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b Fz(JOIN)p Fi(\()p Fp(S)874 56 y Fs(1)891 52 y Fp(;)6
b Fz(JOIN)p Fi(\()p Fp(S)1027 56 y Fs(2)1045 52 y Fp(;)g(S)1085
56 y Fs(3)1103 52 y Fi(\))k(:)h Fg(D)1184 56 y Ff(6)1203
52 y Fi(\))g(:)f Fg(D)1284 56 y Ff(7)1790 52 y Fz(\(2\))123
103 y Fe(ff)232 153 y Fg(D)266 157 y Ff(6)285 153 y Fp(:)p
Fz(attrib)o(utes)h Fi(=)g Fz(union)d Fi(\()p Fg(D)629
157 y Ff(2)648 153 y Fp(:)p Fz(attrib)o(utes)p Fp(;)e
Fg(D)848 157 y Ff(3)867 153 y Fp(:)p Fz(attrib)o(utes)p
Fi(\))k(;)123 203 y Fe(gg)123 253 y Fz(is)p 150 253 12
2 v 14 w(associati)o(v)o(e)d Fi(\()p Fg(D)382 257 y Ff(6)402
253 y Fp(:)p Fz(join)p 473 253 V 13 w(predicate)o Fp(;)f
Fg(D)672 257 y Ff(6)691 253 y Fp(:)p Fz(attrib)o(utes)p
Fp(;)g Fg(D)891 257 y Ff(5)910 253 y Fp(:)p Fz(join)p
981 253 V 13 w(predicate)o Fi(\))123 304 y Fe(ff)232
354 y Fg(D)266 358 y Ff(7)296 354 y Fi(=)11 b Fg(D)371
358 y Ff(5)399 354 y Fi(;)232 404 y Fg(D)266 408 y Ff(7)285
404 y Fp(:)p Fz(join)p 356 404 V 14 w(predicate)e Fi(=)i
Fg(D)590 408 y Ff(4)609 404 y Fp(:)p Fz(join)p 680 404
V 13 w(predicate)d Fi(;)232 454 y Fg(D)266 458 y Ff(6)285
454 y Fp(:)p Fz(tuple)p 373 454 V 13 w(size)i Fi(=)h
Fg(D)528 458 y Ff(2)547 454 y Fp(:)p Fz(tuple)p 635 454
V 13 w(size)c Fi(+)i Fg(D)785 458 y Ff(3)804 454 y Fp(:)p
Fz(tuple)p 892 454 V 13 w(size)f Fi(;)232 504 y Fg(D)266
508 y Ff(6)285 504 y Fp(:)p Fz(num)p 365 504 V 13 w(records)i
Fi(=)g Fz(cardinality)f Fi(\()p Fg(D)755 508 y Ff(2)774
504 y Fp(;)d Fg(D)825 508 y Ff(3)845 504 y Fi(\))j(;)123
555 y Fe(gg)764 631 y Fz(\(a\))g(Join)g(Associati)o(vity)g(T)m(-rule)p
100 682 1745 2 v 319 734 a
 tx@Dict begin tx@NodeDict begin {  } /TheNodejoinr1r2r3 16 { .5 5.384
0.09999 false .5 17.328 InitRnode  } NewNode end end
 319 734 a Fo(JOIN)192 733
y Fv(b)207 738 y Fs(2)234 733 y Ft(=)i Fv(c)287 738 y
Fs(1)248 805 y
 tx@Dict begin tx@NodeDict begin {  } /TheNodejoinr1r2 16 { .5 5.384
0.09999 false .5 17.328 InitRnode  } NewNode end end
 248 805 a Fo(JOIN)120 804 y Fv(a)139 809
y Fs(1)166 804 y Ft(=)f Fv(b)218 809 y Fs(1)181 876 y
 tx@Dict begin tx@NodeDict begin {  } /TheNoderetr1 16 { .5 5.384 0.0
false .5 15.112 InitRnode  } NewNode end end

181 876 a Fo(RET)323 876 y
 tx@Dict begin tx@NodeDict begin {  } /TheNoderetr2 16 { .5 5.384 0.0
false .5 15.112 InitRnode  } NewNode end end
 323 876 a Fo(RET)394 806 y
 tx@Dict begin tx@NodeDict begin {  } /TheNoderetr3 16 { .5 5.384 0.0
false .5 15.112 InitRnode  } NewNode end end

394 806 a Fo(RET)191 945 y
 tx@Dict begin tx@NodeDict begin {  } /TheNoder1 16 { .5 5.46666 1.1111
false .5 10.56842 InitRnode  } NewNode end end
 191 945 a Fv(R)218 950 y Fs(1)333
945 y
 tx@Dict begin tx@NodeDict begin {  } /TheNoder2 16 { .5 5.46666 1.1111
false .5 10.56842 InitRnode  } NewNode end end
 333 945 a Fv(R)360 950 y Fs(2)404 874 y
 tx@Dict begin tx@NodeDict begin {  } /TheNoder3 16 { .5 5.46666 1.1111
false .5 10.56842 InitRnode  } NewNode end end
 404 874
a Fv(R)431 879 y Fs(3)213 936 y
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2
/TheNoderetr1 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray 0
setlinecap stroke  grestore  grestore end
 213 936 a 213 936 a
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2
/TheNoderetr2 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray 0
setlinecap stroke  grestore  grestore end
 213
936 a 213 936 a
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2r3
/TheNodejoinr1r2 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray
0 setlinecap stroke  grestore  grestore end
 213 936 a 213 936 a
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2r3
