F6 1 Tf
2.4452 0 TD
0 Tc
(d)Tj
/TT5 1 Tf
0.5179 0 TD
(.)Tj
-2.2043 -1.2286 TD
[(The)-277(table)-289.1(belo)24.1(w)-277(illustrates)-289.1(the)-277(progress)-277(of)-277(the)-277(iterations)]TJ
-1.1925 -1.2045 TD
[(performed)-144.5(by)-180.7(algorithms)]TJ
/TT7 1 Tf
9.9357 0 TD
(Na)Tj
1.2179 -0.0121 TD
()Tj
/TT9 1 Tf
0.0241 0.0121 TD
()Tj
/TT7 1 Tf
0.2778 0 TD
(ve)Tj
/TT5 1 Tf
1.0804 0 TD
(and)Tj
/TT7 1 Tf
1.6245 0 TD
(Delta)Tj
/TT5 1 Tf
2.2217 0 TD
[(.)-277(While)-192.7(the)-180.7(former)]TJ
-16.3822 -1.1925 TD
(computes)Tj
/F3 1 Tf
4.0614 0 TD
(\()Tj
/F6 1 Tf
0.53 0 TD
(a)Tj
/F3 1 Tf
0.53 0 TD
(,)Tj
/F6 1 Tf
0.53 0 TD
(b)Tj
/F3 1 Tf
0.4336 0 TD
(,)Tj
/F6 1 Tf
0.53 0 TD
(c)Tj
/F3 1 Tf
0.4336 0 TD
(,)Tj
/F6 1 Tf
0.53 0 TD
(d)Tj
/F3 1 Tf
0.5179 0 TD
(\))Tj
/TT5 1 Tf
0.53 0 TD
[(,)-216.8(the)-240.9(latter)-240.9(returns)]TJ
/F3 1 Tf
7.2422 0 TD
(\()Tj
/F6 1 Tf
0.53 0 TD
(a)Tj
/F3 1 Tf
0.53 0 TD
(,)Tj
/F6 1 Tf
0.53 0 TD
(b)Tj
/F3 1 Tf
0.4336 0 TD
(,)Tj
/F6 1 Tf
0.53 0 TD
(c)Tj
/F3 1 Tf
0.4336 0 TD
(\))Tj
/TT5 1 Tf
0.53 0 TD
(.)Tj
ET
q
177.48 0 0 -0.84 79.548 625.6081 cm
/Im1 Do
Q
BT
/TT2 1 Tf
8.9664 0 0 8.9664 85.56 615.42 Tm
(Iteration)Tj
/TT14 1 Tf
6.2126 0 TD
[(Na)26.8()]TJ
/TT15 1 Tf
1.2206 0 TD
()Tj
/TT14 1 Tf
0.2778 0 TD
[(v)13.4(e)-5045.5(Delta)]TJ
/F16 1 Tf
-0.9926 -1.2313 TD
-0.0581 Tc
[(re)-54.3(s)-4188.7(r)0(e)-54.3(s)]TJ
/F19 1 Tf
10.0242 0 TD
0 Tc
()Tj
ET
q
35.88 0 0 -0.36 84.468 599.448 cm
/Im1 Do
Q
q
43.2 0 0 -0.36 130.308 599.448 cm
/Im1 Do
Q
q
68.64 0 0 -0.36 183.348 599.448 cm
/Im1 Do
Q
BT
/TT5 1 Tf
8.9664 0 0 8.9664 100.2 588.66 Tm
(0)Tj
/F4 1 Tf
3.4711 0 TD
(\()Tj
/F18 1 Tf
0.522 0 TD
(a)Tj
/F4 1 Tf
0.5487 0 TD
(,)Tj
/F18 1 Tf
0.522 0 TD
(b)Tj
/F4 1 Tf
0.4417 0 TD
3.3696 Tc
(\)\()Tj
/F18 1 Tf
4.4165 0 TD
0 Tc
(a)Tj
/F4 1 Tf
0.5487 0 TD
(,)Tj
/F18 1 Tf
0.522 0 TD
(b)Tj
/F4 1 Tf
0.4417 0 TD
2.2989 Tc
(\)\()Tj
/F18 1 Tf
3.3459 0 TD
0 Tc
(a)Tj
/F4 1 Tf
0.5487 0 TD
(,)Tj
/F18 1 Tf
0.522 0 TD
(b)Tj
/F4 1 Tf
0.4417 0 TD
(\))Tj
/TT5 1 Tf
-16.2926 -1.2179 TD
(1)Tj
/F4 1 Tf
3.4711 0 TD
(\()Tj
/F18 1 Tf
0.522 0 TD
(a)Tj
/F4 1 Tf
0.5487 0 TD
(,)Tj
/F18 1 Tf
0.522 0 TD
(b)Tj
/F4 1 Tf
0.4417 0 TD
(,)Tj
/F18 1 Tf
0.522 0 TD
(c)Tj
/F4 1 Tf
0.4417 0 TD
2.406 Tc
(\)\()Tj
/F18 1 Tf
3.4529 0 TD
0 Tc
(a)Tj
/F4 1 Tf
0.5487 0 TD
(,)Tj
/F18 1 Tf
0.522 0 TD
(b)Tj
/F4 1 Tf
0.4417 0 TD
(,)Tj
/F18 1 Tf
0.522 0 TD
(c)Tj
/F4 1 Tf
0.4417 0 TD
1.3353 Tc
(\)\()Tj
/F18 1 Tf
2.3823 0 TD
0 Tc
(c)Tj
/F4 1 Tf
0.4417 0 TD
(\))Tj
/TT5 1 Tf
-15.2219 -1.2313 TD
(2)Tj
/F4 1 Tf
3.4711 0 TD
(\()Tj
/F18 1 Tf
0.522 0 TD
(a)Tj
/F4 1 Tf
0.5487 0 TD
(,)Tj
/F18 1 Tf
0.522 0 TD
(b)Tj
/F4 1 Tf
0.4417 0 TD
(,)Tj
/F18 1 Tf
0.522 0 TD
(c)Tj
/F4 1 Tf
0.4417 0 TD
(,)Tj
/F18 1 Tf
0.522 0 TD
(d)Tj
/F4 1 Tf
0.5354 0 TD
1.3487 Tc
(\)\()Tj
/F18 1 Tf
2.3957 0 TD
0 Tc
(a)Tj
/F4 1 Tf
0.5487 0 TD
(,)Tj
/F18 1 Tf
0.522 0 TD
(b)Tj
/F4 1 Tf
0.4417 0 TD
(,)Tj
/F18 1 Tf
0.522 0 TD
(c)Tj
/F4 1 Tf
0.4417 0 TD
1.3353 Tc
[(\)\()1338.3(\))]TJ
/TT5 1 Tf
-12.398 -1.2179 TD
0 Tc
(3)Tj
/F4 1 Tf
3.4711 0 TD
(\()Tj
/F18 1 Tf
0.522 0 TD
(a)Tj
/F4 1 Tf
0.5487 0 TD
(,)Tj
/F18 1 Tf
0.522 0 TD
(b)Tj
/F4 1 Tf
0.4417 0 TD
(,)Tj
/F18 1 Tf
0.522 0 TD
(c)Tj
/F4 1 Tf
0.4417 0 TD
(,)Tj
/F18 1 Tf
0.522 0 TD
(d)Tj
/F4 1 Tf
0.5354 0 TD
(\))Tj
ET
q
177.48 0 0 -0.84 79.548 550.8481 cm
/Im1 Do
Q
BT
/F5 1 Tf
9.9626 0 0 9.9626 278.64 534.54 Tm
()Tj
/TT5 1 Tf
-22.9337 -2.0958 TD
[(What)-228.9(then)-228.9(is)-240.9(an)-228.9(ef)24.1(fecti)24.1(v)12(e)-216.8(characterization)-192.7(of)-228.9(those)-228.9(payloads)]TJ
0 -1.1925 TD
[(for)-228.9(which)]TJ
/TT7 1 Tf
4.0796 0 TD
(Na)Tj
1.172 -0.012 TD
()Tj
/TT9 1 Tf
0.0241 0.012 TD
()Tj
/TT7 1 Tf
0.2778 0 TD
(ve)Tj
/TT5 1 Tf
1.1286 0 TD
[(may)-240.9(safely)-240.9(be)-240.9(traded)-228.9(for)]TJ
/TT7 1 Tf
9.9102 0 TD
(Delta)Tj
/TT5 1 Tf
2.2217 0 TD
(?)Tj
/TT2 1 Tf
11.9552 0 0 11.9552 50.16 476.94 Tm
[(3)10(.)-250.9(T)70.3(rading)]TJ
/TT14 1 Tf
4.6826 0 TD
(Na)Tj
1.1893 -0.01 TD
()Tj
/TT15 1 Tf
0.0301 0.01 TD
()Tj
/TT14 1 Tf
0.2778 0 TD
-0.01 Tc
(ve)Tj
/TT2 1 Tf
1.1186 0 TD
-0.0201 Tc
[(fo)-20.1(r)]TJ
/TT14 1 Tf
1.5077 0 TD
0 Tc
(Delta)Tj
/TT5 1 Tf
9.9626 0 0 9.9626 62.04 450.06 Tm
[(W)84.3(e)-409.5(will)-397.5(no)24.1(w)-385.4(see)-397.5(that)-397.5(a)-397.5(simple)-385.4(notion)-373.4(of)]TJ
/TT7 1 Tf
17.3737 0 TD
[(distrib)24.1(utivity)]TJ
/TT5 1 Tf
-18.5662 -1.2045 TD
[(for)-325.2(XQuery)-325.2(e)12(xpressions)-325.2(suf)]TJ
/TT8 1 Tf
11.2149 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(ces)-337.3(to)-337.3(let)-349.3(an)-337.3(XQuery)-325.2(proces-)]TJ
-11.7711 -1.1925 TD
[(sor)-373.4(safely)-373.4(switch)-385.4(to)-373.4(a)-385.4(more)-373.4(ef)]TJ
/TT8 1 Tf
12.5143 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(cient)-373.4(e)24.1(v)24.1(aluation)-349.3(mode)-373.4(for)]TJ
/F3 1 Tf
-13.0704 -1.2045 TD
0.005 Tc
[(with)-505.9($x)-505.9(seeded)-493.8(by)]TJ
/F6 1 Tf
9.4434 0 TD
0 Tc
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 148.92 412.74 Tm
-0.0454 Tc
[(s)-41.5(eed)]TJ
/F3 1 Tf
9.9626 0 0 9.9626 169.68 414.18 Tm
0.005 Tc
(recurse)Tj
/F6 1 Tf
4.1917 0 TD
0 Tc
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 216.12 412.74 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 227.28 414.18 Tm
0 Tc
[(:)-301.1(whene)24.1(v)12(e)0(r)-216.8(e)12(x-)]TJ
-17.7784 -1.2045 TD
(pression)Tj
/F6 1 Tf
3.7064 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 91.92 400.74 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 106.92 402.18 Tm
0 Tc
(is)Tj
/TT7 1 Tf
1.0645 0 TD
[(distrib)24.1(utive)]TJ
/TT5 1 Tf
4.9165 0 TD
[(\(in)-385.4(the)-385.4(sense)-397.5(de)]TJ
/TT8 1 Tf
6.6107 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(ned)-373.4(belo)24.1(w\),)]TJ
-18.8452 -1.1925 TD
(algorithm)Tj
/TT7 1 Tf
4.1291 0 TD
(Delta)Tj
/TT5 1 Tf
2.4867 0 TD
[(\(Figure)-252.9(3\(b\)\))-252.9(preserv)12(es)-252.9(the)-265(desired)-252.9(IFP)-277(se-)]TJ
-6.6158 -1.2045 TD
[(mantics.)-337.3(While)-252.9(the)]TJ
/TT7 1 Tf
7.8806 0 TD
[(distrib)24.1(utivity)]TJ
/TT5 1 Tf
5.3397 0 TD
[(property)-240.9(is)-265(undecidable)-228.9(in)]TJ
-13.2203 -1.2045 TD
[(general,)-313.2(we)-313.2(present)-313.2(tw)12(o)-313.2(safe)-325.2(and)-301.1(ef)24.1(fecti)24.1(v)12(e)-301.1(approximations)]TJ
0 -1.1925 TD
[(of)-204.8(distrib)24.1(uti)24.1(vity)60.2(,)-204.8(one)-204.8(formulated)-192.7(on)-204.8(the)-216.8(le)24.1(v)12(e)0(l)-216.8(o)0(f)-204.8(XQuery)-204.8(lan-)]TJ
0 -1.2045 TD
[(guage)-204.8(syntax,)-228.9(and)-216.8(one)-228.9(cast)-228.9(in)-228.9(terms)-228.9(of)-228.9(an)-228.9(algebraic)-216.8(XQuery)]TJ
0 -1.1925 TD
[(representation.)-542(The)-337.3(algebraic)-325.2(approximation)-289.1(will)-349.3(turn)-325.2(out)]TJ
0 -1.2045 TD
[(to)-240.9(be)-240.9(particularly)-228.9(simple)-240.9(and)-228.9(uniform)-228.9(\(Section)-228.9(4\).)]TJ
/TT2 1 Tf
10.9589 0 0 10.9589 50.16 295.62 Tm
[(3.1)11(.)-240.9(Distrib)21.9(uti)11(vity)-262.8(in)-251.8(XQuery)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 62.04 269.82 Tm
[(Ob)12(viously)60.2(,)]TJ
/TT7 1 Tf
4.5254 0 TD
(Delta)Tj
/TT5 1 Tf
2.4264 0 TD
[(computes)-180.7(the)-204.8(IFP)-204.8(for)-192.7(gi)24.1(v)12(e)0(n)-180.7(e)12(xpressions)]TJ
/F6 1 Tf
-8.1443 -1.2045 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 54.84 256.38 Tm
-0.0454 Tc
[(s)-41.5(eed)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 73.2 257.82 Tm
0 Tc
(and)Tj
/F6 1 Tf
1.7329 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 95.28 256.38 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 109.32 257.82 Tm
0 Tc
[(if)-301.1(the)-289.1(algorithm)-277(produces)-277(the)-289.1(same)-301.1(result)-289.1(as)]TJ
/TT7 1 Tf
-5.9382 -1.1925 TD
(Na)Tj
1.1443 -0.012 TD
()Tj
/TT9 1 Tf
0.0241 0.012 TD
()Tj
/TT7 1 Tf
0.2778 0 TD
(ve)Tj
/TT5 1 Tf
1.1768 0 TD
[(on)-277(the)-289.1(same)-289.1(inputs.)-433.6(In)-277(particular)36.1(,)-277(the)-289.1(algorithms)-277(are)]TJ
-2.623 -1.2045 TD
[(equi)24.1(v)24.1(alent)-325.2(if)-349.3(both)-337.3(yield)-337.3(equi)24.1(v)24.1(alent)-325.2(intermediate)]TJ
/F9 1 Tf
19.6189 0 TD
-0.0483 Tc
[(re)-46(s)-49(u)-53.7(l)-45.7(t)]TJ
/TT5 1 Tf
2.8186 0 TD
0 Tc
(se-)Tj
-22.4375 -1.2045 TD
[(quences)-228.9(in)-240.9(each)-240.9(iteration)-228.9(of)-240.9(their)]TJ
/TT2 1 Tf
13.2489 0 TD
(do)Tj
/F1 1 Tf
1.2248 0 TD
0.1679 Tc
()Tj
/TT2 1 Tf
1.325 0 TD
0 Tc
(while)Tj
/TT5 1 Tf
2.5308 0 TD
(loops.)Tj
-17.137 -1.2286 TD
[(In)-325.2(its)]TJ
/TT8 1 Tf
2.4403 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(rst)-337.3(loop)-325.2(iteration,)]TJ
/TT7 1 Tf
7.3476 0 TD
(Na)Tj
1.1831 -0.012 TD
()Tj
/TT9 1 Tf
0.0241 0.012 TD
()Tj
/TT7 1 Tf
0.2778 0 TD
(ve)Tj
/TT5 1 Tf
1.225 0 TD
(yields)Tj
/F6 1 Tf
2.7139 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 223.92 208.26 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 234.96 209.7 Tm
0 Tc
(\()Tj
/F6 1 Tf
0.3854 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 243.48 208.26 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 254.64 209.7 Tm
0 Tc
(\()Tj
/F6 1 Tf
0.3854 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 263.16 208.26 Tm
-0.0454 Tc
[(s)-41.5(eed)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 278.64 209.7 Tm
-0.0034 Tc
(\)\))Tj
/F3 1 Tf
-22.9337 -1.1925 TD
0.005 Tc
(union)Tj
/F6 1 Tf
3.1438 0 TD
0 Tc
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 86.16 196.38 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 97.2 197.82 Tm
0 Tc
(\()Tj
/F6 1 Tf
0.3854 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 105.72 196.38 Tm
-0.0454 Tc
[(s)-41.5(eed)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 121.32 197.82 Tm
0 Tc
(\))Tj
/TT5 1 Tf
0.7588 0 TD
[(which)-361.4(is)-373.4(equi)24.1(v)24.1(alent)-349.3(to)]TJ
/TT7 1 Tf
9.463 0 TD
(Delta)Tj
/TT5 1 Tf
2.2217 0 TD
-0.0602 Tc
(s)Tj
/TT8 1 Tf
1.0353 0 TD
0 Tc
()Tj
/TT5 1 Tf
0.5562 0 TD
[(rst)-373.4(in-)]TJ
-21.1777 -1.2045 TD
[(termediate)-566.1(result)]TJ
/F8 1 Tf
7.5857 0 TD
(\()Tj
/F6 1 Tf
0.3854 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 134.52 184.38 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 145.56 185.82 Tm
0 Tc
(\()Tj
/F6 1 Tf
0.3854 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 154.08 184.38 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 165.24 185.82 Tm
0 Tc
(\()Tj
/F6 1 Tf
0.3854 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 173.76 184.38 Tm
-0.0454 Tc
[(s)-41.5(eed)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 189.24 185.82 Tm
-0.0034 Tc
(\)\))Tj
/F3 1 Tf
1.3009 0 TD
0.005 Tc
(except)Tj
/F6 1 Tf
3.6738 0 TD
0 Tc
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 243.48 184.38 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 254.64 185.82 Tm
0 Tc
(\()Tj
/F6 1 Tf
0.3854 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 263.16 184.38 Tm
-0.0454 Tc
[(s)-41.5(eed)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 278.64 185.82 Tm
-0.0034 Tc
(\)\))Tj
/F3 1 Tf
-22.9337 -1.2045 TD
0.005 Tc
(union)Tj
/F6 1 Tf
3.1438 0 TD
0 Tc
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 86.16 172.38 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 97.2 173.82 Tm
0 Tc
(\()Tj
/F6 1 Tf
0.3854 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 105.72 172.38 Tm
-0.0454 Tc
[(s)-41.5(eed)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 121.32 173.82 Tm
0 Tc
(\))Tj
/TT5 1 Tf
0.3854 0 TD
[(.)-289.1(F)12(or)-180.7(the)-192.7(second)-180.7(and)-180.7(further)-168.6(iterations,)-192.7(an)]TJ
-7.5281 -1.1925 TD
[(inducti)24.1(v)12(e)-240.9(proof)-240.9(can)-265(sho)24.1(w)-252.9(the)-265(equi)24.1(v)24.1(alence)-240.9(of)-265(all)-265(subsequent)]TJ
0 -1.2045 TD
(intermediate)Tj
/F9 1 Tf
5.2866 0 TD
-0.0483 Tc
[(re)-46(s)-49(u)-53.7(l)-45.7(t)]TJ
/TT5 1 Tf
2.7824 0 TD
0 Tc
[(sequences,)-313.2(if)-313.2(we)-325.2(may)-301.1(assume)-313.2(that,)-337.3(for)]TJ
-8.0691 -1.2045 TD
[(tw)12(o)-240.9(item)-240.9(sequences)]TJ
/F6 1 Tf
8.0417 0 TD
(X)Tj
/F7 1 Tf
6.9738 0 0 6.9738 138.84 136.5 Tm
(1)Tj
/F6 1 Tf
9.9626 0 0 9.9626 143.28 137.94 Tm
0.1679 Tc
(,X)Tj
/F7 1 Tf
6.9738 0 0 6.9738 156 136.5 Tm
0 Tc
(2)Tj
/TT5 1 Tf
9.9626 0 0 9.9626 160.44 137.94 Tm
0.2409 Tc
[(,w)240.9(e)-12(h)240.9(a)265(v)252.9(e)]TJ
/F6 1 Tf
-9.9612 -2.2524 TD
0 Tc
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 65.88 114.06 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 76.92 115.5 Tm
0 Tc
(\()Tj
/F6 1 Tf
0.3854 0 TD
(X)Tj
/F7 1 Tf
6.9738 0 0 6.9738 89.04 114.06 Tm
(1)Tj
/F3 1 Tf
9.9626 0 0 9.9626 95.76 115.5 Tm
0.005 Tc
(union)Tj
/F6 1 Tf
2.8427 0 TD
0 Tc
(X)Tj
/F7 1 Tf
6.9738 0 0 6.9738 132.36 114.06 Tm
(2)Tj
/F8 1 Tf
9.9626 0 0 9.9626 136.8 115.5 Tm
(\))Tj
/F10 1 Tf
6.9738 0 0 6.9738 144.96 121.14 Tm
(s)Tj
/F8 1 Tf
9.9626 0 0 9.9626 142.92 115.5 Tm
(=)Tj
/F6 1 Tf
0.9997 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 157.56 114.06 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 168.6 115.5 Tm
0 Tc
(\()Tj
/F6 1 Tf
0.3854 0 TD
(X)Tj
/F7 1 Tf
6.9738 0 0 6.9738 180.72 114.06 Tm
(1)Tj
/F8 1 Tf
9.9626 0 0 9.9626 185.28 115.5 Tm
(\))Tj
/F3 1 Tf
0.6023 0 TD
0.005 Tc
(union)Tj
/F6 1 Tf
2.8547 0 TD
0 Tc
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 224.4 114.06 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/F8 1 Tf
9.9626 0 0 9.9626 235.44 115.5 Tm
0 Tc
(\()Tj
/F6 1 Tf
0.3854 0 TD
(X)Tj
/F7 1 Tf
6.9738 0 0 6.9738 247.56 114.06 Tm
(2)Tj
/F8 1 Tf
9.9626 0 0 9.9626 252 115.5 Tm
(\))Tj
/F6 1 Tf
0.8913 0 TD
(.)Tj
/TT5 1 Tf
1.3972 0 TD
(\(3\))Tj
-22.5482 -2.2645 TD
[(F)12(o)0(r)-265(lack)-277(of)-277(space,)-277(we)-277(do)-277(not)-265(reproduce)-240.9(the)-277(straightforw)12(ard)]TJ
0 -1.2045 TD
[(equational)-216.8(reasoning)-228.9(behind)-228.9(the)-240.9(proof)-216.8(here)-240.9(b)24.1(u)0(t)-240.9(refer)-240.9(to)-240.9([2)12(].)]TJ
27.1615 63.1399 TD
[(Note)-445.7(ho)24.1(w)-445.7(\(3\))-433.6(resembles)-445.7(the)]TJ
/TT7 1 Tf
12.2444 0 TD
[(distrib)24.1(utivity)-445.7(pr)48.2(operty)]TJ
/TT5 1 Tf
9.3617 0 TD
(of)Tj
-22.7986 -1.2045 TD
[(functions)-277(de)]TJ
/TT8 1 Tf
4.9426 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(ned)-277(on)-289.1(sets.)-457.7(Such)-289.1(a)-301.1(function)]TJ
/F6 1 Tf
11.8492 0 TD
(e)Tj
/TT5 1 Tf
0.7709 0 TD
(is)Tj
/TT7 1 Tf
0.9681 0 TD
[(distrib)24.1(utive)]TJ
/TT5 1 Tf
-19.087 -1.1925 TD
[(if,)-325.2(for)-301.1(all)-313.2(non-empty)-277(sets)]TJ
/F6 1 Tf
10.4007 0 TD
(X)Tj
/TT5 1 Tf
0.9154 0 TD
(,)Tj
/F6 1 Tf
0.5752 0 TD
(e)Tj
/F8 1 Tf
0.4698 0 TD
(\()Tj
/F6 1 Tf
0.3854 0 TD
(X)Tj
/F8 1 Tf
0.9154 0 TD
0.394 Tc
(\)=)Tj
/F15 1 Tf
2.0086 0.7468 TD
0 Tc
()Tj
/F10 1 Tf
6.9738 0 0 6.9738 473.4 683.1 Tm
(y)Tj
/F14 1 Tf
0.6195 0 TD
()Tj
/F10 1 Tf
0.7744 0 TD
(X)Tj
/F6 1 Tf
9.9626 0 0 9.9626 492.24 686.1 Tm
(e)Tj
/F8 1 Tf
0.4698 0 TD
(\()Tj
/F1 1 Tf
0.3854 0 TD
({)Tj
/F6 1 Tf
0.5059 0 TD
(y)Tj
/F1 1 Tf
0.53 0 TD
(})Tj
/F8 1 Tf
0.5059 0 TD
(\))Tj
/TT5 1 Tf
0.3854 0 TD
[(.)-493.8(This)]TJ
-21.1872 -1.2045 TD
[(property)-252.9(suggests)-277(a)-277(d)0(i)24.1(vide-and-conquer)-216.8(e)24.1(v)24.1(aluation)-252.9(strate)12(gy)]TJ
T*
[(in)-265(which)]TJ
/F6 1 Tf
3.7276 0 TD
(e)Tj
/TT5 1 Tf
0.7347 0 TD
[(is)-277(applied)-240.9(to)-265(subsets)-265(\(singletons\))-240.9(of)]TJ
/F6 1 Tf
14.3738 0 TD
(X)Tj
/TT5 1 Tf
1.1684 0 TD
[(only)60.2(.)-337.3(W)84.3(e)]TJ
-20.0045 -1.1925 TD
(de)Tj
/TT8 1 Tf
0.9438 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(ne)-240.9(the)-252.9(corresponding)]TJ
/TT7 1 Tf
8.5969 0 TD
[(distrib)24.1(utivity)-252.9(pr)48.2(operty)-252.9(for)-252.9(XQuery)]TJ
/TT5 1 Tf
-10.0969 -1.2045 TD
[(as)-252.9(follo)24.1(ws:)]TJ
/TT2 1 Tf
0 -2.3849 TD
(De)Tj
/TT3 1 Tf
1.166 0 TD
()Tj
/TT2 1 Tf
0.5562 0 TD
[(nition)-240.9(3.1)]TJ
/TT14 1 Tf
4.4737 0 TD
[(Distrib)24.1(utivity)-216.8(property)-180.7(f)12(o)0(r)-192.7(XQuery)36.1(.)]TJ
/TT5 1 Tf
14.3464 0 TD
(Let)Tj
/F6 1 Tf
1.5252 0 TD
(e)Tj
/TT5 1 Tf
0.6625 0 TD
(be)Tj
-22.73 -1.2045 TD
[(an)-216.8(XQuery)-216.8(e)12(xpression)-204.8(in)-228.9(which)-216.8(v)24.1(ariable)]TJ
/F3 1 Tf
16.1365 0 TD
0.005 Tc
($x)Tj
/TT5 1 Tf
1.2768 0 TD
0 Tc
[(may)-216.8(occur)-216.8(free.)]TJ
-17.4132 -1.1925 TD
(Expression)Tj
/F6 1 Tf
4.6607 0 TD
(e)Tj
/TT5 1 Tf
0.7107 0 TD
(is)Tj
/TT7 1 Tf
0.9199 0 TD
[(distrib)24.1(utive)-240.9(for)]TJ
/F3 1 Tf
6.204 0 TD
0.005 Tc
($x)Tj
/TT5 1 Tf
1.3009 0 TD
0 Tc
[(if,)-240.9(for)-228.9(an)12(y)-228.9(item)-240.9(sequence)]TJ
/F6 1 Tf
-13.7961 -1.2045 TD
(X)Tj
/F1 1 Tf
1.1804 0 TD
()Tj
/F8 1 Tf
T*
(=)Tj
/F3 1 Tf
1.06 0 TD
0.005 Tc
(\(\))Tj
/TT5 1 Tf
1.3009 0 TD
0 Tc
[(and)-228.9(fresh)-240.9(v)24.1(ariable)]TJ
/F3 1 Tf
7.3376 0 TD
0.005 Tc
($y)Tj
/TT5 1 Tf
1.06 0 TD
0 Tc
(,)Tj
/F3 1 Tf
-9.4817 -2.3969 TD
0.005 Tc
[(for)-505.9($y)-517.9(in)]TJ
/F6 1 Tf
5.2517 0 TD
0 Tc
(X)Tj
/F3 1 Tf
1.4334 0 TD
0.005 Tc
(return)Tj
/F6 1 Tf
3.6738 0 TD
0 Tc
(e)Tj
/F8 1 Tf
0.4698 0 TD
(\()Tj
/F3 1 Tf
0.3854 0 TD
0.005 Tc
($y)Tj
/F8 1 Tf
1.0479 0 TD
0 Tc
(\))Tj
/F10 1 Tf
6.9738 0 0 6.9738 473.52 560.34 Tm
(s)Tj
/F8 1 Tf
9.9626 0 0 9.9626 471.6 554.7 Tm
(=)Tj
/F6 1 Tf
1.9995 0 TD
(e)Tj
/F8 1 Tf
0.4698 0 TD
(\()Tj
/F6 1 Tf
0.3854 0 TD
(X)Tj
/F8 1 Tf
0.9154 0 TD
(\))Tj
/F6 1 Tf
0.8793 0 TD
(.)Tj
/TT5 1 Tf
1.5658 0 TD
(\(4\))Tj
/F5 1 Tf
0.3854 -2.3969 TD
()Tj
/TT5 1 Tf
-22.9337 -2.2886 TD
[(In)-265(particular)36.1(,)-240.9(Equality)-252.9(\(3\))-252.9(is)-277(a)-277(straightforw)12(ard)-228.9(consequence)]TJ
0 -1.1925 TD
[(if)-216.8(we)-216.8(kno)24.1(w)-204.8(that)-216.8(the)-216.8(recursion)-192.7(body)]TJ
/F6 1 Tf
13.8863 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 452.76 494.7 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 465.96 496.14 Tm
0 Tc
[(is)-228.9(distrib)24.1(uti)24.1(v)12(e)-204.8(for)-204.8(its)]TJ
-15.7669 -1.2045 TD
[(free)-277(v)24.1(ariable.)-421.6(Ov)12(erall,)-289.1(we)-289.1(arri)24.1(v)12(e)-277(at)-301.1(the)-277(follo)24.1(wing)-277(suf)]TJ
/TT8 1 Tf
21.1128 0 TD
()Tj
/TT5 1 Tf
0.5561 0 TD
(cient)Tj
-21.6689 -1.2045 TD
[(condition)-216.8(for)-240.9(the)-240.9(applicability)-228.9(of)]TJ
/TT7 1 Tf
13.1649 0 TD
(Delta)Tj
/TT5 1 Tf
2.2217 0 TD
(:)Tj
/TT2 1 Tf
-15.3866 -2.3849 TD
[(Theor)12(em)-240.9(3.2)]TJ
/TT7 1 Tf
5.8483 0 TD
[(Consider)-457.7(the)-457.7(e)24.1(xpr)36.1(ession)]TJ
/F3 1 Tf
10.4664 0 TD
0.005 Tc
[(with)-505.9($x)-517.9(seeded)]TJ
-16.3147 -1.2045 TD
(by)Tj
/F6 1 Tf
1.3731 0 TD
0 Tc
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 327.24 434.94 Tm
-0.0454 Tc
[(s)-41.5(eed)]TJ
/F3 1 Tf
9.9626 0 0 9.9626 346.08 436.38 Tm
0.005 Tc
(recurse)Tj
/F6 1 Tf
3.999 0 TD
0 Tc
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 390.6 434.94 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT7 1 Tf
9.9626 0 0 9.9626 401.64 436.38 Tm
0.542 Tc
[(.I)542(f)]TJ
/F6 1 Tf
1.7281 0 TD
0 Tc
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 423.6 434.94 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT7 1 Tf
9.9626 0 0 9.9626 438 436.38 Tm
0 Tc
[(is)-337.3(distrib)24.1(utive)-325.2(for)]TJ
/F3 1 Tf
7.3769 0 TD
0.005 Tc
($x)Tj
/TT7 1 Tf
1.06 0 TD
0 Tc
[(,)-337.3(then)]TJ
-21.3972 -1.1925 TD
(algorithm)Tj
/TT5 1 Tf
4.1737 0 TD
(Delta)Tj
/TT7 1 Tf
2.4185 0 TD
[(computes)-228.9(the)-240.9(IFP)-240.9(of)]TJ
/F6 1 Tf
8.2826 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 462.36 423.06 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT7 1 Tf
9.9626 0 0 9.9626 475.92 424.5 Tm
0 Tc
(given)Tj
/F6 1 Tf
2.4064 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 504.72 423.06 Tm
-0.0454 Tc
[(s)-41.5(eed)]TJ
/TT7 1 Tf
9.9626 0 0 9.9626 520.2 424.5 Tm
0 Tc
(.)Tj
/TT2 1 Tf
-21.2112 -3.204 TD
[(XP)12(ath)-252.9(Location)-240.9(Steps.)]TJ
/TT5 1 Tf
10.5099 0 TD
[(XP)12(ath)-252.9(location)-240.9(steps)-252.9(are)-252.9(a)-265(pre)24.1(v)24.1(a)0(-)]TJ
-10.5099 -1.1925 TD
[(lent)-373.4(e)12(xample)-349.3(of)-373.4(distrib)24.1(uti)24.1(v)12(e)-361.4(e)12(xpressions)-349.3(in)-373.4(XQuery)60.2(.)-674.5(A)0(n)12(y)]TJ
0 -1.2045 TD
[(e)12(xpression)-385.4(of)-397.5(the)-397.5(form)]TJ
/F6 1 Tf
9.8412 0 TD
(e)Tj
/F8 1 Tf
0.4698 0 TD
(\()Tj
/F3 1 Tf
0.3854 0 TD
0.005 Tc
($x)Tj
/F8 1 Tf
1.0479 0 TD
0.5627 Tc
(\)=)Tj
/F3 1 Tf
2.3127 0 TD
0.005 Tc
($x/)Tj
/F6 1 Tf
1.59 0 TD
0 Tc
(s)Tj
/TT5 1 Tf
0.8552 0 TD
[(is)-421.6(distrib)24.1(uti)24.1(v)12(e)-385.4(for)]TJ
/F3 1 Tf
-16.5022 -1.2045 TD
0.005 Tc
($x)Tj
/TT5 1 Tf
1.5418 0 TD
0 Tc
[(if)-505.9(the)-493.8(step)-493.8(sube)12(xpression)]TJ
/F6 1 Tf
11.0486 0 TD
(s)Tj
/TT5 1 Tf
0.9756 0 TD
[(neither)-481.8(contains)]TJ
/TT7 1 Tf
7.0725 0 TD
(\(i\))Tj
/TT5 1 Tf
1.4377 0 TD
(free)Tj
-22.0762 -1.1925 TD
[(occurrences)-385.4(of)]TJ
/F3 1 Tf
6.4024 0 TD
0.005 Tc
($x)Tj
/TT5 1 Tf
1.06 0 TD
0 Tc
[(,)-433.6(nor)]TJ
/TT7 1 Tf
2.4262 0 TD
(\(ii\))Tj
/TT5 1 Tf
1.6312 0 TD
[(calls)-409.5(to)]TJ
/F3 1 Tf
3.4415 0 TD
0.005 Tc
(fn:position\(\))Tj
/TT5 1 Tf
7.2391 0 TD
0 Tc
(and)Tj
/F3 1 Tf
-22.2003 -1.2045 TD
0.005 Tc
(fn:last\(\))Tj
/TT5 1 Tf
5.059 0 TD
0 Tc
[(that)-337.3(refer)-325.2(to)-337.3(the)-337.3(conte)12(xt)-325.2(item)-325.2(sequence)-325.2(bound)]TJ
-5.059 -1.2045 TD
(to)Tj
/F3 1 Tf
1.1753 0 TD
0.005 Tc
($x)Tj
/TT5 1 Tf
1.06 0 TD
0 Tc
[(,)-433.6(nor)]TJ
/TT7 1 Tf
2.4021 0 TD
(\(iii\))Tj
/TT5 1 Tf
1.897 0 TD
[(node)-385.4(constructors.)-746.8(T)84.3(o)-397.5(see)-409.5(this,)-433.6(note)-397.5(that)]TJ
-6.5344 -1.1925 TD
[(the)-397.5(XQuery)-385.4(Core)-397.5(equi)24.1(v)24.1(alent)-385.4([9)12(])-397.5(o)0(f)]TJ
/F3 1 Tf
14.8514 0 TD
0.005 Tc
($x/)Tj
/F6 1 Tf
1.59 0 TD
0 Tc
(s)Tj
/TT5 1 Tf
0.8672 0 TD
(is)Tj
/F3 1 Tf
1.0765 0 TD
0.005 Tc
(fs:ddo\(for)Tj
-18.3851 -1.2045 TD
[($fs:dot)-493.8(in)-505.9($x)-517.9(return)]TJ
/F6 1 Tf
11.0213 0 TD
0 Tc
(s)Tj
/F3 1 Tf
0.4698 0 TD
(\))Tj
/TT5 1 Tf
0.53 0 TD
[(,)-397.5(and)-349.3(then)-361.4(re)24.1(write)-361.4(the)-361.4(lhs)-361.4(of)]TJ
-12.021 -1.1925 TD
[(Equation)-216.8(\(4\))-240.9(into)-240.9(its)-252.9(rhs,)-240.9(using)-240.9(the)-240.9(de)]TJ