/TheNoderetr3 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray 0
setlinecap stroke  grestore  grestore end
 213 936 a 213 936
a
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1
/TheNoder1 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray 0 setlinecap
stroke  grestore  grestore end
 213 936 a 213 936 a
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2
/TheNoder2 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray 0 setlinecap
stroke  grestore  grestore end
 213 936 a 213 936 a
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr3
/TheNoder3 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray 0 setlinecap
stroke  grestore  grestore end
 213 936 a 497
836 a Ft(=)-6 b Fd(\))679 734 y
 tx@Dict begin tx@NodeDict begin {  } /TheNodejoinr1r2r3 16 { .5 5.384
0.09999 false .5 17.328 InitRnode  } NewNode end end
 679 734 a Fo(JOIN)763
733 y Fv(a)782 738 y Fs(1)809 733 y Ft(=)10 b Fv(b)861
738 y Fs(1)750 805 y
 tx@Dict begin tx@NodeDict begin {  } /TheNodejoinr2r3 16 { .5 5.384
0.09999 false .5 17.328 InitRnode  } NewNode end end
 750 805 a Fo(JOIN)836 804 y Fv(b)851
809 y Fs(2)878 804 y Ft(=)g Fv(c)930 809 y Fs(1)613 806
y
 tx@Dict begin tx@NodeDict begin {  } /TheNoderetr1 16 { .5 5.384 0.0
false .5 15.112 InitRnode  } NewNode end end
 613 806 a Fo(RET)683 876 y
 tx@Dict begin tx@NodeDict begin {  } /TheNoderetr2 16 { .5 5.384 0.0
false .5 15.112 InitRnode  } NewNode end end
 683 876 a Fo(RET)825 876
y
 tx@Dict begin tx@NodeDict begin {  } /TheNoderetr3 16 { .5 5.384 0.0
false .5 15.112 InitRnode  } NewNode end end
 825 876 a Fo(RET)622 874 y
 tx@Dict begin tx@NodeDict begin {  } /TheNoder1 16 { .5 5.46666 1.1111
false .5 10.56842 InitRnode  } NewNode end end
 622 874 a Fv(R)649 879 y
Fs(1)693 945 y
 tx@Dict begin tx@NodeDict begin {  } /TheNoder2 16 { .5 5.46666 1.1111
false .5 10.56842 InitRnode  } NewNode end end
 693 945 a Fv(R)720 950 y Fs(2)835 945
y
 tx@Dict begin tx@NodeDict begin {  } /TheNoder3 16 { .5 5.46666 1.1111
false .5 10.56842 InitRnode  } NewNode end end
 835 945 a Fv(R)862 950 y Fs(3)644 936 y
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2r3
/TheNoderetr1 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray 0
setlinecap stroke  grestore  grestore end
 644 936 a 644
936 a
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2r3
/TheNodejoinr2r3 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray
0 setlinecap stroke  grestore  grestore end
 644 936 a 644 936 a
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr2r3
/TheNoderetr2 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray 0
setlinecap stroke  grestore  grestore end
 644 936 a 644 936 a
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr2r3
/TheNoderetr3 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray 0
setlinecap stroke  grestore  grestore end
 644 936
a 644 936 a
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1
/TheNoder1 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray 0 setlinecap
stroke  grestore  grestore end
 644 936 a 644 936 a
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2
/TheNoder2 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray 0 setlinecap
stroke  grestore  grestore end
 644 936 a 644 936 a
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr3
/TheNoder3 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray 0 setlinecap
stroke  grestore  grestore end
 644
936 a 142 1021 a Fz(\(b\))j(Example)d(of)j(the)e(associati)o(vity)g
(rule)h(applied)f(to)h(an)142 1072 y(operator)d(tree)p
951 1121 2 440 v 1191 734 a
 tx@Dict begin tx@NodeDict begin {  } /TheNodejoinr1r2r3 16 { .5 5.384
0.09999 false .5 17.328 InitRnode  } NewNode end end
 1191 734 a Fo(JOIN)1063 729
y Fv(a)1082 734 y Fs(2)1109 729 y Ft(=)h Fv(c)1161 734
y Fs(1)1121 805 y
 tx@Dict begin tx@NodeDict begin {  } /TheNodejoinr1r2 16 { .5 5.384
0.09999 false .5 17.328 InitRnode  } NewNode end end
 1121 805 a Fo(JOIN)993 804 y Fv(a)1012
809 y Fs(1)1038 804 y Ft(=)h Fv(b)1091 809 y Fs(1)1054
876 y
 tx@Dict begin tx@NodeDict begin {  } /TheNoderetr1 16 { .5 5.384 0.0
false .5 15.112 InitRnode  } NewNode end end
 1054 876 a Fo(RET)1196 876 y
 tx@Dict begin tx@NodeDict begin {  } /TheNoderetr2 16 { .5 5.384 0.0
false .5 15.112 InitRnode  } NewNode end end
 1196 876 a Fo(RET)1267
806 y
 tx@Dict begin tx@NodeDict begin {  } /TheNoderetr3 16 { .5 5.384 0.0
false .5 15.112 InitRnode  } NewNode end end
 1267 806 a Fo(RET)1064 945 y
 tx@Dict begin tx@NodeDict begin {  } /TheNoder1 16 { .5 5.46666 1.1111
false .5 10.56842 InitRnode  } NewNode end end
 1064 945 a Fv(R)1091
950 y Fs(1)1206 945 y
 tx@Dict begin tx@NodeDict begin {  } /TheNoder2 16 { .5 5.46666 1.1111
false .5 10.56842 InitRnode  } NewNode end end
 1206 945 a Fv(R)1233 950 y Fs(2)1276
874 y
 tx@Dict begin tx@NodeDict begin {  } /TheNoder3 16 { .5 5.46666 1.1111
false .5 10.56842 InitRnode  } NewNode end end
 1276 874 a Fv(R)1303 879 y Fs(3)1086 936 y
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2
/TheNoderetr1 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray 0
setlinecap stroke  grestore  grestore end
 1086
936 a 1086 936 a
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2
/TheNoderetr2 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray 0
setlinecap stroke  grestore  grestore end
 1086 936 a 1086 936 a
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2r3
/TheNodejoinr1r2 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray
0 setlinecap stroke  grestore  grestore end
 1086 936 a 1086
936 a
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2r3
/TheNoderetr3 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray 0
setlinecap stroke  grestore  grestore end
 1086 936 a 1086 936 a
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1
/TheNoder1 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray 0 setlinecap
stroke  grestore  grestore end
 1086 936 a 1086 936 a
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2
/TheNoder2 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray 0 setlinecap
stroke  grestore  grestore end
 1086
936 a 1086 936 a
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr3
/TheNoder3 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray 0 setlinecap
stroke  grestore  grestore end
 1086 936 a 1370 836 a Ft(=)-6 b Fd(\))1390
838 y Fv(=)1552 734 y
 tx@Dict begin tx@NodeDict begin {  } /TheNodejoinr1r2r3 16 { .5 5.384
0.09999 false .5 17.328 InitRnode  } NewNode end end
 1552 734 a Fo(JOIN)1623 805 y
 tx@Dict begin tx@NodeDict begin {  } /TheNodejoinr2r3 16 { .5 5.384
0.09999 false .5 17.328 InitRnode  } NewNode end end
 1623
805 a Fo(JOIN)1485 806 y
 tx@Dict begin tx@NodeDict begin {  } /TheNoderetr1 16 { .5 5.384 0.0
false .5 15.112 InitRnode  } NewNode end end
 1485 806 a Fo(RET)1556 876 y
 tx@Dict begin tx@NodeDict begin {  } /TheNoderetr2 16 { .5 5.384 0.0
false .5 15.112 InitRnode  } NewNode end end

1556 876 a Fo(RET)1698 876 y
 tx@Dict begin tx@NodeDict begin {  } /TheNoderetr3 16 { .5 5.384 0.0
false .5 15.112 InitRnode  } NewNode end end
 1698 876 a Fo(RET)1495 874
y
 tx@Dict begin tx@NodeDict begin {  } /TheNoder1 16 { .5 5.46666 1.1111