/TT8 1 Tf
14.7558 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(nition)-228.9(of)]TJ
/F10 1 Tf
6.9738 0 0 6.9738 500.76 290.7 Tm
(s)Tj
/F8 1 Tf
9.9626 0 0 9.9626 498.72 285.06 Tm
(=)Tj
/TT5 1 Tf
0.7709 0 TD
(.)Tj
/TT2 1 Tf
-19.8261 -3.204 TD
[(Regular)-192.7(XP)12(ath.)]TJ
/TT5 1 Tf
7.5844 0 TD
[(These)-204.8(observ)24.1(ations)-180.7(about)-180.7(the)-204.8(distrib)24.1(uti)24.1(v-)]TJ
-7.5844 -1.1925 TD
[(ity)-192.7(of)-180.7(XP)12(ath)-180.7(location)-180.7(steps)-192.7(e)12(xtend)-168.6(to)-192.7(Re)12(gular)-180.7(XP)12(ath)-180.7([21)12.1(])-192.7(and)]TJ
0 -1.2045 TD
[(thus)-337.3(also)-337.3(mak)12(e)-337.3(this)-337.3(XP)12(ath)-337.3(e)12(xtension)-325.2(susceptible)-325.2(to)]TJ
/TT7 1 Tf
21.0798 0 TD
(Delta)Tj
/TT5 1 Tf
2.2217 0 TD
(-)Tj
-23.3014 -1.2045 TD
[(based)-240.9(e)24.1(v)24.1(aluation.)-301.1(Since)-240.9(an)12(y)-240.9(R)0(e)12(gular)-240.9(XP)12(ath)-240.9(step)-252.9(sube)12(xpres-)]TJ
0 -1.1925 TD
(sion)Tj
/F6 1 Tf
1.8718 0 TD
(s)Tj
/TT5 1 Tf
0.6866 0 TD
[(is)-216.8(of)-204.8(the)-204.8(form)-204.8(prescribed)-180.7(by)]TJ
/TT7 1 Tf
11.0466 0 TD
(\(i\))Tj
/TT5 1 Tf
1.1486 0 TD
(to)Tj
/TT7 1 Tf
0.9946 0 TD
(\(iii\))Tj
/TT5 1 Tf
1.7043 0 TD
[(abo)12(v)12(e)-192.7(and)-192.7(Re)12(g-)]TJ
-17.4525 -1.2045 TD
[(ular)-277(XP)12(ath)60.2(s)-289.1(transiti)24.1(v)12(e)-289.1(closure)]TJ
/F6 1 Tf
12.4096 0 TD
(s)Tj
/F11 1 Tf
6.9738 0 0 6.9738 437.64 196.98 Tm
(+)Tj
/TT5 1 Tf
9.9626 0 0 9.9626 444.72 193.38 Tm
[(is)-301.1(equi)24.1(v)24.1(alently)-252.9(e)12(xpressed)]TJ
-13.6349 -1.2045 TD
(as)Tj
/F3 1 Tf
1.2425 0 TD
0.005 Tc
[(with)-505.9($x)-517.9(seeded)-493.8(by)-517.9(.)-517.9(recurse)-481.8($x/)]TJ
/F6 1 Tf
16.285 0 TD
0 Tc
(s)Tj
/TT5 1 Tf
0.8672 0 TD
[(\(for)-397.5(the)-397.5(sim-)]TJ
-18.3948 -1.1925 TD
[(ple)-265(proof)-240.9(see)-277([2)12(]\),)-265(Theorem)-240.9(3.2)-252.9(asserts)-277(that)-265(we)-277(may)-252.9(indeed)]TJ
0 -1.2045 TD
[(use)-240.9(algorithm)]TJ
/TT7 1 Tf
5.6909 0 TD
(Delta)Tj
/TT5 1 Tf
2.4626 0 TD
[(to)-240.9(e)24.1(v)24.1(aluate)]TJ
/F6 1 Tf
4.5425 0 TD
(s)Tj
/F11 1 Tf
6.9738 0 0 6.9738 440.64 161.1 Tm
(+)Tj
/TT5 1 Tf
9.9626 0 0 9.9626 444.84 157.5 Tm
(.)Tj
-13.647 -2.8788 TD
[(In)-337.3(contrast,)-361.4(e)12(xpression)]TJ
/F6 1 Tf
9.5372 0 TD
(e)Tj
/F8 1 Tf
0.4698 0 TD
(\()Tj
/F3 1 Tf
0.3854 0 TD
0.005 Tc
($x)Tj
/F8 1 Tf
1.0479 0 TD
0.4543 Tc
(\)=)Tj
/F3 1 Tf
2.0838 0 TD
0.005 Tc
($x[1])Tj
/TT5 1 Tf
2.9751 0 TD
0 Tc
(is)Tj
/TT7 1 Tf
1.0283 0 TD
(not)Tj
/TT5 1 Tf
1.6271 0 TD
[(distrib)24.1(uti)24.1(v)12(e)]TJ
-19.1547 -1.2045 TD
(for)Tj
/F3 1 Tf
1.4551 0 TD
0.005 Tc
($x)Tj
/TT5 1 Tf
1.349 0 TD
0 Tc
[(in)-289.1(general.)-433.6(W)36.1(ith)-301.1(v)24.1(ariable)]TJ
/F3 1 Tf
10.4306 0 TD
0.005 Tc
($x)Tj
/TT5 1 Tf
1.349 0 TD
0 Tc
[(bound)-277(to)-289.1(the)-289.1(sequence)]TJ
/F3 1 Tf
-14.5838 -1.2045 TD
0.005 Tc
(\(,\))Tj
/TT5 1 Tf
5.8299 0 TD
0 Tc
(,)Tj
/F3 1 Tf
0.4186 0 TD
0.005 Tc
($x[1])Tj
/TT5 1 Tf
2.8427 0 TD
0 Tc
[(e)24.1(v)24.1(aluates)-192.7(to)]TJ
/F3 1 Tf
4.8594 0 TD
0.005 Tc
()Tj
/TT5 1 Tf
2.1199 0 TD
0 Tc
[(,)-204.8(while)]TJ
/F3 1 Tf
2.8812 0 TD
0.005 Tc
[(for)-517.9($y)-505.9(in)]TJ
-18.9517 -1.1925 TD
[($x)-517.9(return)-493.8($y[1])]TJ
/TT5 1 Tf
8.1786 0 TD
0 Tc
(yields)Tj
/F3 1 Tf
2.6898 0 TD
0.005 Tc
(\(,\))Tj
/TT5 1 Tf
5.8298 0 TD
0 Tc
[(.)-421.6(E)0(f)24.1(fecti)24.1(v)12(ely)60.2(,)-289.1(this)]TJ
-16.6983 -1.2045 TD
[(in)36.1(v)24.1(alidates)-228.9(Equation)-216.8(\(4\))12(.)]TJ
-1.3852 -2.9992 TD
(4)Tj
ET
endstream
endobj
44 0 obj
<<
/ProcSet [/PDF /Text /ImageB ]
/Font <<
/F1 4 0 R
/F3 6 0 R
/F4 7 0 R
/F5 8 0 R
/F6 22 0 R
/F7 23 0 R
/F8 24 0 R
/F9 25 0 R
/F10 26 0 R
/F11 27 0 R
/F13 29 0 R
/F14 30 0 R
/F15 37 0 R
/F16 38 0 R
/F18 40 0 R
/F19 41 0 R
/TT2 9 0 R
/TT3 10 0 R
/TT5 11 0 R
/TT7 12 0 R
/TT8 13 0 R
/TT9 14 0 R
/TT14 31 0 R
/TT15 32 0 R
>>
/XObject <<
/Im1 33 0 R
>>
/ExtGState <<
/GS1 17 0 R
>>
>>
endobj
46 0 obj
<<
/Length 21333
>>
stream
BT
/TT2 1 Tf
10.9589 0 0 10.9589 50.16 709.98 Tm
0 g
/GS1 gs
0 Tc
0 Tw
[(3.2)11(.)-240.9(I)0(s)-240.9(Expr)21.9(ession)]TJ
/TT7 1 Tf
11.9552 0 0 11.9552 134.3284 709.98 Tm
(e)Tj
7.9701 0 0 7.9701 140.16 708.1801 Tm
-0.0301 Tc
[(re)-30.1(c)]TJ
/TT2 1 Tf
10.9589 0 0 10.9589 153.24 709.98 Tm
0 Tc
[(Distrib)21.9(uti)11(v)11(e)0(?)]TJ
-7.1613 -1.095 TD
[(\(A)-251.9(Syntactic)-240.9(A)21.9(ppr)21.9(oximation\))]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 62.04 672.0601 Tm
[(Whene)24.1(v)12(e)0(r)-289.1(a)0(n)-301.1(XQuery)-289.1(processor)-289.1(plans)-301.1(the)-301.1(e)24.1(v)24.1(aluation)-277(of)]TJ
/F3 1 Tf
-1.1925 -1.1924 TD
0.005 Tc
[(with)-505.9($x)-505.9(seeded)-493.8(by)]TJ
/F6 1 Tf
9.4434 0 TD
0 Tc
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 148.92 658.7401 Tm
-0.0454 Tc
[(s)-41.5(eed)]TJ
/F3 1 Tf
9.9626 0 0 9.9626 169.68 660.1801 Tm
0.005 Tc
(recurse)Tj
/F6 1 Tf
4.1917 0 TD
0 Tc
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 216.12 658.7401 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 227.28 660.1801 Tm
0 Tc
[(,)-517.9(kno)24.1(wing)-433.6(the)]TJ
-17.7784 -1.2045 TD
[(answer)-240.9(to)-240.9()]TJ
/TT7 1 Tf
4.5355 0 TD
(Is)Tj
/F6 1 Tf
0.9751 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 109.92 646.7401 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT7 1 Tf
9.9626 0 0 9.9626 123.48 648.1801 Tm
0 Tc
[(distrib)24.1(utive)-240.9(for)]TJ
/F3 1 Tf
6.216 0 TD
0.005 Tc
($x)Tj
/TT7 1 Tf
1.06 0 TD
0 Tc
(?)Tj
/TT5 1 Tf
0.5 0 TD
[()-301.1(i)0(s)-252.9(particularly)-228.9(v)24.1(alu-)]TJ
-15.1355 -1.2045 TD
[(able:)-289.1(we)-240.9(may)-216.8(le)12(gitimately)-216.8(e)12(xpect)]TJ
/TT7 1 Tf
13.3731 0 TD
(Delta)Tj
/TT5 1 Tf
2.4505 0 TD
[(to)-228.9(be)-228.9(a)-240.9(signi)]TJ
/TT8 1 Tf
4.809 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
(cantly)Tj
-21.1888 -1.1925 TD
[(more)-204.8(ef)]TJ
/TT8 1 Tf
3.0122 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(cient)-216.8(IFP)-216.8(e)24.1(v)24.1(aluation)-204.8(strate)12(gy)-204.8(than)]TJ
/TT7 1 Tf
13.4407 0 TD
(Na)Tj
1.2271 -0.0121 TD
()Tj
/TT9 1 Tf
0.0241 0.0121 TD
()Tj
/TT7 1 Tf
0.2778 0 TD
(ve)Tj
/TT5 1 Tf
1.1045 0 TD
[(\(Section)-216.8(5)]TJ
-19.6426 -1.2045 TD
[(will)-277(indeed)-265(mak)12(e)-277(this)-277(e)24.1(vident\).)-385.4(While,)-289.1(unfortunately)60.2(,)-228.9(there)]TJ
0 -1.1925 TD
[(is)-313.2(no)-301.1(complete)-301.1(procedure)-277(to)-301.1(decide)-301.1(this)-313.2(question)]TJ
6.9738 0 0 6.9738 247.08 604.02 Tm
(2)Tj
9.9626 0 0 9.9626 250.92 600.42 Tm
[(,)-325.2(still)-325.2(we)]TJ
-20.1513 -1.2045 TD
[(can)-313.2(safely)-325.2(approximate)-289.1(the)-325.2(answer)60.2(.)-554.1(Here,)-337.3(we)-325.2(will)-337.3(present)]TJ
T*
[(purely)-265(syntactic,)-277(suf)]TJ
/TT8 1 Tf
8.099 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(cient)-277(conditions)-265(for)-265(XQuery)-277(distrib)24.1(u-)]TJ
-8.6551 -1.1925 TD
[(ti)24.1(vity)60.2(.)-313.2(Section)-240.9(4)-252.9(approaches)-228.9(the)-252.9(same)-252.9(challenge)-228.9(on)-252.9(an)-240.9(alge-)]TJ
0 -1.2045 TD
[(braic)-228.9(le)24.1(v)12(el.)]TJ
0 -1.5658 TD
[(Intuiti)24.1(v)12(ely)60.2(,)-385.4(w)0(e)-397.5(may)]TJ
/TT7 1 Tf
8.3757 0 TD
(not)Tj
/TT5 1 Tf
1.6753 0 TD
[(apply)-373.4(a)-397.5(d)0(i)24.1(vide-and-conquer)-325.2(e)24.1(v)24.1(al-)]TJ
-10.051 -1.2045 TD
[(uation)-325.2(strate)12(gy)-325.2(for)-337.3(an)-337.3(e)12(xpression)]TJ
/F6 1 Tf
13.6658 0 TD
(e)Tj
/F8 1 Tf
0.4698 0 TD
(\()Tj
/F3 1 Tf
0.3854 0 TD
0.005 Tc
($x)Tj
/F8 1 Tf
1.0479 0 TD
0 Tc
(\))Tj
/TT5 1 Tf
0.3854 0 TD
[(,)-373.4(i)0(f)-349.3(a)0(n)12(y)-325.2(sube)12(xpres-)]TJ
-15.9544 -1.1925 TD
[(sion)-301.1(of)]TJ
/F6 1 Tf
3.1023 0 TD
(e)Tj
/TT5 1 Tf
0.7709 0 TD
[(inspects)-301.1(the)-313.2(sequence)-289.1(bound)-277(to)]TJ
/F3 1 Tf
12.8673 0 TD
0.005 Tc
($x)Tj
/TT5 1 Tf
1.3611 0 TD
0 Tc
[(as)-313.2(a)-313.2(whole:)]TJ
/F6 1 Tf
5.0465 0 TD
(e)Tj
/TT5 1 Tf
-23.148 -1.2045 TD
[(is)-313.2(only)-301.1(e)24.1(v)24.1(aluated)-289.1(after)]TJ
/F3 1 Tf
9.2637 0 TD
0.005 Tc
($x)Tj
/TT5 1 Tf
1.3611 0 TD
0 Tc
[(has)-313.2(been)-289.1(di)24.1(vided)-289.1(into)-313.2(indi)24.1(vidual)]TJ
-10.6248 -1.2045 TD
[(items)-361.4(\(see)-373.4(Equation)-337.3(4\).)-662.5(Ob)12(vious)-349.3(e)12(xamples)-361.3(of)-361.3(such)-361.4(prob-)]TJ
0 -1.1925 TD
[(lematic)-216.8(sube)12(xpressions)-192.7(are)]TJ
/F3 1 Tf
10.833 0 TD
0.005 Tc
(count\($x\))Tj
/TT5 1 Tf
4.9626 0 TD
0 Tc
(and)Tj
/F3 1 Tf
1.6486 0 TD
0.005 Tc
($x[1])Tj
/TT5 1 Tf
2.6499 0 TD
0 Tc
[(,)-204.8(b)24.1(ut)-228.9(also)]TJ
-20.0942 -1.2045 TD
[(the)-313.2(general)-313.2(comparison)]TJ
/F3 1 Tf
9.745 0 TD
0.5229 Tc
[($)517.9(x=1)517.9(0)]TJ
/TT5 1 Tf
4.011 0 TD
0 Tc
[(\(that)-313.2(in)36.1(v)24.1(olv)12(es)-301.1(e)12(xistential)]TJ
-13.756 -1.2045 TD
(quanti)Tj
/TT8 1 Tf
2.4995 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(cation)-216.8(o)12(v)12(e)0(r)-228.9(the)-240.9(sequence)-228.9(bound)-216.8(to)]TJ
/F3 1 Tf
13.7454 0 TD
0.005 Tc
($x)Tj
/TT5 1 Tf
1.06 0 TD
0 Tc
(\).)Tj
-16.6685 -1.2286 TD
[(Sube)12(xpressions)-385.4(whose)-397.5(v)24.1(alue)-385.4(is)]TJ
/TT7 1 Tf
13.1637 0 TD
(independent)Tj
/TT5 1 Tf
5.2726 0 TD
(of)Tj
/F3 1 Tf
1.2305 0 TD
0.005 Tc
($x)Tj
/TT5 1 Tf
1.06 0 TD
0.4336 Tc
[(,o)433.6(n)]TJ
-21.9192 -1.2045 TD
0 Tc
[(the)-277(other)-277(hand,)-289.1(are)-277(distrib)24.1(uti)24.1(v)12(e)0(.)-421.6(The)-277(only)-277(e)12(xception)-265(of)-277(this)]TJ
0 -1.1925 TD
[(rule)-265(are)-277(XQuery)60.2(s)-265(node)-265(constructors,)]TJ
/TT7 1 Tf
15.0771 0 TD
-0.012 Tc
[(e.)-12(g.)]TJ
/TT5 1 Tf
1.4198 0 TD
0 Tc
(,)Tj
/F3 1 Tf
0.515 0 TD
0.005 Tc
[(text)-156.6({)]TJ
/F1 1 Tf
2.8065 0 TD
0 Tc
()Tj
/F3 1 Tf
0.277 0 TD
(})Tj
/TT5 1 Tf
0.53 0 TD
[(,)-277(which)]TJ
-20.6254 -1.2045 TD
[(create)-313.2(ne)24.1(w)-313.2(node)-313.2(identities)-313.2(upon)-301.1(each)-313.2(in)36.1(v)24.1(ocation.)-505.9(W)36.1(ith)]TJ
/F3 1 Tf
22.542 0 TD
0.005 Tc
($x)Tj
/TT5 1 Tf
-22.542 -1.2045 TD
0 Tc
[(bound)-216.8(to)]TJ
/F3 1 Tf
3.7355 0 TD
0.005 Tc
(\(,\))Tj
/TT5 1 Tf
5.8299 0 TD
0 Tc
[(,)-192.7(for)-240.9(e)12(xample,)]TJ
/F3 1 Tf
-9.3847 -2.2645 TD
0.005 Tc
[(text)-156.6({)-168.6("c")-168.6(})]TJ
/F1 1 Tf
5.6492 0 TD
0 Tc
()Tj
/F8 1 Tf
T*
(=)Tj
/F10 1 Tf
6.9738 0 0 6.9738 110.16 376.14 Tm
(s)Tj
/F3 1 Tf
9.9626 0 0 9.9626 119.76 370.5 Tm
0.005 Tc
[(for)-517.9($y)-517.9(in)-505.9($x)-517.9(return)-493.8(text)-156.6({)-168.6("c")-156.6(})]TJ
/F6 1 Tf
16.2609 0 TD
0 Tc
(,)Tj
/TT5 1 Tf
-23.247 -2.2645 TD
[(since)-192.7(the)-192.7(rhs)-192.7(will)-204.8(yield)-192.7(a)-192.7(sequence)-180.7(of)-192.7(tw)12(o)-204.8(distinct)-192.7(te)12(xt)-192.7(nodes.)]TJ
0 -1.5658 TD
[(The)-289.1(inference)-289.1(rules)-301.1(of)-301.1(Figure)-289.1(5)-301.1(h)0(a)24.1(v)12(e)-301.1(been)-289.1(designed)-289.1(to)-301.1(im-)]TJ
0 -1.2045 TD
[(plement)-204.8(these)-216.8(considerations.)-265(The)-204.8(rules)-216.8(syntactically)-204.8(assess)]TJ
T*
(the)Tj
/TT7 1 Tf
1.571 0 TD
[(distrib)24.1(utivity)-361.4(safety)]TJ
/F9 1 Tf
8.142 0 TD
-0.0052 Tc
(ds)Tj
/F11 1 Tf
6.9738 0 0 6.9738 157.08 306.9 Tm
0.0022 Tc
($x)Tj
/F8 1 Tf
9.9626 0 0 9.9626 166.56 308.34 Tm
0 Tc
(\()Tj
/F6 1 Tf
0.3975 0 TD
(e)Tj
/F8 1 Tf
0.4698 0 TD
(\))Tj
/TT5 1 Tf
0.7468 0 TD
[(of)-349.3(an)-349.3(arbitrary)-337.3(LiXQuery)]TJ
-13.2977 -1.1925 TD
[([19)24.1(])-433.6(input)-421.6(e)12(xpression)]TJ
/F6 1 Tf
9.2151 0 TD
(e)Tj
/TT5 1 Tf
0.9034 0 TD
[(by)-421.6(tra)24.1(v)12(ersing)]TJ
/F6 1 Tf
5.7935 0 TD
(e)Tj
/TT5 1 Tf
0.4698 0 TD
[()60.2(s)-433.6(parse)-421.6(tree)-433.6(in)-421.6(a)]TJ
-16.3817 -1.2045 TD
[(bottom-up)-240.9(f)12(ashion.)-385.4(LiXQuery)-252.9(is)-289.1(a)-277(sublanguage)-240.9(of)-277(XQuery)]TJ
T*
[(that)-469.8(preserv)12(es)-469.8(T)48.2(uring-completeness,)-493.8(remo)12(v)12(e)0(s)-457.7(all)-481.8(b)24.1(u)0(t)-481.8(the)]TJ
0 -1.1925 TD
[(most)-517.9(basic)-517.9(types,)-590.2(and)-517.9(e)12(xcludes)-505.9(selected)-517.9(rather)-505.9(esoteric)]TJ
0 -1.2045 TD
[(language)-373.4(features.)-746.8(LiXQuery)60.2(s)-385.4(simpli)]TJ
/TT8 1 Tf
15.8018 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(cation)-385.4(of)-397.5(the)-397.5(v)12(e)0(r)24.1(-)]TJ
-16.358 -1.1925 TD
[(bose)-313.2(XQuery)-301.1(syntax)-301.1(and)-313.2(semantics)-313.2(ha)24.1(v)12(e)-313.2(been)-313.2(designed)-301.1(to)]TJ
0 -1.2045 TD
[(mak)12(e)-301.1(LiXQuery)-301.1(ideal)-313.2(for)-301.1(in)36.1(v)12(estigations)-289.1(of)-301.1(interesting)-301.1(lan-)]TJ
T*
[(guage)-228.9(properties,)-228.9(yet)-240.9(allo)24.1(w)]TJ
/TT8 1 Tf
10.995 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(ndings)-240.9(to)-240.9(be)-252.9(transposed)-228.9(to)-240.9(full)]TJ
-11.5512 -1.1925 TD
[(XQuery)60.2(.)]TJ
1.1925 -1.2406 TD
[(Rules)-252.9(F)]TJ
7.9701 0 0 7.9701 93.274 188.46 Tm
0.0602 Tc
(OR)Tj
9.9626 0 0 9.9626 105.3057 188.46 Tm
0 Tc
[(1)-252.9(and)-240.9(F)]TJ
7.9701 0 0 7.9701 135.6123 188.46 Tm
0.0602 Tc
(OR)Tj
9.9626 0 0 9.9626 147.6441 188.46 Tm
0 Tc
[(2)-252.9(ensure)-216.8(that)-216.8(the)-216.8(recursion)-204.8(v)24.1(ariable)]TJ
/F3 1 Tf
-9.785 -1.1925 TD
0.005 Tc
($x)Tj
/TT5 1 Tf
1.3731 0 TD
0 Tc
[(occurs)-301.1(either)-313.2(in)-313.2(the)-313.2(body)]TJ
/F6 1 Tf
10.4275 0 TD
(e)Tj
/F7 1 Tf
6.9738 0 0 6.9738 173.04 175.14 Tm
(2)Tj
/TT5 1 Tf
9.9626 0 0 9.9626 180.72 176.58 Tm
[(or)-313.2(in)-313.2(the)-313.2(range)-313.2(e)12(xpression)]TJ
/F6 1 Tf
-13.105 -1.2045 TD
(e)Tj
/F7 1 Tf
6.9738 0 0 6.9738 54.84 163.14 Tm
(1)Tj
/TT5 1 Tf
9.9626 0 0 9.9626 62.16 164.58 Tm
[(of)-301.1(a)]TJ
/F3 1 Tf
1.8671 0 TD
0.005 Tc
(for)Tj
/TT5 1 Tf
1.59 0 TD
0 Tc
[(-iteration)-265(b)24.1(u)0(t)-301.1(not)-289.1(both.)-433.6(This)-301.1(coincides)-277(with)-301.1(the)]TJ
-4.6615 -1.2045 TD
[(linearity)-252.9(constraint)-252.9(of)-265(SQL:1999.)-349.3(A)-277(similar)-265(remark)-252.9(applies)]TJ
0 -1.1925 TD
[(to)-301.1(Rules)-325.2(S)]TJ
7.9701 0 0 7.9701 92.8632 140.7 Tm
0.0602 Tc
(TEP)Tj
9.9626 0 0 9.9626 108.4728 140.7 Tm
0 Tc
[(1)-325.2(and)-626.3(S)]TJ
7.9701 0 0 7.9701 143.3394 140.7 Tm
0.0602 Tc
(TEP)Tj
9.9626 0 0 9.9626 158.9489 140.7 Tm
0 Tc
[(2)-325.2(\(in)-289.1(XQuery)60.2(,)-301.1(the)-301.1(step)-301.1(operator)]TJ
-10.9197 -1.2045 TD
()Tj
/F3 1 Tf
0.333 0 TD
(/)Tj
/TT5 1 Tf
0.53 0 TD
[()-192.7(essentially)-204.8(describes)-192.7(an)-204.8(iteration)-192.7(o)12(v)12(e)0(r)-192.7(a)-204.8(sequence)-192.7(of)-192.7(type)]TJ
ET
q
94.56 0 0 -0.48 50.148 119.328 cm
/Im1 Do
Q
BT
5.9776 0 0 5.9776 60.96 112.14 Tm
(2)Tj
7.9701 0 0 7.9701 64.44 109.38 Tm
[(If,)-225.8(for)-225.8(tw)15.1(o)-240.9(arbitrary)-256(e)15.1(xpression)]TJ
/F20 1 Tf
12.4606 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 167.04 108.3 Tm
(1)Tj
/TT5 1 Tf
7.9701 0 0 7.9701 171.24 109.38 Tm
(,)Tj
/F20 1 Tf
0.4608 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 178.92 108.3 Tm
(2)Tj
/TT5 1 Tf
7.9701 0 0 7.9701 184.8 109.38 Tm
[(in)-240.9(which)]TJ
/F11 1 Tf
3.6884 0 TD
-0.0042 Tc
($x)Tj
/TT5 1 Tf
1.2949 0 TD
0 Tc
[(does)-225.8(not)-225.8(occur)-256(free,)]TJ
-21.8764 -1.1894 TD
[(an)-361.3(XQuery)-376.4(processor)-391.5(could)-376.4(assess)-376.4(whether)]TJ
/F11 1 Tf
18.1573 0 TD
-0.0043 Tc
[(if)-527(\(deep-equal\()]TJ
/F20 1 Tf
7.905 0 TD
0 Tc
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 261 98.82 Tm
(1)Tj
/F11 1 Tf
7.9701 0 0 7.9701 265.56 99.9 Tm
(,)Tj
/F20 1 Tf
0.527 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 273.72 98.82 Tm
(2)Tj
/F11 1 Tf
7.9701 0 0 7.9701 277.92 99.9 Tm
-0.0042 Tc
(\)\))Tj
-28.5768 -1.1894 TD
[(then)-542($x)-542(else)-542($x[1])]TJ
/TT5 1 Tf
10.0129 0 TD
0 Tc
[(is)-466.7(distrib)15.1(uti)30.1(v)15.1(e)-527(for)]TJ
/F11 1 Tf
7.7884 0 TD
-0.0042 Tc
($x)Tj
/TT5 1 Tf
1.054 0 TD
0 Tc
[(,)-511.9(i)0(t)-481.8(could)-481.8(also)-481.8(decide)-496.9(the)]TJ
-18.8553 -1.1894 TD
[(equi)30.1(v)30.1(alence)-316.2(of)]TJ
/F20 1 Tf
6.1198 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 102.36 79.86 Tm
(1)Tj
/TT5 1 Tf
7.9701 0 0 7.9701 108.48 80.94 Tm
(and)Tj
/F20 1 Tf
1.6998 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 125.88 79.86 Tm
(2)Tj
/TT5 1 Tf
7.9701 0 0 7.9701 132 80.94 Tm
[(\(which)-271(is)-256(impossible\).)]TJ
/F3 1 Tf
9.9626 0 0 9.9626 308.88 709.98 Tm
0.005 Tc
(node\(\)*)Tj
/TT5 1 Tf
3.9869 0 TD
0 Tc
[([9)12(]\).)-505.9(Also)-313.2(note)-301.1(ho)24.1(w)-301.1(Rule)-337.3(F)]TJ
7.9701 0 0 7.9701 461.1531 709.98 Tm
0.0602 Tc
(UN)Tj
9.9626 0 0 9.9626 473.6246 709.98 Tm
0 Tc
(C)Tj
7.9701 0 0 7.9701 480.7496 709.98 Tm
0.0602 Tc
(ALL)Tj
9.9626 0 0 9.9626 500.6823 709.98 Tm
0 Tc
[(recursi)24.1(v)12.1(ely)]TJ
-19.2522 -1.2045 TD
[(infers)-192.7(the)-192.7(distrib)24.1(uti)24.1(vity)-180.7(of)-180.7(the)-204.8(body)-168.6(of)-192.7(a)-204.8(called)-180.7(function)-180.7(if)-192.7(the)]TJ
0 -1.1925 TD
[(recursion)-228.9(v)24.1(ariable)-228.9(occurs)-228.9(free)-240.9(in)-240.9(the)-240.9(function)-228.9(ar)12(gument\(s\).)]TJ
1.1925 -1.2165 TD
[(In)-337.3(our)-313.2(conte)12(xt,)-337.3(whene)24.1(v)12(e)0(r)-301.1(the)-337.3(XQuery)-313.2(processor)-313.2(is)-337.3(able)]TJ
-1.1925 -1.1925 TD
[(to)-240.9(infer)]TJ
/F9 1 Tf
3.1353 0 TD
-0.0052 Tc
(ds)Tj
/F11 1 Tf
6.9738 0 0 6.9738 350.28 660.66 Tm
0.0022 Tc
($x)Tj
/F8 1 Tf
9.9626 0 0 9.9626 359.88 662.1 Tm
0 Tc
(\()Tj
/F6 1 Tf
0.3854 0 TD
(e)Tj
/F8 1 Tf
0.4698 0 TD
(\))Tj
/TT5 1 Tf
0.6263 0 TD
[(for)-240.9(an)-228.9(input)-228.9(e)12(xpression)]TJ
/F6 1 Tf
9.3578 0 TD
(e)Tj
/TT5 1 Tf
0.4698 0 TD
[(,)-228.9(then)-240.9(it)-240.9(is)-252.9(guaran-)]TJ
-16.4282 -1.2045 TD
[(teed)-313.2(that)]TJ
/F6 1 Tf
3.8034 0 TD
(e)Tj
/TT5 1 Tf
0.7829 0 TD
[(is)-337.3(indeed)-301.1(distrib)24.1(uti)24.1(v)12(e)-301.1(for)]TJ
/F3 1 Tf
10.2462 0 TD
0.005 Tc
($x)Tj
/TT5 1 Tf
1.06 0 TD
0 Tc
[(.)-530(The)-313.2(proof)-289.1(of)-325.2(this)]TJ
-15.8925 -1.1925 TD
[(implication,)-313.2(by)-313.2(induction)-289.1(on)-313.2(the)-313.2(syntactical)-301.1(structure)-301.1(of)]TJ
/F6 1 Tf
22.8683 0 TD
(e)Tj
/TT5 1 Tf
0.4698 0 TD
(,)Tj
-23.3381 -1.2045 TD
[(is)-252.9(to)-240.9(be)-240.9(found)-228.9(in)-240.9([2)12(].)]TJ
/TT2 1 Tf
0 -2.6981 TD
[(Distrib)24.1(uti)12(vity)-493.8(Hints.)]TJ
/TT5 1 Tf
9.8072 0 TD
[(Still,)-578.2(the)-493.8(inference)-469.8(rules)-493.8(of)-493.8(Fig-)]TJ
-9.8072 -1.2045 TD
[(ure)-385.4(5)-385.4(can)-397.5(only)-373.4(check)]TJ
/TT7 1 Tf
9.2011 0 TD
(suf)Tj
/TT9 1 Tf
1.1549 0 TD
()Tj
/TT7 1 Tf
0.5 0 TD
[(cient)-373.4(syntactical)-385.4(conditions)]TJ
/TT5 1 Tf
11.5741 0 TD
(for)Tj
-22.4302 -1.2045 TD
[(distrib)24.1(uti)24.1(vity)-517.9(to)-530(hold.)-1156.3(The)-517.9(processor)-517.9(might)-530(thus)-530(actu-)]TJ
0 -1.1925 TD
[(ally)-517.9(miss)-542(distrib)24.1(uti)24.1(v)12(e)-505.9(e)12(xpressions)-505.9(and)-517.9(will)-530(f)12(ail)-530(to)-530(infer)]TJ
/F9 1 Tf
0 -1.2045 TD
-0.0052 Tc
(ds)Tj
/F11 1 Tf
6.9738 0 0 6.9738 318.84 550.02 Tm
0.0022 Tc
($x)Tj
/F8 1 Tf
9.9626 0 0 9.9626 328.44 551.46 Tm
0 Tc
(\()Tj
/F3 1 Tf
0.3854 0 TD
0.005 Tc
[(count\($x\))-481.8(>=)-517.9(1)]TJ
/F8 1 Tf
7.3475 0 TD
0 Tc
(\))Tj
/TT5 1 Tf
0.3975 0 TD
[(,)-373.4(for)-337.3(e)12(xample.)-590.2(Ho)24.1(we)24.1(v)12(e)0(r)36.1(,)-349.3(it)-361.4(is)-349.3(in-)]TJ
-10.0938 -1.2045 TD
[(teresting)-240.9(to)-240.9(note)-240.9(users)-252.9(can)-240.9(support)-228.9(the)-252.9(XQuery)-228.9(processor)-228.9(in)]TJ
0 -1.1925 TD
[(its)-216.8(distrib)24.1(uti)24.1(vity)-192.7(assessment,)-216.8(since)-216.8(e)24.1(v)12(ery)-180.7(distrib)24.1(uti)24.1(v)12(e)-204.8(e)12(xpres-)]TJ
0 -1.2045 TD
[(sion)-240.9(is)-252.9(equi)24.1(v)24.1(alent)-228.9(to)-240.9(a)-252.9(distrib)24.1(uti)24.1(vity-safe)-216.8(e)12(xpression:)]TJ
/TT7 1 Tf
0.9997 -2.0236 TD
[(If)-240.9(e)24.1(xpr)36.1(ession)]TJ
/F6 1 Tf
5.3213 0 TD
(e)Tj
/F8 1 Tf
0.4698 0 TD
(\()Tj
/F3 1 Tf
0.3854 0 TD
0.005 Tc
($x)Tj
/F8 1 Tf
1.0479 0 TD
0 Tc
(\))Tj
/TT7 1 Tf
0.6384 0 TD
[(is)-252.9(distrib)24.1(utive)-240.9(for)]TJ
/F3 1 Tf
7.136 0 TD
0.005 Tc
($x)Tj
/TT5 1 Tf
1.06 0 TD
0 Tc
[(,)-240.9(then)-240.9(it)-252.9(is)-252.9(set-)]TJ
-16.0588 -1.1925 TD
[(equal)-493.8(to)]TJ
/F3 1 Tf
3.9431 0 TD
0.005 Tc
[(for)-517.9($y)-517.9(in)-505.9($x)-517.9(return)]TJ
/F6 1 Tf
10.5033 0 TD
0 Tc
(e)Tj
/F8 1 Tf
0.4698 0 TD
(\()Tj
/F3 1 Tf
0.3854 0 TD
0.005 Tc
($y)Tj
/F8 1 Tf
1.0479 0 TD
0 Tc
(\))Tj
/TT5 1 Tf
0.3854 0 TD
[(,)-578.2(for)-505.9(which)]TJ
-16.735 -1.2045 TD
[(the)-349.3(rules)-361.3(of)-349.3(Figure)-349.3(5)-361.4(will)-361.4(successfully)-349.3(infer)-349.3(distrib)24.1(u-)]TJ
T*
[(ti)24.1(vity)-240.9(safety)]TJ
/F9 1 Tf
4.9567 0 TD
-0.0052 Tc
(ds)Tj
/F11 1 Tf
6.9738 0 0 6.9738 378.36 458.1 Tm
0.0022 Tc
($x)Tj
/F8 1 Tf
9.9626 0 0 9.9626 387.96 459.54 Tm
0 Tc
(\()Tj
/F1 1 Tf
0.3854 0 TD
()Tj
/F8 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.3854 0 TD
(.)Tj
-8.9856 -2.0115 TD
[(This)-301.1(is)-325.2(a)-313.2(direct)-301.1(consequence)-277(of)-301.1(Rule)-337.3(F)]TJ
7.9701 0 0 7.9701 465.8464 439.5 Tm
0.0602 Tc
(OR)Tj
9.9626 0 0 9.9626 477.8782 439.5 Tm
0 Tc
[(2)-337.3(\(Figure)-301.1(5\))-301.1(and)]TJ
-16.9632 -1.2045 TD
(De)Tj
/TT8 1 Tf
1.166 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(nition)-240.9(3.1.)-337.3(Thus,)-252.9(at)-265(the)-252.9(e)12(xpense)-240.9(of)-252.9(a)-265(slight)-252.9(query)-240.9(refor)24.1(-)]TJ
-1.7222 -1.2045 TD
[(mulation,)-180.7(we)-204.8(may)-192.7(pro)12(vide)-168.6(a)-204.8(syntactic)-192.7(distrib)24.1(uti)24.1(vity)-180.7(hint)-192.7(to)]TJ
0 -1.1925 TD
[(the)-301.1(XQuery)-301.1(processor)-289.1(which)-289.1(ef)24.1(fecti)24.1(v)12(ely)-289.1(pa)24.1(v)12(e)0(s)-301.1(the)-301.1(w)12(a)0(y)-313.2(for)]TJ
0 -1.2045 TD
[(IFP)-252.9(e)24.1(v)24.1(aluation)-216.8(via)-240.9(algorithm)]TJ
/TT7 1 Tf
11.6115 0 TD
(Delta)Tj
/TT5 1 Tf
2.2217 0 TD
(.)Tj
/TT2 1 Tf
11.9552 0 0 11.9552 308.88 367.5 Tm
[(4.)-240.9(Distrib)20.1(uti)10(vity)-250.9(and)-261(Relational)-240.9(XQuery)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 320.76 341.34 Tm