false .5 10.56842 InitRnode  } NewNode end end
 1495 874 a Fv(R)1522 879 y Fs(1)1566 945 y
 tx@Dict begin tx@NodeDict begin {  } /TheNoder2 16 { .5 5.46666 1.1111
false .5 10.56842 InitRnode  } NewNode end end
 1566 945
a Fv(R)1593 950 y Fs(2)1707 945 y
 tx@Dict begin tx@NodeDict begin {  } /TheNoder3 16 { .5 5.46666 1.1111
false .5 10.56842 InitRnode  } NewNode end end
 1707 945 a Fv(R)1734
950 y Fs(3)1517 936 y
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2r3
/TheNoderetr1 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray 0
setlinecap stroke  grestore  grestore end
 1517 936 a 1517 936 a
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2r3
/TheNodejoinr2r3 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray
0 setlinecap stroke  grestore  grestore end
 1517 936
a 1517 936 a
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr2r3
/TheNoderetr2 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray 0
setlinecap stroke  grestore  grestore end
 1517 936 a 1517 936 a
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr2r3
/TheNoderetr3 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray 0
setlinecap stroke  grestore  grestore end
 1517 936 a 1517 936
a
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1
/TheNoder1 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray 0 setlinecap
stroke  grestore  grestore end
 1517 936 a 1517 936 a
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2
/TheNoder2 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray 0 setlinecap
stroke  grestore  grestore end
 1517 936 a 1517 936 a
 tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray  /ArrowA { moveto
} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr3
/TheNoder3 InitNC { NCLine  } if end gsave 0.8 SLW 0. setgray 0 setlinecap
stroke  grestore  grestore end
 1517 936
a 1015 1021 a Fz(\(c\))11 b(Example)f(of)i(an)e(operator)h(tree)g
(where)f(the)h(associa-)1015 1072 y(ti)o(vity)f(rule)g(does)d(not)j
(apply)p 1868 1134 2 1122 v 75 1136 1796 2 v 1869 1144
10 1126 v 83 1144 1796 10 v 727 1247 a FG(Figure)i(3:)j(Join)10
b(associati)o(vity)p 85 1392 1773 2 v 85 1806 2 414 v
122 1432 a Fp(E)r Fi(\()p Fp(x)189 1436 y Fs(1)206 1432
y Fp(;)c(:)g(:)g(:)g(;)g(x)313 1436 y Fh(n)334 1432 y
Fi(\))11 b(:)f Fg(D)415 1436 y Ff(1)445 1432 y Fi(=)-6
b Fe(\))11 b Fp(A)p Fi(\()p Fp(x)584 1436 y Fs(1)600
1432 y Fp(;)6 b(:)h(:)f(:)g(;)g(x)708 1436 y Fh(n)729
1432 y Fi(\))k(:)h Fg(D)810 1436 y Ff(2)1788 1432 y Fz(\(3\))122
1482 y(test)122 1533 y Fe(ff)230 1583 y Fz(pre-opt)f(statements)122
1633 y Fe(gg)122 1683 y(ff)230 1734 y Fz(post-opt)f(statements)122
1784 y Fe(gg)p 1855 1806 V 85 1808 1773 2 v 1856 1816
10 418 v 93 1816 1773 10 v 654 1919 a FG(Figure)i(4:)16
b(General)11 b(form)h(of)f(an)h(I-rule)75 2099 y Fy(2.4)50
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b(Let)10 b Fw(E)i FG(be)e(an)g(e)o(xpression)f(and)h
Fw(A)g FG(be)g(an)g(algorithm)f(that)h(implements)f Fw(E)s
FG(.)15 b(The)10 b(general)75 2316 y(form)i(of)f(an)g(I-rule)h(is)e(gi)
o(v)o(en)h(by)g(Equation)e(\(3\))i(\(sho)o(wn)f(in)h(Figure)g(4\).)137
2378 y(The)f(actions)e(associated)h(with)f(an)i(I-rule)f(are)i
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FB(test)p FG(,)f(is)g(a)h(boolean)75 2440 y(e)o(xpression)g(whose)h(v)o
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(statements)p FG(,)h(is)g(a)g(set)g(of)g(descriptor)f(assignment)g
(statements)g(that)h(are)75 2565 y(e)o(x)o(ecuted)f(only)f(if)h(the)g
(test)f(is)g(true)h(and)g FB(befor)n(e)g FG(an)o(y)g(of)g(the)f(inputs)
g Fw(x)1249 2572 y Fv(i)1279 2565 y FG(of)h Fw(E)i FG(are)f(optimized.)