[(In)-409.5(this)-421.6(section)-409.5(we)-409.5(will,)-457.7(literally)60.2(,)-445.7(follo)24.1(w)-397.5(a)0(n)-409.5(alternati)24.1(v)12(e)]TJ
-1.1925 -1.1925 TD
[(route)-252.9(to)-277(decide)-265(the)-265(applicability)-252.9(of)]TJ
/TT7 1 Tf
14.073 0 TD
(Delta)Tj
/TT5 1 Tf
2.4987 0 TD
[(for)-252.9(the)-277(e)24.1(v)24.1(aluation)]TJ
-16.5717 -1.2045 TD
[(of)-289.1(the)-289.1(IFP)-301.1(of)-277(an)-289.1(XQuery)-289.1(e)12(xpression)]TJ
/F6 1 Tf
14.7623 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 461.4 316.02 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 472.44 317.46 Tm
0 Tc
[(.)-457.7(W)84.3(e)-301.1(lea)24.1(v)12(e)-289.1(syntax)]TJ
-16.4173 -1.2045 TD
[(aside)-252.9(and)-252.9(instead)-252.9(inspect)]TJ
/TT7 1 Tf
10.1754 0 TD
[(r)36.1(elational)-252.9(alg)12(ebr)12(aic)-240.9(code)]TJ
/TT5 1 Tf
10.3391 0 TD
[(that)-265(has)]TJ
-20.5144 -1.1925 TD
[(been)-301.1(compiled)-289.1(for)]TJ
/F6 1 Tf
7.6783 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 390.6 292.14 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 401.64 293.58 Tm
0 Tc
[(:)-445.7(the)-313.2(equi)24.1(v)24.1(alent)-289.1(algebraic)-301.1(represen-)]TJ
-9.3108 -1.2045 TD
[(tation)-252.9(of)]TJ
/F6 1 Tf
3.6283 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 349.92 280.14 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 363.6 281.58 Tm
0 Tc
[(renders)-252.9(the)-265(check)-252.9(for)-252.9(the)-252.9(inherently)-240.9(algebraic)]TJ
-5.4925 -1.2045 TD
[(distrib)24.1(uti)24.1(vity)-228.9(property)-216.8(particularly)-216.8(uniform)-228.9(and)-228.9(simple.)]TJ
/TT2 1 Tf
0 -2.6981 TD
[(Relational)-277(XQuery)72.3(.)]TJ
/TT5 1 Tf
9.275 0 TD
[(This)-289.1(alternati)24.1(v)12(e)-277(route)-289.1(is)-301.1(inspired)-289.1(by)]TJ
-9.275 -1.2045 TD
(the)Tj
/TT7 1 Tf
1.7637 0 TD
[(P)84.3(ath)]TJ
/TT9 1 Tf
1.8044 0 TD
()Tj
/TT7 1 Tf
0.5 0 TD
(nder)Tj
/TT5 1 Tf
2.3871 0 TD
(project)Tj
6.9738 0 0 6.9738 401.4 234.42 Tm
(3)Tj
9.9626 0 0 9.9626 410.76 230.7 Tm
[(which)-530(fully)-542(implements)-542(such)-542(a)]TJ
-10.2262 -1.1925 TD
[(purely)-252.9(relational)-252.9(approach)-240.9(to)-277(XQuery)60.2(.)]TJ
/TT7 1 Tf
15.557 0 TD
[(P)84.3(ath)]TJ
/TT9 1 Tf
1.8044 0 TD
()Tj
/TT7 1 Tf
0.5 0 TD
(nder)Tj
/TT5 1 Tf
2.11 0 TD
(compiles)Tj
-19.9714 -1.2045 TD
[(instances)-313.2(of)-325.2(the)-313.2(XQuery)-313.2(Data)-313.2(Model)-313.2(\(XDM\))-313.2(and)-313.2(XQuery)]TJ
0 -1.1925 TD
[(e)12(xpressions)-325.2(into)-337.3(relational)-325.2(tables)-349.3(and)-325.2(algebraic)-325.2(plans)-349.3(o)12(v)12(e)0(r)]TJ
0 -1.2045 TD
[(these)-277(tables,)-289.1(respecti)24.1(v)12(ely)60.2(,)-252.9(and)-277(thus)-277(follo)24.1(ws)-265(the)-277(dashed)-277(path)]TJ
T*
[(in)-265(Figure)-252.9(6.)-349.3(The)-252.9(translation)-252.9(strate)12(gy)-252.9(b)24.1(uilt)-252.9(into)-265(the)-252.9(compiler)]TJ
0 -1.1925 TD
[(has)-409.5(been)-409.5(carefully)-397.5(designed)-397.5(\()]TJ
/TT7 1 Tf
12.2757 0 TD
(i\))Tj
/TT5 1 Tf
1.0204 0 TD
[(to)-409.5(f)12(aithfully)-397.5(preserv)12(e)-397.5(the)]TJ
-13.296 -1.2045 TD
[(XQuery)-277(semantics)-301.1(\(including)-277(compositionality)60.2(,)-265(node)-289.1(iden-)]TJ
T*
[(tity)60.2(,)-325.2(iteration)-313.2(and)-301.1(sequence)-301.1(order\),)-313.2(and)-313.2(\()]TJ
/TT7 1 Tf
16.3004 0 TD
(ii\))Tj
/TT5 1 Tf
1.2018 0 TD
[(yield)-313.2(relational)]TJ
-17.5022 -1.1925 TD
[(plans)-228.9(which)-240.9(e)12(xclusi)24.1(v)12(ely)-204.8(rely)-240.9(on)-228.9(re)12(gular)-216.8(relational)-228.9(query)-228.9(en-)]TJ
0 -1.2045 TD
[(gine)-349.3(technology)-313.2(\(no)-349.3(speci)]TJ
/TT8 1 Tf
10.5645 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(c)-349.3(operators)-337.3(or)-349.3(inde)12(x)-337.3(structures)]TJ
-11.1207 -1.1925 TD
[(are)-240.9(required,)-216.8(in)-240.9(particular\))-228.9([15)12(].)]TJ
ET
q
94.56 0 0 -0.48 308.868 90.888 cm
/Im1 Do
Q
BT
5.9776 0 0 5.9776 319.68 83.7 Tm
(3)Tj
/F11 1 Tf
7.9701 0 0 7.9701 323.16 80.94 Tm
-0.0042 Tc
[(http://www.pathfinder-)-75.2(xqu)-15(ery)-15(.org)-15(/)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 295.08 51.06 Tm
0 Tc
(5)Tj
ET
endstream
endobj
47 0 obj
<<
/ProcSet [/PDF /Text /ImageB ]
/Font <<
/F1 4 0 R
/F3 6 0 R
/F6 22 0 R
/F7 23 0 R
/F8 24 0 R
/F9 25 0 R
/F10 26 0 R
/F11 27 0 R
/F13 29 0 R
/F20 48 0 R
/F21 49 0 R
/TT2 9 0 R
/TT5 11 0 R
/TT7 12 0 R
/TT8 13 0 R
/TT9 14 0 R
>>
/XObject <<
/Im1 33 0 R
>>
/ExtGState <<
/GS1 17 0 R
>>
>>
endobj
51 0 obj
<<
/Length 35884
>>
stream
0 g
/GS1 gs
q
28.8 0 0 -0.48 64.188 707.928 cm
/Im1 Do
Q
BT
/F16 1 Tf
8.9664 0 0 8.9664 64.2 698.7001 Tm
-0.0027 Tc
0 Tw
(ds)Tj
/F11 1 Tf
5.9776 0 0 5.9776 73.32 697.62 Tm
-0.0092 Tc
($x)Tj
/F19 1 Tf
8.9664 0 0 8.9664 81.72 698.7001 Tm
0 Tc
(\()Tj
/F18 1 Tf
0.4015 0 TD
(c)Tj
/F19 1 Tf
0.4417 0 TD
(\))Tj
0.5353 0.7495 TD
(\()Tj
/TT5 1 Tf
0.4283 0 TD
(C)Tj
7.1731 0 0 7.1731 104.3806 705.42 Tm
0.0669 Tc
(ONST)Tj
/F19 1 Tf
8.9664 0 0 8.9664 124.5519 705.42 Tm
0 Tc
(\))Tj
ET
q
34.32 0 0 -0.48 138.348 707.928 cm
/Im1 Do
Q
BT
/F16 1 Tf
8.9664 0 0 8.9664 138.36 698.7001 Tm
-0.0027 Tc
(ds)Tj
/F11 1 Tf
5.9776 0 0 5.9776 147.6 697.62 Tm
-0.0092 Tc
($x)Tj
/F19 1 Tf
8.9664 0 0 8.9664 155.88 698.7001 Tm
0 Tc
(\()Tj
/F4 1 Tf
0.4015 0 TD
($)Tj
/F18 1 Tf
0.5354 0 TD
(v)Tj
/F19 1 Tf
0.5353 0 TD
(\))Tj
0.5219 0.7495 TD
(\()Tj
/TT5 1 Tf
0.4283 0 TD
(V)Tj
7.1731 0 0 7.1731 183.4753 705.42 Tm
0.0669 Tc
(AR)Tj
/F19 1 Tf
8.9664 0 0 8.9664 194.0399 705.42 Tm
0 Tc
(\))Tj
/F4 1 Tf
1.5391 0.7628 TD
-0.003 Tc
($x)Tj
/F18 1 Tf
1.4454 0 TD
0 Tc
(/)Tj
/F17 1 Tf
-0.107 0 TD
()Tj
/F16 1 Tf
0.9636 0 TD
0.0064 Tc
(fv)Tj
/F19 1 Tf
0.8967 0 TD
0 Tc
(\()Tj
/F18 1 Tf
0.4015 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 244.44 711.3 Tm
(1)Tj
/F19 1 Tf
8.9664 0 0 8.9664 248.52 712.26 Tm
(\))Tj
/F16 1 Tf
1.4053 0 TD
-0.0027 Tc
(ds)Tj
/F11 1 Tf
5.9776 0 0 5.9776 270.24 711.1801 Tm
-0.0092 Tc
($x)Tj
/F19 1 Tf
8.9664 0 0 8.9664 278.64 712.26 Tm
0 Tc
(\()Tj
/F18 1 Tf
0.4015 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 286.56 711.3 Tm
(2)Tj
/F19 1 Tf
8.9664 0 0 8.9664 290.64 712.26 Tm
(\))Tj
/F16 1 Tf
1.5792 0 TD
-0.0027 Tc
(ds)Tj
/F11 1 Tf
5.9776 0 0 5.9776 313.92 711.1801 Tm
-0.0092 Tc
($x)Tj
/F19 1 Tf
8.9664 0 0 8.9664 322.32 712.26 Tm
0 Tc
(\()Tj
/F18 1 Tf
0.4015 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 330.24 711.3 Tm
(3)Tj
/F19 1 Tf
8.9664 0 0 8.9664 334.32 712.26 Tm
(\))Tj
ET
q
130.2 0 0 -0.48 207.828 707.928 cm
/Im1 Do
Q
BT
/F16 1 Tf
8.9664 0 0 8.9664 207.84 698.7001 Tm
-0.0027 Tc
(ds)Tj
/F11 1 Tf
5.9776 0 0 5.9776 217.08 697.62 Tm
-0.0092 Tc
($x)Tj
/F19 1 Tf
8.9664 0 0 8.9664 225.48 698.7001 Tm
0 Tc
(\()Tj
/F4 1 Tf
0.3881 0 TD
-0.003 Tc
[(if)-535.3(\()]TJ
/F18 1 Tf
2.1012 0 TD
0 Tc
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 252.12 697.7401 Tm
(1)Tj
/F4 1 Tf
8.9664 0 0 8.9664 256.32 698.7001 Tm
-0.003 Tc
[(\))-521.9(then)]TJ
/F18 1 Tf
3.6671 0 TD
0 Tc
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 293.52 697.7401 Tm
(2)Tj
/F4 1 Tf
8.9664 0 0 8.9664 302.4 698.7001 Tm
-0.003 Tc
(else)Tj
/F18 1 Tf
2.6232 0 TD
0 Tc
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 330.24 697.7401 Tm
(3)Tj
/F19 1 Tf
8.9664 0 0 8.9664 334.32 698.7001 Tm
(\))Tj
0.5353 0.7495 TD
(\()Tj
/TT5 1 Tf
0.4283 0 TD
(I)Tj
7.1731 0 0 7.1731 346.426 705.42 Tm
(F)Tj
/F19 1 Tf
8.9664 0 0 8.9664 350.6553 705.42 Tm
(\))Tj
/F17 1 Tf
1.524 0.7628 TD
0.2847 Tc
[()-7.1({)]TJ
/F4 1 Tf
2.5697 0 TD
0 Tc
(,)Tj
/F18 1 Tf
0.522 0 TD
(,)Tj
/F4 1 Tf
0.4684 0 TD
(|)Tj
/F17 1 Tf
0.522 0 TD
(})Tj
/F16 1 Tf
1.5123 0 TD
-0.0027 Tc
(ds)Tj
/F11 1 Tf
5.9776 0 0 5.9776 423.72 711.1801 Tm
-0.0092 Tc
($x)Tj
/F19 1 Tf
8.9664 0 0 8.9664 432 712.26 Tm
0 Tc
(\()Tj
/F18 1 Tf
0.4015 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 439.92 711.3 Tm
(1)Tj
/F19 1 Tf
8.9664 0 0 8.9664 444.12 712.26 Tm
(\))Tj
/F16 1 Tf
1.5659 0 TD
-0.0027 Tc
(ds)Tj
/F11 1 Tf
5.9776 0 0 5.9776 467.4 711.1801 Tm
-0.0092 Tc
($x)Tj
/F19 1 Tf
8.9664 0 0 8.9664 475.8 712.26 Tm
0 Tc
(\()Tj
/F18 1 Tf
0.3881 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 483.6 711.3 Tm
(2)Tj
/F19 1 Tf
8.9664 0 0 8.9664 487.8 712.26 Tm
(\))Tj
ET
q
127.08 0 0 -0.48 364.308 707.928 cm
/Im1 Do
Q
BT
/F16 1 Tf
8.9664 0 0 8.9664 401.4 698.7001 Tm
-0.0027 Tc
(ds)Tj
/F11 1 Tf
5.9776 0 0 5.9776 410.64 697.62 Tm
-0.0092 Tc
($x)Tj
/F19 1 Tf
8.9664 0 0 8.9664 419.04 698.7001 Tm
0 Tc
(\()Tj
/F18 1 Tf
0.3881 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 426.84 697.7401 Tm
(1)Tj
/F17 1 Tf
8.9664 0 0 8.9664 433.08 698.7001 Tm
()Tj
/F18 1 Tf
1.0305 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 446.64 697.7401 Tm
(2)Tj
/F19 1 Tf
8.9664 0 0 8.9664 450.72 698.7001 Tm
(\))Tj
4.6708 0.7495 TD
(\()Tj
/TT5 1 Tf
0.4283 0 TD
(C)Tj
7.1731 0 0 7.1731 502.9006 705.42 Tm
0.0669 Tc
[(ONCA)117.1(T)]TJ
/F19 1 Tf
8.9664 0 0 8.9664 528.6872 705.42 Tm
0 Tc
(\))Tj
/F4 1 Tf
-41.4445 -2.7971 TD
-0.003 Tc
($x)Tj
/F18 1 Tf
1.4588 0 TD
0 Tc
(/)Tj
/F17 1 Tf
-0.1204 0 TD
()Tj
/F16 1 Tf
0.9636 0 TD
0.0064 Tc
(fv)Tj
/F19 1 Tf
0.8967 0 TD
0 Tc
(\()Tj
/F18 1 Tf
0.4015 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 193.68 679.38 Tm
(1)Tj
/F19 1 Tf
8.9664 0 0 8.9664 197.88 680.34 Tm
(\))Tj
/F16 1 Tf
1.3919 0 TD
-0.0027 Tc
(ds)Tj
/F11 1 Tf
5.9776 0 0 5.9776 219.6 679.26 Tm
-0.0092 Tc
($x)Tj
/F19 1 Tf
8.9664 0 0 8.9664 228 680.34 Tm
0 Tc
(\()Tj
/F18 1 Tf
0.3881 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 235.8 679.38 Tm
(2)Tj
/F19 1 Tf
8.9664 0 0 8.9664 240 680.34 Tm
(\))Tj
ET
q
154.68 0 0 -0.48 122.988 676.008 cm
/Im1 Do
Q
BT
/F16 1 Tf
8.9664 0 0 8.9664 123 666.66 Tm
-0.0027 Tc
(ds)Tj
/F11 1 Tf
5.9776 0 0 5.9776 132.24 665.5801 Tm
-0.0092 Tc
($x)Tj
/F19 1 Tf
8.9664 0 0 8.9664 140.64 666.66 Tm
0 Tc
(\()Tj
/F4 1 Tf
0.4015 0 TD
-0.003 Tc
[(for)-535.3($)]TJ
/F18 1 Tf
2.6232 0 TD
0 Tc
(v)Tj
/F4 1 Tf
1.0573 0 TD
-0.003 Tc
[(at)-535.3($)]TJ
/F18 1 Tf
2.1012 0 TD
0 Tc
(p)Tj
/F4 1 Tf
1.0439 0 TD
-0.003 Tc
(in)Tj
/F18 1 Tf
1.5659 0 TD
0 Tc
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 223.8 665.7001 Tm
(1)Tj
/F4 1 Tf
8.9664 0 0 8.9664 232.68 666.66 Tm
-0.003 Tc
(return)Tj
/F18 1 Tf
3.6671 0 TD
0 Tc
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 269.88 665.7001 Tm
(2)Tj
/F19 1 Tf
8.9664 0 0 8.9664 274.08 666.66 Tm
(\))Tj
0.5353 0.7495 TD
(\()Tj
/TT5 1 Tf
0.4283 0 TD
(F)Tj
7.1731 0 0 7.1731 288.1868 673.38 Tm
0.0669 Tc
(OR)Tj
8.9664 0 0 8.9664 299.1114 673.38 Tm
0 Tc
(1)Tj
/F19 1 Tf
0.5 0 TD
(\))Tj
/F16 1 Tf
3.681 0.7762 TD
-0.0027 Tc
(ds)Tj
/F11 1 Tf
5.9776 0 0 5.9776 345.84 679.26 Tm
-0.0092 Tc
($x)Tj
/F19 1 Tf
8.9664 0 0 8.9664 354.24 680.34 Tm
0 Tc
(\()Tj
/F18 1 Tf
0.3881 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 362.04 679.38 Tm
(1)Tj
/F19 1 Tf
8.9664 0 0 8.9664 366.24 680.34 Tm
(\))Tj
/F4 1 Tf
1.5659 0 TD
-0.003 Tc
($x)Tj
/F18 1 Tf
1.4454 0 TD
0 Tc
(/)Tj
/F17 1 Tf
-0.107 0 TD
()Tj
/F16 1 Tf
0.9636 0 TD
0.0064 Tc
(fv)Tj
/F19 1 Tf
0.8967 0 TD
0 Tc
(\()Tj
/F18 1 Tf
0.4015 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 416.88 679.38 Tm
(2)Tj
/F19 1 Tf
8.9664 0 0 8.9664 420.96 680.34 Tm
(\))Tj
ET
q
126.48 0 0 -0.48 317.388 676.008 cm
/Im1 Do
Q
BT
/F16 1 Tf
8.9664 0 0 8.9664 317.4 666.66 Tm
-0.0027 Tc
(ds)Tj
/F11 1 Tf
5.9776 0 0 5.9776 326.52 665.5801 Tm
-0.0092 Tc
($x)Tj
/F19 1 Tf
8.9664 0 0 8.9664 334.92 666.66 Tm
0 Tc
(\()Tj
/F4 1 Tf
0.4015 0 TD
-0.003 Tc
[(for)-535.3($)]TJ
/F18 1 Tf
2.6232 0 TD
0 Tc
(v)Tj
/F4 1 Tf
1.0707 0 TD
-0.003 Tc
(in)Tj
/F18 1 Tf
1.5659 0 TD
0 Tc
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 390 665.7001 Tm
(1)Tj
/F4 1 Tf
8.9664 0 0 8.9664 398.88 666.66 Tm
-0.003 Tc
(return)Tj
/F18 1 Tf
3.6671 0 TD
0 Tc
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 436.08 665.7001 Tm
(2)Tj
/F19 1 Tf
8.9664 0 0 8.9664 440.28 666.66 Tm
(\))Tj
0.522 0.7495 TD
(\()Tj
/TT5 1 Tf
0.4283 0 TD
(F)Tj
7.1731 0 0 7.1731 454.2668 673.38 Tm
0.0669 Tc
(OR)Tj
8.9664 0 0 8.9664 465.1914 673.38 Tm
0 Tc
(2)Tj
/F19 1 Tf
0.5134 0 TD
(\))Tj
/F4 1 Tf
-35.0503 -2.7971 TD
-0.003 Tc
($x)Tj
/F18 1 Tf
1.4588 0 TD
0 Tc
(/)Tj
/F17 1 Tf
-0.1204 0 TD
()Tj
/F16 1 Tf
0.977 0 TD
0.0064 Tc
(fv)Tj
/F19 1 Tf
0.8967 0 TD
0 Tc
(\()Tj
/F18 1 Tf
0.4015 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 192.24 647.34 Tm
(1)Tj
/F19 1 Tf
8.9664 0 0 8.9664 196.32 648.3 Tm
(\))Tj
/F16 1 Tf
1.3919 0 TD
-0.0027 Tc
(ds)Tj
/F11 1 Tf
5.9776 0 0 5.9776 218.04 647.22 Tm
-0.0092 Tc
($x)Tj
/F19 1 Tf
8.9664 0 0 8.9664 226.44 648.3 Tm
0 Tc
(\()Tj
/F18 1 Tf
0.4015 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 234.36 647.34 Tm
(2)Tj
/F19 1 Tf
8.9664 0 0 8.9664 238.44 648.3 Tm
(\))Tj
ET
q
126.48 0 0 -0.48 135.588 643.968 cm
/Im1 Do
Q
BT
/F16 1 Tf
8.9664 0 0 8.9664 135.6 634.7401 Tm
-0.0027 Tc
(ds)Tj
/F11 1 Tf
5.9776 0 0 5.9776 144.72 633.66 Tm
-0.0092 Tc
($x)Tj
/F19 1 Tf
8.9664 0 0 8.9664 153.12 634.7401 Tm
0 Tc
(\()Tj
/F4 1 Tf
0.4015 0 TD
-0.003 Tc
[(let)-535.3($)]TJ
/F18 1 Tf
2.6232 0 TD
0 Tc
(v)Tj
/F4 1 Tf
1.0707 0 TD
-0.003 Tc
(:=)Tj
/F18 1 Tf
1.5659 0 TD
0 Tc
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 208.2 633.78 Tm
(1)Tj
/F4 1 Tf
8.9664 0 0 8.9664 217.08 634.7401 Tm
-0.003 Tc
(return)Tj
/F18 1 Tf
3.6671 0 TD
0 Tc
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 254.28 633.78 Tm
(2)Tj
/F19 1 Tf
8.9664 0 0 8.9664 258.48 634.7401 Tm
(\))Tj
0.5219 0.7495 TD
(\()Tj
/TT5 1 Tf
0.4283 0 TD
(L)Tj
7.1731 0 0 7.1731 272.9572 641.46 Tm
0.0669 Tc
(ET)Tj
8.9664 0 0 8.9664 282.6804 641.46 Tm
0 Tc
(1)Tj
/F19 1 Tf
0.5 0 TD
(\))Tj
/F16 1 Tf
1.5521 0.7629 TD
-0.0027 Tc
(ds)Tj
/F11 1 Tf
5.9776 0 0 5.9776 310.2 647.22 Tm
-0.0092 Tc
($x)Tj
/F19 1 Tf
8.9664 0 0 8.9664 318.6 648.3 Tm
0 Tc
(\()Tj
/F18 1 Tf
0.4015 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 326.52 647.34 Tm
(1)Tj
/F19 1 Tf
8.9664 0 0 8.9664 330.6 648.3 Tm
(\))Tj
/F4 1 Tf
1.5792 0 TD
-0.003 Tc
($x)Tj
/F18 1 Tf
1.4454 0 TD
0 Tc
(/)Tj
/F17 1 Tf
-0.1071 0 TD
()Tj
/F16 1 Tf
0.9636 0 TD
0.0064 Tc
(fv)Tj
/F19 1 Tf
0.8967 0 TD
0 Tc
(\()Tj
/F18 1 Tf
0.4015 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 381.36 647.34 Tm
(2)Tj
/F19 1 Tf
8.9664 0 0 8.9664 385.44 648.3 Tm
(\))Tj
/F16 1 Tf
1.4053 0 TD
-0.0027 Tc
(ds)Tj
/F11 1 Tf
5.9776 0 0 5.9776 407.16 647.22 Tm
0 Tc
($)Tj
/F22 1 Tf
0.522 0 TD
(v)Tj
/F19 1 Tf
8.9664 0 0 8.9664 416.4 648.3 Tm
(\()Tj
/F18 1 Tf
0.4015 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 424.32 647.34 Tm
(2)Tj
/F19 1 Tf
8.9664 0 0 8.9664 428.4 648.3 Tm
(\))Tj
ET
q
130.92 0 0 -0.48 301.068 643.968 cm
/Im1 Do
Q
BT
/F16 1 Tf
8.9664 0 0 8.9664 303.24 634.7401 Tm
-0.0027 Tc
(ds)Tj
/F11 1 Tf
5.9776 0 0 5.9776 312.48 633.66 Tm
-0.0092 Tc
($x)Tj
/F19 1 Tf
8.9664 0 0 8.9664 320.88 634.7401 Tm
0 Tc
(\()Tj
/F4 1 Tf
0.4015 0 TD
-0.003 Tc
[(let)-535.3($)]TJ
/F18 1 Tf
2.6232 0 TD
0 Tc
(v)Tj
/F4 1 Tf
1.0573 0 TD
-0.003 Tc
(:=)Tj
/F18 1 Tf
1.5793 0 TD
0 Tc
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 375.96 633.78 Tm
(1)Tj
/F4 1 Tf
8.9664 0 0 8.9664 384.72 634.7401 Tm
-0.003 Tc
(return)Tj
/F18 1 Tf
3.6805 0 TD
0 Tc
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 422.04 633.78 Tm
(2)Tj
/F19 1 Tf
8.9664 0 0 8.9664 426.12 634.7401 Tm
(\))Tj
0.7896 0.7495 TD
(\()Tj
/TT5 1 Tf
0.4283 0 TD
(L)Tj
7.1731 0 0 7.1731 442.9971 641.46 Tm
0.0669 Tc
(ET)Tj
8.9664 0 0 8.9664 452.7204 641.46 Tm
0 Tc
(2)Tj
/F19 1 Tf
0.4866 0 TD
(\))Tj
/F4 1 Tf
-34.4491 -2.8105 TD
-0.003 Tc
($x)Tj
/F18 1 Tf
1.4588 0 TD
0 Tc
(/)Tj
/F17 1 Tf
-0.1204 0 TD
()Tj
/F16 1 Tf
0.977 0 TD
0.0064 Tc
(fv)Tj
/F19 1 Tf
0.8833 0 TD
0 Tc
(\()Tj
/F18 1 Tf
0.4015 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 184.8 615.3 Tm
(1)Tj
/F19 1 Tf
8.9664 0 0 8.9664 189 616.26 Tm
(\))Tj
/F16 1 Tf
1.3919 0 TD
-0.0027 Tc
(ds)Tj
/F11 1 Tf
5.9776 0 0 5.9776 210.72 615.1801 Tm
-0.0092 Tc
($x)Tj
/F19 1 Tf
8.9664 0 0 8.9664 219.12 616.26 Tm
0 Tc
(\()Tj
/F18 1 Tf
0.4015 0 TD
(c)Tj
/F22 1 Tf
5.9776 0 0 5.9776 226.68 615.3 Tm
(i)Tj
/F19 1 Tf
8.9664 0 0 8.9664 229.8 616.26 Tm
(\))Tj
/F22 1 Tf
5.9776 0 0 5.9776 233.4 613.6201 Tm
(i)Tj
/F21 1 Tf
0.4417 0 TD
0.0085 Tc
(=1)Tj
/F22 1 Tf
1.546 0 TD
0.0019 Tc
(...n)Tj
/F21 1 Tf
1.9074 0 TD
0.0085 Tc
(+1)Tj
ET
q
131.4 0 0 -0.48 141.588 611.688 cm
/Im1 Do
Q
BT
/F16 1 Tf
8.9664 0 0 8.9664 141.6 580.86 Tm
-0.0027 Tc
(ds)Tj
/F11 1 Tf
5.9776 0 0 5.9776 150.84 579.78 Tm
-0.0092 Tc
($x)Tj
/F23 1 Tf
8.9664 0 0 8.9664 159.24 609.66 Tm
0 Tc
(0)Tj
0 -1.7532 TD
(B)Tj
0 -0.6023 TD
(B)Tj
T*
(B)Tj
T*
(B)Tj
0 -0.6424 TD
(@)Tj
/F4 1 Tf
1.4588 3.3994 TD
-0.003 Tc
[(typeswitch)-200.7(\()]TJ
/F18 1 Tf
5.9424 0 TD
0 Tc
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 229.92 601.5 Tm
(1)Tj
/F4 1 Tf
8.9664 0 0 8.9664 234 602.46 Tm
(\))Tj
-6.4374 -1.2313 TD
-0.003 Tc
(case)Tj
/F18 1 Tf
2.6232 0 TD
0 Tc
()Tj
/F21 1 Tf
5.9776 0 0 5.9776 203.88 590.46 Tm
(1)Tj
/F4 1 Tf
8.9664 0 0 8.9664 213.72 591.42 Tm
-0.003 Tc
(return)Tj
/F18 1 Tf
3.6671 0 TD
0 Tc
(c)Tj
/F21 1 Tf
5.9776 0 0 5.9776 250.56 590.46 Tm
(1)Tj
/TT5 1 Tf
8.9664 0 0 8.9664 215.04 585.3 Tm
(.)Tj
0 -0.4417 TD
(.)Tj
T*
(.)Tj
/F4 1 Tf
-4.3228 -0.7762 TD
-0.003 Tc
(case)Tj
/F18 1 Tf
2.6232 0 TD
0 Tc
()Tj
/F22 1 Tf
5.9776 0 0 5.9776 203.88 569.46 Tm
(n)Tj
/F4 1 Tf
8.9664 0 0 8.9664 213.72 570.42 Tm
-0.003 Tc
(return)Tj
/F18 1 Tf
3.6671 0 TD
0 Tc
(c)Tj
/F22 1 Tf
5.9776 0 0 5.9776 250.56 569.46 Tm
(n)Tj
/F4 1 Tf
8.9664 0 0 8.9664 176.28 559.5 Tm
-0.003 Tc
[(default)-521.9(return)]TJ
/F18 1 Tf
7.8429 0 TD
0 Tc
(c)Tj
/F22 1 Tf
5.9776 0 0 5.9776 250.56 558.54 Tm
(n)Tj
/F21 1 Tf
0.763 0 TD
0.0085 Tc
(+1)Tj
/F23 1 Tf
8.9664 0 0 8.9664 264.96 609.66 Tm
0 Tc
(1)Tj
0 -1.7532 TD
(C)Tj
0 -0.6023 TD
(C)Tj
T*
(C)Tj
T*
(C)Tj
0 -0.6424 TD
(A)Tj
/F19 1 Tf
1.0305 4.1488 TD
(\()Tj
/TT5 1 Tf
0.4283 0 TD
(T)Tj
7.1731 0 0 7.1731 283.9971 609.1801 Tm
0.0669 Tc
(YPE)Tj
8.9664 0 0 8.9664 298.9883 609.1801 Tm
0 Tc
(S)Tj
7.1731 0 0 7.1731 304.4549 609.1801 Tm
(W)Tj
/F19 1 Tf
8.9664 0 0 8.9664 311.2253 609.1801 Tm
(\))Tj
/F4 1 Tf
2.5356 0.7628 TD
-0.003 Tc
($x)Tj
/F18 1 Tf
1.4454 0 TD
0 Tc
(/)Tj
/F17 1 Tf
-0.1071 0 TD
()Tj
/F16 1 Tf
0.9636 0 TD
0.0064 Tc
(fv)Tj
/F19 1 Tf
0.8967 0 TD
0 Tc
(\()Tj
/F18 1 Tf
0.4015 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 370.56 615.0601 Tm
(1)Tj
/F19 1 Tf
8.9664 0 0 8.9664 374.64 616.02 Tm
(\))Tj
/F16 1 Tf
1.4053 0 TD
-0.0027 Tc
(ds)Tj
/F11 1 Tf
5.9776 0 0 5.9776 396.48 614.9401 Tm
-0.0092 Tc
($x)Tj
/F19 1 Tf
8.9664 0 0 8.9664 404.88 616.02 Tm
0 Tc
(\()Tj
/F18 1 Tf
0.3881 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 412.68 615.0601 Tm
(2)Tj
/F19 1 Tf
8.9664 0 0 8.9664 416.88 616.02 Tm
(\))Tj
ET
q
86.52 0 0 -0.48 333.948 611.688 cm
/Im1 Do
Q
BT
/F16 1 Tf
8.9664 0 0 8.9664 354 602.46 Tm
-0.0027 Tc
(ds)Tj
/F11 1 Tf
5.9776 0 0 5.9776 363.24 601.38 Tm
-0.0092 Tc
($x)Tj
/F19 1 Tf
8.9664 0 0 8.9664 371.64 602.46 Tm
0 Tc
(\()Tj
/F18 1 Tf
0.4015 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 379.56 601.5 Tm
(1)Tj
/F4 1 Tf
8.9664 0 0 8.9664 383.64 602.46 Tm
(/)Tj
/F18 1 Tf
0.522 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 392.64 601.5 Tm
(2)Tj
/F19 1 Tf
8.9664 0 0 8.9664 396.84 602.46 Tm
(\))Tj
2.7704 0.7495 TD
(\()Tj
/TT5 1 Tf
0.4283 0 TD
(S)Tj
7.1731 0 0 7.1731 430.9868 609.1801 Tm
0.0669 Tc
(TEP)Tj
8.9664 0 0 8.9664 445.1794 609.1801 Tm
0 Tc
(1)Tj
/F19 1 Tf
0.4866 0 TD
(\))Tj
/F16 1 Tf
-12.8907 -2.7971 TD
-0.0027 Tc
(ds)Tj
/F11 1 Tf
5.9776 0 0 5.9776 343.2 583.02 Tm
-0.0092 Tc
($x)Tj
/F19 1 Tf
8.9664 0 0 8.9664 351.6 584.1 Tm
0 Tc
(\()Tj
/F18 1 Tf
0.4015 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 359.52 583.14 Tm
(1)Tj
/F19 1 Tf
8.9664 0 0 8.9664 363.6 584.1 Tm
(\))Tj
/F4 1 Tf
1.5659 0 TD
-0.003 Tc
($x)Tj
/F18 1 Tf
1.4588 0 TD
0 Tc
(/)Tj
/F17 1 Tf
-0.1204 0 TD
()Tj
/F16 1 Tf
0.977 0 TD
0.0064 Tc
(fv)Tj
/F19 1 Tf
0.8833 0 TD
0 Tc
(\()Tj
/F18 1 Tf
0.4015 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 414.24 583.14 Tm
(2)Tj
/F19 1 Tf
8.9664 0 0 8.9664 418.44 584.1 Tm
(\))Tj
ET
q
88.08 0 0 -0.48 333.948 579.648 cm
/Im1 Do
Q
BT
/F16 1 Tf
8.9664 0 0 8.9664 354.84 570.42 Tm
-0.0027 Tc
(ds)Tj
/F11 1 Tf
5.9776 0 0 5.9776 363.96 569.34 Tm
-0.0092 Tc
($x)Tj
/F19 1 Tf
8.9664 0 0 8.9664 372.36 570.42 Tm
0 Tc
(\()Tj
/F18 1 Tf
0.4015 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 380.28 569.46 Tm
(1)Tj
/F4 1 Tf
8.9664 0 0 8.9664 384.36 570.42 Tm
(/)Tj
/F18 1 Tf
0.522 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 393.36 569.46 Tm
(2)Tj
/F19 1 Tf
8.9664 0 0 8.9664 397.56 570.42 Tm
(\))Tj
2.8506 0.7495 TD
(\()Tj
/TT5 1 Tf
0.4283 0 TD
(S)Tj
7.1731 0 0 7.1731 432.4268 577.14 Tm
0.0669 Tc
(TEP)Tj
8.9664 0 0 8.9664 446.6194 577.14 Tm
0 Tc
(2)Tj
/F19 1 Tf
0.5 0 TD
(\))Tj
/F4 1 Tf
-38.8276 -3.9749 TD
-0.003 Tc
[(declare)-548.7(function)]TJ
/F18 1 Tf
8.9269 0 TD
0 Tc
(f)Tj
/F4 1 Tf
0.6023 0 TD
-0.003 Tc
(\($)Tj
/F18 1 Tf
1.0439 0 TD
0 Tc
(v)Tj
/F21 1 Tf
5.9776 0 0 5.9776 202.2 540.54 Tm
(1)Tj
/F4 1 Tf
8.9664 0 0 8.9664 206.52 541.5 Tm
(,)Tj
/F18 1 Tf
0.522 0 TD
0.1696 Tc
(...)Tj
/F4 1 Tf
1.3651 0 TD
-0.003 Tc
(,$)Tj
/F18 1 Tf
1.0439 0 TD
0 Tc
(v)Tj
/F22 1 Tf
5.9776 0 0 5.9776 237.24 540.54 Tm
(n)Tj
/F4 1 Tf
8.9664 0 0 8.9664 242.52 541.5 Tm
0.1709 Tc
(\){)Tj
/F18 1 Tf
1.3919 0 TD
0 Tc
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 259.32 540.54 Tm
(0)Tj
/F4 1 Tf
8.9664 0 0 8.9664 265.08 541.5 Tm
(})Tj
/F19 1 Tf
1.5257 0 TD
(\()Tj
/F4 1 Tf
0.4015 0 TD
-0.003 Tc
($x)Tj
/F17 1 Tf
1.325 0 TD
0 Tc
()Tj
/F16 1 Tf
0.977 0 TD
0.0064 Tc
(fv)Tj
/F19 1 Tf
0.8967 0 TD
0 Tc
(\()Tj
/F18 1 Tf
0.4015 0 TD
(e)Tj
/F22 1 Tf
5.9776 0 0 5.9776 318.96 540.54 Tm
(i)Tj
/F19 1 Tf
8.9664 0 0 8.9664 322.08 541.5 Tm
(\))Tj
/F17 1 Tf
0.6826 0 TD
()Tj
/F16 1 Tf
1.3116 0 TD
-0.0027 Tc
(ds)Tj
/F11 1 Tf
5.9776 0 0 5.9776 349.2 540.42 Tm
-0.0092 Tc
($x)Tj
/F19 1 Tf
8.9664 0 0 8.9664 357.48 541.5 Tm
0 Tc
(\()Tj
/F18 1 Tf
0.4015 0 TD
(e)Tj
/F22 1 Tf
5.9776 0 0 5.9776 365.4 540.54 Tm
(i)Tj
/F19 1 Tf
8.9664 0 0 8.9664 368.52 541.5 Tm
(\))Tj
/F17 1 Tf
0.629 0 TD
()Tj
/F16 1 Tf
0.9235 0 TD
-0.0027 Tc
(ds)Tj
/F11 1 Tf
5.9776 0 0 5.9776 391.56 540.42 Tm
0 Tc
($)Tj
/F22 1 Tf
0.522 0 TD
(v)Tj
/F24 1 Tf
4.9813 0 0 4.9813 398.4 539.1 Tm
(i)Tj
/F19 1 Tf
8.9664 0 0 8.9664 403.68 541.5 Tm
(\()Tj
/F18 1 Tf
0.4015 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 411.6 540.54 Tm
(0)Tj
/F19 1 Tf
8.9664 0 0 8.9664 415.68 541.5 Tm
0.0018 Tc
(\)\))Tj
/F22 1 Tf
5.9776 0 0 5.9776 422.88 540.54 Tm
0 Tc
(i)Tj
/F21 1 Tf
0.4417 0 TD
0.0085 Tc
(=1)Tj
/F22 1 Tf
1.546 0 TD
0.0019 Tc
(...n)Tj
ET
q
343.8 0 0 -0.48 102.948 537.168 cm
/Im1 Do
Q
BT
/F16 1 Tf
8.9664 0 0 8.9664 235.32 527.9401 Tm
-0.0027 Tc
(ds)Tj
/F11 1 Tf
5.9776 0 0 5.9776 244.44 526.86 Tm
-0.0092 Tc
($x)Tj
/F19 1 Tf
8.9664 0 0 8.9664 252.84 527.9401 Tm
0 Tc
(\()Tj
/F18 1 Tf
0.4015 0 TD
(f)Tj
/F4 1 Tf
0.6023 0 TD
(\()Tj
/F18 1 Tf
0.522 0 TD
(e)Tj
/F21 1 Tf
5.9776 0 0 5.9776 270.84 526.98 Tm
(1)Tj
/F4 1 Tf
8.9664 0 0 8.9664 275.04 527.9401 Tm
(,)Tj
/F18 1 Tf
0.522 0 TD
0.1696 Tc
(...)Tj
/F4 1 Tf
1.3785 0 TD
0 Tc
(,)Tj
/F18 1 Tf
0.522 0 TD
(e)Tj
/F22 1 Tf
5.9776 0 0 5.9776 301.08 526.98 Tm
(n)Tj
/F4 1 Tf
8.9664 0 0 8.9664 306.12 527.9401 Tm
(\))Tj
/F19 1 Tf
0.522 0 TD
(\))Tj
15.2837 0.7495 TD
(\()Tj
/TT5 1 Tf
0.4283 0 TD
(F)Tj
7.1731 0 0 7.1731 457.1468 534.66 Tm
0.0669 Tc
(UN)Tj
8.9664 0 0 8.9664 468.4672 534.66 Tm
0 Tc
(C)Tj
7.1731 0 0 7.1731 474.9277 534.66 Tm
0.0669 Tc
(ALL)Tj
/F19 1 Tf
8.9664 0 0 8.9664 489.7111 534.66 Tm
0 Tc
(\))Tj
/TT11 1 Tf
9.9626 0 0 9.9626 62.04 506.22 Tm
[(Figure)-433.6(5.)-445.7(Distrib)24.1(utivity-saf)12(ety)]TJ
/F9 1 Tf
14.5019 0 TD
-0.0052 Tc
(ds)Tj
/F11 1 Tf
6.9738 0 0 6.9738 216.6 504.78 Tm
0.0022 Tc
($x)Tj
/F8 1 Tf
9.9626 0 0 9.9626 226.2 506.22 Tm
0 Tc
(\()Tj
/F1 1 Tf
0.3854 0 TD
()Tj
/F8 1 Tf
0.277 0 TD
(\))Tj
/TT11 1 Tf
0.3854 0 TD
[(:)-662.5(A)-445.7(syntactic)-433.6(appr)24.1(o)24.1(ximation)-421.6(of)-433.6(the)-433.6(distrib)24.1(utivity)-433.6(pr)24.1(oper)-24.1(ty)-433.6(f)24.1(o)0(r)]TJ
-17.5255 -1.2045 TD
[(LiXQuer)-12(y)-277(e)12(xpressions.)]TJ
ET
0 G
0 J 0 j 0.598 w 10 M []0 d
1 i
168.24 413.852 m
S
BT
/TT5 1 Tf
8.9664 0 0 8.9664 98.2524 444.8733 Tm
[(XDM)-10944.6(XDM)]TJ
-0.1265 -3.795 TD
[(T)80.3(ables)-10692.9(T)80.3(ables)]TJ
6.3215 4.7121 TD
(XQuery)Tj
-2.1805 -5.4255 TD
[(Relational)-254.3(Algebra)]TJ
ET
[2.989 1.993 ]0 d
108.712 441.586 m
108.712 420.831 l
S
1 J 1 j 0.478 w []0 d
110.545 422.206 m
109.857 422.091 108.826 420.831 108.712 420.488 c
108.597 420.831 107.566 422.091 106.879 422.206 c
S
0 J 0 j 0.598 w [2.989 1.993 ]0 d
227.768 420.248 m
227.768 441.003 l
S
1 J 1 j 0.478 w []0 d
225.935 439.628 m
226.623 439.743 227.654 441.003 227.768 441.347 c
227.883 441.003 228.914 439.743 229.601 439.628 c
S
0 J 0 j 0.598 w
122.458 447.868 m
213.439 447.868 l
S
1 J 1 j 0.478 w
212.064 449.701 m
212.179 449.014 213.439 447.983 213.782 447.868 c
213.439 447.754 212.179 446.722 212.064 446.035 c
S
0 J 0 j 0.598 w [2.989 1.993 ]0 d
123.593 413.852 m
212.305 413.852 l
S
1 J 1 j 0.478 w []0 d
210.93 415.685 m
211.044 414.998 212.305 413.967 212.648 413.852 c
212.305 413.737 211.044 412.706 210.93 412.019 c
S
BT
/TT11 1 Tf
9.9626 0 0 9.9626 62.04 377.7 Tm
[(Figure)-554.1(6.)-566.1(Relational)-554.1(XQuer)-12(y)-566.1(\(dashed)-554.1(path\))]TJ
0 -1.2045 TD
[(faithfull)12(y)-265(implements)-265(the)-277(XQuer)-12(y)-277(semantics.)]TJ
/TT5 1 Tf
0 -5.2637 TD
[(The)-373.4(compiler)-361.4(emits)-385.4(a)-385.4(dialect)-373.4(of)-373.4(relational)-373.4(algebra)-361.4(that)]TJ
-1.1925 -1.1925 TD
[(mimics)-265(the)-277(capabilities)-277(of)-265(modern)-252.9(SQL)-277(query)-252.9(engines)-265(\(T)84.3(a-)]TJ
0 -1.2045 TD
[(ble)-325.2(1\).)-530(Note)-325.2(that)-325.2(the)-325.2(non-te)12(xtbook)-277(operators,)-325.2(lik)12(e)]TJ
/F6 1 Tf
20.5067 0 TD
()Tj
/TT5 1 Tf
0.795 0 TD
(or)Tj
ET
0 J 0.398 w
275.4 288.9 m
275.4 291.31 l
277.81 291.31 l
277.81 293.719 l
280.219 293.719 l
280.219 296.129 l
282.629 296.129 l
282.629 288.9 l
s
BT
9.9626 0 0 9.9626 283.92 289.38 Tm
(,)Tj
-23.4637 -1.1925 TD
[(merely)-216.8(are)-228.9(macros)-228.9(representing)-204.8(micro)-216.8(plans)-228.9(composed)-204.8(of)]TJ
0 -1.2045 TD
[(standard)-204.8(relational)-204.8(operators:)-277(e)12(xpanding)]TJ
ET
212.64 265.02 m
212.64 267.43 l
215.05 267.43 l
215.05 269.839 l
217.459 269.839 l
217.459 272.249 l
219.869 272.249 l
219.869 265.02 l
s
BT
/F10 1 Tf
6.9738 0 0 6.9738 221.04 264.06 Tm
()Tj
/F11 1 Tf
0.74 0 TD
0.0022 Tc
(::)Tj
/F10 1 Tf
1.0669 0 TD
0 Tc
(n)Tj
/TT5 1 Tf
9.9626 0 0 9.9626 241.32 265.5 Tm
[(re)24.1(v)12(eals)]TJ
/F25 1 Tf
3.0122 0 TD
()Tj
0.0121 0 TD
()Tj
/F10 1 Tf
6.9738 0 0 6.9738 279.24 264.06 Tm
(p)Tj
/TT5 1 Tf
9.9626 0 0 9.9626 283.92 265.5 Tm
(,)Tj
-23.4637 -1.2045 TD
(where)Tj
/F6 1 Tf
2.6476 0 TD
(p)Tj
/TT5 1 Tf
0.7227 0 TD
[(is)-216.8(a)-228.9(conjuncti)24.1(v)12(e)-180.7(range)-204.8(predicate)-192.7(that)-216.8(realizes)-216.8(the)-216.8(se-)]TJ
-3.3703 -1.1925 TD
[(mantics)-313.2(of)-325.2(an)-325.2(XP)12(ath)-325.2(location)-313.2(step)-325.2(along)-313.2(axis)]TJ
/F6 1 Tf
18.6053 0 TD
()Tj
/TT5 1 Tf
0.9757 0 TD
[(with)-325.2(node)]TJ
-19.581 -1.2045 TD
(test)Tj
/F6 1 Tf
1.6416 0 TD
(n)Tj
/TT5 1 Tf
0.6023 0 TD
[(,)-252.9(for)-240.9(e)12(xample.)-301.1(The)-240.9(ro)24.1(w)-240.9(numbering)-216.8(operator)]TJ
/F6 1 Tf
17.5135 0 TD
()Tj
/TT5 1 Tf
0.7709 0 TD
(directly)Tj
-20.5282 -1.2045 TD
[(compares)-313.2(with)-325.2(SQL:1999)60.2(s)]TJ
/F3 1 Tf
11.3899 0 TD
0.005 Tc
(ROW_NUMBER)Tj
/TT5 1 Tf
5.2999 0 TD
0 Tc
[(.)-289.1(The)-325.2(plans)-325.2(oper)24.1(-)]TJ
-16.6897 -1.1925 TD
[(ate)-216.8(o)12(v)12(e)0(r)-192.7(relational)-192.7(encodings)-192.7(of)-216.8(XQuery)-192.7(item)-216.8(sequence)-192.7(held)]TJ
0 -1.2045 TD
(in)Tj
/TT8 1 Tf
1.0549 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(at)-289.1(\(1NF\))-265(tables)-277(with)-289.1(schema)]TJ
/F26 1 Tf
11.6601 0 TD
0.0012 Tc
(iter)Tj
/F1 1 Tf
1.3972 0 TD
0 Tc
(|)Tj
/F26 1 Tf
0.277 0 TD
0.0254 Tc
[(po)19.5(s)]TJ
/F1 1 Tf
1.4334 0 TD
0 Tc
(|)Tj
/F26 1 Tf
0.277 0 TD
0.0012 Tc
(item)Tj
/TT5 1 Tf
1.8429 0 TD
0 Tc
[(.)-409.5(I)0(n)-277(these)-277(ta-)]TJ
-18.4987 -1.1925 TD
[(bles,)-252.9(columns)]TJ
/F26 1 Tf
5.7313 0 TD
0.0012 Tc
(iter)Tj
/TT5 1 Tf
1.6622 0 TD
0 Tc
(and)Tj
/F26 1 Tf
1.6847 0 TD
0.0254 Tc
[(po)19.5(s)]TJ
/TT5 1 Tf
1.6863 0 TD
0 Tc
[(are)-240.9(used)-252.9(to)-252.9(properly)-216.8(re)]TJ
/TT8 1 Tf
8.9597 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
(ect)Tj
/F3 1 Tf
1.4185 0 TD
0.005 Tc
(for)Tj
/TT5 1 Tf
1.59 0 TD
0 Tc
(-)Tj
-23.2889 -1.2045 TD
[(iteration)-397.5(and)-397.5(sequence)-397.5(order)36.1(,)-421.6(respecti)24.1(v)12(ely)60.2(.)-770.9(Column)]TJ
/F26 1 Tf
21.7539 0 TD
0.0012 Tc
(item)Tj
/TT5 1 Tf
-21.7539 -1.2045 TD
0 Tc
[(carries)-349.3(encodings)-337.3(of)-361.3(XQuery)-337.3(items,)]TJ
/TT7 1 Tf
14.9726 0 TD
[(i.e)12(.)]TJ
/TT5 1 Tf
1.2096 0 TD
[(,)-373.4(atomic)-361.3(v)24.1(alues)-349.3(or)]TJ
-16.1822 -1.1925 TD
(nodes.)Tj
1.1925 -1.7224 TD
[(Further)-349.3(details)-361.4(of)-361.4(Relational)-361.3(XQuery)-337.3(do)-361.3(not)-349.3(af)24.1(fect)-361.4(our)]TJ
-1.1925 -1.2045 TD
[(present)-385.4(discussion)-397.5(of)-397.5(distrib)24.1(uti)24.1(vity)-397.5(or)-397.5(IFP)-409.5(e)24.1(v)24.1(aluation)-373.4(and)]TJ
T*
[(may)-289.1(be)-289.1(found)-277(in)-301.1([15)24.1(].)-457.7(In)-301.1(the)-289.1(follo)24.1(wing,)-289.1(let)]TJ
ET
0 j 0.199 w
228.127 102.291 m
237.473 102.291 l
238.026 102.291 238.278 102.693 238.04 103.193 c
233.229 113.295 l
232.991 113.796 232.609 113.796 232.371 113.295 c
227.56 103.193 l
227.322 102.693 227.574 102.291 228.127 102.291 c
s
BT
/F10 1 Tf
6.9738 0 0 6.9738 230.91 104.7586 Tm
(e)Tj
/TT5 1 Tf
9.9626 0 0 9.9626 244.56 104.82 Tm
[(denote)-289.1(the)]TJ
-19.5129 -1.1925 TD
[(algebraic)-301.1(plan)-301.1(that)-313.2(has)-325.2(been)-301.1(compiled)-301.1(for)-301.1(XQuery)-301.1(e)12(xpres-)]TJ
0 -1.2045 TD
(sion)Tj
/F6 1 Tf
1.9079 0 TD
(e)Tj
/TT5 1 Tf
0.4698 0 TD
(.)Tj
ET
q
229.56 0 0 -0.84 312.228 462.288 cm
/Im1 Do
Q
BT
8.9664 0 0 8.9664 312.24 452.1 Tm
[(Operator)-3533.2(Semantics)-12018.2(Push?)]TJ
ET
q
52.56 0 0 -0.36 312.228 447.168 cm
/Im1 Do
Q
q
140.64 0 0 -0.36 374.748 447.168 cm
/Im1 Do
Q
q
21.48 0 0 -0.36 520.308 447.168 cm
/Im1 Do
Q
BT
/F18 1 Tf
8.9664 0 0 8.9664 312.24 436.26 Tm
()Tj
/F27 1 Tf
5.9776 0 0 5.9776 317.52 435.18 Tm
(a)Tj
/F28 1 Tf
4.9813 0 0 4.9813 320.52 433.98 Tm
(1)Tj
/F21 1 Tf
5.9776 0 0 5.9776 324.48 435.18 Tm
(:)Tj
/F27 1 Tf
0.3614 0 TD
(b)Tj
/F28 1 Tf
4.9813 0 0 4.9813 329.88 433.98 Tm
(1)Tj
/F22 1 Tf
5.9776 0 0 5.9776 333.72 435.18 Tm
0.0019 Tc
(,...,)Tj
/F27 1 Tf
1.9074 0 TD
0 Tc
(a)Tj
/F24 1 Tf
4.9813 0 0 4.9813 348.12 434.22 Tm
(n)Tj
/F21 1 Tf
5.9776 0 0 5.9776 353.04 435.18 Tm
(:)Tj
/F27 1 Tf
0.3614 0 TD
(b)Tj
/F24 1 Tf
4.9813 0 0 4.9813 358.44 434.22 Tm
(n)Tj
/TT5 1 Tf
8.9664 0 0 8.9664 375.72 436.26 Tm
[(project)-254.3(onto)-267.7(col.s)]TJ
/F29 1 Tf
7.1779 0 TD
(a)Tj
/F22 1 Tf
5.9776 0 0 5.9776 444.36 435.3 Tm
(i)Tj
/TT5 1 Tf
8.9664 0 0 8.9664 447.6 436.26 Tm
[(,)-240.9(rename)]TJ
/F29 1 Tf
3.701 0 TD
(b)Tj
/F22 1 Tf
5.9776 0 0 5.9776 485.52 435.3 Tm
(i)Tj
/TT5 1 Tf
8.9664 0 0 8.9664 490.8 436.26 Tm
(into)Tj
/F29 1 Tf
1.81 0 TD
(a)Tj
/F22 1 Tf
5.9776 0 0 5.9776 511.44 435.3 Tm
(i)Tj
/F17 1 Tf
8.9664 0 0 8.9664 527.4 436.26 Tm
()Tj
/F18 1 Tf
-23.9963 -1.1108 TD
()Tj
/F27 1 Tf
5.9776 0 0 5.9776 317.52 425.22 Tm
(b)Tj
/TT5 1 Tf
8.9664 0 0 8.9664 375.72 426.3 Tm
[(select)-254.3(ro)26.8(ws)-254.3(with)-240.9(column)]TJ
/F29 1 Tf
9.9884 0 TD
(b)Tj
/F19 1 Tf
0.8164 0 TD
(=)Tj
/F16 1 Tf
1.0841 0 TD
-0.0039 Tc
(true)Tj
/F17 1 Tf
5.0456 0 TD
0 Tc
()Tj
/F25 1 Tf
-24.0143 -1.1242 TD
()Tj
0.0134 0 TD
()Tj
/F22 1 Tf
5.9776 0 0 5.9776 319.56 414.9 Tm
(p)Tj
/TT5 1 Tf
8.9664 0 0 8.9664 375.72 416.22 Tm
[(join)-254.3(with)-240.9(predicate)]TJ
/F18 1 Tf
7.7604 0 TD
(p)Tj
/F30 1 Tf
9.1676 0 TD
()Tj
/F17 1 Tf
-24.0078 -1.1242 TD
()Tj
/TT5 1 Tf
7.0798 0 TD
[(Cartesian)-254.3(product)]TJ
/F30 1 Tf
16.9355 0 TD
()Tj
/F18 1 Tf
-24.0153 -1.1242 TD
()Tj
/TT5 1 Tf
7.0798 0 TD
[(duplicate)-267.7(elimination)-254.3(\()]TJ
/F4 1 Tf
9.0747 0 TD
-0.003 Tc
(DISTINCT)Tj
/TT5 1 Tf
4.1757 0 TD
0 Tc
(\))Tj
/F17 1 Tf
3.6788 0 TD
()Tj
-24.0091 -1.1242 TD
()Tj
/TT5 1 Tf
7.0798 0 TD
(union)Tj
/F30 1 Tf
16.9326 0 TD
()Tj
/F17 1 Tf
-24.0124 -1.1242 TD
(\\)Tj
/TT5 1 Tf
7.0798 0 TD
[(disjoint)-254.3(dif)26.8(ference)-267.7(\()]TJ
/F4 1 Tf
7.8809 0 TD
-0.003 Tc
[(EXCEPT)-535.3(ALL)]TJ
/TT5 1 Tf
5.233 0 TD
0 Tc
(\))Tj
/F17 1 Tf
3.8127 0 TD
()Tj
/F4 1 Tf
-24.0065 -1.1242 TD
-0.003 Tc
(count)Tj
/F27 1 Tf
5.9776 0 0 5.9776 335.76 364.38 Tm
0 Tc
(a)Tj
/F21 1 Tf
0.5019 0 TD
(:)Tj
/F22 1 Tf
0.3614 0 TD
(/)Tj
/F27 1 Tf
0.6425 0 TD
(b)Tj
/TT5 1 Tf
8.9664 0 0 8.9664 375.72 365.82 Tm
[(aggre)13.4(gates)-267.7(\(group)-267.7(by)]TJ
/F29 1 Tf
8.7176 0 TD
(b)Tj
/TT5 1 Tf
0.5354 0 TD
[(,)-240.9(result)-254.3(in)]TJ
/F29 1 Tf
3.999 0 TD
(a)Tj
/TT5 1 Tf
0.4952 0 TD
(\))Tj
/F17 1 Tf
3.2104 0 TD
()Tj
/F5 1 Tf
-24.0374 -1.1108 TD
()Tj
/F27 1 Tf
5.9776 0 0 5.9776 319.44 354.42 Tm
(a)Tj
/F21 1 Tf
0.5019 0 TD
(:)Tj
/F31 1 Tf
0.3614 0 TD
()Tj
/F27 1 Tf
0.5019 0 TD
(b)Tj
/F28 1 Tf
4.9813 0 0 4.9813 330.84 353.22 Tm
(1)Tj
/F22 1 Tf
5.9776 0 0 5.9776 334.8 354.42 Tm
0.0019 Tc
[(,...)20.1(,)]TJ
/F27 1 Tf
1.8873 0 TD
0 Tc
(b)Tj
/F24 1 Tf
4.9813 0 0 4.9813 349.32 353.46 Tm
(n)Tj
/F31 1 Tf
5.9776 0 0 5.9776 354.24 354.42 Tm
()Tj
/F18 1 Tf
8.9664 0 0 8.9664 375.72 355.86 Tm
(n)Tj
/TT5 1 Tf
0.6157 0 TD
[(-ary)-254.3(arithmetic/comparison)-267.7(operator)]TJ
/F17 1 Tf
14.7281 0 TD
1.0921 Tc
()Tj
/TT5 1 Tf
7.9701 0 0 7.9701 312.24 345.78 Tm
0 Tc
(#)Tj
/F27 1 Tf
5.9776 0 0 5.9776 316.2 344.82 Tm
(a)Tj
/TT5 1 Tf
8.9664 0 0 8.9664 375.72 345.78 Tm
[(unique)-267.7(ro)26.8(w)-254.3(tagging)-267.7(\(tag)-254.3(in)]TJ
/F29 1 Tf
10.8803 0 TD
(a)Tj
/TT5 1 Tf
0.4952 0 TD
(\))Tj
/F17 1 Tf
5.5793 0 TD
()Tj
/F18 1 Tf
-24.0346 -1.1242 TD
()Tj
/F27 1 Tf
5.9776 0 0 5.9776 317.04 334.26 Tm
(a)Tj
/F21 1 Tf
0.5019 0 TD
(:)Tj
/F31 1 Tf
0.3614 0 TD
()Tj
/F27 1 Tf
0.5019 0 TD
(b)Tj
/F28 1 Tf
4.9813 0 0 4.9813 328.44 333.06 Tm
(1)Tj
/F22 1 Tf
5.9776 0 0 5.9776 332.4 334.26 Tm
0.0019 Tc
[(,...)20.1(,)]TJ
/F27 1 Tf
1.8873 0 TD
0 Tc
(b)Tj
/F24 1 Tf
4.9813 0 0 4.9813 346.92 333.3 Tm
(n)Tj
/F31 1 Tf
5.9776 0 0 5.9776 351.84 334.26 Tm
()Tj
/F22 1 Tf
0.522 0 TD
0.0036 Tc
(/p)Tj
/TT5 1 Tf
8.9664 0 0 8.9664 375.72 335.7 Tm
0 Tc
[(ordered)-267.7(ro)26.8(w)-254.3(numbering)-267.7(\(by)]TJ
/F29 1 Tf
11.3049 0 TD
(b)Tj
/F21 1 Tf
5.9776 0 0 5.9776 481.44 334.74 Tm
(1)Tj
/F18 1 Tf
8.9664 0 0 8.9664 485.52 335.7 Tm
0.1696 Tc
(,...,)Tj
/F29 1 Tf
2.2886 0 TD
0 Tc
(b)Tj
/F22 1 Tf
5.9776 0 0 5.9776 510.84 334.74 Tm
(n)Tj
/TT5 1 Tf
8.9664 0 0 8.9664 515.88 335.7 Tm
(\))Tj
/F17 1 Tf
1.2832 0 TD
()Tj
ET
1 j 0.398 w
312.48 325.26 m
312.48 327.67 l
314.89 327.67 l
314.89 330.079 l
317.299 330.079 l
317.299 332.489 l
319.709 332.489 l
319.709 325.26 l
s
BT
/F22 1 Tf
5.9776 0 0 5.9776 320.88 324.54 Tm
()Tj
/F11 1 Tf
0.8031 0 TD
-0.0092 Tc
(::)Tj
/F22 1 Tf
1.0641 0 TD
0 Tc
(n)Tj
/TT5 1 Tf
8.9664 0 0 8.9664 375.72 325.62 Tm
[(XP)13.4(ath)-240.9(step)-254.3(join)-254.3(\(axis)]TJ
/F18 1 Tf
8.6007 0 TD
()Tj
/TT5 1 Tf
0.6558 0 TD
[(,)-254.3(node)-267.7(test)]TJ
/F18 1 Tf
4.3454 0 TD
(n)Tj
/TT5 1 Tf
0.6157 0 TD
(\))Tj
/F17 1 Tf
2.7152 0 TD
()Tj
/F18 1 Tf
-24.0126 -1.1242 TD
0.1696 Tc
[()164.9(,)0()113.4(,...)]TJ
/TT5 1 Tf
7.0799 0 TD
0 Tc
[(node)-267.7(constructors)]TJ
/F17 1 Tf
16.9493 0 TD
()Tj
/F18 1 Tf
-24.0292 -1.151 TD
-0.0036 Tc
[(,)-173.2()]TJ
/F21 1 Tf
5.9776 0 0 5.9776 327.36 309.06 Tm
0 Tc
()Tj
/TT8 1 Tf
8.9664 0 0 8.9664 375.72 305.22 Tm
()Tj
/TT5 1 Tf
0.5562 0 TD
[(xpoint)-254.3(operators)]TJ
/F17 1 Tf
16.3808 0 TD
()Tj
ET
q
229.56 0 0 -0.84 312.228 301.248 cm
/Im1 Do
Q
BT
/TT11 1 Tf
9.9626 0 0 9.9626 320.76 282.18 Tm
[(T)84.3(a)0(b)12(l)0(e)-301.1(1)0(.)-289.1(Relational)-289.1(alg)-12(ebra)-289.1(dialect)-289.1(emitted)-289.1(b)24.1(y)]TJ
0 -1.2045 TD
[(the)-277(P)24.1(ath)]TJ
/TT12 1 Tf
3.9199 0 TD
()Tj
/TT11 1 Tf
0.6108 0 TD
[(nder)-265(compiler)60.2(.)]TJ
/TT2 1 Tf
10.9589 0 0 10.9589 308.88 227.1 Tm
[(4.1)11(.)-251.9(I)0(s)-240.9(Expr)21.9(ession)]TJ
/TT7 1 Tf
11.9552 0 0 11.9552 393.0484 227.1 Tm
(e)Tj
7.9701 0 0 7.9701 398.88 225.3 Tm
-0.0301 Tc
[(re)-30.1(c)]TJ
/TT2 1 Tf
10.9589 0 0 10.9589 412.08 227.1 Tm
0 Tc
[(Distrib)21.9(uti)10.9(v)11(e)0(?)]TJ
-7.1722 -1.095 TD
[(\(An)-251.8(Algebraic)-240.9(Account\))]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 320.76 188.58 Tm
[(An)-349.3(occurrence)-313.2(of)-337.3(the)-337.3(ne)24.1(w)]TJ
/F3 1 Tf
10.9783 0 TD
0.005 Tc
[(with)-505.9($x)-517.9(seeded)-493.8(by)]TJ
/F6 1 Tf
9.4554 0 TD
0 Tc
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 529.68 187.14 Tm
-0.0454 Tc
[(s)-41.5(eed)]TJ
/F3 1 Tf
9.9626 0 0 9.9626 308.88 176.58 Tm
0.005 Tc
(recurse)Tj
/F6 1 Tf
4.2038 0 TD
0 Tc
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 355.44 175.14 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 369.12 176.58 Tm
0 Tc
[(form)-252.9(in)-265(a)-277(source)-252.9(XQuery)-252.9(e)12(xpression)-240.9(will)-277(be)]TJ
ET
0 j
530.16 158.43 m
S
0.299 w
518.455 80.537 m
541.974 80.537 l
542.527 80.537 542.703 80.894 542.37 81.338 c
530.815 96.744 l
530.482 97.189 529.947 97.189 529.614 96.744 c
518.059 81.338 l
517.726 80.894 517.902 80.537 518.455 80.537 c
s
BT
/F10 1 Tf
6.9738 0 0 6.9738 523.12 85.2337 Tm
(e)Tj
/F13 1 Tf
4.9813 0 0 4.9813 526 84.1537 Tm
-0.0387 Tc
[(s)-34.7(eed)]TJ
ET
518.455 120.223 m
541.974 120.223 l
542.527 120.223 542.703 120.579 542.37 121.024 c
530.815 136.43 l
530.482 136.874 529.947 136.874 529.614 136.43 c
518.059 121.024 l
517.726 120.579 517.902 120.223 518.455 120.223 c
s
BT
/F10 1 Tf
6.9738 0 0 6.9738 524.2878 124.8888 Tm
0 Tc
(e)Tj
/F13 1 Tf
4.9813 0 0 4.9813 528.0078 123.9288 Tm
-0.0408 Tc
(rec)Tj
ET
0.398 w
530.16 98.331 m
530.16 105.607 l
S
530.16 109.91 m
528.966 109.91 528.008 108.953 528.008 107.759 c
528.008 106.564 528.966 105.607 530.16 105.607 c
531.354 105.607 532.312 106.564 532.312 107.759 c
532.312 108.953 531.354 109.91 530.16 109.91 c
h
530.16 107.759 m
S
530.16 138.016 m
530.16 143.308 l
S
530.16 147.612 m
528.966 147.612 528.008 146.654 528.008 145.46 c
528.008 144.266 528.966 143.308 530.16 143.308 c
531.354 143.308 532.312 144.266 532.312 145.46 c
532.312 146.654 531.354 147.612 530.16 147.612 c
h
530.16 145.46 m
S
530.16 112.999 m
530.16 119.315 l
S
1 J
527.57 111.704 m
528.865 113.647 531.455 113.647 532.75 111.704 c
S
0 J
530.16 149.206 m
530.16 157.732 l
S
[2.989 1.993 ]0 d
530.16 149.206 m
530.16 149.185 l
530.16 151.95 527.943 154.166 525.179 154.166 c
515.299 154.166 l
512.534 154.166 510.317 151.95 510.317 149.185 c
510.317 104.58 l
510.317 101.816 512.534 99.599 515.299 99.599 c
519.78 99.599 l
S
1 J 1 j 0.319 w []0 d
518.585 101.193 m
518.685 100.595 519.78 99.698 520.079 99.599 c
519.78 99.499 518.685 98.603 518.585 98.005 c
S
BT
/F11 1 Tf
6.9738 0 0 6.9738 502.21 124.7516 Tm
0.0022 Tc
($x)Tj
ET
0 J 0 j 0.398 w [2.989 1.993 ]0 d
520.936 99.599 m
525.179 99.599 l
527.943 99.599 530.16 101.816 530.16 104.58 c
530.16 104.559 l
S
[]0 d
544.688 148.508 m
545.435 148.135 545.933 147.263 545.933 146.018 c
545.933 128.763 l
545.933 127.517 546.431 126.646 547.178 126.272 c
546.431 125.898 545.933 125.027 545.933 123.781 c
545.933 106.526 l
545.933 105.281 545.435 104.409 544.688 104.036 c
S
BT
/F10 1 Tf
6.9738 0 0 6.9738 548.2198 125.3619 Tm
0 Tc
()Tj
/TT5 1 Tf
9.9626 0 0 9.9626 308.88 164.58 Tm
[(compiled)-228.9(into)-240.9(a)-252.9(plan)-240.9(fragment)-216.8(as)-252.9(sho)24.1(wn)-240.9(here)]TJ
0 -1.1925 TD
[(on)-252.9(the)-252.9(right.)-325.2(Operator)]TJ
/F6 1 Tf
8.9861 0 TD
()Tj
/TT5 1 Tf
0.6023 0 TD
[(,)-252.9(the)-265(algebraic)-240.9(repre-)]TJ
-9.5883 -1.2045 TD
[(sentation)-192.7(of)-204.8(algorithm)]TJ
/TT7 1 Tf
8.9097 0 TD
(Na)Tj
1.1961 -0.012 TD
()Tj
/TT9 1 Tf
0.0241 0.012 TD
()Tj
/TT7 1 Tf
0.2778 0 TD
(ve)Tj
/TT5 1 Tf
1.0925 0 TD
[(\(Figure)-192.7(3\(a\)\),)-192.7(it-)]TJ
-11.5001 -1.1925 TD
[(erates)-228.9(the)-240.9(e)24.1(v)24.1(aluation)-204.8(of)-228.9(the)-240.9(algebraic)-216.8(plan)-228.9(for)]TJ
/F6 1 Tf
0 -1.2045 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 313.56 115.38 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 327 116.82 Tm
0 Tc
[(and)-228.9(feeds)-228.9(its)-240.9(output)]TJ
ET
410.04 116.34 m
410.04 118.853 l
S
410.04 123.157 m
408.846 123.157 407.888 122.199 407.888 121.005 c
407.888 119.811 408.846 118.853 410.04 118.853 c
411.234 118.853 412.192 119.811 412.192 121.005 c
412.192 122.199 411.234 123.157 410.04 123.157 c
h
410.04 121.005 m
S
BT
9.9626 0 0 9.9626 415.44 116.82 Tm
[(back)-228.9(to)-240.9(its)-240.9(input)]TJ
ET
484.68 117.834 m
484.68 123.356 l
S
1 J
482.09 116.539 m
483.385 118.482 485.975 118.482 487.27 116.539 c
S
BT
9.9626 0 0 9.9626 308.88 104.82 Tm
[(until)-265(the)-265(IFP)-277(is)-289.1(reached.)-361.4(If)-265(we)-277(can)-265(guarantee)]TJ
0 -1.1925 TD
[(that)-301.1(the)-301.1(plan)-289.1(for)]TJ
/F6 1 Tf
6.7893 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 381.6 91.5 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 395.76 92.94 Tm
0 Tc
[(is)-313.2(distrib)24.1(uti)24.1(v)12(e)0(,)-301.1(w)0(e)-301.1(may)]TJ
-8.7206 -1.2045 TD
[(safely)-265(trade)]TJ
/F6 1 Tf
4.9283 0 TD
()Tj
/TT5 1 Tf
0.8793 0 TD
[(for)-265(its)]TJ
/TT7 1 Tf
2.6649 0 TD
(Delta)Tj
/TT5 1 Tf
2.2217 0 TD
[(-based)-252.9(v)24.1(ariant)]TJ
/F6 1 Tf
5.8801 0 TD
()Tj
/F7 1 Tf
6.9738 0 0 6.9738 480.72 84.54 Tm
()Tj
/TT5 1 Tf
9.9626 0 0 9.9626 295.08 51.06 Tm
(6)Tj
ET
endstream
endobj
52 0 obj
<<
/ProcSet [/PDF /Text /ImageB ]
/Font <<
/F1 4 0 R
/F3 6 0 R
/F4 7 0 R
/F5 8 0 R
/F6 22 0 R
/F7 23 0 R
/F8 24 0 R
/F9 25 0 R
/F10 26 0 R
/F11 27 0 R
/F13 29 0 R
/F16 38 0 R
/F17 39 0 R
/F18 40 0 R
/F19 41 0 R
/F21 49 0 R
/F22 53 0 R
/F23 54 0 R
/F24 55 0 R
/F25 56 0 R
/F26 57 0 R
/F27 58 0 R
/F28 59 0 R
/F29 60 0 R
/F30 61 0 R
/F31 62 0 R
/TT2 9 0 R
/TT5 11 0 R
/TT7 12 0 R
/TT8 13 0 R
/TT9 14 0 R
/TT11 15 0 R
/TT12 16 0 R
>>
/XObject <<
/Im1 33 0 R
>>
/ExtGState <<
/GS1 17 0 R
>>
>>
endobj
64 0 obj
<<
/Length 33455
>>
stream
0 G
0 J 0 j 0.398 w 10 M []0 d
/GS1 gs
1 i
65.76 664.013 m
S
0.299 w
54.055 673.287 m
77.574 673.287 l
78.127 673.287 78.303 673.644 77.97 674.088 c
66.415 689.494 l
66.082 689.939 65.547 689.939 65.214 689.494 c
53.659 674.088 l
53.326 673.644 53.502 673.287 54.055 673.287 c
s
BT
/F10 1 Tf
6.9738 0 0 6.9738 59.8878 677.9534 Tm
0 g
0 Tc
0 Tw
(e)Tj
/F13 1 Tf
4.9813 0 0 4.9813 63.6078 676.9934 Tm
-0.0408 Tc
(rec)Tj
/F17 1 Tf
8.9664 0 0 8.9664 62.6882 661.5226 Tm
0 Tc
()Tj
ET
0.398 w
75.681 651.334 m
75.681 656.927 l
S
1 J
73.091 650.039 m
74.386 651.982 76.977 651.982 78.272 650.039 c
S
0 J
55.839 651.334 m
55.839 656.927 l
S
1 J
53.248 650.039 m
54.544 651.982 57.134 651.982 58.429 650.039 c
S
0 J
75.681 656.927 m
69.529 661.321 l
55.839 656.927 m
61.991 661.321 l
65.76 667.201 m
65.76 672.379 l
65.76 691.081 m
65.76 694.944 l
S
65.76 699.248 m
64.566 699.248 63.608 698.29 63.608 697.096 c
63.608 695.901 64.566 694.944 65.76 694.944 c
66.954 694.944 67.912 695.901 67.912 697.096 c
67.912 698.29 66.954 699.248 65.76 699.248 c
h
65.76 697.096 m
S
BT
/F21 1 Tf
5.9776 0 0 5.9776 93.7403 674.6639 Tm
(?)Tj
/F19 1 Tf
8.9664 0 0 8.9664 91.9403 669.5039 Tm
(=)Tj
ET
130.249 688.108 m
S
0.299 w
103.662 659.114 m
127.181 659.114 l
127.734 659.114 127.91 659.47 127.577 659.915 c
116.022 675.321 l
115.689 675.766 115.154 675.766 114.821 675.321 c
103.266 659.915 l
102.933 659.47 103.109 659.114 103.662 659.114 c
s
BT
/F10 1 Tf
6.9738 0 0 6.9738 109.4946 663.78 Tm
(e)Tj
/F13 1 Tf
4.9813 0 0 4.9813 113.2146 662.8201 Tm
-0.0408 Tc
(rec)Tj
ET
133.426 659.114 m