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b(An)17 b(introduction)d(to)j(distrib)o(uted)e(query)i(compilation)e
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FB(Pr)n(oceedings)f(2nd)171 139 y(International)9 b(Confer)n(ence)i(on)
g(Distrib)o(uted)d(Databases)p FG(,)i(pages)h(291\261309,)f(Berlin,)h
(September)h(1982.)98 233 y([5])20 b(Dinesh)12 b(Das)h(and)f(Don)g
(Batory)m(.)21 b(Prairie:)e(An)13 b(algebraic)f(frame)o(work)h(for)g
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b(In)15 b FB(Pr)n(oceedings)e(of)i(the)f(W)l(orkshop)f(on)i(Database)e
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(Optimizers)p FG(,)f(pages)i(139\261154,)f(Dallas,)h(September)g(1993.)
98 451 y([6])20 b(Johann)8 b(Christoph)e(Fre)o(ytag.)12
b(A)c(rule-based)g(vie)o(w)f(of)h(query)g(optimization.)i(In)e
FB(Pr)n(oceedings)e(1987)h(A)o(CM)171 514 y(SIGMOD)13
b(International)d(Confer)n(ence)j(on)f(Management)f(of)h(Data)p
FG(,)h(pages)g(173\261180,)f(San)h(Francisco,)171 576
y(May)f(1987.)98 670 y([7])20 b(Goetz)13 b(Graefe.)23
b FB(Rule-Based)12 b(Query)h(Optimizatio)o(n)d(in)j(Extensible)f
(Database)f(Systems)p FG(.)21 b(PhD)13 b(thesis,)171
732 y(Uni)o(v)o(ersity)d(of)h(W)n(isconsin\261Madison,)e(1987.)98
826 y([8])20 b(Goetz)12 b(Graefe.)19 b(V)-6 b(olcano,)12
b(an)g(e)o(xtensible)e(and)i(parallel)f(query)h(e)o(v)o(aluation)e
(system.)17 b(T)m(echnical)11 b(Report)171 888 y
(CU\261CS\261481\26190,)g(Uni)o(v)o(ersity)e(of)i(Colorado)g(at)g
(Boulder)n(,)h(July)e(1990.)98 983 y([9])20 b(Goetz)c(Graefe.)31
b(Query)15 b(e)o(v)o(aluation)g(techniques)f(for)i(lar)o(ge)h
(databases.)29 b FB(A)o(CM)15 b(Computing)g(Surve)o(ys)p
FG(,)171 1045 y(25\(2\):73\261170,)10 b(June)g(1993.)75
1139 y([10])20 b(Goetz)f(Graefe)i(and)e(Da)o(vid)f(J.)i(DeW)n(itt.)37
b(The)19 b(EXODUS)g(optimizer)f(generator)m(.)39 b(In)19
b FB(Pr)n(oceedings)171 1201 y(1987)12 b(A)o(CM)f(SIGMOD)h
(International)d(Confer)n(ence)j(on)f(Management)f(of)i(Data)p
FG(,)f(pages)h(387\261394,)f(San)171 1263 y(Francisco,)h(May)g(1987.)75
1358 y([11])20 b(L.)15 b(M.)g(Haas,)h(J.)e(C.)h(Fre)o(ytag,)h(G.)e(M.)i
(Lohman,)f(and)f(H.)g(Pirahesh.)25 b(Extensible)12 b(query)i
(processing)f(in)171 1420 y(Starb)o(urst.)j(Research)c(Report)f(RJ)h
(6610,)e(IBM)j(Almaden)e(Research)h(Center)n(,)g(December)g(1988.)75
1514 y([12])20 b(W)l(on)9 b(Kim,)g(Da)o(vid)e(S.)j(Reiner)n(,)f(and)f
(Don)g(S.)h(Batory)m(,)g(editors.)i FB(Query)d(Pr)n(ocessing)e(in)i
(Database)f(Systems)p FG(.)171 1576 y(Springer)o(-V)-5
b(erlag,)12 b(1985.)75 1671 y([13])20 b(Guy)12 b(M.)i(Lohman.)19
b(Grammar)o(-like)12 b(functional)f(rules)h(for)h(representing)e(query)