156.945 659.114 l
157.498 659.114 157.674 659.47 157.341 659.915 c
145.786 675.321 l
145.453 675.766 144.918 675.766 144.585 675.321 c
133.03 659.915 l
132.697 659.47 132.873 659.114 133.426 659.114 c
s
BT
/F10 1 Tf
6.9738 0 0 6.9738 139.2587 663.78 Tm
0 Tc
(e)Tj
/F13 1 Tf
4.9813 0 0 4.9813 142.9787 662.8201 Tm
-0.0408 Tc
(rec)Tj
/F17 1 Tf
8.9664 0 0 8.9664 127.1771 685.6173 Tm
0 Tc
()Tj
ET
0.398 w
115.367 651.334 m
115.367 658.206 l
S
1 J
112.777 650.039 m
114.072 651.982 116.662 651.982 117.957 650.039 c
S
0 J
145.131 651.334 m
145.131 658.206 l
S
1 J
142.541 650.039 m
143.836 651.982 146.426 651.982 147.721 650.039 c
S
0 J
115.367 676.908 m
115.367 677.478 l
145.131 676.908 m
145.131 677.478 l
115.367 677.478 m
126.48 685.416 l
145.131 677.478 m
134.018 685.416 l
130.249 691.296 m
130.249 694.944 l
S
130.249 699.248 m
129.055 699.248 128.097 698.29 128.097 697.096 c
128.097 695.901 129.055 694.944 130.249 694.944 c
131.443 694.944 132.401 695.901 132.401 697.096 c
132.401 698.29 131.443 699.248 130.249 699.248 c
h
130.249 697.096 m
S
BT
/TT5 1 Tf
8.9664 0 0 8.9664 64.32 638.7001 Tm
[(\(a\))-361.3(Is)]TJ
/F18 1 Tf
2.4343 0 TD
(e)Tj
/F13 1 Tf
5.9776 0 0 5.9776 90.48 637.7401 Tm
-0.0607 Tc
(rec)Tj
/TT5 1 Tf
8.9664 0 0 8.9664 102.36 638.7001 Tm
0 Tc
[(distrib)13.4(uti)26.8(v)13.4(e)0(?)]TJ
ET
202.881 657.753 m
S
0.8 g
181.849 709.244 8.07 -28.347 re
f
0.5 G
0.398 w [2.989 1.993 ]0 d
181.849 709.244 m
181.849 680.897 l
204.093 680.897 l
204.093 709.244 l
h
204.093 680.897 m
S
BT
/F17 1 Tf
8.9664 0 0 8.9664 189.8882 669.4359 Tm
0 g
()Tj
ET
0 G
0.299 w []0 d
176.912 650.362 m
189.093 650.362 l
189.646 650.362 189.898 650.763 189.66 651.264 c
183.432 664.342 l
183.194 664.843 182.811 664.843 182.573 664.342 c
176.345 651.264 l
176.107 650.763 176.359 650.362 176.912 650.362 c
s
BT
/F10 1 Tf
6.9738 0 0 6.9738 179.1684 654.3196 Tm
(e)Tj
/F28 1 Tf
4.9813 0 0 4.9813 182.8884 653.3596 Tm
(1)Tj
ET
196.755 650.362 m
208.936 650.362 l
209.489 650.362 209.741 650.763 209.503 651.264 c
203.275 664.342 l
203.036 664.843 202.654 664.843 202.416 664.342 c
196.188 651.264 l
195.95 650.763 196.202 650.362 196.755 650.362 c
s
BT
/F10 1 Tf
6.9738 0 0 6.9738 199.0111 654.3196 Tm
(e)Tj
/F28 1 Tf
4.9813 0 0 4.9813 202.7311 653.3596 Tm
(2)Tj
ET
0.398 w
192.96 713.749 m
192.96 710.099 l
192.96 679.959 m
192.96 675.115 l
189.191 669.691 m
183.039 666.041 l
196.729 669.691 m
202.881 666.041 l
S
BT
/F17 1 Tf
8.9664 0 0 8.9664 213.1557 684.431 Tm
( )Tj
ET
272.331 657.753 m
S
BT
8.9664 0 0 8.9664 254.3771 704.8694 Tm
()Tj
ET
0.8 g
231.456 700.314 8.07 -28.347 re
f
0.5 G
0.398 w [2.989 1.993 ]0 d
231.456 700.314 m
231.456 671.967 l
253.699 671.967 l
253.699 700.314 l
h
253.699 671.967 m
S
261.22 700.314 8.07 -28.347 re
f
261.22 700.314 m
261.22 671.967 l
283.464 671.967 l
283.464 700.314 l
h
283.464 671.967 m
S
0 G
0.299 w []0 d
236.44 650.362 m
248.621 650.362 l
249.174 650.362 249.426 650.763 249.188 651.264 c
242.96 664.342 l
242.722 664.843 242.34 664.843 242.101 664.342 c
235.873 651.264 l
235.635 650.763 235.887 650.362 236.44 650.362 c
s
BT
/F10 1 Tf
6.9738 0 0 6.9738 238.6966 654.3196 Tm
0 g
(e)Tj
/F28 1 Tf
4.9813 0 0 4.9813 242.4166 653.3596 Tm
(1)Tj
ET
266.204 650.362 m
278.385 650.362 l
278.938 650.362 279.19 650.763 278.952 651.264 c
272.724 664.342 l
272.486 664.843 272.104 664.843 271.866 664.342 c
265.638 651.264 l
265.399 650.763 265.652 650.362 266.204 650.362 c
s
BT
/F10 1 Tf
6.9738 0 0 6.9738 268.4608 654.3196 Tm
(e)Tj
/F28 1 Tf
4.9813 0 0 4.9813 272.1808 653.3596 Tm
(2)Tj
ET
0.398 w
257.449 713.749 m
257.449 710.548 l
253.68 705.792 m
242.567 701.17 l
261.218 705.792 m
272.331 701.17 l
242.567 671.03 m
242.567 666.041 l
272.331 671.03 m
272.331 666.041 l
S
BT
/TT5 1 Tf
8.9664 0 0 8.9664 173.04 638.7001 Tm
[(\(b\))-361.3(T)80.3(aking)-267.7(a)]TJ
/TT7 1 Tf
5.2454 0 TD
[(big)-254.3(step)]TJ
/TT5 1 Tf
3.143 0 TD
[(:)-307.8(Pushing)]TJ
/F17 1 Tf
-8.3883 -1.2179 TD
()Tj
/TT5 1 Tf
0.9369 0 TD
[(through)-267.7(a)-254.3(plan)-254.3(template)]TJ
/TT11 1 Tf
9.9626 0 0 9.9626 62.04 602.58 Tm
[(Figure)-216.8(7.)-216.8(Alg)-12(ebraic)-228.9(distrib)24.1(utivity)-204.8(assessment.)]TJ
ET
79.881 544.833 m
S
BT
/F17 1 Tf
8.9664 0 0 8.9664 66.3762 570.9384 Tm
()Tj
0.0571 -1.6085 TD
()Tj
ET
0.299 w
54.032 537.442 m
66.213 537.442 l
66.766 537.442 67.018 537.843 66.78 538.344 c
60.552 551.422 l
60.314 551.923 59.931 551.923 59.693 551.422 c
53.465 538.344 l
53.227 537.843 53.479 537.442 54.032 537.442 c
s
BT
/F10 1 Tf
6.9738 0 0 6.9738 56.2884 541.3996 Tm
(e)Tj
/F28 1 Tf
4.9813 0 0 4.9813 60.0084 540.4396 Tm
(1)Tj
ET
73.875 537.442 m
86.056 537.442 l
86.609 537.442 86.861 537.843 86.623 538.344 c
80.395 551.422 l
80.156 551.923 79.774 551.923 79.536 551.422 c
73.308 538.344 l
73.07 537.843 73.322 537.442 73.875 537.442 c
s
BT
/F10 1 Tf
6.9738 0 0 6.9738 76.1311 541.3996 Tm
(e)Tj
/F28 1 Tf
4.9813 0 0 4.9813 79.8511 540.4396 Tm
(2)Tj
ET
0.398 w
69.96 569.411 m
69.96 562.195 l
66.191 556.771 m
60.039 553.121 l
73.729 556.771 m
79.881 553.121 l
S
BT
/F17 1 Tf
8.9664 0 0 8.9664 90.1556 560.8809 Tm
( )Tj
ET
129.488 544.833 m
S
BT
8.9664 0 0 8.9664 116.495 570.6893 Tm
()Tj
-1.1636 -1.1578 TD
1.4136 Tc
()Tj
ET
0.299 w
103.639 537.442 m
115.82 537.442 l
116.373 537.442 116.625 537.843 116.387 538.344 c
110.159 551.422 l
109.92 551.923 109.538 551.923 109.3 551.422 c
103.072 538.344 l
102.834 537.843 103.086 537.442 103.639 537.442 c
s
BT
/F10 1 Tf
6.9738 0 0 6.9738 105.8952 541.3996 Tm
0 Tc
(e)Tj
/F28 1 Tf
4.9813 0 0 4.9813 109.6152 540.4396 Tm
(1)Tj
ET
123.482 537.442 m
135.663 537.442 l
136.215 537.442 136.468 537.843 136.229 538.344 c
130.001 551.422 l
129.763 551.923 129.381 551.923 129.143 551.422 c
122.915 538.344 l
122.676 537.843 122.929 537.442 123.482 537.442 c
s
BT
/F10 1 Tf
6.9738 0 0 6.9738 125.738 541.3996 Tm
(e)Tj
/F28 1 Tf
4.9813 0 0 4.9813 129.458 540.4396 Tm
(2)Tj
ET
0.398 w
116.591 569.992 m
113.163 566.319 l
122.542 569.992 m
125.97 566.319 l
109.645 558.781 m
109.645 553.121 l
129.488 558.781 m
129.488 553.121 l
S
BT
/TT5 1 Tf
8.9664 0 0 8.9664 54.48 525.78 Tm
[(\(a\))-361.3(Unary)-267.7(operators)]TJ
/F17 1 Tf
8.2129 0 TD
()Tj
ET
189.522 554.046 m
S
BT
/F30 1 Tf
8.9664 0 0 8.9664 173.5362 567.3951 Tm
()Tj
/F17 1 Tf
-1.326 -1.2133 TD
()Tj
ET
0.299 w
148.79 537.442 m
160.971 537.442 l
161.524 537.442 161.776 537.843 161.538 538.344 c
155.31 551.422 l
155.072 551.923 154.69 551.923 154.451 551.422 c
148.223 538.344 l
147.985 537.843 148.237 537.442 148.79 537.442 c
s
BT
/F10 1 Tf
6.9738 0 0 6.9738 151.0467 541.3996 Tm
(e)Tj
/F28 1 Tf
4.9813 0 0 4.9813 154.7667 540.4396 Tm
(1)Tj
ET
168.633 537.442 m
180.814 537.442 l
181.367 537.442 181.619 537.843 181.381 538.344 c
175.153 551.422 l
174.915 551.923 174.532 551.923 174.294 551.422 c
168.066 538.344 l
167.828 537.843 168.08 537.442 168.633 537.442 c
s
BT
/F10 1 Tf
6.9738 0 0 6.9738 170.8894 541.3996 Tm
(e)Tj
/F28 1 Tf
4.9813 0 0 4.9813 174.6094 540.4396 Tm
(2)Tj
ET
183.515 546.655 m
195.696 546.655 l
196.249 546.655 196.501 547.056 196.263 547.556 c
190.035 560.635 l
189.797 561.135 189.414 561.135 189.176 560.635 c
182.948 547.556 l
182.71 547.056 182.962 546.655 183.515 546.655 c
s
BT
/F10 1 Tf
6.9738 0 0 6.9738 185.7715 550.6122 Tm
(e)Tj
/F28 1 Tf
4.9813 0 0 4.9813 189.4915 549.6522 Tm
(3)Tj
ET
0.398 w
172.839 565.967 m
168.438 562.195 l
181.401 567.116 m
189.522 562.334 l
160.949 556.771 m
154.797 553.121 l
168.488 556.771 m
174.64 553.121 l
S
BT
/F17 1 Tf
8.9664 0 0 8.9664 199.796 560.8809 Tm
( )Tj
ET
276.334 544.833 m
S
BT
8.9664 0 0 8.9664 243.4978 567.146 Tm
()Tj
/F30 1 Tf
-2.2701 -1.1578 TD
3.627 Tc
()Tj
ET
0.299 w
210.799 537.442 m
222.98 537.442 l
223.533 537.442 223.785 537.843 223.547 538.344 c
217.319 551.422 l
217.08 551.923 216.698 551.923 216.46 551.422 c
210.232 538.344 l
209.994 537.843 210.246 537.442 210.799 537.442 c
s
BT
/F10 1 Tf
6.9738 0 0 6.9738 213.0552 541.3996 Tm
0 Tc
(e)Tj
/F28 1 Tf
4.9813 0 0 4.9813 216.7752 540.4396 Tm
(1)Tj
ET
230.642 537.442 m
242.823 537.442 l
243.375 537.442 243.628 537.843 243.389 538.344 c
237.161 551.422 l
236.923 551.923 236.541 551.923 236.303 551.422 c
230.075 538.344 l
229.837 537.843 230.089 537.442 230.642 537.442 c
s
BT
/F10 1 Tf
6.9738 0 0 6.9738 232.898 541.3996 Tm
(e)Tj
/F28 1 Tf
4.9813 0 0 4.9813 236.618 540.4396 Tm
(3)Tj
ET
250.484 537.442 m
262.665 537.442 l
263.218 537.442 263.47 537.843 263.232 538.344 c
257.004 551.422 l
256.766 551.923 256.384 551.923 256.146 551.422 c
249.918 538.344 l
249.679 537.843 249.932 537.442 250.484 537.442 c
s
BT
/F10 1 Tf
6.9738 0 0 6.9738 252.7408 541.3996 Tm
(e)Tj
/F28 1 Tf
4.9813 0 0 4.9813 256.4608 540.4396 Tm
(2)Tj
ET
270.327 537.442 m
282.508 537.442 l
283.061 537.442 283.313 537.843 283.075 538.344 c
276.847 551.422 l
276.609 551.923 276.227 551.923 275.988 551.422 c
269.76 538.344 l
269.522 537.843 269.774 537.442 270.327 537.442 c
s
BT
/F10 1 Tf
6.9738 0 0 6.9738 272.5835 541.3996 Tm
(e)Tj
/F28 1 Tf
4.9813 0 0 4.9813 276.3035 540.4396 Tm
(3)Tj
ET
0.398 w
242.8 567.618 m
231.008 561.3 l
250.339 567.618 m
262.131 561.3 l
222.446 556.467 m
216.805 553.121 l
231.008 556.467 m
236.648 553.121 l
262.131 556.467 m
256.491 553.121 l
270.694 556.467 m
276.334 553.121 l
S
BT
/TT5 1 Tf
8.9664 0 0 8.9664 174 525.78 Tm
[(\(b\))-374.7(Binary)-254.3(operators)]TJ
/F30 1 Tf
8.5051 0 TD
()Tj
/TT11 1 Tf
9.9626 0 0 9.9626 62.04 500.7 Tm
[(Figure)-445.7(8.)-445.7(Pushing)]TJ
/F1 1 Tf
9.1589 0 TD
()Tj
/TT11 1 Tf
1.1081 0 TD
[(thr)24.1(ough)-433.6(unar)-12(y)-433.6(\()]TJ
/F1 1 Tf
7.6877 0 TD
()Tj
/TT11 1 Tf
0.7829 0 TD
[(\))-433.6(and)]TJ
-18.7377 -1.2045 TD
[(binar)-12(y)-277(\()]TJ
/F32 1 Tf
3.6231 0 TD
()Tj
/TT11 1 Tf
0.7829 0 TD
[(\))-265(operator)12(s.)]TJ
/TT5 1 Tf
-5.5985 -4.2398 TD
[(which,)-265(in)-265(general,)-265(will)-277(feed)-252.9(signi)]TJ
/TT8 1 Tf
13.2102 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(cantly)-265(less)-277(items)-277(back)-265(in)]TJ
-13.7664 -1.2045 TD
[(each)-228.9(iteration)-240.9(\(see)-240.9(Figure)-240.9(3\(b\))-228.9(and)-240.9(Section)-228.9(5\).)]TJ
0 -1.5297 TD
[(In)-337.3(this)-349.3(algebraic)-337.3(setting,)-361.4(if)-349.3(the)-349.3(recursion)-325.2(body)]TJ
/F6 1 Tf
19.1579 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 246.72 417.78 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 261.24 419.22 Tm
0 Tc
[(is)-361.3(dis-)]TJ
-21.1872 -1.2045 TD
[(trib)24.1(uti)24.1(v)12(e)0(,)-301.1(its)-313.2(relational)-289.1(plan)-301.1(will)-313.2(satisfy)-301.1(the)-301.1(equality)-301.1(sho)24.1(wn)]TJ
T*
[(in)-397.5(Figure)-397.5(7\(a\).)-770.9(This)-397.5(equality)-397.5(is)-409.5(the)-397.5(algebraic)-397.5(e)12(xpression)]TJ
0 -1.1925 TD
[(of)-337.3(a)-361.4(d)0(i)24.1(vide-and-conquer)-289.1(e)24.1(v)24.1(aluation)-325.2(strate)12(gy)-349.3(for)]TJ
/F6 1 Tf
19.5187 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 250.68 381.9 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 265.32 383.34 Tm
0 Tc
(\(Sec-)Tj
-21.5967 -1.2045 TD
[(tion)-204.8(3.1\):)-277(e)24.1(v)24.1(aluating)]TJ
/F6 1 Tf
8.1958 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 137.04 369.9 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 150.24 371.34 Tm
0 Tc
[(o)12(v)12(e)0(r)-192.7(a)-216.8(composite)-192.7(input)-204.8(\(lhs,)]TJ
ET
272.47 377.204 m
S
BT
/F1 1 Tf
9.9626 0 0 9.9626 269.1491 374.4366 Tm
()Tj
ET
265.383 370.194 m
265.383 374.369 l
S
1 J
262.793 368.899 m
264.088 370.842 266.678 370.842 267.974 368.899 c
S
0 J
279.557 370.194 m
279.557 374.369 l
S
1 J
276.966 368.899 m
278.262 370.842 280.852 370.842 282.147 368.899 c
S
0 J
265.383 374.369 m
267.954 377.204 l
279.557 374.369 m
276.986 377.204 l
S
BT
/TT5 1 Tf
9.9626 0 0 9.9626 283.08 371.34 Tm
(\))Tj
-23.3793 -1.2045 TD
[(yields)-252.9(the)-252.9(same)-265(result)-252.9(as)-265(the)-265(union)-240.9(of)-252.9(the)-252.9(e)24.1(v)24.1(aluation)-240.9(of)]TJ
/F6 1 Tf
22.0182 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 275.28 357.9 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 50.16 347.46 Tm
0 Tc
[(o)12(v)12(e)0(r)-252.9(a)-277(partitioned)-252.9(input)-265(\(rhs\).)-385.4(Ef)24.1(fecti)24.1(v)12(ely)60.2(,)-252.9(the)-277(union)-252.9(opera-)]TJ
0 -1.2045 TD
(tor)Tj
/F1 1 Tf
1.2915 0 TD
()Tj
/TT5 1 Tf
0.8552 0 TD
[(has)-192.7(been)-180.7(completely)-168.6(pushed)-168.6(up)-192.7(through)-156.6(all)-192.7(branches)-168.6(of)]TJ
-2.1467 -1.1925 TD
[(the)-289.1(D)36.1(A)36.1(G-shaped)-265(algebraic)-277(plan)-277(for)]TJ
/F6 1 Tf
14.3627 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 198.72 322.14 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 209.88 323.58 Tm
0 Tc
[(.)-445.7(Zooming)-265(in)-289.1(from)]TJ
-16.0319 -1.2045 TD
[(the)-373.4(plan)-385.4(to)-373.4(the)-385.4(operator)-361.3(le)24.1(v)12(el,)-409.5(Figure)-373.4(8)-385.4(depicts)-373.4(ho)24.1(w)]TJ
/F1 1 Tf
21.8673 0 TD
()Tj
/TT5 1 Tf
1.06 0 TD
(is)Tj
-22.9272 -1.2045 TD
[(pushed)-168.6(up)-180.7(through)-168.6(unary)-168.6(\()]TJ
/F1 1 Tf
10.2403 0 TD
()Tj
/TT5 1 Tf
0.7829 0 TD
[(\))-180.7(and)-180.7(binary)-180.7(\()]TJ
/F32 1 Tf
5.2066 0 TD
()Tj
/TT5 1 Tf
0.7829 0 TD
[(\))-180.7(operators.)-265(Col-)]TJ
-17.0127 -1.1925 TD
[(umn)-228.9(Push?)-301.1(of)-240.9(T)84.3(able)-240.9(1)-240.9(indicates)-240.9(whether)]TJ
/F1 1 Tf
16.8675 0 TD
()Tj
/TT5 1 Tf
0.9154 0 TD
[(may)-240.9(indeed)-228.9(be)]TJ
-17.7829 -1.2045 TD
[(v)24.1(alidly)-204.8(pushed)-192.7(through)-192.7(a)-228.9(g)0(i)24.1(v)12(en)-192.7(operator)60.2(.)-277(Note)-216.8(that)-216.8(this)-228.9(push)]TJ
T*
[(through)-180.7(is)-228.9(prohibited)-192.7(by)-216.8(e)12(xactly)-204.8(those)-216.8(operators)-192.7(that)-216.8(require)]TJ
0 -1.1925 TD
[(to)-252.9(consume)-228.9(their)]TJ
/TT7 1 Tf
6.8998 0 TD
(complete)Tj
/TT5 1 Tf
3.8503 0 TD
[(input)-240.9(to)-265(produce)-228.9(the)-240.9(result.)-337.3(This)]TJ
-10.7501 -1.2045 TD
[(af)24.1(fects,)]TJ
/TT7 1 Tf
3.1434 0 TD
-0.012 Tc
[(e.)-12(g.)]TJ
/TT5 1 Tf
1.4198 0 TD
0 Tc
[(,)-240.9(aggre)12(gates,)-228.9(dif)24.1(ference,)-228.9(and)-252.9(the)-252.9(ro)24.1(w)-252.9(numbering)]TJ
-4.5632 -1.1925 TD
[(operator)60.2(.)-662.5(A)0(s)-385.4(before,)-385.4(the)-373.4(occurrence)-337.3(of)-373.4(node)-361.4(constructors)]TJ
0 -1.2045 TD
(renders)Tj
/F6 1 Tf
3.1717 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 86.64 214.5 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 100.2 215.94 Tm
0 Tc
[(non-distrib)24.1(uti)24.1(v)12(e)0(.)]TJ
-5.0228 -1.5297 TD
[(Because)-385.4(our)-373.4(primary)-373.4(goal)-385.4(is)-397.5(distrib)24.1(uti)24.1(vity)-373.4(assessment)-397.5(\(as)]TJ
0 -1.2045 TD
[(opposed)-289.1(to)-325.2(query)]TJ
/TT7 1 Tf
7.3031 0 TD
[(e)12(valuation)]TJ
/TT5 1 Tf
4.2091 0 TD
[(b)24.1(ut)-277(see)-325.2(Section)-313.2(5\),)-337.3(we)-313.2(may)]TJ
-11.5123 -1.2045 TD
[(actually)-301.1(emplo)12(y)-313.2(simpli)]TJ
/TT8 1 Tf
9.2673 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(ed)-313.2(v)24.1(ariants)-313.2(of)]TJ
/F6 1 Tf
5.8578 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 211.8 175.26 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 226.08 176.7 Tm
0 Tc
[(in)-313.2(this)-325.2(conte)12(xt.)]TJ
-17.658 -1.1925 TD
[(In)-228.9(particular)36.1(,)-204.8(since)-240.9(the)-228.9(de)]TJ
/TT8 1 Tf
10.0015 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(nition)-216.8(of)-240.9(distrib)24.1(uti)24.1(vity)-216.8(disre)12(gards)]TJ
-10.5577 -1.2045 TD
[(duplicates)-457.7(and)-457.7(order)-457.7(\(De)]TJ
/TT8 1 Tf
10.4801 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(nition)-457.7(3.1\),)-505.9(the)-469.8(compiler)-445.7(may)]TJ
-11.0362 -1.1925 TD
[(choose)-301.1(to)-325.2(remo)12(v)12(e)-301.1(code)-313.2(from)]TJ
/F6 1 Tf
11.9024 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 174.24 139.5 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 188.64 140.94 Tm
0 Tc
[(that)-325.2(is)-325.2(used)-325.2(to)-313.2(eliminate)]TJ
-13.8999 -1.2045 TD
[(duplicate)-301.1(nodes)-313.2(after)-313.2(XP)12(ath)-325.2(location)-313.2(steps)-325.2(as)-325.2(well)-337.3(as)-325.2(omit)]TJ
T*
[(those)-240.9(parts)-252.9(of)-240.9(the)-252.9(plan)-240.9(that)-252.9(realize)-240.9(the)-252.9(proper)-228.9(XQuery)-228.9(order)]TJ
0 -1.1925 TD
[(semantics)-240.9([14)24.1(].)]TJ
1.1925 -1.2165 TD
[(Further)36.1(,)-469.8(the)-433.6(plans)-433.6(generated)-409.5(by)-433.6(the)-433.6(XQuery)-421.6(compiler)]TJ
-1.1925 -1.2045 TD
[(typically)-192.7(contain)-204.8(numerous)-180.7(instantiations)-204.8(of)]TJ
/TT7 1 Tf
17.5399 0 TD
[(plan)-192.7(templates)]TJ
/TT5 1 Tf
5.8031 0 TD
(,)Tj
ET
337.2 718.901 m
S
BT
/F18 1 Tf
8.9664 0 0 8.9664 322.8971 547.9749 Tm
()Tj
/F27 1 Tf
5.9776 0 0 5.9776 328.1771 547.0149 Tm
0.0086 Tc
[(it)10.8(er)]TJ
/F22 1 Tf
1.4858 0 TD
0 Tc
(,)Tj
/F27 1 Tf
0.3815 0 TD
0.0086 Tc
[(it)10.8(em)]TJ
/TT5 1 Tf
7.9701 0 0 7.9701 328.3813 563.67 Tm
0 Tc
(#)Tj
/F27 1 Tf
5.9776 0 0 5.9776 332.4614 562.71 Tm
-0.0065 Tc
[(i)-14(nne)-16.1(r)]TJ
/F18 1 Tf
8.9664 0 0 8.9664 321.9034 627.6221 Tm
0 Tc
()Tj
/F27 1 Tf
5.9776 0 0 5.9776 327.1835 626.6621 Tm
-0.0065 Tc
[(i)-14(nne)-16.1(r)]TJ
/F22 1 Tf
2.2085 0 TD
0 Tc
(,)Tj
/F27 1 Tf
-2.2085 -0.9636 TD
-0.0079 Tc
[(out)-5.7(e)-17.5(r)]TJ
/F21 1 Tf
2.329 0 TD
0 Tc
(:)Tj
/F27 1 Tf
0.3614 0 TD
0.0086 Tc
[(it)10.8(er)]TJ
/F18 1 Tf
8.9664 0 0 8.9664 369.1274 581.991 Tm
0 Tc
()Tj
/F27 1 Tf
5.9776 0 0 5.9776 374.4074 581.031 Tm
0.0086 Tc
[(it)10.8(er)]TJ
/F21 1 Tf
1.5058 0 TD
0 Tc
(:)Tj
/F27 1 Tf
0.3614 0 TD
-0.0065 Tc
[(i)-14(nne)-16.1(r)]TJ
/F22 1 Tf
2.1684 0 TD
0 Tc
(,)Tj
/F27 1 Tf
0.3815 0 TD
0.0086 Tc
[(it)10.8(em)]TJ
ET
1 j 0.398 w
386.977 607.25 m
386.977 609.66 l
389.387 609.66 l
389.387 612.069 l
391.796 612.069 l
391.796 614.479 l
394.206 614.479 l
394.206 607.25 l
s
BT
/F11 1 Tf
5.9776 0 0 5.9776 380.017 601.7302 Tm
-0.0092 Tc
(child::)Tj
-1.606 -0.9235 TD
(prerequisites)Tj
ET
386.996 634.463 m
386.996 636.873 l
389.406 636.873 l
389.406 639.282 l
391.816 639.282 l
391.816 641.692 l
394.225 641.692 l
394.225 634.463 l
s
BT
5.9776 0 0 5.9776 380.0362 628.9431 Tm
(child::)Tj
-0.2811 -0.9234 TD
(pre_code)Tj
ET
q
6.84 0 0 -7.68 436.9493 641.8957 cm
/Im1 Do
Q
BT
/F27 1 Tf
5.9776 0 0 5.9776 438.0413 636.6277 Tm
1 g
0.0075 Tc
(id)Tj
ET
0 g
q
9.48 0 0 -7.68 443.6693 641.8957 cm
/Im1 Do
Q
BT
5.9776 0 0 5.9776 444.6419 636.6277 Tm
1 g
-0.0014 Tc
[(re)-11(f)]TJ
ET
0 g
q
0.48 0 0 -17.16 436.8293 638.2957 cm
/Im1 Do
Q
BT
/TT5 1 Tf
8.9664 0 0 8.9664 439.1213 631.4677 Tm
0 Tc
(.)Tj
0 -0.455 TD
(.)Tj
0 -0.4417 TD
(.)Tj
ET
q
0.48 0 0 -17.16 443.3093 638.2957 cm
/Im1 Do
Q
BT
8.9664 0 0 8.9664 447.0413 631.4677 Tm
(.)Tj
0 -0.455 TD
(.)Tj
0 -0.4417 TD
(.)Tj
ET
q
0.48 0 0 -17.16 452.6693 638.2957 cm
/Im1 Do
Q
q
16.2 0 0 -0.48 436.8293 621.2557 cm
/Im1 Do
Q
BT
/F25 1 Tf
8.9664 0 0 8.9664 414.3984 651.9478 Tm
()Tj
0.0134 0 TD
()Tj
/F27 1 Tf
5.9776 0 0 5.9776 406.9584 645.4678 Tm
0.0086 Tc
[(it)10.8(em)]TJ
/F21 1 Tf
1.9676 0 TD
0 Tc
(=)Tj
/F27 1 Tf
0.9436 0 TD
0.0075 Tc
(id)Tj
/F18 1 Tf
8.9664 0 0 8.9664 398.9471 667.0588 Tm
0 Tc
()Tj
/F27 1 Tf
5.9776 0 0 5.9776 404.2271 665.9788 Tm
0.0086 Tc
[(it)10.8(er)]TJ
/F22 1 Tf
1.4857 0 TD
0 Tc
(,)Tj
/F27 1 Tf
0.3815 0 TD
0.0086 Tc
[(it)10.8(em)]TJ
/F21 1 Tf
1.9676 0 TD
0 Tc
(:)Tj
/F27 1 Tf
0.3614 0 TD
-0.0014 Tc
[(re)-11(f)]TJ
/F25 1 Tf
8.9664 0 0 8.9664 333.5835 685.9365 Tm
0 Tc
()Tj
0.0134 0 TD
()Tj
/F27 1 Tf
5.9776 0 0 5.9776 323.3835 679.5765 Tm
-0.0065 Tc
[(i)-14(nne)-16.1(r)]TJ
/F21 1 Tf
2.2085 0 TD
0 Tc
(=)Tj
/F27 1 Tf
0.9437 0 TD
0.0086 Tc
[(it)10.8(er)]TJ
/F18 1 Tf
8.9664 0 0 8.9664 314.9312 701.0476 Tm
0 Tc
()Tj
/F27 1 Tf
5.9776 0 0 5.9776 320.2112 700.0876 Tm
0.0086 Tc
[(it)10.8(er)]TJ
/F21 1 Tf
1.4857 0 TD
0 Tc
(:)Tj
/F27 1 Tf
0.3614 0 TD
-0.0079 Tc
[(out)-5.7(e)-17.5(r)]TJ
/F22 1 Tf
2.3089 0 TD
0 Tc
(,)Tj
/F27 1 Tf
0.3815 0 TD
0.0086 Tc
[(it)10.8(em)]TJ
ET
0 j 0.398 w
337.2 534.502 m
337.2 544.609 l
S
1 J
334.61 533.207 m
335.905 535.149 338.495 535.149 339.79 533.207 c
S
0 J
337.2 553.031 m
337.2 561.467 l
337.2 570.19 m
337.2 618.035 l
347.214 567.409 m
391.059 574.332 l
391.059 578.625 l
337.2 632.678 m
337.2 677.314 l
337.2 692.456 m
337.2 697.682 l
391.059 587.047 m
391.059 592.362 l
391.059 615.83 m
391.059 619.575 l
391.059 643.043 m
391.059 646.616 l
405.763 648.939 l
444.918 643.1 m
444.918 646.616 l
430.214 648.939 l
417.988 658.467 m
417.988 663.638 l
417.988 672.115 m
417.988 676.381 l
352.212 683.305 l
337.2 706.104 m
337.2 713.202 l
S
337.2 717.506 m
336.006 717.506 335.048 716.548 335.048 715.354 c
335.048 714.16 336.006 713.202 337.2 713.202 c
338.394 713.202 339.352 714.16 339.352 715.354 c
339.352 716.548 338.394 717.506 337.2 717.506 c
h
337.2 715.354 m
S
387.288 617.703 m
S
0.8 g
312.27 693.713 8.07 -133.23 re
f
BT
/TT5 1 Tf
0 6.9738 -6.9738 0 317.9284 620.8983 Tm
0.2 g
0 Tc
(loop)Tj
ET
0.5 G
0.398 w [2.989 1.993 ]0 d
312.27 693.713 m
312.27 560.483 l
456.405 560.483 l
456.405 693.713 l
h
456.405 560.483 m
S
0.8 g
362.004 643.256 8.07 -51.024 re
f
BT
0 6.9738 -6.9738 0 367.3033 612.1261 Tm
0.2 g
(step)Tj
ET
362.004 643.256 m
362.004 592.231 l
412.594 592.231 l
412.594 643.256 l
h
412.594 592.231 m
S
BT
8.9664 0 0 8.9664 347.04 519.9 Tm
0 g
(\(a\))Tj
/F18 1 Tf
1.4712 0 TD
(e)Tj
/F13 1 Tf
5.9776 0 0 5.9776 364.56 518.9401 Tm
-0.0607 Tc
(rec)Tj
/TT5 1 Tf
8.9664 0 0 8.9664 376.44 519.9 Tm
0 Tc
[(of)-240.9(Query)-267.7(Q1)]TJ
ET
0 G
0.398 w []0 d
517.677 642.396 m
S
BT
/F18 1 Tf
8.9664 0 0 8.9664 480.6971 548.0068 Tm
()Tj
/F27 1 Tf
5.9776 0 0 5.9776 485.9771 547.0468 Tm
0.0086 Tc
[(it)10.8(er)]TJ
/F22 1 Tf
1.4857 0 TD
0 Tc
(,)Tj
/F27 1 Tf
0.3815 0 TD
0.0086 Tc
[(it)10.8(em)]TJ
ET
1 j 0.398 w
513.523 591.011 m
513.523 593.421 l
515.932 593.421 l
515.932 595.831 l
518.342 595.831 l
518.342 598.24 l
520.752 598.24 l
520.752 591.011 l
s
BT
/F11 1 Tf
5.9776 0 0 5.9776 506.5626 585.3713 Tm
-0.0092 Tc
(self::a)Tj
/F18 1 Tf
8.9664 0 0 8.9664 510.3468 606.9539 Tm
0 Tc
()Tj
/F27 1 Tf
5.9776 0 0 5.9776 515.6268 605.9939 Tm
0.0086 Tc
[(it)10.8(er)]TJ
/F4 1 Tf
8.9664 0 0 8.9664 493.4685 624.3511 Tm
-0.003 Tc
(count)Tj
/F27 1 Tf
5.9776 0 0 5.9776 516.9885 622.9111 Tm
0.0086 Tc
[(it)10.8(em)]TJ
/F22 1 Tf
1.9475 0 TD
0 Tc
(/)Tj
/F27 1 Tf
0.6425 0 TD
0.0086 Tc
[(it)10.8(er)]TJ
/F25 1 Tf
8.9664 0 0 8.9664 491.3956 651.9523 Tm
0 Tc
()Tj
0.0134 0 TD
()Tj
/F27 1 Tf
5.9776 0 0 5.9776 490.5556 645.5922 Tm
0.0086 Tc
[(it)10.8(er)]TJ
ET
490.817 671.8 m
490.817 674.209 l
493.227 674.209 l
493.227 676.619 l
495.637 676.619 l
495.637 679.029 l
498.046 679.029 l
498.046 671.8 l
s
BT
/F11 1 Tf
5.9776 0 0 5.9776 482.2972 666.1597 Tm
-0.0092 Tc
(child::*)Tj
ET
0 j 0.398 w
492.165 672.161 m
S
0.8 g
496.645 601.334 8.07 -19.843 re
f
BT
/TT5 1 Tf
0 6.9738 -6.9738 0 501.9443 585.7955 Tm
0.2 g
0 Tc
(step)Tj
ET
0.5 G
0.398 w [2.989 1.993 ]0 d
496.645 601.334 m
496.645 581.492 l
533.062 581.492 l
533.062 601.334 l
h
533.062 581.492 m
S
0.8 g
473.968 682.123 8.07 -19.843 re
f
BT
0 6.9738 -6.9738 0 479.2669 666.5839 Tm
0.2 g
(step)Tj
ET
473.968 682.123 m
473.968 662.28 l
510.385 662.28 l
510.385 682.123 l
h
510.385 662.28 m
S
0 G
0.398 w []0 d
495 534.534 m
495 544.641 l
S
1 J
492.41 533.239 m
493.705 535.181 496.295 535.181 497.59 533.239 c
S
0 J
495 553.063 m
495 565.86 l
495 565.86 m
517.677 574.364 l
517.677 583.153 l
517.677 599.592 m
517.677 604.75 l
517.677 612.01 m
517.677 620.266 l
495 565.86 m
472.323 574.364 l
472.323 642.396 l
489.36 648.786 l
495 658.472 m
495 663.941 l
513.692 643.891 m
500.64 648.786 l
S
[0.398 0.996 ]0 d
517.677 630.51 m
517.677 638.411 l
S
[]0 d
495 680.38 m
495 687.722 l
S
495 692.026 m
493.806 692.026 492.848 691.068 492.848 689.874 c
492.848 688.68 493.806 687.722 495 687.722 c
496.194 687.722 497.152 688.68 497.152 689.874 c
497.152 691.068 496.194 692.026 495 692.026 c
h
495 689.874 m
S
BT
8.9664 0 0 8.9664 469.92 519.9 Tm
0 g
(\(b\))Tj
/F18 1 Tf
1.5274 0 TD
(e)Tj
/F13 1 Tf
5.9776 0 0 5.9776 487.92 518.9401 Tm
-0.0607 Tc
(rec)Tj
/TT5 1 Tf
8.9664 0 0 8.9664 499.8 519.9 Tm
0 Tc
[(of)-254.3(Query)-254.3(Q2)]TJ
/TT11 1 Tf
9.9626 0 0 9.9626 320.76 494.7 Tm
[(Figure)-240.9(9.)-240.9(Relational)-228.9(representations)-240.9(of)-228.9(the)-228.9(re-)]TJ
0 -1.1925 TD
[(cur)12(sion)-277(bodies)]TJ
/F6 1 Tf
7.3765 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 399 481.38 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT11 1 Tf
9.9626 0 0 9.9626 412.8 482.82 Tm
0 Tc
[(of)-277(Queries)-277(Q1)-277(and)-265(Q2.)]TJ
/TT5 1 Tf
-10.431 -4.2037 TD
[(closed)-240.9(plan)-228.9(fragments)-228.9(with)-240.9(single)-240.9(entry)-228.9(and)-228.9(e)12(xit)-240.9(points)-240.9(\(en-)]TJ
0 -1.2045 TD
[(closed)-228.9(by)]TJ
ET
363.84 430.26 m
S
0.8 g
352.586 435.291 8.966 -8.966 re
f
0.5 G
0.398 w [2.989 1.993 ]0 d
352.586 435.291 m
352.586 426.325 l
375.002 426.325 l
375.002 435.291 l
h
375.002 426.325 m
S
BT
9.9626 0 0 9.9626 380.88 428.94 Tm
0 g
[(in)-240.9(Figure)-228.9(9\).)-289.1(These)-228.9(templates)-240.9(embody)-204.8(al-)]TJ
-7.227 -1.2045 TD
[(gebraic)-313.2(implementations)-301.1(of)-325.2(basic)-325.2(XQuery)-325.2(constructs,)]TJ
/TT7 1 Tf
21.9366 0 TD
-0.0121 Tc
[(e.)-12.1(g.)]TJ
/TT5 1 Tf
1.4198 0 TD
0 Tc
(,)Tj
-23.3564 -1.1925 TD
[(the)-265(semantics)-252.9(of)]TJ
/F3 1 Tf
6.781 0 TD
0.005 Tc
(for)Tj
/TT5 1 Tf
1.59 0 TD
0 Tc
[(-iteration)-228.9(or)-252.9(XP)12(ath)-265(location)-252.9(steps.)-361.3(As-)]TJ
-8.3709 -1.2045 TD
[(sessing)-192.7(the)-180.7(distrib)24.1(uti)24.1(vity)-168.6(of)-192.7(such)-180.7(plan)-180.7(templates)-180.7(is)-192.7(a)-192.7(one)-180.7(time)]TJ
T*
[(ef)24.1(fort.)-710.7(Once)-385.4(this)-385.4(has)-385.4(been)-373.4(done,)-409.5(whene)24.1(v)12(e)0(r)-361.3(a)-385.4(distrib)24.1(uti)24.1(v)12(e)]TJ
0 -1.1925 TD
[(template)-277(is)-313.2(encountered,)-265(the)]TJ
/F1 1 Tf
11.6121 0 TD
()Tj
/TT5 1 Tf
0.9636 0 TD
[(push)-277(up)-289.1(process)-289.1(may)-289.1(disre-)]TJ
-12.5757 -1.2045 TD
[(gard)-349.3(the)-361.4(template)60.2(s)-349.3(contents)-361.4(and)-349.3(instead)-361.4(perform)-337.3(a)-361.4(single)]TJ
/TT7 1 Tf
0 -1.1925 TD
[(big)-240.9(step)]TJ
/TT5 1 Tf
3.3705 0 TD
[(across)-240.9(the)-252.9(template)-228.9(\(see)-252.9(Figure)-228.9(7\(b\)\).)]TJ
-3.3705 -1.5658 TD
[(F)12(o)0(r)-252.9(the)-265(XQuery)-252.9(processor)36.1(,)-240.9(this)-265(suggests)-265(the)-265(follo)24.1(wing)-240.9(sim-)]TJ
0 -1.1925 TD
[(ple)-265(procedure)-228.9(as)-277(a)-277(replacement)-240.9(for)]TJ
/F9 1 Tf
14.0896 0 TD
-0.0052 Tc
(ds)Tj
/F11 1 Tf
6.9738 0 0 6.9738 460.2 316.38 Tm
0.0022 Tc
($x)Tj
/F8 1 Tf
9.9626 0 0 9.9626 469.68 317.82 Tm
0 Tc
(\()Tj
/F1 1 Tf
0.3975 0 TD
()Tj
/F8 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.6625 0 TD
[(\(Section)-252.9(3.2\))-252.9(to)]TJ
-17.4773 -1.2045 TD
[(assess)-265(the)-240.9(distrib)24.1(uti)24.1(vity)-228.9(of)]TJ
/F6 1 Tf
10.5935 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 419.4 304.38 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 430.44 305.82 Tm
0 Tc
(:)Tj
-11.3705 -1.8911 TD
[(Start)-240.9(with)-252.9(the)-240.9(algebraic)-228.9(plan)-240.9(for)]TJ
/F6 1 Tf
12.8733 0 TD
(e)Tj
/F13 1 Tf
6.9738 0 0 6.9738 450.72 285.54 Tm
-0.053 Tc
[(re)-7.6(c)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 464.28 286.98 Tm
0 Tc
[(with)-252.9(its)-252.9(input)]TJ
ET
0 G
0.398 w []0 d
522.48 287.994 m
522.48 293.516 l
S
1 J
519.89 286.699 m
521.185 288.642 523.775 288.642 525.07 286.699 c
S
BT
9.9626 0 0 9.9626 317.16 275.1 Tm
[(replaced)-228.9(by)]TJ
ET
0 J
376.39 280.844 m
S
BT
/F1 1 Tf
9.9626 0 0 9.9626 373.0691 278.0766 Tm
()Tj
ET
369.303 273.834 m
369.303 278.009 l
S
1 J
366.713 272.539 m
368.008 274.482 370.598 274.482 371.894 272.539 c
S
0 J
383.477 273.834 m
383.477 278.009 l
S
1 J
380.886 272.539 m
382.182 274.482 384.772 274.482 386.067 272.539 c
S
0 J
369.303 278.009 m
371.874 280.844 l
383.477 278.009 m
380.906 280.844 l
S
BT
/TT5 1 Tf
9.9626 0 0 9.9626 387.12 275.1 Tm
(;)Tj
/TT2 1 Tf
-7.0222 -1.2045 TD
(while)Tj
/TT5 1 Tf
2.5308 0 TD
[(not)-228.9(all)]TJ
/F1 1 Tf
2.7591 0 TD
()Tj
/TT5 1 Tf
0.9154 0 TD
[(ha)24.1(v)12(e)-240.9(reached)]TJ
ET
436.68 262.62 m
436.68 265.133 l
S
436.68 269.437 m
435.486 269.437 434.528 268.479 434.528 267.285 c
434.528 266.09 435.486 265.133 436.68 265.133 c
437.874 265.133 438.832 266.09 438.832 267.285 c
438.832 268.479 437.874 269.437 436.68 269.437 c
h
436.68 267.285 m
S
BT
/TT2 1 Tf
9.9626 0 0 9.9626 442.32 263.1 Tm
(do)Tj
ET
q
0.48 0 0 -21.36 322.068 259.608 cm
/Im1 Do
Q
BT
/TT5 1 Tf
9.9626 0 0 9.9626 332.52 252.78 Tm
[(Perform)-216.8(a)]TJ
/TT7 1 Tf
4.1905 0 TD
[(big)-240.9(step)]TJ
/TT5 1 Tf
3.3705 0 TD
[(or)-240.9(push)]TJ
/F1 1 Tf
3.204 0 TD
()Tj
/TT5 1 Tf
0.9154 0 TD
[(up)-240.9(through)-216.8(its)-252.9(parent)]TJ
-11.6803 -1.2045 TD
[(operator)36.1(,)-204.8(i)0(f)-252.9(possible.)-301.1(Otherwise)]TJ
/TT2 1 Tf
12.7937 0 TD
[(r)12(etur)12(n)]TJ
/F9 1 Tf
2.9816 0 TD
-0.004 Tc
[(fals)-4.6(e)]TJ
/TT5 1 Tf
2.0236 0 TD
0 Tc
(;)Tj
ET
q
5.04 0 0 -0.48 322.548 238.728 cm
/Im1 Do
Q
BT
/TT2 1 Tf
9.9626 0 0 9.9626 317.16 228.42 Tm
[(r)12(etur)12(n)]TJ
/F9 1 Tf
2.9816 0 TD
0.0052 Tc
[(tr)5.3(ue)]TJ
/TT5 1 Tf
1.8309 0 TD
0 Tc
(;)Tj
-5.6436 -1.602 TD
[(Figure)-289.1(9)-289.1(depicts)-289.1(the)-301.1(algebraic)-277(representations)-277(of)-289.1(the)-289.1(recur)24.1(-)]TJ
0 -1.2045 TD
[(sion)-409.5(bodies)-409.5(of)-409.5(the)-409.5(Queries)-409.5(Q1)-409.5(and)-409.5(Q2)-409.5(\(Section)-409.5(2\).)-807(F)12(o)0(r)]TJ
0 -1.1925 TD
[(Query)-385.4(Q1,)-421.6(to)-397.5(push)]TJ
/F1 1 Tf
8.2281 0 TD
()Tj
/TT5 1 Tf
1.072 0 TD
[(through)-361.4(from)]TJ
ET
463.44 189.594 m
463.44 195.116 l
S
1 J
460.85 188.299 m
462.145 190.242 464.735 190.242 466.03 188.299 c
S
BT
9.9626 0 0 9.9626 470.52 188.58 Tm
(to)Tj
ET
0 J
485.4 188.1 m
485.4 190.613 l
S
485.4 194.917 m
484.206 194.917 483.248 193.959 483.248 192.765 c
483.248 191.57 484.206 190.613 485.4 190.613 c
486.594 190.613 487.552 191.57 487.552 192.765 c
487.552 193.959 486.594 194.917 485.4 194.917 c
h
485.4 192.765 m
S
BT
9.9626 0 0 9.9626 488.52 188.58 Tm
[(,)-433.6(the)-397.5(distrib)24.1(u-)]TJ
-18.0314 -1.2045 TD
[(ti)24.1(vity)-349.3(check)-337.3(will)-349.3(succeed)-349.3(after)-337.3(it)-361.4(has)-349.3(performed)-313.2(tw)12(o)-361.3(steps)]TJ
T*
[(across)-385.4(the)-373.4(tw)12(o)-397.5(peripheral)-349.3(projections)-373.4(plus)-373.4(one)-385.4(intermedi-)]TJ
0 -1.1925 TD
(ate)Tj
/TT7 1 Tf
1.3944 0 TD
[(big)-228.9(step)]TJ
/TT5 1 Tf
3.3584 0 TD
[(across)-228.9(the)]TJ
/F3 1 Tf
4.1784 0 TD
0.005 Tc
(for)Tj
/TT5 1 Tf
1.59 0 TD
0 Tc
[(-iteration)-204.8(that)-228.9(implements)-228.9(the)-228.9(se-)]TJ
-10.5212 -1.2045 TD
[(mantics)-277(of)-289.1(the)]TJ
/F3 1 Tf
6.0082 0 TD
0.005 Tc
($x/id\()Tj
/F1 1 Tf
3.1799 0 TD
0 Tc
()Tj
/F3 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.7829 0 TD
[(lookup.)-409.5(F)12(o)0(r)-277(Query)-265(Q2,)]TJ
/F1 1 Tf
9.6168 0 TD
()Tj
/TT5 1 Tf
0.9636 0 TD
[(will)-289.1(be)]TJ
-20.8285 -1.1925 TD
[(pushed)-192.7(through)]TJ
/F6 1 Tf
6.3052 0 TD
()Tj
/F27 1 Tf
6.9738 0 0 6.9738 377.88 127.38 Tm
0.0047 Tc
[(it)9.8(e)12.3(r)]TJ
/F10 1 Tf
1.4972 0 TD
0 Tc
(,)Tj
/F27 1 Tf
0.3442 0 TD
0.0047 Tc
[(it)9.8(e)12.3(m)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 406.92 128.82 Tm
0 Tc
[(and)-204.8(then)-192.7(upw)12(ards)-192.7(the)-204.8(tw)12(o)-216.8(branches)]TJ
-9.8408 -1.2045 TD
[(of)-252.9(the)-265(D)36.1(A)36.1(G-shaped)-228.9(plan.)-337.3(In)-265(the)-252.9(right)-252.9(branch,)-240.9(the)-265(aggre)12(gate)]TJ
/F3 1 Tf
T*
0.005 Tc
(count)Tj
/F27 1 Tf
6.9738 0 0 6.9738 335.04 103.02 Tm
0.0047 Tc
[(it)9.8(e)12.3(m)]TJ
/F10 1 Tf
1.9446 0 TD
0 Tc
(/)Tj
/F27 1 Tf
0.5851 0 TD
0.0047 Tc
[(it)9.8(e)12.3(r)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 366.48 104.82 Tm
0 Tc
[(blocks)-277(the)-277(process)-277(\(T)84.3(able)-277(1\))-289.1(which)-265(indicates)]TJ
-5.7816 -1.1925 TD
[(that)-289.1(the)-301.1(processor)-277(may)]TJ
/TT7 1 Tf
9.4312 0 TD
(not)Tj
/TT5 1 Tf
1.579 0 TD
[(use)-301.1(algorithm)]TJ
/TT7 1 Tf
5.7873 0 TD
(Delta)Tj
/TT5 1 Tf
2.5228 0 TD
[(\(or)-289.1(the)]TJ
/F6 1 Tf
2.9659 0 TD
()Tj
/F7 1 Tf
6.9738 0 0 6.9738 538.08 96.54 Tm
()Tj
/TT5 1 Tf
9.9626 0 0 9.9626 308.88 80.94 Tm
[(v)24.1(ariant)-228.9(of)-240.9(the)]TJ
/TT8 1 Tf
5.5176 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(x)12(e)0(d)-240.9(point)-228.9(operator\))-216.8(to)-252.9(e)24.1(v)24.1(aluate)-228.9(Query)-228.9(Q2.)]TJ
-7.4589 -2.9992 TD
(7)Tj
ET
endstream
endobj
65 0 obj
<<
/ProcSet [/PDF /Text /ImageB ]
/Font <<
/F1 4 0 R
/F3 6 0 R
/F4 7 0 R
/F6 22 0 R
/F7 23 0 R
/F8 24 0 R
/F9 25 0 R
/F10 26 0 R
/F11 27 0 R
/F13 29 0 R
/F17 39 0 R
/F18 40 0 R
/F19 41 0 R
/F21 49 0 R
/F22 53 0 R
/F25 56 0 R
/F27 58 0 R
/F28 59 0 R
/F30 61 0 R
/F32 66 0 R
/TT2 9 0 R
/TT5 11 0 R
/TT7 12 0 R
/TT8 13 0 R
/TT11 15 0 R
>>
/XObject <<
/Im1 33 0 R
>>
/ExtGState <<
/GS1 17 0 R
>>
>>
endobj
68 0 obj
<<
/Length 16171
>>
stream
BT
/TT2 1 Tf
9.9626 0 0 9.9626 50.16 709.98 Tm
0 g
/GS1 gs
0 Tc
0 Tw
[(Algebraic)-421.6(vs.)-433.6(Syntactic)-421.6(A)24.1(ppr)12(oximation.)]TJ
/TT5 1 Tf
18.2589 0 TD
[(Compared)-421.6(to)]TJ
-18.2589 -1.2045 TD
[(the)-228.9(syntactic)-228.9(approximation)]TJ
/F9 1 Tf
11.2583 0 TD
-0.0052 Tc
(ds)Tj
/F8 1 Tf
1.072 0 TD
0 Tc
(\()Tj
/F1 1 Tf
0.3975 0 TD
()Tj
/F8 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.3854 0 TD
[(,)-240.9(this)-228.9(algebraic)-216.8(account)-216.8(of)]TJ
-13.3903 -1.1925 TD
[(distrib)24.1(uti)24.1(vity)-373.4(dra)12(ws)-385.4(its)-397.5(conciseness)-385.4(from)-373.4(the)-397.5(f)12(act)-385.4(that)-397.5(the)]TJ
0 -1.2045 TD
[(rather)-313.2(in)36.1(v)24.1(olv)12(ed)-301.1(XQuery)-325.2(semantics)-325.2(and)-325.2(substantial)-325.2(number)]TJ
T*
[(of)-240.9(b)24.1(uilt-in)-252.9(functions)-228.9(ne)24.1(v)12(ertheless)-240.9(map)-240.9(to)-252.9(a)-265(small)-252.9(number)-228.9(of)]TJ
0 -1.1925 TD
[(algebraic)-265(primiti)24.1(v)12(e)0(s)-265(\(gi)24.1(v)12(e)0(n)-265(suitable)-289.1(relational)-265(encodings)-265(of)]TJ
0 -1.2045 TD
[(the)-301.1(XDM\).)-301.1(Further)36.1(,)-313.2(for)-301.1(these)-301.1(primiti)24.1(v)12(es,)-313.2(the)-301.1(algebraic)-301.1(dis-)]TJ
0 -1.1925 TD
[(trib)24.1(uti)24.1(vity)-228.9(property)-216.8(is)-252.9(readily)-228.9(decided.)]TJ
1.1925 -1.2045 TD
[(T)84.3(o)-252.9(mak)12(e)-252.9(this)-252.9(point,)-240.9(consider)-240.9(a)-252.9(slight)-252.9(yet)-252.9(equi)24.1(v)24.1(alent)-228.9(v)24.1(ari-)]TJ
-1.1925 -1.2045 TD
[(ation)-265(of)-265(Query)-252.9(Q1)-277(in)-277(which)-252.9(v)24.1(ariable)]TJ
/F3 1 Tf
14.8264 0 TD
0.005 Tc
($x)Tj
/TT5 1 Tf
1.325 0 TD
0 Tc
[(no)24.1(w)-265(occurs)-265(free)-265(in)]TJ
-16.1514 -1.1925 TD
[(the)-240.9(ar)12(gument)-216.8(of)-240.9(function)]TJ
/F3 1 Tf
10.067 0 TD
0.005 Tc
(id\()Tj
/F1 1 Tf
1.59 0 TD
0 Tc
()Tj
/F3 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.53 0 TD
(:)Tj
/F3 1 Tf
-11.0667 -1.9151 TD
0.005 Tc
[(with)-505.9($x)-517.9(seeded)-493.8(by)-517.9(doc)-156.6(\("curriculum.xml")12.1(\))]TJ
10.5032 -1.1925 TD
[(/course[@code="c1)12.1("])]TJ
-10.5032 -1.2045 TD
[(recurse)-493.8(id)-168.6(\($x/prerequisite)12.1(s/)12.1(pre)12.1(_c)12.1(od)12.1(e\))]TJ
/TT5 1 Tf
20.6574 0 TD
0 Tc
(.)Tj
-22.0546 -1.9031 TD
[(If)-433.6(we)-445.7(unfold)-421.6(the)-433.6(implementation)-409.5(of)-445.7(the)-433.6(XQuery)-433.6(b)24.1(uilt-in)]TJ
0 -1.2045 TD
(function)Tj
/F3 1 Tf
3.7782 0 TD
0.005 Tc
(id\()Tj
/F1 1 Tf
1.59 0 TD
0 Tc
()Tj
/F3 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.9997 0 TD
[(\(ef)24.1(fecti)24.1(v)12(ely)60.2(,)-493.8(this)-493.8(e)12(xpansion)-445.7(is)-493.8(performed)]TJ
-6.6449 -1.1925 TD
[(when)-228.9(Rule)-252.9(F)]TJ
7.9701 0 0 7.9701 101.3761 504.66 Tm
0.0602 Tc
(UN)Tj
9.9626 0 0 9.9626 113.8476 504.66 Tm
0 Tc
(C)Tj
7.9701 0 0 7.9701 120.9726 504.66 Tm
0.0602 Tc
(ALL)Tj
9.9626 0 0 9.9626 140.1853 504.66 Tm
0 Tc
[(recursi)24.1(v)12(ely)-216.8(in)36.1(v)24.1(o)0(k)12(e)0(s)]TJ
/F9 1 Tf
7.8784 0 TD
-0.0052 Tc
(ds)Tj
/F11 1 Tf
6.9738 0 0 6.9738 229.32 503.22 Tm
0.0022 Tc
($x)Tj
/F8 1 Tf
9.9626 0 0 9.9626 238.92 504.66 Tm
0 Tc
(\()Tj
/F1 1 Tf
0.3854 0 TD
()Tj
/F8 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.6384 0 TD
[(to)-228.9(assess)]TJ
-20.2477 -1.2045 TD
[(the)-240.9(distrib)24.1(uti)24.1(vity)-228.9(of)-240.9(the)-240.9(function)-216.8(body)-228.9(of)]TJ
/F3 1 Tf
16.1988 0 TD
0.005 Tc
(id\()Tj
/F1 1 Tf
1.59 0 TD
0 Tc
()Tj
/F3 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.53 0 TD
[(\),)-228.9(we)-240.9(obtain)]TJ
/F3 1 Tf
-18.0297 -1.9031 TD
0.005 Tc
[(with)-505.9($x)-517.9(seeded)-493.8(by)-505.9(doc\("curriculum.x)12.1(ml")12.1(\))]TJ
10.5032 -1.2045 TD
[(/course[@code=")12.1(c1")12.1(])]TJ
-10.5032 -1.2045 TD
(recurse)Tj
1.0479 -1.1925 TD
[(for)-505.9($c)-517.9(in)-517.9(doc\("curriculum.)12.1(xm)12.1(l"\))12.1(/c)12.1(our)12.1(se)]TJ
0 -1.2045 TD
[(where)-505.9($c/@code)-481.8(=)-517.9($x/prerequisite/)12.1(pre)12.1(_c)12.1(od)12.1(e)]TJ
T*
[(return)-493.8($c)]TJ
/TT5 1 Tf
5.7696 0 TD
0 Tc
(.)Tj
-7.3836 -2.0958 TD
[(The)-385.4(syntactic)-385.4(approximation)-349.3(will)]TJ
/TT8 1 Tf
14.0143 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(ag)-385.4(the)-397.5(recursion)-361.4(body)]TJ
-14.5704 -1.1925 TD
[(as)-361.4(non-distrib)24.1(uti)24.1(v)12(e)-313.2(because)-349.3(of)-349.3(the)-361.3(general)-337.3(comparison)-325.2(\()]TJ
/F3 1 Tf
22.7181 0 TD
(=)Tj
/TT5 1 Tf
0.53 0 TD
(\))Tj
-23.2481 -1.2045 TD
[(in)-289.1(the)]TJ
/F3 1 Tf
2.5777 0 TD
0.005 Tc
(where)Tj
/TT5 1 Tf
2.9149 0 TD
0 Tc
[(clause)-289.1(\(Section)-289.1(3.2\).)-421.6(While)-289.1(the)-289.1(algebraic)-277(ap-)]TJ
-5.4926 -1.2045 TD
[(proach)-228.9(w)12(ould)-252.9(be)-252.9(unaf)24.1(fected)-228.9(by)-252.9(the)-265(v)24.1(ariation,)-240.9(the)-252.9(rule)-252.9(set)-265(of)]TJ
0 -1.1925 TD
[(Figure)-265(5)-289.1(w)12(ould)-265(need)-277(a)-289.1(speci)]TJ
/TT8 1 Tf
11.3702 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(c)-289.1(rule)-277(for)]TJ
/F3 1 Tf
3.9957 0 TD
0.005 Tc
(id\()Tj
/F1 1 Tf
1.59 0 TD
0 Tc
()Tj
/F3 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.807 0 TD
[(to)-277(be)-289.1(able)-277(to)]TJ
-18.596 -1.2045 TD
[(infer)-228.9(its)-252.9(actual)-240.9(distrib)24.1(uti)24.1(vity)60.2(.)]TJ
/TT2 1 Tf
11.9552 0 0 11.9552 50.16 309.66 Tm
[(5)10(.)-250.9(Practical)-250.9(Impact)-250.9(of)-250.9(Distrib)20.1(uti)10(vity)-250.9(and)]TJ
/TT14 1 Tf
17.3249 0 TD
(Delta)Tj
/TT5 1 Tf
9.9626 0 0 9.9626 62.04 284.22 Tm
[(Recasting)-373.4(a)-373.4(recursi)24.1(v)12(e)-349.3(XQuery)-349.3(query)-349.3(as)-373.4(an)-373.4(in)]TJ
/TT8 1 Tf
18.6099 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
(ationary)Tj
/TT8 1 Tf
-20.3585 -1.2045 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(x)12(e)0(d)-289.1(point)-289.1(computation)-277(imposes)-301.1(restrictions.)-469.8(Such)-301.1(recast-)]TJ
-0.5562 -1.2045 TD
[(ing,)-469.8(ho)24.1(we)24.1(v)12(e)0(r)36.1(,)-445.7(also)-433.6(puts)-433.6(the)-433.6(query)-409.5(processor)-421.6(into)-421.6(control)]TJ
0 -1.1925 TD
[(since)-265(the)-277(applicability)-252.9(of)-277(a)-277(promising)-252.9(optimization,)-252.9(trading)]TJ
/TT7 1 Tf
0 -1.2045 TD
(Na)Tj
1.1443 -0.0121 TD
()Tj
/TT9 1 Tf
0.0241 0.0121 TD
()Tj
/TT7 1 Tf
0.2778 0 TD
(ve)Tj
/TT5 1 Tf
1.2129 0 TD
(for)Tj
/TT7 1 Tf
1.4792 0 TD
(Delta)Tj
/TT5 1 Tf
2.2217 0 TD
[(,)-349.3(becomes)-313.2(ef)24.1(fecti)24.1(v)12(ely)-301.1(decidable.)-530(This)-325.2(sec-)]TJ
-6.36 -1.1925 TD
[(tion)-252.9(pro)12(vides)-240.9(the)-265(e)24.1(vidence)-240.9(that)-265(signi)]TJ
/TT8 1 Tf
14.4473 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(cant)-252.9(gains)-252.9(can)-265(indeed)]TJ
-15.0035 -1.2045 TD
[(be)-240.9(realized,)-228.9(much)-228.9(lik)12(e)-252.9(i)0(n)-240.9(the)-240.9(relational)-240.9(domain.)]TJ
1.1925 -1.2045 TD
[(T)84.3(o)-674.5(quantify)-650.4(the)-674.5(impact,)-770.9(we)-674.5(implemented)-650.4(the)-674.5(tw)12(o)]TJ
/TT8 1 Tf
-1.1925 -1.1925 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(x)12(e)0(d)-602.3(point)-590.2(operator)-590.2(v)24.1(ariants)]TJ
/F6 1 Tf
12.3454 0 TD
()Tj
/TT5 1 Tf
1.2166 0 TD
(and)Tj
/F6 1 Tf
2.0461 0 TD
()Tj
/F7 1 Tf
6.9738 0 0 6.9738 218.04 192.18 Tm
()Tj
/TT5 1 Tf
9.9626 0 0 9.9626 231.24 188.58 Tm
[(\(Section)-602.3(4.1\))]TJ
-18.1759 -1.2045 TD
(in)Tj
/TT7 1 Tf
1.2837 0 TD
[(MonetDB/XQuery)-481.8(0.18)]TJ
/TT5 1 Tf
9.989 0 TD
[([8],)-566.1(an)-493.8(ef)]TJ
/TT8 1 Tf
4.1726 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(cient)-505.9(and)-493.8(scalable)]TJ
-16.0015 -1.2045 TD
[(XQuery)-397.5(processor)-409.5(that)-421.6(consequently)-385.4(implements)-409.5(the)-409.5(Re-)]TJ
0 -1.1925 TD
[(lational)-337.3(XQuery)-325.2(approach)-313.2(\(Section)-337.3(4\).)-590.2(Its)-349.3(algebraic)-325.2(com-)]TJ
0 -1.2045 TD
[(piler)-433.6(front-end)]TJ
/TT7 1 Tf
6.4084 0 TD
[(P)84.3(ath)]TJ
/TT9 1 Tf
1.8044 0 TD
()Tj
/TT7 1 Tf
0.5 0 TD
(nder)Tj
/TT5 1 Tf
2.2787 0 TD
[(has)-445.7(been)-433.6(enhanced)-421.6(\()]TJ
/TT7 1 Tf
8.63 0 TD
(i\))Tj
/TT5 1 Tf
1.0565 0 TD
[(to)-445.7(pro-)]TJ
-20.6779 -1.1925 TD
[(cess)-397.5(the)-385.4(syntactic)-385.4(form)]TJ
/F3 1 Tf
9.9275 0 TD
0.005 Tc
(with)Tj
/F1 1 Tf
2.2645 0 TD
0.1679 Tc
()Tj
/F3 1 Tf
1.337 0 TD
0.005 Tc
[(seeded)-493.8(by)]TJ
/F1 1 Tf
4.8903 0 TD
0.1679 Tc
()Tj
/F3 1 Tf
1.325 0 TD
0.005 Tc
(recurse)Tj
/TT5 1 Tf
3.6858 0 TD
0 Tc
(,)Tj
-23.4301 -1.2045 TD
[(and)-240.9(\()]TJ
/TT7 1 Tf
2.0178 0 TD
(ii\))Tj
/TT5 1 Tf
1.1296 0 TD
[(to)-252.9(implement)-240.9(the)-240.9(algebraic)-240.9(distrib)24.1(uti)24.1(vity)-240.9(check.)-301.1(All)]TJ
-3.1473 -1.2045 TD
[(queries)-216.8(in)-228.9(this)-240.9(section)-228.9(were)-216.8(recognized)-204.8(as)-240.9(being)-216.8(distrib)24.1(uti)24.1(v)12(e)]TJ
0 -1.1925 TD
(by)Tj
/TT7 1 Tf
1.3011 0 TD
[(P)84.3(ath)]TJ
/TT9 1 Tf
1.8044 0 TD
()Tj
/TT7 1 Tf
0.5 0 TD
(nder)Tj
/TT5 1 Tf
1.833 0 TD
[(.)-481.8(T)84.3(o)-313.2(demonstrate)-289.1(that)-313.2(an)12(y)-301.1(XQuery)-301.1(processor)]TJ
-5.4385 -1.2045 TD
[(can)-180.7(bene)]TJ
/TT8 1 Tf
3.4561 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(t)-180.7(from)-180.7(optimized)-180.7(IFP)-192.7(e)24.1(v)24.1(aluation)-168.6(in)-192.7(the)-180.7(presence)-180.7(of)]TJ
/F4 1 Tf
8.9664 0 0 8.9664 308.88 713.7001 Tm
-0.003 Tc
[(declare)-548.7(variable)-548.7($doc)-535.3(:=)-535.3(doc\("auction.xml"\);)]TJ
0 -2.1949 TD
[(declare)-548.7(function)-548.7(bidder)-187.3(\($in)-535.3(as)-535.3(node\(\)*\))-548.7(as)-535.3(node\(\)*)]TJ
0 -1.0974 TD
[({)-521.9(for)-535.3($id)-535.3(in)-535.3($in/@id)]TJ
1.0439 -1.1108 TD
[(let)-535.3($b)-535.3(:=)-535.3($doc//open_auction[seller/@pers)-13.3(on)-602.2(=)-535.3($id])]TJ
6.3036 -1.0974 TD
(/bidder/personref)Tj
-6.3036 -1.0974 TD
[(return)-548.7($doc//people/person[@id)-588.8(=)-535.3($b/@person])]TJ
-1.0439 -1.0974 TD
(};)Tj
0 -2.2083 TD
[(for)-535.3($p)-521.9(in)-535.3($doc//people/person)]TJ
0 -1.0974 TD
[(return)-535.3()]TJ
4.2024 -1.0974 TD
[({)-521.9($p/@id)-548.7(})]TJ
T*
[({)-521.9(data)-535.3(\(\(with)-548.7($x)-535.3(seeded)-535.3(by)-535.3($p)]TJ
4.7243 -1.0974 TD
[(recurse)-548.7(bidder)-187.3(\($x\)\)/@id\))-548.7(})]TJ
-5.2597 -1.1108 TD
()Tj
/TT11 1 Tf
9.9626 0 0 9.9626 334.2 553.7401 Tm
0 Tc
[(Figure)-277(10.)-277(XMark)-289.1(bid)12(der)-277(netw)24.1(ork)-277(quer)-12(y)84.3(.)]TJ
/TT5 1 Tf
-2.5415 -3.1678 TD
[(distrib)24.1(uti)24.1(vity)60.2(,)-301.1(w)0(e)-301.1(also)-313.2(performed)-265(the)-301.1(transition)-301.1(from)]TJ
/TT7 1 Tf
21.2646 0 TD
(Na)Tj
1.2595 -0.0121 TD
()Tj
/TT9 1 Tf
0.0241 0.0121 TD
()Tj
/TT7 1 Tf
0.2778 0 TD
(ve)Tj
/TT5 1 Tf
-22.8261 -1.2045 TD
(to)Tj
/TT7 1 Tf
1.091 0 TD
(Delta)Tj
/TT5 1 Tf
2.5348 0 TD
[(on)-301.1(the)-313.2(XQuery)-301.1(source)-301.1(le)24.1(v)12(e)0(l)-301.1(and)-301.1(let)]TJ
/TT7 1 Tf
14.5473 0 TD
[(Saxon-SA)-277(8.9)]TJ
/TT5 1 Tf
-18.1732 -1.1925 TD
[([20)12(])-204.8(process)-204.8(the)-216.8(resulting)-204.8(user)24.1(-de)]TJ
/TT8 1 Tf
13.1241 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(ned)-192.7(recursi)24.1(v)12(e)-192.7(queries)-204.8(\(cf.)]TJ
-13.6802 -1.2045 TD
[(Figures)-397.5(2)-397.5(and)-397.5(4\).)-770.9(All)-397.5(e)12(xperiments)-385.4(were)-397.5(conducted)-373.4(on)-397.5(a)]TJ
T*
[(Linux-based)-313.2(host)-349.3(\(64)-144.5(bit\),)-373.4(with)-349.3(tw)12(o)-337.3(3.2)-156.6(GHz)-349.3(Intel)-337.3(Xeon)]TJ
4.9813 0 0 4.9813 539.04 478.14 Tm
(R)Tj
/F14 1 Tf
6.9738 0 0 6.9738 536.76 477.9 Tm
()Tj
/TT5 1 Tf
9.9626 0 0 9.9626 308.88 462.42 Tm
[(CPUs,)-337.3(8)-168.6(G)0(B)-325.2(o)0(f)-301.1(primary)-301.1(and)-301.1(280)-156.6(GB)-313.2(SCSI)-325.2(disk-based)-301.1(sec-)]TJ
T*
[(ondary)-216.8(memory)60.2(.)]TJ
1.1925 -1.2045 TD
[(T)84.3(able)-505.9(2)-505.9(summarizes)-493.8(our)-493.8(observ)24.1(ations)-481.8(for)-493.8(four)-493.8(query)]TJ
-1.1925 -1.1925 TD
[(types,)-277(chosen)-265(to)-289.1(inspect)-277(the)-277(systems)-277(beha)24.1(vior)-252.9(for)-277(gro)24.1(wing)]TJ
0 -1.2045 TD
[(input)-168.6(XML)-192.7(instance)-180.7(sizes)-192.7(and)-180.7(v)24.1(arying)-156.6(result)-180.7(sizes)-204.8(at)-180.7(each)-180.7(re-)]TJ
T*
[(cursion)-252.9(le)24.1(v)12(e)0(l)-252.9(\(the)-252.9(maximum)-240.9(recursion)-240.9(depth)-252.9(ranged)-240.9(from)-252.9(5)]TJ
0 -1.1925 TD
[(to)-240.9(33\).)]TJ
/TT2 1 Tf
0 -2.6499 TD
[(XMark)-265(Bidder)-289.1(Netw)12(ork.)]TJ
/TT5 1 Tf
11.6117 0 TD
[(T)84.3(o)-265(assess)-289.1(scalability)60.2(,)-252.9(w)0(e)-277(com-)]TJ
-11.6117 -1.2045 TD
[(puted)-397.5(a)-409.5(bidder)-397.5(netw)12(orkrecursi)24.1(v)12(ely)-361.4(connecting)-385.4(the)-409.5(sell-)]TJ
T*
[(ers)-301.1(and)-289.1(bidders)-277(of)-289.1(auctions)-289.1(\(Figure)-289.1(10\)o)12(v)12(e)0(r)-252.9(XMark)-289.1([25)12(])]TJ
0 -1.1925 TD
[(XML)-252.9(data)-240.9(of)-252.9(increasing)-228.9(size)-265(\(from)-228.9(scale)-252.9(f)12(actor)-240.9(0.01,)-240.9(small,)]TJ
0 -1.2045 TD
[(to)-301.1(0.33,)-289.1(huge\).)-457.7(If)]TJ
/TT7 1 Tf
7.3077 0 TD
(Delta)Tj
/TT5 1 Tf
2.5228 0 TD
[(is)-313.2(used)-301.1(to)-301.1(compute)-277(the)-301.1(IFP)-301.1(of)-301.1(this)]TJ
-9.8305 -1.1925 TD
[(netw)12(ork,)]TJ
/TT7 1 Tf
3.7437 0 TD
(MonetDB/XQuery)Tj
/TT5 1 Tf
7.5042 0 TD
[(\(2.2)-240.9(to)-252.9(3.3)-240.9(times)-252.9(f)12(aster\))-240.9(as)-265(well)]TJ
-11.2479 -1.2045 TD
(as)Tj
/TT7 1 Tf
1.0739 0 TD
(Saxon)Tj
/TT5 1 Tf
2.6486 0 TD
[(\(1.2)-228.9(to)-228.9(2.7)-216.8(times)-240.9(f)12(aster\))-228.9(bene)]TJ
/TT8 1 Tf
11.351 0 TD
()Tj
/TT5 1 Tf
0.5561 0 TD
[(t)-228.9(signi)]TJ
/TT8 1 Tf
2.4515 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(cantly)60.2(.)-277(Most)]TJ
-18.6373 -1.2045 TD
[(importantly)60.2(,)-301.1(note)-313.2(that)-313.2(the)-325.2(number)-289.1(of)-313.2(nodes)-313.2(in)-313.2(the)-313.2(netw)12(ork)]TJ
0 -1.1925 TD
[(gro)24.1(ws)-361.4(quadratically)-337.3(with)-373.4(the)-373.4(input)-361.4(document)-337.3(size.)-686.6(Algo-)]TJ
0 -1.2045 TD
(rithm)Tj
/TT7 1 Tf
2.4676 0 TD
(Delta)Tj
/TT5 1 Tf
2.5228 0 TD
[(feeds)-313.2(signi)]TJ
/TT8 1 Tf
4.3679 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(cantly)-289.1(less)-325.2(nodes)-301.1(back)-301.1(in)-301.1(each)-301.1(re-)]TJ
-9.9144 -1.2045 TD
[(cursion)-385.4(le)24.1(v)12(e)0(l)-397.5(which)-397.5(positi)24.1(v)12(ely)-385.4(impacts)-409.5(the)-397.5(comple)12(xity)-373.4(of)]TJ
0 -1.1925 TD
[(the)-349.3(v)24.1(alue-based)-325.2(join)-349.3(inside)-349.3(recursion)-337.3(payload)]TJ
/F3 1 Tf
18.8512 0 TD
0.005 Tc
(bidder\()Tj
/F1 1 Tf
3.7099 0 TD
0 Tc
()Tj
/F3 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.53 0 TD
(:)Tj
-23.3681 -1.2045 TD
[(for)-277(the)-289.1(huge)-277(netw)12(ork,)]TJ
/TT7 1 Tf
8.9665 0 TD
(Delta)Tj
/TT5 1 Tf
2.5108 0 TD
[(e)12(xactly)-277(feeds)-289.1(those)-277(10)-289.1(million)]TJ
-11.4773 -1.1925 TD
[(nodes)-337.3(into)]TJ
/F3 1 Tf
4.5632 0 TD
0.005 Tc
(bidder\()Tj
/F1 1 Tf
3.7099 0 TD
0 Tc
()Tj
/F3 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.8432 0 TD
[(that)-337.3(mak)12(e)-337.3(u)0(p)-349.3(the)-337.3(result)]TJ
/TT7 1 Tf
10.4574 0 TD
(Na)Tj
1.216 -0.012 TD
()Tj
/TT9 1 Tf
0.0241 0.012 TD
()Tj
/TT7 1 Tf
0.2778 0 TD
(ve)Tj
/TT5 1 Tf
1.225 0 TD
(re-)Tj
-22.5936 -1.2045 TD
[(peatedly)-252.9(re)24.1(visits)-265(intermediate)-252.9(results)-265(and)-265(processes)-265(9)-265(times)]TJ
T*
[(as)-252.9(man)12(y)-228.9(nodes.)]TJ
/TT2 1 Tf
0 -2.6499 TD
[(Romeo)-277(and)-277(J)12(uliet)-277(Dialogs.)]TJ
/TT5 1 Tf
12.2237 0 TD
[(F)12(a)0(r)-277(less)-289.1(nodes)-265(are)-277(processed)]TJ
-12.2237 -1.1925 TD
[(by)-469.8(a)-481.8(recursi)24.1(v)12(e)-469.8(e)12(xpression)-457.7(that)-481.8(queries)-469.7(XML)-469.8(markup)-457.7(of)]TJ
0 -1.2045 TD
[(Shak)12(espeare)60.2(s)-421.6(Romeo)-433.6(and)-433.6(Juliet)]TJ
6.9738 0 0 6.9738 443.28 138.18 Tm
(4)Tj
9.9626 0 0 9.9626 451.56 134.58 Tm
[(to)-445.7(determine)-421.6(the)-433.6(max-)]TJ
-14.3215 -1.2045 TD
[(imum)-457.7(length)-457.7(of)-457.7(an)12(y)-457.7(uninterrupted)-421.6(dialog.)-963.6(Seeded)-457.7(with)]TJ
/F3 1 Tf
0 -1.1925 TD
0.005 Tc
(SPEECH)Tj
/TT5 1 Tf
3.6497 0 TD
0 Tc
[(element)-481.8(nodes,)-542(each)-481.8(le)24.1(v)12(e)0(l)-481.8(o)0(f)-493.8(the)-493.8(recursion)-469.8(e)12(x)0(-)]TJ
-3.6497 -1.2045 TD
[(pands)-325.2(the)-325.2(currently)-313.2(considered)-313.2(dialog)-325.2(sequences)-325.2(by)-325.2(a)-337.3(sin-)]TJ
ET
q
94.56 0 0 -0.48 308.868 90.888 cm
/Im1 Do
Q
BT
5.9776 0 0 5.9776 319.68 83.7 Tm
(4)Tj
/F11 1 Tf
7.9701 0 0 7.9701 323.16 80.94 Tm
-0.0042 Tc
[(http://www.ibiblio.org)-15(/xm)-15(l/ex)-15(amp)-15(les/)-15(sha)-15(k)0.1(esp)-15(ear)-15(e)0.1(/)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 295.08 51.06 Tm
0 Tc
(8)Tj
ET
endstream
endobj
69 0 obj
<<
/ProcSet [/PDF /Text /ImageB ]
/Font <<
/F1 4 0 R
/F3 6 0 R
/F4 7 0 R
/F6 22 0 R
/F7 23 0 R
/F8 24 0 R
/F9 25 0 R
/F11 27 0 R
/F14 30 0 R
/TT2 9 0 R
/TT5 11 0 R
/TT7 12 0 R
/TT8 13 0 R
/TT9 14 0 R
/TT11 15 0 R
/TT14 31 0 R
>>
/XObject <<
/Im1 33 0 R
>>
/ExtGState <<
/GS1 17 0 R
>>
>>
endobj
71 0 obj
<<
/Length 16421
>>
stream
0 g
/GS1 gs
q
490.44 0 0 -0.84 52.428 719.928 cm
/Im1 Do
Q
BT
/TT2 1 Tf
8.9664 0 0 8.9664 56.88 709.7401 Tm
0 Tc
0 Tw
(Query)Tj
/TT14 1 Tf
13.6157 0 TD
[(MonetDB/XQuery)-5246.3(Saxon-SA)-240.9(8.9)]TJ
/TT2 1 Tf
22.5838 0 TD
[(T)93.7(otal)-254.3(#)-254.3(o)0(f)-254.3(Nodes)-254.3(F)26.8(e)0(d)-240.9(Back)-2020.9(Recursion)]TJ
/TT7 1 Tf
-22.8162 -1.2179 TD
[(Na)26.8()]TJ
/TT9 1 Tf
1.1654 0 TD
()Tj
/TT7 1 Tf
0.2778 0 TD
[(ve)-3158.5(Delta)-4403.1(Na)26.8()]TJ
/TT9 1 Tf
11.8364 0 TD
()Tj
/TT7 1 Tf
0.2778 0 TD
[(ve)-3158.5(Delta)-4081.9(Na)26.8()]TJ
/TT9 1 Tf
11.5152 0 TD
()Tj
/TT7 1 Tf
0.2778 0 TD
[(ve)-3800.9(Delta)]TJ
/TT2 1 Tf
11.4873 0 TD
(Depth)Tj
ET
q
92.76 0 0 -0.36 57.348 693.888 cm
/Im1 Do
Q
q
87.48 0 0 -0.36 169.068 693.888 cm
/Im1 Do
Q
q
87.48 0 0 -0.36 275.508 693.888 cm
/Im1 Do
Q
q
99 0 0 -0.36 381.948 693.888 cm
/Im1 Do
Q
q
38.04 0 0 -0.36 499.908 693.888 cm
/Im1 Do
Q
BT
/TT5 1 Tf
8.9664 0 0 8.9664 56.88 682.98 Tm
[(Bidder)-267.7(netw)13.4(ork)-254.3(\(small\))-4389.7(362)-254.3(ms)-2770.4(165)-267.7(ms)-3024.6(2,307)-267.7(ms)-1512.3(1,872)-267.7(ms)-3774.1(40,254)-4403.1(9,319)-5366.7(10)]TJ
0 -1.2179 TD
[(Bidder)-267.7(netw)13.4(ork)-254.3(\(medium\))-2542.8(5,010)-254.3(ms)-2020.9(1,995)-267.7(ms)-2516.1(15,027)-281.1(ms)-1512.3(7,284)-267.7(ms)-3265.5(683,225)-3412.8(122,532)-5380.1(16)]TJ
T*
[(Bidder)-267.7(netw)13.4(ork)-254.3(\(lar)13.4(ge\))-3319.1(40,785)-267.7(ms)-1525.7(13,805)-267.7(ms)-2020.9(123,316)-281(ms)-1003.8(52,436)-281(ms)-2516.1(5,694,390)-3412.8(961,356)-5380.1(15)]TJ
0 -1.2313 TD
[(Bidder)-267.7(netw)13.4(ork)-254.3(\(huge\))-4122.1(9)-254.3(m)-254.3(4)0(6)-267.7(s)-1003.8(176,890)-281(ms)-2770.4(32)-267.7(m)-240.9(4)0(0)-267.7(s)-1258(12)-254.3(m)-254.3(0)0(4)-267.7(s)-2020.9(87,528,919)-2663.3(9,799,342)-5380.1(24)]TJ
0 -1.6595 TD
[(Romeo)-267.7(and)-267.7(Juliet)-5955.6(6,795)-254.3(ms)-2020.9(1,260)-267.7(ms)-3024.6(1,150)-267.7(ms)-2261.8(818)-267.7(ms)-3774.1(37,841)-4403.1(5,638)-5366.7(33)]TJ
0 -1.6729 TD
[(Curriculum)-267.7(\(medium\))-4911.7(183)-254.3(ms)-2770.4(135)-267.7(ms)-3024.6(1,308)-267.7(ms)-1512.3(1,040)-267.7(ms)-3774.1(12,301)-4403.1(3,044)-5366.7(18)]TJ
0 -1.2313 TD
[(Curriculum)-267.7(\(lar)13.4(ge\))-5447(1,466)-254.3(ms)-2770.3(646)-267.7(ms)-3024.6(3,485)-267.7(ms)-1512.3(2,176)-267.7(ms)-3265.5(127,992)-3907.9(19,780)-5380.1(35)]TJ
0 -1.6729 TD
[(Hospital)-254.3(\(medium\))-6143(734)-254.3(ms)-2770.3(497)-267.7(ms)-3024.6(1,301)-267.7(ms)-1512.3(1,290)-267.7(ms)-3774.1(99,381)-3894.5(50,000)-5875.3(5)]TJ
ET
q
490.44 0 0 -0.84 52.428 589.248 cm
/Im1 Do
Q
BT
/TT11 1 Tf
9.9626 0 0 9.9626 62.52 570.0601 Tm
0.277 Tc
[(T)361.3(a)277(b)289(l)277(e2)277(.N)277(a)301.1()]TJ
/TT12 1 Tf
5.1896 0 TD
0 Tc
()Tj
/TT11 1 Tf
0.2778 0 TD
[(ve)-277(vs.)-289.1(Delta:)-337.3(Comparison)-265(of)-277(quer)-12(y)-277(e)12(v)24.1(aluation)-265(times)-277(and)-277(total)-265(n)12(umber)-277(of)-265(nodes)-277(f)12(e)0(d)-277(bac)24.1(k.)]TJ
/TT5 1 Tf
-6.7081 -3.204 TD
(gle)Tj
/F3 1 Tf
1.5951 0 TD
0.005 Tc
(SPEECH)Tj
/TT5 1 Tf
3.5413 0 TD
0 Tc
[(node)-361.4(gi)24.1(v)12(e)0(n)-373.4(that)-373.4(the)-385.4(associated)]TJ
/F3 1 Tf
12.8269 0 TD
0.005 Tc
(SPEAKER)Tj
/TT5 1 Tf
3.7099 0 TD
0 Tc
[(s)-361.3(are)]TJ
-21.6732 -1.2045 TD
[(found)-481.8(to)-493.8(alternate)-493.8(\(horizontal)-481.8(structural)-493.8(recursion)-481.8(along)]TJ
T*
(the)Tj
/F3 1 Tf
1.5951 0 TD
0.005 Tc
[(following-siblin)12.1(g)]TJ
/TT5 1 Tf
9.2989 0 TD
0 Tc
[(axiswe)-385.4(do)-361.3(not)-373.4(reproduce)-349.3(the)]TJ
-10.8939 -1.1925 TD
[(query)-349.3(here)-373.4(for)-361.4(space)-373.4(reasons.\))-674.5(Although)-361.4(the)-373.4(recursion)-349.3(is)]TJ
0 -1.2045 TD
[(shallo)24.1(w)-421.6(\(depth)-421.6(6)-433.6(o)0(n)-433.6(a)24.1(v)12(erage\),)-457.7(T)84.3(able)-433.6(2)-433.6(sho)24.1(ws)-433.6(ho)24.1(w)-433.6(both,)]TJ
/TT7 1 Tf
T*
(MonetDB/XQuery)Tj
/TT5 1 Tf
7.6127 0 TD
(and)Tj
/TT7 1 Tf
1.8052 0 TD
(Saxon)Tj
/TT5 1 Tf
2.4438 0 TD
[(,)-361.4(completed)-349.3(e)24.1(v)24.1(aluation)-337.3(up)-361.3(to)]TJ
-11.8617 -1.1925 TD
[(5)-216.8(times)-240.9(f)12(aster)-228.9(because)-216.8(the)-228.9(query)-204.8(had)-216.8(been)-216.8(speci)]TJ
/TT8 1 Tf
18.6951 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(ed)-228.9(in)-228.9(a)-228.9(dis-)]TJ
-19.2512 -1.2045 TD
[(trib)24.1(uti)24.1(v)12(e)-228.9(f)12(ashion.)]TJ
/TT2 1 Tf
0 -3.0715 TD
[(T)72.3(ransiti)12(v)12(e)-445.7(Closur)12(es.)]TJ
/TT5 1 Tf
9.6858 0 TD
[(T)84.3(w)12(o)-445.7(more)-445.7(queries,)-481.8(tak)12(en)-445.7(directly)]TJ
-9.6858 -1.2045 TD
[(from)-180.7(related)-192.7(w)12(ork)-192.7([23)12(,)-204.8(1)0(1)12(])0(,)-204.8(compute)-180.7(transiti)24.1(v)12(e)-192.7(closure)-192.7(prob-)]TJ
T*
[(lems)-216.8(\(we)-216.8(generated)-192.7(the)-228.9(data)-204.8(instances)-216.8(with)-228.9(the)-216.8(help)-204.8(of)-216.8(T)84.3(oX-)]TJ
0 -1.1925 TD
[(gene)-289.1([6)12(]\).)-457.7(The)]TJ
/TT8 1 Tf
6.2152 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(rst)-301.1(query)-289.1(implements)-277(a)-301.1(consistenc)12(y)-289.1(check)]TJ
-6.7714 -1.2045 TD
[(o)12(v)12(e)0(r)-168.6(the)-192.7(curriculum)-168.6(data)-192.7(\(cf.)-192.7(Figure)-180.7(1\))-192.7(and)]TJ
/TT8 1 Tf
16.7442 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(nds)-192.7(courses)-192.7(that)]TJ
-17.3004 -1.2045 TD
[(are)-192.7(among)-168.6(their)-192.7(o)24.1(w)0(n)-180.7(prerequisites)-180.7(\(Rule)-192.7(5)-192.7(i)0(n)-204.8(the)-192.7(Curriculum)]TJ
0 -1.1925 TD
[(Case)-277(Study)-265(in)-265(Appendix)-240.9(B)-289.1(o)0(f)-265([23)24.1(]\).)-373.4(Much)-265(lik)12(e)-277(for)-252.9(the)-277(bid-)]TJ
0 -1.2045 TD
[(der)-301.1(netw)12(ork)-301.1(query)60.2(,)-301.1(the)-313.2(lar)12(ger)-301.1(the)-313.2(query)-301.1(input)-301.1(\(medium)-289.1(in-)]TJ
0 -1.1925 TD
[(stance:)-361.4(800)-265(courses,)-265(lar)12(ge:)-349.3(4,000)-252.9(courses\),)-277(the)-265(better)]TJ
/TT7 1 Tf
21.4324 0 TD
(Mon-)Tj
-21.4324 -1.2045 TD
(etDB/XQuery)Tj
/TT5 1 Tf
5.6712 0 TD
(and)Tj
/TT7 1 Tf
1.6847 0 TD
(Saxon)Tj
/TT5 1 Tf
2.6727 0 TD
[(e)12(xploited)]TJ
/TT7 1 Tf
3.926 0 TD
(Delta)Tj
/TT5 1 Tf
2.2217 0 TD
(.)Tj
-14.9839 -1.2768 TD
[(The)-265(last)-277(query)-252.9(in)-265(the)-265(e)12(xperiment)-240.9(e)12(xplores)-252.9(50,000)-240.9(hospi-)]TJ
-1.1925 -1.2045 TD
[(tal)-192.7(patient)-180.7(records)-180.7(to)-192.7(in)36.1(v)12(estigate)-168.6(a)-192.7(hereditary)-168.6(disease)-192.7([11)12(].)-277(In)]TJ
0 -1.1925 TD
[(this)-252.9(case,)-265(the)-252.9(recursion)-240.9(follo)24.1(ws)-252.9(the)-252.9(hierarchical)-240.9(structure)-240.9(of)]TJ
0 -1.2045 TD
[(the)-204.8(XML)-216.8(input)-192.7(\(from)-204.8(patient)-204.8(to)-204.8(parents\),)-204.8(recursing)-192.7(into)-204.8(sub-)]TJ
T*
[(trees)-289.1(of)-289.1(a)-301.1(maximum)-265(depth)-289.1(of)-277(5.)-457.7(Again,)]TJ
/TT7 1 Tf
16.1754 0 TD
(Delta)Tj
/TT5 1 Tf
2.5108 0 TD
[(mak)12(es)-289.1(a)-301.1(no-)]TJ
-18.6862 -1.1925 TD
[(table)-228.9(dif)24.1(ference)-216.8(e)24.1(v)12(en)-228.9(for)-240.9(this)-240.9(computationally)-204.8(rather)-228.9(light)]TJ
0 -1.2045 TD
[(query)60.2(.)]TJ
1.1925 -1.2768 TD
[(W)84.3(e)-457.7(belie)24.1(v)12(e)-433.6(that)-433.6(this)-457.7(renders)-421.6(this)-445.7(particular)-433.6(controlled)]TJ
-1.1925 -1.1925 TD
[(form)-313.2(of)-325.2(XQuery)-325.2(recursion)-313.2(and)-325.2(its)-349.3(associated)-325.2(distrib)24.1(uti)24.1(vity)]TJ
0 -1.2045 TD
[(notion)-216.8(attracti)24.1(v)12(e)0(,)-216.8(e)24.1(v)12(e)0(n)-228.9(for)-228.9(processors)-216.8(that)-240.9(do)-228.9(not)-228.9(implement)]TJ
T*
[(a)-240.9(dedicated)]TJ
/TT8 1 Tf
4.7447 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(x)12(e)0(d)-240.9(point)-228.9(operator)-216.8(\(lik)12(e)]TJ
/TT7 1 Tf
9.579 0 TD
(Saxon)Tj
/TT5 1 Tf
2.4438 0 TD
(\).)Tj
/TT2 1 Tf
11.9552 0 0 11.9552 50.16 156.9 Tm
[(6)10(.)-250.9(Mor)20.1(e)-261(Related)-250.9(W)70.3(ork)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 62.04 128.82 Tm
[(Bringing)-385.4(adequate)-385.4(support)-385.4(for)-397.5(recursion)-373.4(to)-409.5(XQuery)-385.4(is)]TJ
-1.1925 -1.2045 TD
[(a)-385.4(core)-385.4(research)-373.4(matter)-373.4(on)-385.4(v)24.1(arious)-373.4(le)24.1(v)12(els)-385.4(of)-385.4(the)-385.4(language.)]TJ
T*
[(While)-337.3(the)-337.3(ef)]TJ
/TT8 1 Tf
5.0923 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(cient)-337.3(e)24.1(v)24.1(aluation)-313.2(of)-337.3(the)-337.3(recursi)24.1(v)12(e)-313.2(XP)12(ath)-337.3(ax)12(es)]TJ
-5.6485 -1.1925 TD
(\()Tj
/TT7 1 Tf
0.333 0 TD
-0.012 Tc
[(e.)-12(g.)]TJ
/TT5 1 Tf
1.4198 0 TD
0 Tc
(,)Tj
/F3 1 Tf
0.4186 0 TD
0.005 Tc
(descendant)Tj
/TT5 1 Tf
5.4565 0 TD
0 Tc
(or)Tj
/F3 1 Tf
1.0137 0 TD
0.005 Tc
(ancestor)Tj
/TT5 1 Tf
4.2399 0 TD
0 Tc
[(\))-144.5(i)0(s)-204.8(well)-192.7(understood)-156.6(by)-180.7(no)24.1(w)]TJ
-12.8814 -1.2045 TD
[([3)12(,)-228.9(1)0(6)12(])0(,)-240.9(the)-228.9(optimization)-204.8(of)-228.9(recursi)24.1(v)12(e)-216.8(user)24.1(-de)]TJ
/TT8 1 Tf
17.6475 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(ned)-204.8(functions)]TJ
7.7653 45.8914 TD
[(has)-337.3(been)-325.2(found)-313.2(to)-349.3(be)-325.2(tractable)-337.3(only)-325.2(in)-337.3(the)-337.3(presence)-325.2(of)-325.2(re-)]TJ
0 -1.2045 TD
[(strictions:)-301.1([24)12(,)-240.9(1)0(3)12(])-240.9(propose)-228.9(e)12(xhausti)24.1(v)12(e)-216.8(inlining)-228.9(of)-240.9(functions)]TJ
T*
[(b)24.1(u)0(t)-457.7(require)-433.6(that)-457.7(functions)-445.7(are)]TJ
/TT7 1 Tf
12.7675 0 TD
[(structur)12(ally)]TJ
/TT5 1 Tf
5.1122 0 TD
[(recursi)24.1(v)12(e)-433.6(\(use)]TJ
-17.8797 -1.1925 TD
[(ax)12(es)]TJ
/F3 1 Tf
1.9455 0 TD
0.005 Tc
(child)Tj
/TT5 1 Tf
2.8186 0 TD
0 Tc
(and)Tj
/F3 1 Tf
1.6245 0 TD
0.005 Tc
(descendant)Tj
/TT5 1 Tf
5.4444 0 TD
0 Tc
[(to)-192.7(na)24.1(vigate)-168.6(into)-180.7(subtrees)-180.7(only\))]TJ
-11.833 -1.2045 TD
-0.012 Tc
[(ove)-12(r)]TJ
/TT7 1 Tf
1.9696 0 TD
0 Tc
(acyclic)Tj
/TT5 1 Tf
3.072 0 TD
[(schemata)-228.9(to)-240.9(guarantee)-216.8(that)-240.9(inlining)-228.9(terminates.)]TJ
-5.0415 -1.2045 TD
[(Note)-313.2(that,)-325.2(be)12(yond)-277(inlining,)-313.2(this)-325.2(type)-301.1(of)-313.2(recursion)-289.1(does)-301.1(not)]TJ
0 -1.1925 TD
[(come)-204.8(packaged)-192.7(with)-216.8(an)-216.8(ef)24.1(fecti)24.1(v)12(e)-204.8(optimization)-192.7(hook)-204.8(compa-)]TJ
0 -1.2045 TD
[(rable)-240.9(to)-240.9(what)-240.9(the)-240.9(in)]TJ
/TT8 1 Tf
7.6833 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
(ationary)Tj
/TT8 1 Tf
3.5052 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(x)12(e)0(d)-228.9(point)-240.9(of)24.1(fers.)]TJ
-11.1084 -1.325 TD
[(The)-385.4(distinguished)-373.4(use)-385.4(case)-397.5(for)-373.4(in)]TJ
/TT8 1 Tf
13.8009 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
(ationary)Tj
/TT8 1 Tf
3.6377 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(x)12(e)0(d)-385.4(point)]TJ
-19.7434 -1.2045 TD
[(computation)-277(is)-325.2(transiti)24.1(v)12(e)-301.1(closure.)-493.9(This)-313.2(is)-313.2(also)-313.2(re)]TJ
/TT8 1 Tf
19.658 0 TD
()Tj
/TT5 1 Tf
0.5561 0 TD
[(ected)-313.2(by)]TJ
-20.2142 -1.1925 TD
[(the)-192.7(adv)12(ent)-180.7(of)-192.7(XP)12(ath)-192.7(dialects)-192.7(lik)12(e)-192.7(R)0(e)12(gular)-192.7(XP)12(ath)-192.7([21)24.1(])-204.8(and)-180.7(the)]TJ
0 -1.2045 TD
[(inclusion)-289.1(of)-301.1(a)-301.1(dedicated)]TJ
/F3 1 Tf
9.9548 0 TD
0.005 Tc
(dyn:closure\()Tj
/F1 1 Tf
6.3598 0 TD
0 Tc
()Tj
/F3 1 Tf
0.277 0 TD
(\))Tj
/TT5 1 Tf
0.7829 0 TD
[(construct)-289.1(in)-301.1(the)]TJ
-17.3746 -1.1925 TD
[(EXSL)96.4(T)-265(function)-240.9(library)-240.9([10)12(].)-349.3(W)84.3(e)-277(ha)24.1(v)12(e)-252.9(seen)-265(applications)-240.9(in)]TJ
0 -1.2045 TD
[(Section)-277(5)-289.1([23)12(,)-289.1(1)0(1)12(])-289.1(and)-277(recent)-289.1(w)12(ork)-277(on)-277(data)-289.1(inte)12(gration)-265(and)]TJ
T*
[(XML)-240.9(vie)24.1(ws)-240.9(adds)-240.9(to)-252.9(this)-240.9([12)12(].)]TJ
0 -1.7465 TD
[(In)-349.3(the)-361.4(domain)-337.3(of)-349.3(relational)-349.3(query)-337.3(languages,)]TJ
/TT7 1 Tf
18.6457 0 TD
(Na)Tj
1.2647 -0.0121 TD
()Tj
/TT9 1 Tf
0.0241 0.0121 TD
()Tj
/TT7 1 Tf
0.2778 0 TD
(ve)Tj
/TT5 1 Tf
1.2491 0 TD
[(is)-361.4(the)]TJ
-21.4614 -1.2045 TD
[(most)-240.9(widely)-240.9(described)-228.9(algorithmic)-228.9(account)-240.9(of)-240.9(the)-240.9(in)]TJ
/TT8 1 Tf
20.712 0 TD
()Tj
/TT5 1 Tf
0.5561 0 TD
(ation-)Tj
-21.2682 -1.2045 TD
(ary)Tj
/TT8 1 Tf
1.5418 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(x)12(e)0(d)-265(point)-265(operator)-252.9([5)12.1(].)-397.5(Its)-277(optimized)]TJ
/TT7 1 Tf
14.9324 0 TD
(Delta)Tj
/TT5 1 Tf
2.4987 0 TD
[(v)24.1(ariant,)-265(in)]TJ
-19.5291 -1.1925 TD
[(focus)-216.8(since)-228.9(the)-228.9(1980)60.2(s,)-216.8(has)-240.9(been)-216.8(coined)]TJ
/TT7 1 Tf
15.8064 0 TD
[(delta)-216.8(iter)12(ation)]TJ
/TT5 1 Tf
5.8775 0 TD
[([17)24.1(],)]TJ
/TT7 1 Tf
-21.6839 -1.2045 TD
(semi-na)Tj
3.1558 -0.012 TD
()Tj
/TT9 1 Tf
0.0241 0.012 TD
()Tj
/TT7 1 Tf
0.2778 0 TD
(ve)Tj
/TT5 1 Tf
1.3695 0 TD
[([5)12(],)-240.9(or)]TJ
/TT7 1 Tf
2.7188 0 TD
[(wavefr)48.2(ont)]TJ
/TT5 1 Tf
4.2163 0 TD
[([18)24.1(])-252.9(strate)12(gy)-228.9(in)-252.9(earlier)-228.9(w)12(ork.)]TJ
-10.5699 -1.3249 TD
[(Since)-373.4(our)-373.4(w)12(ork)-361.4(rests)-385.4(on)-361.4(the)-373.4(adaption)-361.4(of)-361.3(these)-373.4(original)]TJ
-1.1925 -1.2045 TD
[(ideas)-373.4(to)-373.4(the)-373.4(XQuery)-349.3(Data)-373.4(Model)-373.4(and)-361.4(language,)-373.4(the)-373.4(lar)12(ge)]TJ
0 -1.1925 TD
[(relational)-385.4(body)-373.4(of)-385.4(w)12(ork)-397.5(in)-397.5(this)-397.5(area)-385.4(should)-385.4(be)-397.5(directly)]TJ
0 -1.2045 TD
[(transferable,)-349.3(e)24.1(v)12.1(en)-325.2(more)-337.3(so)-349.3(in)-349.3(the)-349.3(Relational)-337.3(XQuery)-337.3(con-)]TJ
0 -1.1925 TD
[(te)12(xt.)-530(In)-313.2(particular)36.1(,)-313.2(optimization)-301.1(techniques)-301.1(lik)12(e)]TJ
/TT7 1 Tf
19.5177 0 TD
[(Ma)12(gic)-313.2(Set)]TJ
/TT5 1 Tf
-19.5177 -1.2045 TD
[(re)24.1(writing)-216.8([4)12(])-240.9(should)-228.9(apply)-228.9(\(this)-228.9(has)-240.9(not)-240.9(been)-228.9(in)36.1(v)12(estigated)-204.8(in)]TJ
T*
[(the)-240.9(present)-240.9(paper\).)]TJ
0 -1.7465 TD
[(The)-240.9(adoption)-216.8(of)-240.9(in)]TJ
/TT8 1 Tf
7.3636 0 TD
()Tj
/TT5 1 Tf
0.5561 0 TD
(ationary)Tj
/TT8 1 Tf
3.5052 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(x)12(e)0(d)-240.9(point)-228.9(semantics)-240.9(by)-240.9(Data-)]TJ
-11.9812 -1.2045 TD
[(log)-289.1(and)-301.1(SQL:1999)-277(with)-301.1(its)]TJ
/F3 1 Tf
11.0929 0 TD
0.005 Tc
[(WITH)-505.9(RECURSIVE)]TJ
/TT5 1 Tf
7.6607 0 TD
0 Tc
[(clause)-289.1(\(Sec-)]TJ
-18.7536 -1.1925 TD
[(tion)-397.5(2\))-409.5(led)-409.5(to)-397.5(in)36.1(v)12(estigations)-385.4(of)-409.5(the)-397.5(applicability)-397.5(of)]TJ
/TT7 1 Tf
21.3829 0 TD
(Delta)Tj
/TT5 1 Tf
-21.3829 -1.2045 TD
[(for)-349.3(these)-361.4(recursi)24.1(v)12(e)-337.3(relational)-349.3(query)-349.3(languages.)-626.3(F)12(o)0(r)-361.4(strati-)]TJ
/TT8 1 Tf
T*
()Tj
/TT5 1 Tf
0.5562 0 TD
[(ed)-289.1(Datalog)-277(programs)-252.9([1],)]TJ
/TT7 1 Tf
10.4104 0 TD
(Delta)Tj
/TT5 1 Tf
2.5108 0 TD
[(is)-289.1(applicable)-277(in)]TJ
/TT7 1 Tf
6.3969 0 TD
(all)Tj
/TT5 1 Tf
1.3447 0 TD
(cases:)Tj
-21.2189 -1.1925 TD
[(positi)24.1(v)12(e)-252.9(Datalog)-252.9(maps)-252.9(onto)-252.9(the)-265(distrib)24.1(uti)24.1(v)12.1(e)-252.9(operators)-240.9(of)-252.9(re-)]TJ
0 -1.2045 TD
[(lational)-325.2(algebra)-325.2(\()]TJ
/F6 1 Tf
6.9248 0 TD
()Tj
/TT5 1 Tf
0.6023 0 TD
(,)Tj
/F6 1 Tf
0.6114 0 TD
()Tj
/TT5 1 Tf
0.6023 0 TD
(,)Tj
/F25 1 Tf
0.6114 0 TD
()Tj
0.0121 0 TD
()Tj
/TT5 1 Tf
0.7829 0 TD
(,)Tj
/F1 1 Tf
0.6114 0 TD
()Tj
/TT5 1 Tf
0.6625 0 TD
(,)Tj
/F1 1 Tf
0.6114 0 TD
()Tj
/TT5 1 Tf
0.6625 0 TD
[(\))-337.3(while)-337.3(strati)]TJ
/TT8 1 Tf
5.2287 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(cation)-325.2(yields)]TJ
-18.4796 -1.2045 TD
[(partial)-204.8(applications)-180.7(of)-204.8(the)-204.8(dif)24.1(ference)-180.7(operator)]TJ
/F6 1 Tf
17.9569 0 TD
(x)Tj
/F1 1 Tf
0.6504 0 TD
(\\)Tj
/F6 1 Tf
0.5902 0 TD
(R)Tj
/TT5 1 Tf
0.9756 0 TD
[(in)-204.8(which)]TJ
/F6 1 Tf
-20.1732 -1.1925 TD
(R)Tj
/TT5 1 Tf
1.0118 0 TD
(is)Tj
/TT8 1 Tf
0.9199 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
-0.012 Tc
[(xe)-12(d)-252.9(\()]TJ
/F6 1 Tf
2.0057 0 TD
0 Tc
(f)Tj
/F8 1 Tf
0.6023 0 TD
(\()Tj
/F6 1 Tf
0.3854 0 TD
(x)Tj
/F8 1 Tf
0.5661 0 TD
0.2736 Tc
(\)=)Tj
/F6 1 Tf
1.7225 0 TD
0 Tc
(x)Tj
/F1 1 Tf
0.795 0 TD
(\\)Tj
/F6 1 Tf
0.7227 0 TD
(R)Tj
/TT5 1 Tf
1.0118 0 TD
[(is)-252.9(distrib)24.1(uti)24.1(v)12(e\).)]TJ
-9.1069 -1.325 TD
[(SQL:1999,)-433.6(on)-409.5(the)-409.5(other)-409.5(hand,)-433.6(imposes)-409.5(rigid)]TJ
/TT7 1 Tf
18.9686 0 TD
(syntacti-)Tj
-20.1611 -1.2045 TD
(cal)Tj
/TT5 1 Tf
1.6673 0 TD
[(restrictions)-445.7([22)12(])-457.7(o)0(n)-445.7(the)-445.7(iterati)24.1(v)12(e)-445.7(fullselect)-445.7(\(recursion)]TJ
-3.0525 -2.9992 TD
(9)Tj
ET
endstream
endobj
72 0 obj
<<
/ProcSet [/PDF /Text /ImageB ]
/Font <<
/F1 4 0 R
/F3 6 0 R
/F6 22 0 R
/F8 24 0 R
/F25 56 0 R
/TT2 9 0 R
/TT5 11 0 R
/TT7 12 0 R
/TT8 13 0 R
/TT9 14 0 R
/TT11 15 0 R
/TT12 16 0 R
/TT14 31 0 R
>>
/XObject <<
/Im1 33 0 R
>>
/ExtGState <<
/GS1 17 0 R
>>
>>
endobj
74 0 obj
<<
/Length 18032
>>
stream
BT
/TT5 1 Tf
9.9626 0 0 9.9626 50.16 709.98 Tm
0 g
/GS1 gs
0 Tc
0 Tw
[(body\))-192.7(inside)]TJ
/F3 1 Tf
5.1433 0 TD
0.005 Tc
[(WITH)-505.9(RECURSIVE)]TJ
/TT5 1 Tf
7.5764 0 TD
0 Tc
[(that)-228.9(mak)12(e)]TJ
/TT7 1 Tf
4.0987 0 TD
(Delta)Tj
/TT5 1 Tf
2.4385 0 TD
(applicable:)Tj
-19.2568 -1.2045 TD
[(grouping,)-156.6(ordering,)-180.7(usage)-180.7(of)-192.7(column)-168.6(functions)-180.7(\(aggre)12(gates\),)]TJ
0 -1.1925 TD
[(and)-313.2(nested)-313.2(subqueries)-313.2(are)-325.2(ruled)-313.2(out,)-337.3(as)-325.2(are)-325.2(repeated)-313.2(refer)24.1(-)]TJ
0 -1.2045 TD
[(ences)-337.3(to)-337.3(the)-337.3(virtual)-325.2(table)-337.3(computed)-325.2(by)-325.2(the)-337.3(recursion.)-566.1(Re-)]TJ
T*
[(placing)-216.8(this)-240.9(coarse)-216.8(syntactic)-228.9(check)-228.9(by)-216.8(an)-240.9(algebraic)-216.8(distrib)24.1(u-)]TJ
0 -1.1925 TD
[(ti)24.1(vity)-252.9(assessment)-277(\(Section)-252.9(4\))-265(w)12(ould)-252.9(render)-240.9(a)-277(lar)12(ger)-240.9(class)-277(of)]TJ
0 -1.2045 TD
[(queries)-228.9(admissible)-240.9(for)-240.9(ef)]TJ
/TT8 1 Tf
9.7945 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
(cient)Tj
/TT8 1 Tf
2.1722 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(x)12(e)0(d)-240.9(point)-228.9(computation.)]TJ
/TT2 1 Tf
11.9552 0 0 11.9552 50.16 613.86 Tm
[(7)10(.)-250.9(Wrap-Up)]TJ
/TT5 1 Tf
9.9626 0 0 9.9626 62.04 587.46 Tm
[(This)-252.9(paper)-228.9(may)-228.9(be)-252.9(read)-228.9(in)-252.9(tw)12(o)-240.9(w)12(ays:)]TJ
/TT7 1 Tf
0 -1.2165 TD
(\(i\))Tj
/TT5 1 Tf
1.4377 0 TD
[(As)-277(a)-277(proposal)-252.9(to)-265(add)-265(an)-265(in)]TJ
/TT8 1 Tf
10.5444 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
(ationary)Tj
/TT8 1 Tf
3.5293 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(x)12(e)0(d)-252.9(point)-265(con-)]TJ
-17.8161 -1.2045 TD
[(struct,)-252.9(along)-252.9(the)-252.9(lines)-265(of)]TJ
/F3 1 Tf
9.9135 0 TD
0.005 Tc
(with)Tj
/F1 1 Tf
2.2645 0 TD
0.1679 Tc
()Tj
/F3 1 Tf
1.337 0 TD
0.005 Tc
[(seeded)-493.8(by)]TJ
/F1 1 Tf
4.8903 0 TD
0.1679 Tc
()Tj
/F3 1 Tf
1.325 0 TD
0.005 Tc
(recurse)Tj
/TT5 1 Tf
3.6858 0 TD
0 Tc
(,)Tj
-23.4161 -1.1925 TD
[(to)-674.5(XQuery)-674.5(\(this)-674.5(has)-686.6(actually)-674.5(been)-674.5(discussed)-674.5(by)-674.5(the)]TJ
0 -1.2045 TD
[(W3C)-204.8(XQuery)-204.8(w)12(orking)-180.7(group)-180.7(in)-216.8(the)-204.8(v)12(ery)-192.7(early)-192.7(XQuery)-192.7(days)]TJ
T*
[(of)-265(2001)]TJ
6.9738 0 0 6.9738 81.36 531.1801 Tm
(5)Tj
9.9626 0 0 9.9626 87.84 527.46 Tm
[(b)24.1(u)0(t)-277(then)-265(dismissed)-265(because)-265(the)-277(group)-252.9(aimed)-265(for)-252.9(a)]TJ
/TT8 1 Tf
-3.7821 -1.1925 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(rst-order)-216.8(language)-228.9(design)-228.9(at)-252.9(that)-240.9(time\).)]TJ
/TT7 1 Tf
0.6363 -1.2165 TD
(\(ii\))Tj
/TT5 1 Tf
1.7155 0 TD
[(As)-421.6(a)-421.6(guideline)-397.5(for)-397.5(query)-397.5(authors)-397.5(as)-421.6(well)-421.6(XQuery)]TJ
-2.908 -1.2045 TD
[(processor)-289.1(designers)-301.1(to)-313.2(check)-301.1(for)-301.1(and)-301.1(then)-301.1(e)12(xploit)-301.1(distrib)24.1(u-)]TJ
0 -1.1925 TD
[(ti)24.1(vity)-240.9(during)-216.8(the)-240.9(e)24.1(v)24.1(aluation)-228.9(of)-240.9(recursi)24.1(v)12(e)-216.8(queries.)]TJ
1.1925 -1.2165 TD
[(W)84.3(e)-240.9(ha)24.1(v)12(e)-204.8(seen)-228.9(ho)24.1(w)-204.8(such)-216.8(distrib)24.1(uti)24.1(vity)-204.8(checks)-216.8(can)-216.8(be)-216.8(used)]TJ
-1.1925 -1.2045 TD
[(to)-385.4(safely)-385.4(unlock)-373.4(the)-385.4(optimization)-361.4(potential,)-421.6(namely)-373.4(algo-)]TJ
T*
(rithm)Tj
/TT7 1 Tf
2.4676 0 TD
(Delta)Tj
/TT5 1 Tf
2.2217 0 TD
[(,)-325.2(that)-313.2(comes)-313.2(tightly)-301.1(coupled)-301.1(with)-313.2(the)-313.2(in)]TJ
/TT8 1 Tf
16.0385 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
(ation-)Tj
-21.284 -1.1925 TD
(ary)Tj
/TT8 1 Tf
1.6503 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(x)12(e)0(d)-361.4(point)-373.4(semantics.)]TJ
/TT7 1 Tf
9.1262 0 TD
(MonetDB/XQuery)Tj
/TT5 1 Tf
7.6367 0 TD
(implements)Tj
-18.9694 -1.2045 TD
[(this)-337.3(distrib)24.1(uti)24.1(vity)-325.2(check)-325.2(on)-325.2(the)-337.3(algebraic)-325.2(le)24.1(v)12(e)0(l)-337.3(and)-325.2(signi)]TJ
/TT8 1 Tf
22.7147 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
(-)Tj
-23.2708 -1.2045 TD
[(cantly)-252.9(bene)]TJ
/TT8 1 Tf
4.584 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(ts)-265(whene)24.1(v)12(e)0(r)-240.9(the)]TJ
/TT7 1 Tf
6.4981 0 TD
(Delta)Tj
/TT5 1 Tf
2.2217 0 TD
[(-based)-252.9(operator)]TJ
/F6 1 Tf
6.4353 0 TD
()Tj
/F7 1 Tf
6.9738 0 0 6.9738 259.44 411.18 Tm
()Tj
/TT5 1 Tf
9.9626 0 0 9.9626 269.16 407.58 Tm
(may)Tj
-21.9821 -1.1925 TD
[(be)-313.2(used)-325.2(for)]TJ
/TT8 1 Tf
4.8944 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(xpoint)-313.2(computation.)-517.9(Ev)12(en)-313.2(if)-325.2(the)-325.2(approach)-301.1(is)]TJ
-5.4506 -1.2045 TD
[(realized)-252.9(on)-252.9(the)-265(coarser)-252.9(syntactic)-252.9(le)24.1(v)12(e)0(l)]TJ
/TT7 1 Tf
15.2636 0 TD
[(on)-265(top)-252.9(of)]TJ
/TT5 1 Tf
3.9831 0 TD
[(an)-265(e)12(xisting)]TJ
-19.2467 -1.2045 TD
[(XQuery)-313.2(processor)36.1(,)-337.3(feeding)-313.2(back)-337.3(less)-337.3(nodes)-325.2(in)-337.3(each)-337.3(recur)24.1(-)]TJ
0 -1.1925 TD
[(sion)-240.9(le)24.1(v)12(e)0(l)-240.9(yields)-240.9(substantial)-240.9(performance)-204.8(impro)12(v)12(ements.)]TJ
0 -1.5297 TD
[(Remember)-301.1(that)-325.2(the)-313.2(distrib)24.1(uti)24.1(vity)-313.2(notion)-301.1(suggests)-313.2(a)-325.2(d)0(i)24.1(vide-)]TJ
0 -1.2045 TD
[(and-conquer)-144.5(e)24.1(v)24.1(aluation)-168.6(strate)12(gy)-168.6(\(Section)-180.7(3.1\))-180.7(in)-192.7(which)-180.7(parts)]TJ
T*
[(of)-277(a)-289.1(computation)-265(may)-277(be)-289.1(performed)-252.9(independently)-252.9(\(before)]TJ
0 -1.1925 TD
[(a)-433.6(mer)12(ge)-421.6(step)-433.6(forms)-421.6(the)]TJ
/TT8 1 Tf
10.2519 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(nal)-433.6(result\).)-867.2(Be)12(yond)-421.6(recursion,)]TJ
-10.8081 -1.2045 TD
[(this)-361.4(may)-349.3(lead)-349.3(to)-361.4(impro)12(v)12(e)0(d)-325.2(XQuery)-337.3(compilation)-337.3(strate)12(gies)]TJ
T*
[(for)-277(back-ends)-265(that)-289.1(can)-289.1(e)12(xploit)-277(such)-289.1(independence,)]TJ
/TT7 1 Tf
20.3916 0 TD
-0.012 Tc
[(e.)-12(g)]TJ
/TT5 1 Tf
1.1818 0 TD
0 Tc
[(,)-289.1(set-)]TJ
-21.5734 -1.1925 TD
[(oriented)-168.6(relational)-192.7(query)-180.7(processors)-180.7(\(cf.)-180.7(loop-lifting)-168.6([15)12(]\))-192.7(as)]TJ
0 -1.2045 TD
[(well)-240.9(as)-252.9(parallel)-240.9(or)-240.9(distrib)24.1(uted)-228.9(e)12(x)12(ecution)-216.8(platforms.)]TJ
/TT2 1 Tf
0 -2.7463 TD
[(Ackno)12(wledgments.)]TJ
/TT5 1 Tf
9.0591 0 TD
[(Loredana)-710.7(Af)12(anasie)24.1(v)-734.7(i)0(s)-746.8(supported)]TJ
-9.0591 -1.2045 TD
[(by)-457.7(the)-469.8(Netherlands)-457.7(Or)12(ganization)-433.6(for)-457.7(Scienti)]TJ
/TT8 1 Tf
18.4813 0 TD
()Tj
/TT5 1 Tf
0.5562 0 TD
[(c)-469.8(Research)]TJ
-19.0374 -1.2045 TD
[(\(NW)12(O\))-349.3(under)-337.3(project)-337.3(number)-325.2(612.000.207.)-578.2(Jan)-349.3(Rittinger)]TJ
0 -1.1925 TD
[(is)-397.5(supported)-373.4(by)-385.4(the)-385.4(German)-385.4(Research)-385.4(F)12(oundation)-361.4(\(DFG\))]TJ
0 -1.2045 TD
[(under)-216.8(grant)-240.9(GR)-252.9(2036/2-1.)]TJ
/TT2 1 Tf
11.9552 0 0 11.9552 50.16 162.54 Tm
[(Refer)20.1(ences)]TJ
/TT5 1 Tf
8.9664 0 0 8.9664 56.28 138.3 Tm
[([1])-548.7(S.)-548.7(Abiteboul,)-629(R.)-535.3(Hull,)-615.6(and)-562.1(V)133.8(.)-548.7(V)53.5(ianu.)]TJ
/TT7 1 Tf
19.3754 0 TD
[(F)107.1(oundations)-575.5(of)]TJ
-17.6624 -1.0974 TD
(Databases)Tj
/TT5 1 Tf
4.2222 0 TD
[(.)-374.7(Addison)-267.7(W)80.3(esle)13.4(y)66.9(,)-254.3(1995.)]TJ
-5.9352 -1.084 TD
[([2])-548.7(L.)-896.7(Af)13.4(anasie)26.8(v)66.9(.)-2449.1(Distrib)13.4(uti)26.8(vity)-896.7(for)-896.7(XQuery)-910.1(Expres-)]TJ
1.7131 -1.0974 TD
[(sions.)-2020.9(T)66.9(echnical)-762.8(report,)-896.7(Uni)26.8(v)13.4(ersity)-776.2(of)-762.8(Amsterdam,)]TJ
ET
q
94.56 0 0 -0.48 50.148 100.368 cm
/Im1 Do
Q
BT
5.9776 0 0 5.9776 60.96 93.18 Tm
(5)Tj
/F11 1 Tf
7.9701 0 0 7.9701 64.44 90.42 Tm
-0.0042 Tc
[(http://www.w3.org/TR/20)-15(0)0.1(1/)-15(WD-)-75.2(quer)-15(y)0(-)-60.2(s)-15(ema)-15(ntic)-15(s-)-60.2(2)-15(001)-15(0607)-15(/)]TJ
/TT5 1 Tf
-1.7917 -1.1894 TD
0 Tc
[(\(Issue)-256(0008\).)]TJ
8.9664 0 0 8.9664 330.48 709.98 Tm
[(2007.)-1365.1(A)80.3(v)26.8(ailable)-575.5(at)]TJ
/F4 1 Tf
9.2545 0 TD
-0.003 Tc
(http://staff.science.uva.nl/)Tj
-9.2545 -1.0974 TD
[(~lafanasi/Publications/2007/dis)-13.3(tr-)-66.9(repor)-13.3(t.pd)-13.4(f)]TJ
/TT5 1 Tf
23.0736 0 TD
0 Tc
(.)Tj
-24.8001 -0.9636 TD
[([3])-562.1(S.)-187.4(Al-Khalif)13.4(a,)-214.1(H.)-200.8(V)133.8(.)-214.1(Jagadish,)-227.5(J.)-200.8(M.)-200.8(P)13.4(atel,)-214.1(Y)133.8(.)-200.7(W)53.5(u)0(,)-214.1(N)0(.)-200.7(K)40.1(oudas,)]TJ
1.7265 -1.0974 TD
[(and)-227.5(D.)-227.5(Sri)26.8(v)26.8(asta)13.4(v)26.8(a)0(.)-294.4(Structural)-214.1(Joins:)-307.8(A)-214.1(Primiti)26.8(v)13.4(e)-214.1(for)-227.5(Ef)]TJ
/TT8 1 Tf
21.4297 0 TD
()Tj
/TT5 1 Tf
0.5561 0 TD
(cient)Tj
-21.9858 -1.0974 TD
[(XML)-240.9(Query)-267.7(P)13.4(attern)-240.9(Matching.)-374.7(In)]TJ
/TT7 1 Tf
13.8343 0 TD
[(Pr)40.1(oc.)-240.9(ICDE)]TJ
/TT5 1 Tf
4.7276 0 TD
[(,)-240.9(2002.)]TJ
-20.2884 -0.9502 TD
[([4])-562.1(F)80.3(.)-281.1(Bancilhon,)-307.8(D.)-281(Maier)40.1(,)-307.8(Y)133.8(.)-294.4(Sagi)26.8(v)66.9(,)-307.8(and)-294.4(J.)-294.4(D.)-281(Ullman.)-495.2(Magic)]TJ
1.7265 -1.1108 TD
[(Sets)-214.1(and)-227.5(Other)-227.5(Strange)-227.5(W)80.3(ays)-227.5(to)-214.1(Implement)-240.9(Logic)-227.5(Programs.)]TJ
0 -1.0974 TD
(In)Tj
/TT7 1 Tf
1.0873 0 TD
[(Pr)40.1(oc.)-240.9(PODS)]TJ
/TT5 1 Tf
4.9498 0 TD
[(,)-240.9(1985.)]TJ
-7.7635 -0.9502 TD
[([5])-562.1(F)80.3(.)-361.4(Bancilhon)-401.5(and)-388.1(R.)-374.7(Ramakrishnan.)-789.6(An)-388.1(Amateur)53.5(s)-374.7(Intro-)]TJ
1.7265 -1.0974 TD
[(duction)-294.4(to)-294.4(Recursi)26.8(v)13.4(e)-294.4(Query)-307.8(Processing)-294.4(Strate)13.4(gies.)-468.4(In)]TJ
/TT7 1 Tf
21.8291 0 TD
[(Pr)40.2(oc.)]TJ
-21.8291 -1.1108 TD
(SIGMOD)Tj
/TT5 1 Tf
3.8325 0 TD
[(,)-240.9(1986.)]TJ
-5.559 -0.9502 TD
[([6])-562.1(D.)-334.6(Barbosa,)-374.7(A.)-334.6(Mendelzon,)-388.1(J.)-348(K)26.8(eenle)13.4(yside,)-374.7(and)-361.4(K.)-334.6(L)53.5(yons.)]TJ
1.7265 -1.0974 TD
[(T)80.3(oXgene:)-508.6(A)-348(template-based)-361.4(Data)-348(Generator)-348(for)-348(XML.)-655.8(In)]TJ
/TT7 1 Tf
T*
[(Pr)40.2(oc.)-240.9(SIGMOD)]TJ
/TT5 1 Tf
6.2271 0 TD
[(,)-254.3(2002.)]TJ
-7.9536 -0.9636 TD
[([7])-562.1(S.)-455(Boag,)-521.9(D.)-455(Chamberlin,)-535.3(M.)-455(F)80.3(.)-455(Fern)-53.5()]TJ
17.4123 0 TD
[(andez,)-535.3(D.)-468.4(Florescu,)]TJ
-15.6859 -1.0974 TD
[(J.)-281.1(Robie,)-307.8(and)-307.8(J.)-294.4(Sim)-53.5()]TJ
8.1622 0 TD
[(eon.)-495.2(XQuery)-294.4(1.0:)-401.5(An)-294.4(XML)-294.4(query)-307.8(lan-)]TJ
-8.1622 -1.0974 TD
[(guage.)-374.7(W3C)-240.9(Recommendation,)-281.1(2007.)]TJ
-1.7265 -0.9502 TD
[([8])-562.1(P)107.1(.)-174(Boncz,)-214.1(T)80.3(.)-200.7(Grust,)-200.7(M.)-200.7(v)26.8(a)0(n)-214.1(K)26.8(eulen,)-214.1(S.)-187.4(Mane)13.4(gold,)-227.5(J.)-187.4(Rittinger)40.2(,)]TJ
1.7265 -1.1108 TD
[(and)-267.7(J.)-254.3(T)66.9(eubner)53.5(.)-401.5(MonetDB/XQuery:)-348(A)-254.3(F)13.4(ast)-254.3(XQuery)-281(Proces-)]TJ
0 -1.0974 TD
[(sor)-388.1(Po)26.8(wered)-401.5(by)-401.5(a)-388.1(Relational)-401.5(Engine.)-803(In)]TJ
/TT7 1 Tf
17.3489 0 TD
[(Pr)40.1(oc.)-388.1(SIGMOD)]TJ
/TT5 1 Tf
6.3743 0 TD
(,)Tj
-23.7232 -1.0974 TD
(2006.)Tj
-1.7265 -0.9502 TD
[([9])-562.1(D.)-388.1(Draper)40.1(,)-441.7(P)107.1(.)-388.1(F)13.4(ankhauser)40.2(,)-455(M)0(.)-401.5(F)80.3(.)-388.1(Fern)-53.5()]TJ
17.3504 0 TD
[(andez,)-441.6(A.)-401.5(Malhotra,)]TJ
-15.624 -1.1108 TD
[(K.)-361.4(Rose,)-401.5(M.)-374.7(Rys,)-388.1(J.)-374.7(Sim)-53.5()]TJ
10.3173 0 TD
[(eon,)-401.5(and)-374.7(P)107.1(.)-361.3(W)80.3(adler)53.5(.)-736.1(XQuery)-374.7(1.0)]TJ
-10.3173 -1.0974 TD
[(and)-321.2(XP)13.4(ath)-307.8(2.0)-307.8(F)13.4(ormal)-307.8(Semantics.)-562.1(W3C)-307.8(Recommendation,)]TJ
T*
(2007.)Tj
-2.2216 -0.9502 TD
[([10])-562.1(EXSL)93.7(T)53.5(:)-348(A)-361.4(Community)-388.1(Initiati)26.8(v)13.4(e)-361.4(to)-374.7(Pro)13.4(vide)-374.7(Extensions)-374.7(to)]TJ
2.2216 -1.1108 TD
[(XSL)93.7(T.)]TJ
/F4 1 Tf
2.9909 0 TD
-0.003 Tc
(http://www.exslt.org/)Tj
/TT5 1 Tf
10.9613 0 TD
0 Tc
(.)Tj
-16.1739 -0.9502 TD
[([11])-562.1(W)93.7(.)-240.9(F)13.4(an,)-240.9(F)80.3(.)-240.9(Geerts,)-254.3(X.)-240.9(Jia,)-254.3(and)-254.3(A.)-254.3(K)26.8(ementsietsidis.)-361.4(SMOQE:)]TJ
2.2216 -1.0974 TD
[(A)-334.6(System)-348(for)-348(Pro)13.4(viding)-348(Secure)-348(Access)-348(to)-348(XML.)-642.4(In)]TJ
/TT7 1 Tf
21.8129 0 TD
[(Pr)40.2(oc.)]TJ
-21.8129 -1.0974 TD
(VLDB)Tj
/TT5 1 Tf
2.5 0 TD
[(,)-227.5(2006.)]TJ
-4.7216 -0.9636 TD
[([12])-562.1(W)93.7(.)-294.4(F)13.4(an,)-334.6(F)80.3(.)-307.8(Geerts,)-321.2(X.)-307.8(Jia,)-321.2(and)-334.6(A.)-307.8(K)26.8(ementsietsidis.)-562.1(Re)26.8(writ-)]TJ
2.2216 -1.0974 TD
[(ing)-254.3(Re)13.4(gular)-267.7(XP)13.4(ath)-240.9(Queries)-267.7(on)-254.3(XML)-267.7(V)53.5(i)0(e)26.8(ws.)-361.4(In)]TJ
/TT7 1 Tf
18.9746 0 TD
[(Pr)40.1(oc.)-254.3(ICDE)]TJ
/TT5 1 Tf
4.741 0 TD
(,)Tj
-23.7156 -1.0974 TD
(2007.)Tj
-2.2216 -0.9502 TD
[([13])-562.1(M.)-321.2(Grine)26.8(v)-321.2(and)-334.6(D.)-321.2(Lizorkin.)-588.9(XQuery)-321.2(Function)-334.6(Inlining)-321.2(for)]TJ
2.2216 -1.1108 TD
[(Optimizing)-254.3(XQuery)-254.3(Queries.)-361.4(In)]TJ
/TT7 1 Tf
13.0934 0 TD
[(Pr)40.1(oc.)-240.9(ADBIS)]TJ
/TT5 1 Tf
5.1715 0 TD
[(,)-240.9(2004.)]TJ
-20.4865 -0.9502 TD
[([14])-562.1(T)80.3(.)-254.3(Grust,)-267.7(J.)-267.7(Rittinger)40.1(,)-267.7(and)-267.7(J.)-267.7(T)66.9(eubner)53.5(.)-414.9(eXrQuy:)-348(Order)-267.7(Indif-)]TJ
2.2216 -1.0974 TD
[(ference)-254.3(in)-254.3(XQuery.)-361.4(In)]TJ
/TT7 1 Tf
9.1476 0 TD
[(Pr)40.1(oc.)-240.9(ICDE)]TJ
/TT5 1 Tf
4.7276 0 TD
[(,)-240.9(2007.)]TJ
-16.0969 -0.9636 TD
[([15])-562.1(T)80.3(.)-227.5(Grust,)-240.9(S.)-227.5(Sakr)40.2(,)-240.9(and)-240.9(J.)-240.9(T)66.9(eubner)53.5(.)-334.6(XQuery)-254.3(on)-240.9(SQL)-227.5(Hosts.)-334.6(In)]TJ
/TT7 1 Tf
2.2216 -1.0974 TD
[(Pr)40.2(oc.)-240.9(VLDB)]TJ
/TT5 1 Tf
4.8946 0 TD
[(,)-227.5(2004.)]TJ
-7.1162 -0.9502 TD
[([16])-562.1(T)80.3(.)-374.7(Grust,)-414.9(M.)-388.1(v)26.8(a)0(n)-388.1(K)26.8(eulen,)-428.3(and)-401.5(J.)-374.7(T)66.9(eubner)53.5(.)-789.6(Staircase)-374.7(Join:)]TJ
2.2216 -1.0974 TD
[(T)66.9(each)-187.4(a)-200.8(Relational)-200.8(DBMS)-187.4(to)-187.4(W)80.3(atch)-200.7(its)-187.4(\(Axis\))-187.4(Steps.)-227.5(In)]TJ
/TT7 1 Tf
21.7879 0 TD
[(Pr)40.2(oc.)]TJ
-21.7879 -1.1108 TD
(VLDB)Tj
/TT5 1 Tf
2.5 0 TD
[(,)-227.5(2003.)]TJ
-4.7216 -0.9502 TD
[([17])-562.1(U.)-334.6(G)-80.3()]TJ
4.2555 0 TD
[(untzer)40.2(,)-374.7(W)93.7(.)-348(Kieling,)-361.4(and)-361.3(R.)-334.6(Bayer)53.5(.)-669.2(O)0(n)-361.3(the)-348(Ev)26.8(aluation)]TJ
-2.0338 -1.0974 TD
[(of)-307.8(Recursion)-307.8(in)-307.8(\(Deducti)26.8(v)13.4(e)0(\))-321.2(Database)-307.8(Systems)-307.8(by)-307.8(Ef)]TJ
/TT8 1 Tf
21.4845 0 TD
()Tj
/TT5 1 Tf
0.5561 0 TD
(cient)Tj
-22.0406 -1.0974 TD
[(Dif)26.8(ferential)-240.9(Fixpoint)-254.3(Iteration.)-361.4(In)]TJ
/TT7 1 Tf
13.608 0 TD
[(Pr)40.1(oc.)-240.9(ICDE)]TJ
/TT5 1 Tf
4.7276 0 TD
[(,)-240.9(1987.)]TJ
-20.5572 -0.9636 TD
[([18])-562.1(J.)-361.4(Han,)-401.5(G.)-374.7(Z.)-361.3(Qadah,)-401.5(and)-388.1(C.)-361.3(Chaou.)-749.5(The)-374.7(Processing)-388.1(and)]TJ
2.2216 -1.0974 TD
[(Ev)26.8(aluation)-334.6(of)-334.6(T)40.2(ransiti)26.8(v)13.4(e)-348(Closure)-334.6(Queries.)-629(In)]TJ
/TT7 1 Tf
18.7312 0 TD
[(Pr)40.1(oc.)-321.2(EDBT)]TJ
/TT5 1 Tf
4.9749 0 TD
(,)Tj
-23.7061 -1.0974 TD
(1988.)Tj
-2.2216 -0.9502 TD
[([19])-562.1(J.)-374.7(Hidders,)-414.9(P)107.1(.)-361.4(Michiels,)-414.9(J.)-374.7(P)13.4(aredaens,)-414.9(and)-388.1(R.)-374.7(V)107.1(ercammen.)]TJ
2.2216 -1.1108 TD
[(LiXQuery:)-414.9(A)-294.4(F)13.4(oundation)-321.2(for)-307.8(XQuery)-307.8(Research.)]TJ
/TT7 1 Tf
20.1354 0 TD
(SIGMOD)Tj
-20.1354 -1.0974 TD
[(Recor)40.1(d)]TJ
/TT5 1 Tf
2.8475 0 TD
[(,)-254.3(3\(4\),)-254.3(2005.)]TJ
-5.0692 -0.9502 TD
[([20])-562.1(M.)-321.2(Kay)66.9(.)-575.5(The)-321.2(Saxon)-321.2(XSL)93.7(T)-307.8(and)-334.6(XQuery)-321.2(Processor.)]TJ
/F4 1 Tf
23.5588 0 TD
-0.003 Tc
(http:)Tj
-21.3371 -1.0974 TD
(//saxon.sf.net/)Tj
/TT5 1 Tf
7.8295 0 TD
0 Tc
(.)Tj
-10.0511 -0.9636 TD
[([21])-562.1(M.)-535.3(Marx.)-1284.8(Conditional)-548.7(XP)13.4(ath.)]TJ
/TT7 1 Tf
16.869 0 TD
[(A)26.8(C)0(M)-535.3(T)53.5(r)13.4(ansactions)-548.7(on)]TJ
-14.6473 -1.0974 TD
[(Database)-267.7(Systems)-254.3(\(T)13.4(ODS\))]TJ
/TT5 1 Tf
10.6741 0 TD
[(,)-240.9(30\(4\),)-254.3(2005.)]TJ
-12.8957 -0.9502 TD
[([22])-562.1(J.)-227.5(Melton)-240.9(and)-240.9(A.)-227.5(R.)-227.5(Simon.)]TJ
/TT7 1 Tf
13.4229 0 TD
[(SQL:)-227.5(1999)-254.3(-)-227.5(Under)13.4(standing)-267.7(Re-)]TJ
-11.2013 -1.1108 TD
[(lational)-254.3(Langua)13.4(g)13.4(e)-281(Components)]TJ
/TT5 1 Tf
12.6199 0 TD
[(.)-374.7(Mor)13.4(gan)-267.7(Kaufmann,)-254.3(2002.)]TJ
-14.8415 -0.9502 TD
[([23])-562.1(C.)-321.2(Nentwich,)-374.7(L.)-321.2(Capra,)-361.4(W)93.7(.)-334.6(Emmerich,)-361.3(and)-348(A.)-334.6(Fink)13.4(elstein.)]TJ
2.2216 -1.0974 TD
[(xlinkit:)-281(A)-187.4(Consistenc)13.4(y)-214.1(Checking)-214.1(and)-214.1(Smart)-187.4(Link)-200.8(Generation)]TJ
T*
(Service.)Tj
/TT7 1 Tf
3.9712 0 TD
[(A)26.8(C)0(M)-348(T)53.5(r)13.4(ansactions)-388.1(on)-374.7(Internet)-361.4(T)93.7(e)0(c)13.4(hnolo)13.4(gy)]TJ
/TT5 1 Tf
17.4231 0 TD
[(,)-414.9(2\(2\),)]TJ
-21.3943 -1.1108 TD
(2002.)Tj
-2.2216 -0.9502 TD
[([24])-562.1(C.-W)93.7(.)-281.1(P)13.4(ark,)-307.8(J.-K.)-294.4(Min,)-321.2(and)-307.8(C.-W)93.7(.)-294.4(Chung.)-535.3(Structural)-294.4(Func-)]TJ
2.2216 -1.0974 TD
[(tion)-495.2(Inlining)-508.6(T)66.9(echnique)-522(for)-495.2(Structurally)-495.2(Recursi)26.8(v)13.4(e)-522(XML)]TJ
T*
[(Queries.)-361.4(In)]TJ
/TT7 1 Tf
4.8085 0 TD
[(Pr)40.1(oc.)-240.9(VLDB)]TJ
/TT5 1 Tf
4.8946 0 TD
[(,)-227.5(2002.)]TJ
-11.9247 -0.9636 TD
[([25])-562.1(A.)-682.5(Schmidt,)-803(F)80.3(.)-695.9(W)80.3(aas,)-803(M.)-695.9(L.)-682.5(K)26.8(ersten,)-816.4(M.)-695.9(J.)-682.5(Care)13.4(y)66.9(,)]TJ
2.2216 -1.0974 TD
[(I.)-401.5(Manolescu,)-481.8(and)-428.3(R.)-401.5(Busse.)-896.7(XMark:)-642.4(A)-414.9(Benchmark)-428.3(for)]TJ
T*
[(XML)-240.9(Data)-254.3(Management.)-388.1(In)]TJ
/TT7 1 Tf
11.5507 0 TD
[(Pr)40.1(oc.)-240.9(VLDB)]TJ
/TT5 1 Tf
4.8946 0 TD
[(,)-227.5(2002.)]TJ
9.9626 0 0 9.9626 292.68 51.06 Tm
(10)Tj
ET
endstream
endobj
75 0 obj
<<
/ProcSet [/PDF /Text /ImageB ]
/Font <<
/F1 4 0 R
/F3 6 0 R
/F4 7 0 R
/F6 22 0 R
/F7 23 0 R
/F11 27 0 R
/TT2 9 0 R
/TT5 11 0 R
/TT7 12 0 R
/TT8 13 0 R
>>
/XObject <<
/Im1 33 0 R
>>
/ExtGState <<
/GS1 17 0 R
>>
>>
endobj
33 0 obj
<<
/Type /XObject
/Subtype /Image
/Width 1
/Height 1
/BitsPerComponent 1
/ImageMask true
/Length 2
>>
stream
endstream
endobj
17 0 obj
<<
/Type /ExtGState
/SA false
/SM 0.02
/OP false
/op false
/OPM 1
/BG2 /Default
/UCR2 /Default
/HT /Default
/TR2 /Default
>>
endobj
76 0 obj
<<
/Type /FontDescriptor
/Ascent 698
/CapHeight 0
/Descent 0
/Flags 32
/FontBBox [-65 -250 1062 761]
/FontName /GPHJOL+CMSS8
/ItalicAngle 0
/StemV 87
/StemH 66
/CharSet (/a/b/i/t/e/r/m/n/o/u/d/f)
/FontFile3 77 0 R
>>
endobj
77 0 obj
<<
/Filter /FlateDecode
/Length 976
/Subtype /Type1C
>>
stream
Hl}L[UiǽÕ"w5FӤ
lv1Fvn|JemHƖ*mѡ`:dLPKncL,<{6(8bGNn˳\59tb)vEc&uHx>jO 9LuMN^ozOJI15nsmr攋jZgM|Fu5_h(-0([)W0!UqKQD*2!}>x{EDy7r}N¶i<RJAf5mFo)=Zc\a/-CZ;M'H|ub\IZbל
c*o䚪ڎOLCkC>~ff͋8
K%S)G~u=\GTD/@yp#/D+%{H<.եꈆhuwE[,g;R64!j_T+o@zFa)0cZ^N~<'n}a/K2|ϯ)Kfg.{[]O׳Omk
Q~ZΖnغrwZ&Bq=O+nA~_E(䵓0\"U
\oYv.uXwiߥw۳k9r%~`d~6yDaLnk:6 #ͽm@1b`^ʙ0_+&JBeMZ-$2"*@MNr-ohkenhI Dty .jgW֭[L5TԱ98ҦǔFphpjfNqʂ5||J}@snSAU1q{*xNَEs8ai/ {
endstream
endobj
78 0 obj
<<
/Type /FontDescriptor
/Ascent 0
/CapHeight 0
/Descent 0
/Flags 4
/FontBBox [0 -82 720 582]
/FontName /GPHKCM+stmary10
/ItalicAngle 0
/StemV 25
/StemH 25
/CharSet (/varoplus)
/FontFile3 79 0 R
>>
endobj
79 0 obj
<<
/Filter /FlateDecode
/Length 345
/Subtype /Type1C
>>
stream
Hbd`ab`ddpv..M,44 )a!CG7̗_ng]M79=rJ*23J45B