h(optimization)e(alterna-)171 1733 y(ti)o(v)o(es.)15
b(In)10 b FB(Pr)n(oceedings)e(1988)i(A)o(CM)f(SIGMOD)h(International)d
(Confer)n(ence)j(on)g(Management)e(of)i(Data)p FG(,)171
1795 y(pages)h(18\26127,)g(Chicago,)g(June)g(1988.)75
1889 y([14])20 b(Guy)13 b(M.)h(Lohman,)g(C.)g(Mohan,)h(Laura)e(M.)h
(Haas,)h(Bruce)f(G.)f(Lindsay)m(,)g(P)o(atricia)h(G.)f(Selinger)n(,)h
(P)o(aul)g(F)l(.)171 1951 y(W)n(ilms,)e(and)f(Dean)h(Daniels.)k(Query)c
(processing)e(in)h(R)1075 1935 y Fd(\003)1095 1951 y
FG(.)17 b(Research)c(Report)e(RJ)h(4272,)f(IBM)h(Research)171
2013 y(Laboratory)m(,)f(San)h(Jose,)f(April)f(1984.)75
2108 y([15])20 b(P)-5 b(.)14 b(Schwarz,)f(W)l(.)g(Chang,)f(J.)h(C.)g
(Fre)o(ytag,)h(G.)e(Lohman,)h(J.)g(McPherson,)g(C.)g(Mohan,)g(and)f(H.)
h(Pirahesh.)171 2170 y(Extensibility)i(in)i(the)g(Starb)o(urst)g
(database)h(system.)33 b(In)18 b FB(Pr)n(oceedings)e(International)f(W)
l(orkshop)h(on)171 2232 y(Object-Oriented)10 b(Database)f(Systems)p
FG(,)i(pages)g(85\26192,)f(Asilomar)n(,)h(September)h(1986.)75
2326 y([16])20 b(P)-5 b(.)13 b(G.)g(Selinger)e(and)h(M.)h(Adiba.)18
b(Access)12 b(path)f(selection)g(in)h(distrib)o(uted)d(data)j(base)g
(management)h(sys-)171 2388 y(tems.)19 b(In)13 b(Deen)f(and)g
(Hammersly)m(,)h(editors,)e FB(Pr)n(oceedings)g(International)e(Confer)
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(v)o(ersity)g(of)h(Aberdeen,)g(July)f(1980.)75 2545 y([17])20
b(P)-5 b(.)14 b(G.)e(Selinger)n(,)h(M.)g(M.)h(Astrahan,)e(D.)g(D.)h
(Chamberlin,)g(R.)g(A.)g(Lorie,)f(and)g(T)m(.)h(G.)f(Price.)21
b(Access)12 b(path)171 2607 y(selection)h(in)h(a)g(relational)f
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h(A)o(CM)h(SIGMOD)171 2669 y(International)9 b(Confer)n(ence)i(on)g
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%%Page: 25 25
25 24 bop 75 14 a FG([18])20 b(Michael)14 b(Stonebraker)f(and)h(La)o
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b(In)14 b FB(Pr)n(oceedings)e(1986)171 77 y(A)o(CM)g(SIGMOD)f
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FG(,)h(pages)f(340\261355,)g(W)l(ashing-)171 139 y(ton,)g(May)h(1986.)
75 234 y([19])20 b(Da)o(vid)14 b(L.)f(W)l(ells,)i(Jos)s(\302)-18
b(e)13 b(A.)h(Blakele)o(y)m(,)g(and)g(Craig)f(W)l(.)h(Thompson.)22
b(Architecture)13 b(of)h(an)g(open)f(object-)171 296
y(oriented)e(database)g(management)g(system.)16 b FB(IEEE)11
b(Computer)p FG(,)g(25\(10\):74\26182,)e(October)i(1992.)75
391 y([20])20 b(C.)11 b(T)m(.)e(Y)-5 b(u)9 b(and)h(C.)g(C.)g(Chang.)k
(Distrib)o(uted)7 b(query)i(processing.)k FB(A)o(CM)c(Computing)f
(Surve)o(ys)p FG(,)h(16\(4\):399\261)171 453 y(433,)i(December)i(1984.)
952 2793 y(25)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF