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3806 y(approac)m(hes)e(are)g(dev)m(elop)s(ed)g(to)f(roughly)f(the)i
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1959 1208 4 308 v 1959 1955 4 474 v 1959 2702 V 1959
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eop
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1831 y(\001)2110 1914 y(\001)2093 1948 y(\001)p 2233
1956 V 2234 1748 a(A)2276 1831 y(A)2318 1914 y(A)2334
1948 y(A)p 2382 2205 4 125 v 2525 2039 a Fr(x)115 b Fu(:=)63
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4 291 v 2733 1748 a(A)2774 1831 y(A)2816 1914 y(A)2832
1948 y(A)p 2880 2205 4 125 v 2940 1624 a Fr(y)115 b Fu(:=)63
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4 291 v 3148 1333 a(A)3189 1416 y(A)3231 1499 y(A)3247
1533 y(A)p 3296 1790 4 125 v 973 794 a Fs(S)906 918 y
Fq(\000)823 1001 y(\000)740 1084 y(\000)699 1126 y(\000)640
1209 y Fs(S)616 1333 y Fq(\001)574 1416 y(\001)533 1499
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1533 y(A)782 1624 y Fs(a)p 805 1790 4 125 v 782 1873
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1001 y(@)1155 1084 y(@)1197 1126 y(@)1305 1209 y Fs(S)1259
1333 y Fq(\023)1197 1416 y(\023)1134 1499 y(\023)1114
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b Fs(a)1197 2288 y Fr(y)1031 1748 y Fq(\001)989 1831
y(\001)948 1914 y(\001)931 1948 y(\001)p 1071 1956 V
1072 1748 a(A)1114 1831 y(A)1155 1914 y(A)1172 1948 y(A)p
1220 2205 4 125 v 1320 1541 4 291 v 1313 1624 a Fu(;)1321
1333 y Fq(S)1384 1416 y(S)1446 1499 y(S)1467 1527 y(S)1056
1624 y Fs(S)1388 2039 y Fr(y)90 b Fu(:=)63 b Fs(a)1695
2288 y Fr(z)1529 1748 y Fq(\001)1487 1831 y(\001)1446
1914 y(\001)1429 1948 y(\001)p 1569 1956 V 1570 1748
a(A)1612 1831 y(A)1653 1914 y(A)1670 1948 y(A)p 1718
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281 1019 135 10 v 135 w({z)p 490 1019 V 135 w(})279 1124
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4603 y Fs(x)12 b Fu(.)42 b(F)-8 b(rom)0 4724 y(the)31
b(assumptions)f(of)g(the)h(lemma)d(w)m(e)j(get)g Fs(s)38
b(x)k Fu(=)31 b Fs(s)1927 4687 y Fi(0)1980 4724 y Fs(x)42
b Fu(b)s(ecause)32 b Fs(x)42 b Ft(2)31 b Fu(FV\()p Fs(x)12
b Fu(\))30 b(so)h(clearly)e(the)0 4844 y(lemma)h(holds)j(in)e(this)i
(case.)146 4966 y(Next)h(w)m(e)f(turn)g(to)f(the)h(comp)s(osite)f
(elemen)m(ts)h(of)f Fw(Aexp)p Fu(:)0 5133 y Fw(The)f(case)g
Fs(a)509 5148 y Fn(1)579 5133 y Fu(+)f Fs(a)742 5148
y Fn(2)781 5133 y Fu(:)43 b(F)-8 b(rom)29 b(T)-8 b(able)30
b(1.1)g(w)m(e)h(ha)m(v)m(e)h Ft(A)o Fu([)-17 b([)q Fs(a)2064
5148 y Fn(1)2134 5133 y Fu(+)30 b Fs(a)2297 5148 y Fn(2)2337
5133 y Fu(])-17 b(])p Fs(s)39 b Fu(=)30 b Ft(A)o Fu([)-17
b([)q Fs(a)2733 5148 y Fn(1)2773 5133 y Fu(])g(])p Fs(s)38
b Fu(+)31 b Ft(A)o Fu([)-17 b([)q Fs(s)3160 5148 y Fn(2)3199
5133 y Fu(])g(])q Fs(s)38 b Fu(and)0 5254 y(similarly)24
b Ft(A)p Fu([)-17 b([)p Fs(a)568 5269 y Fn(1)636 5254
y Fu(+)28 b Fs(a)797 5269 y Fn(2)836 5254 y Fu(])-17
b(])q Fs(s)922 5218 y Fi(0)973 5254 y Fu(=)28 b Ft(A)o
Fu([)-17 b([)q Fs(a)1251 5269 y Fn(1)1291 5254 y Fu(])g(])p
Fs(s)1376 5218 y Fi(0)1427 5254 y Fu(+)28 b Ft(A)p Fu([)-17
b([)p Fs(s)1696 5269 y Fn(2)1736 5254 y Fu(])g(])p Fs(s)1821
5218 y Fi(0)1845 5254 y Fu(.)42 b(Since)28 b Fs(a)2221
5269 y Fn(i)2273 5254 y Fu(\(for)f(i)g(=)g(1,2\))h(is)f(an)h(immediate)
0 5374 y(sub)s(expression)35 b(of)e Fs(a)789 5389 y Fn(1)862
5374 y Fu(+)g Fs(a)1028 5389 y Fn(2)1101 5374 y Fu(and)g(FV\()p
Fs(a)1523 5389 y Fn(i)1547 5374 y Fu(\))g Ft(\022)h Fu(FV\()p
Fs(a)1961 5389 y Fn(1)2033 5374 y Fu(+)f Fs(a)2199 5389
y Fn(2)2239 5374 y Fu(\))g(w)m(e)h(can)g(apply)f(the)g(induction)0
5494 y(h)m(yp)s(othesis)i(\(that)f(is)g(the)g(lemma\))e(to)i
Fs(a)1534 5509 y Fn(i)1592 5494 y Fu(and)g(get)h Ft(A)o
Fu([)-17 b([)q Fs(a)2122 5509 y Fn(i)2146 5494 y Fu(])g(])p
Fs(s)43 b Fu(=)34 b Ft(A)o Fu([)-17 b([)q Fs(a)2550 5509
y Fn(i)2574 5494 y Fu(])g(])p Fs(s)2659 5458 y Fi(0)2683
5494 y Fu(.)48 b(It)34 b(is)g(no)m(w)h(easy)g(to)p eop
%%Page: 16 26
16 25 bop 251 130 a Fw(16)2575 b(1)113 b(In)m(tro)s(duction)p
251 193 3473 4 v 283 515 a Fu(see)34 b(that)f(the)g(lemma)d(holds)i
(for)g Fs(a)1596 530 y Fn(1)1668 515 y Fu(+)h Fs(a)1834
530 y Fn(2)1906 515 y Fu(as)g(w)m(ell.)283 683 y Fw(The)38
b(cases)h Fs(a)851 698 y Fn(1)928 683 y Ft(\000)f Fs(a)1100
698 y Fn(2)1177 683 y Fu(and)g Fs(a)1429 698 y Fn(1)1506
683 y Fo(?)f Fs(a)1649 698 y Fn(2)1726 683 y Fu(follo)m(w)f(the)i(same)
g(pattern)f(and)h(are)g(omitted.)57 b(This)283 803 y(completes)33
b(the)g(pro)s(of.)2529 b Fh(2)430 1009 y Fu(In)41 b(a)f(similar)e(w)m
(a)m(y)k(w)m(e)g(ma)m(y)e(de\014ne)j(the)e(set)g(FV\()p
Fs(b)6 b Fu(\))41 b(of)f(free)h(v)-5 b(ariables)40 b(in)g(a)g(b)s(o)s
(olean)283 1130 y(expression)34 b Fs(b)39 b Fu(b)m(y)577
1336 y(FV\()p Fr(true)p Fu(\))231 b(=)100 b Ft(;)577
1504 y Fu(FV\()p Fr(false)p Fu(\))180 b(=)100 b Ft(;)577
1672 y Fu(FV\()p Fs(a)809 1687 y Fn(1)881 1672 y Fu(=)32
b Fs(a)1046 1687 y Fn(2)1086 1672 y Fu(\))101 b(=)f(FV\()p
Fs(a)1633 1687 y Fn(1)1672 1672 y Fu(\))33 b Ft([)g Fu(FV\()p
Fs(a)2074 1687 y Fn(2)2113 1672 y Fu(\))577 1839 y(FV\()p
Fs(a)809 1854 y Fn(1)881 1839 y Ft(\024)g Fs(a)1048 1854
y Fn(2)1088 1839 y Fu(\))99 b(=)h(FV\()p Fs(a)1633 1854
y Fn(1)1672 1839 y Fu(\))33 b Ft([)g Fu(FV\()p Fs(a)2074
1854 y Fn(2)2113 1839 y Fu(\))577 2007 y(FV\()p Ft(:)p
Fs(b)6 b Fu(\))318 b(=)100 b(FV\()p Fs(b)6 b Fu(\))577
2175 y(FV\()p Fs(b)803 2190 y Fn(1)875 2175 y Ft(^)33
b Fs(b)1025 2190 y Fn(2)1064 2175 y Fu(\))123 b(=)100
b(FV\()p Fs(b)1627 2190 y Fn(1)1666 2175 y Fu(\))32 b
Ft([)h Fu(FV\()p Fs(b)2061 2190 y Fn(2)2100 2175 y Fu(\))283
2421 y Fw(Exercise)k(1.12)49 b(\(Essen)m(tial\))31 b
Fu(Let)j Fs(s)41 b Fu(and)34 b Fs(s)2024 2385 y Fi(0)2080
2421 y Fu(b)s(e)g(t)m(w)m(o)g(states)h(satisfying)d(that)h
Fs(s)42 b(x)j Fu(=)33 b Fs(s)3654 2385 y Fi(0)3711 2421
y Fs(x)283 2541 y Fu(for)f(all)f Fs(x)44 b Fu(in)32 b(FV\()p
Fs(b)6 b Fu(\).)43 b(Pro)m(v)m(e)34 b(that)f Ft(B)s Fu([)-17
b([)q Fs(b)6 b Fu(])-17 b(])p Fs(s)41 b Fu(=)32 b Ft(B)t
Fu([)-17 b([)p Fs(b)6 b Fu(])-17 b(])q Fs(s)2218 2505
y Fi(0)2241 2541 y Fu(.)1413 b Fh(2)283 2845 y Fp(Substitutions)283
3034 y Fu(W)-8 b(e)46 b(shall)d(later)g(b)s(e)i(in)m(terested)h(in)e
(replacing)f(eac)m(h)j(o)s(ccurrence)g(of)e(a)h(v)-5
b(ariable)42 b Fs(y)54 b Fu(in)44 b(an)283 3155 y(arithmetic)j
(expression)i Fs(a)56 b Fu(with)48 b(another)g(arithmetic)e(expression)
k Fs(a)3003 3170 y Fn(0)3042 3155 y Fu(.)91 b(This)48
b(is)g(called)283 3275 y Fs(substitution)39 b Fu(and)30
b(w)m(e)i(write)e Fs(a)7 b Fu([)p Fs(y)i Ft(7!)p Fs(a)1685
3290 y Fn(0)1725 3275 y Fu(])30 b(for)g(the)h(arithmetic)d(expression)k
(so)f(obtained.)42 b(The)283 3395 y(formal)31 b(de\014nition)g(is)h(as)
h(follo)m(ws:)577 3583 y Fs(n)7 b Fu([)p Fs(y)i Ft(7!)p
Fs(a)879 3598 y Fn(0)919 3583 y Fu(])449 b(=)100 b Fs(n)577
3840 y(x)12 b Fu([)p Fs(y)d Ft(7!)p Fs(a)874 3855 y Fn(0)913
3840 y Fu(])455 b(=)1571 3666 y Fg(8)1571 3741 y(<)1571
3890 y(:)1686 3756 y Fs(a)1743 3771 y Fn(0)1866 3756
y Fu(if)31 b Fs(x)44 b Fu(=)33 b Fs(y)1686 3923 y(x)135
b Fu(if)31 b Fs(x)44 b Ft(6)p Fu(=)33 b Fs(y)577 4103
y Fu(\()p Fs(a)672 4118 y Fn(1)744 4103 y Fu(+)g Fs(a)910
4118 y Fn(2)949 4103 y Fu(\)[)p Fs(y)9 b Ft(7!)p Fs(a)1227
4118 y Fn(0)1267 4103 y Fu(])101 b(=)f(\()p Fs(a)1666
4118 y Fn(1)1705 4103 y Fu([)p Fs(y)9 b Ft(7!)p Fs(a)1945
4118 y Fn(0)1985 4103 y Fu(]\))32 b(+)h(\()p Fs(a)2286
4118 y Fn(2)2325 4103 y Fu([)p Fs(y)9 b Ft(7!)p Fs(a)2565
4118 y Fn(0)2605 4103 y Fu(]\))577 4270 y(\()p Fs(a)672
4285 y Fn(1)744 4270 y Fo(?)33 b Fs(a)883 4285 y Fn(2)922
4270 y Fu(\)[)p Fs(y)9 b Ft(7!)p Fs(a)1200 4285 y Fn(0)1240
4270 y Fu(])128 b(=)100 b(\()p Fs(a)1666 4285 y Fn(1)1705
4270 y Fu([)p Fs(y)9 b Ft(7!)p Fs(a)1945 4285 y Fn(0)1985
4270 y Fu(]\))32 b Fo(?)h Fu(\()p Fs(a)2259 4285 y Fn(2)2298
4270 y Fu([)p Fs(y)9 b Ft(7!)p Fs(a)2538 4285 y Fn(0)2578
4270 y Fu(]\))577 4438 y(\()p Fs(a)672 4453 y Fn(1)744
4438 y Ft(\000)33 b Fs(a)911 4453 y Fn(2)951 4438 y Fu(\)[)p
Fs(y)9 b Ft(7!)p Fs(a)1229 4453 y Fn(0)1268 4438 y Fu(])100
b(=)g(\()p Fs(a)1666 4453 y Fn(1)1705 4438 y Fu([)p Fs(y)9
b Ft(7!)p Fs(a)1945 4453 y Fn(0)1985 4438 y Fu(]\))32
b Ft(\000)h Fu(\()p Fs(a)2287 4453 y Fn(2)2327 4438 y
Fu([)p Fs(y)9 b Ft(7!)p Fs(a)2567 4453 y Fn(0)2606 4438
y Fu(]\))283 4652 y(As)34 b(an)e(example)g(\()p Fr(x)p
Fu(+)p Fr(1)p Fu(\)[)p Fr(x)p Ft(7!)p Fr(3)p Fu(])h(=)g
Fr(3)p Fu(+)p Fr(1)g Fu(and)f(\()p Fr(x)p Fu(+)p Fr(y)p
Fo(?)p Fr(x)p Fu(\)[)p Fr(x)p Ft(7!)q Fr(y)p Ft(\000)p
Fr(5)p Fu(])h(=)g(\()p Fr(y)p Ft(\000)p Fr(5)p Fu(\)+)p
Fr(y)p Fo(?)p Fu(\()p Fr(y)p Ft(\000)p Fr(5)p Fu(\).)430
4775 y(W)-8 b(e)48 b(also)e(ha)m(v)m(e)j(a)e(notion)f(of)h
(substitution)g(\(or)g(up)s(dating\))f(for)h(states.)89
b(W)-8 b(e)48 b(de\014ne)283 4895 y Fs(s)8 b Fu([)p Fs(y)h
Ft(7!)p Fs(v)i Fu(])33 b(to)f(b)s(e)h(the)g(state)g(that)f(is)g(as)h
Fs(s)40 b Fu(except)35 b(that)d(the)h(v)-5 b(alue)32
b(b)s(ound)h(to)f Fs(y)41 b Fu(is)33 b Fs(v)11 b Fu(,)32
b(that)g(is)527 5198 y(\()p Fs(s)8 b Fu([)p Fs(y)h Ft(7!)p
Fs(v)i Fu(]\))32 b Fs(x)45 b Fu(=)1147 5023 y Fg(8)1147
5098 y(<)1147 5247 y(:)1262 5113 y Fs(v)176 b Fu(if)31
b Fs(x)44 b Fu(=)33 b Fs(y)1262 5281 y(s)41 b(x)95 b
Fu(if)31 b Fs(x)44 b Ft(6)p Fu(=)33 b Fs(y)283 5494 y
Fu(The)h(relationship)d(b)s(et)m(w)m(een)j(the)f(t)m(w)m(o)h(concepts)g
(is)e(sho)m(wn)i(in)e(the)h(follo)m(wing)c(exercise:)p
eop
%%Page: 17 27
17 26 bop 0 130 a Fw(1.4)112 b(Prop)s(erties)36 b(of)i(the)f(seman)m
(tics)1763 b(17)p 0 193 3473 4 v 0 515 a(Exercise)36
b(1.13)49 b(\(Essen)m(tial\))37 b Fu(Pro)m(v)m(e)k(that)e
Ft(A)p Fu([)-17 b([)p Fs(a)7 b Fu([)p Fs(y)i Ft(7!)p
Fs(a)2164 530 y Fn(0)2204 515 y Fu(]])-17 b(])q Fs(s)47
b Fu(=)39 b Ft(A)p Fu([)-17 b([)p Fs(a)7 b Fu(])-17 b(])q(\()p
Fs(s)8 b Fu([)p Fs(y)h Ft(7!A)p Fu([)-17 b([)p Fs(a)3126
530 y Fn(0)3166 515 y Fu(])g(])q Fs(s)8 b Fu(]\))39 b(for)0
636 y(all)30 b(states)k Fs(s)8 b Fu(.)2910 b Fh(2)0 864
y Fw(Exercise)36 b(1.14)49 b(\(Essen)m(tial\))25 b Fu(De\014ne)i
(substitution)f(for)g(b)s(o)s(olean)g(expressions:)42
b Fs(b)6 b Fu([)p Fs(y)j Ft(7!)p Fs(a)3406 879 y Fn(0)3445
864 y Fu(])0 984 y(is)44 b(to)h(b)s(e)g(the)h(b)s(o)s(olean)d
(expression)j(that)f(is)f(as)i Fs(b)k Fu(except)d(that)e(all)e(o)s
(ccurrences)j(of)f(the)0 1105 y(v)-5 b(ariable)26 b Fs(y)37
b Fu(are)28 b(replaced)h(b)m(y)g(the)f(arithmetic)e(expression)k
Fs(a)2268 1120 y Fn(0)2307 1105 y Fu(.)42 b(Pro)m(v)m(e)30
b(that)e(y)m(our)g(de\014nition)0 1225 y(satis\014es)244
1429 y Ft(B)s Fu([)-17 b([)q Fs(b)6 b Fu([)p Fs(y)j Ft(7!)p
Fs(a)641 1444 y Fn(0)680 1429 y Fu(]])-17 b(])q Fs(s)41
b Fu(=)32 b Ft(B)s Fu([)-17 b([)q Fs(b)6 b Fu(])-17 b(])q(\()p
Fs(s)8 b Fu([)p Fs(y)h Ft(7!)o(A)p Fu([)-17 b([)q Fs(a)1572
1444 y Fn(0)1611 1429 y Fu(])g(])q Fs(s)8 b Fu(]\))0
1632 y(for)32 b(all)f(states)i Fs(s)8 b Fu(.)2761 b Fh(2)p
eop
%%Page: 18 28
18 27 bop 251 130 a Fw(18)2575 b(1)113 b(In)m(tro)s(duction)p
251 193 3473 4 v eop
%%Page: 19 29
19 28 bop 0 1180 a Fv(Chapter)78 b(2)0 1595 y(Op)6 b(erational)77
b(Seman)-6 b(tics)0 2047 y Fu(The)27 b(role)e(of)g(a)h(statemen)m(t)g
(in)f Fw(While)f Fu(is)h(to)h(c)m(hange)h(the)f(state.)41
b(F)-8 b(or)25 b(example,)i(if)e Fr(x)h Fu(is)f(b)s(ound)0
2168 y(to)i Fw(3)g Fu(in)g Fs(s)35 b Fu(and)27 b(w)m(e)i(execute)g(the)
f(statemen)m(t)f Fr(x)h Fu(:=)f Fr(x)h Fu(+)f Fr(1)g
Fu(then)h(w)m(e)g(get)g(a)f(new)h(state)g(where)g Fr(x)0
2288 y Fu(is)k(b)s(ound)h(to)f Fw(4)p Fu(.)44 b(So)33
b(while)f(the)h(seman)m(tics)g(of)f(arithmetic)e(and)j(b)s(o)s(olean)e
(expressions)k(only)0 2408 y Fs(insp)-5 b(e)g(ct)43 b
Fu(the)34 b(state)h(in)e(order)h(to)g(determine)g(the)g(v)-5
b(alue)34 b(of)f(the)i(expression,)h(the)e(seman)m(tics)0
2529 y(of)e(statemen)m(ts)i(will)c Fs(mo)-5 b(dify)41
b Fu(the)33 b(state)g(as)f(w)m(ell.)146 2649 y(In)38
b(an)g(op)s(erational)e(seman)m(tics)i(w)m(e)g(are)g(concerned)i(with)d
Fs(how)48 b Fu(to)37 b(execute)j(programs)0 2769 y(and)27
b(not)g(merely)f(what)h(the)h(results)f(of)g(execution)g(are.)42
b(More)27 b(precisely)-8 b(,)28 b(w)m(e)g(are)f(in)m(terested)0
2890 y(in)39 b(ho)m(w)h(the)f(states)i(are)e(mo)s(di\014ed)f(during)h
(the)h(execution)g(of)f(the)h(statemen)m(t.)64 b(W)-8
b(e)40 b(shall)0 3010 y(consider)33 b(t)m(w)m(o)g(di\013eren)m(t)g
(approac)m(hes)h(to)e(op)s(erational)e(seman)m(tics:)145
3211 y Ft(\017)49 b Fs(Natur)-5 b(al)36 b(semantics)p
Fu(:)43 b(its)33 b(purp)s(ose)h(is)e(to)h(describ)s(e)h(ho)m(w)g(the)f
Fs(over)-5 b(al)5 b(l)43 b Fu(results)33 b(of)g(exe-)244
3332 y(cutions)f(are)h(obtained.)145 3535 y Ft(\017)49
b Fs(Structur)-5 b(al)26 b(op)-5 b(er)g(ational)24 b(semantics)p
Fu(:)37 b(its)21 b(purp)s(ose)i(is)e(to)h(describ)s(e)h(ho)m(w)f(the)g
Fs(individual)244 3655 y(steps)40 b Fu(of)32 b(the)h(computations)f
(tak)m(e)h(place.)0 3856 y(W)-8 b(e)46 b(shall)e(see)i(that)f(for)g
(the)h(language)e Fw(While)g Fu(w)m(e)i(can)g(easily)e(sp)s(ecify)i(b)s
(oth)f(kinds)h(of)0 3977 y(seman)m(tics)41 b(and)g(that)g(they)h(will)d
(b)s(e)i(\\equiv)-5 b(alen)m(t")40 b(in)h(a)f(sense)j(to)e(b)s(e)g
(made)g(clear)f(later.)0 4097 y(Ho)m(w)m(ev)m(er,)33
b(w)m(e)f(shall)d(also)h(giv)m(e)h(examples)f(of)g(programming)e
(constructs)k(where)g(one)f(of)f(the)0 4217 y(approac)m(hes)k(is)e(sup)
s(erior)g(to)g(the)h(other.)146 4338 y(F)-8 b(or)43 b(b)s(oth)h(kinds)g
(of)f(op)s(erational)e(seman)m(tics,)47 b(the)d(meaning)e(of)h
(statemen)m(ts)i(will)c(b)s(e)0 4458 y(sp)s(eci\014ed)33
b(b)m(y)h(a)e Fs(tr)-5 b(ansition)35 b(system)p Fu(.)43
b(It)33 b(will)d(ha)m(v)m(e)k(t)m(w)m(o)f(t)m(yp)s(es)h(of)e
(con\014gurations:)294 4651 y Ft(h)o Fs(S)12 b Fu(,)33
b Fs(s)8 b Ft(i)99 b Fu(represen)m(ting)39 b(that)f(the)g(statemen)m(t)
g Fs(S)49 b Fu(is)38 b(to)f(b)s(e)h(executed)i(from)645
4771 y(the)33 b(state)g Fs(s)8 b Fu(,)33 b(and)294 4939
y Fs(s)311 b Fu(represen)m(ting)34 b(a)e(terminal)e(\(that)j(is)f
(\014nal\))g(state.)0 5133 y(The)24 b Fs(terminal)i(c)-5
b(on\014gur)g(ations)31 b Fu(will)21 b(b)s(e)i(those)h(of)f(the)h
(latter)e(form.)39 b(The)25 b Fs(tr)-5 b(ansition)26
b(r)-5 b(elation)0 5254 y Fu(will)31 b(then)j(describ)s(e)g(ho)m(w)g
(the)g(execution)g(tak)m(es)h(place.)45 b(The)34 b(di\013erence)g(b)s
(et)m(w)m(een)i(the)e(t)m(w)m(o)0 5374 y(approac)m(hes)40
b(to)f(op)s(erational)d(seman)m(tics)j(amoun)m(ts)g(to)f(di\013eren)m
(t)i(w)m(a)m(ys)g(of)f(sp)s(ecifying)f(the)0 5494 y(transition)31
b(relation.)1687 5849 y(19)p eop
%%Page: 20 30
20 29 bop 251 130 a Fw(20)2086 b(2)112 b(Op)s(erational)37
b(Seman)m(tics)p 251 193 3473 4 v 283 419 V 283 2467
4 2049 v 609 528 a Fu([ass)761 543 y Fn(ns)833 528 y
Fu(])372 b Ft(h)p Fs(x)44 b Fu(:=)33 b Fs(a)7 b Fu(,)33
b Fs(s)8 b Ft(i)32 b(!)g Fs(s)8 b Fu([)p Fs(x)k Ft(7!A)o
Fu([)-17 b([)q Fs(a)7 b Fu(])-17 b(])q Fs(s)8 b Fu(])609
743 y([skip)807 758 y Fn(ns)879 743 y Fu(])326 b Ft(h)p
Fr(skip)p Fu(,)34 b Fs(s)8 b Ft(i)32 b(!)g Fs(s)609 1035
y Fu([comp)864 1050 y Fn(ns)935 1035 y Fu(])1242 948
y Ft(h)p Fs(S)1348 963 y Fn(1)1387 948 y Fu(,)h Fs(s)8
b Ft(i)32 b(!)g Fs(s)1746 912 y Fi(0)1770 948 y Fu(,)g
Ft(h)p Fs(S)1935 963 y Fn(2)1974 948 y Fu(,)h Fs(s)2082
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1688 y Fn(2)1803 1673 y Fu(,)h Fs(s)8 b Ft(i)32 b(!)g
Fs(s)2162 1636 y Fi(0)p 1242 1736 V 1242 1841 a Ft(h)p
Fr(if)h Fs(b)38 b Fr(then)c Fs(S)1804 1856 y Fn(1)1876
1841 y Fr(else)f Fs(S)2180 1856 y Fn(2)2220 1841 y Fu(,)f
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2085 y Fn(tt)859 2146 y(ns)930 2121 y Fu(])1242 2035
y Ft(h)p Fs(S)12 b Fu(,)32 b Fs(s)8 b Ft(i)33 b(!)f Fs(s)1707
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2035 y Ft(i)g(!)g Fs(s)2785 1998 y Fi(00)p 1242 2098
1586 4 v 1528 2203 a Ft(h)o Fr(while)i Fs(b)39 b Fr(do)33
b Fs(S)12 b Fu(,)32 b Fs(s)8 b Ft(i)32 b(!)h Fs(s)2500
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b Fu(if)31 b Ft(B)t Fu([)-17 b([)p Fs(b)6 b Fu(])-17
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%%Page: 21 31
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2603 y Fs(S)67 2618 y Fn(1)134 2603 y Fu(and)i Fs(S)385
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2723 y(itself.)42 b(The)34 b(follo)m(wing)c(is)i(an)g
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3723 y Fn(0)1602 3708 y Ft(i)f(!)g Fs(s)1853 3723 y Fn(0)0
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%%Page: 22 32
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23 32 bop 0 130 a Fw(2.1)112 b(Natural)37 b(seman)m(tics)2216
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1245 y Fu(and)g Ft(h)p Fr(x)p Fu(:=)p Fr(y)p Fu(,)h Fs(s)3138
1260 y Fn(1)3178 1245 y Ft(i)f(!)g Fs(s)3433 1260 y Fn(2)0
1365 y Fu(with)e(the)h(in)m(ternal)f(no)s(de)g(lab)s(elled)f
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y Ft(i)g(!)f Fs(s)1904 1540 y Fn(3)p 254 1589 1690 4
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(ards.)58 b(So)37 b(w)m(e)h(will)c(start)j(b)m(y)h(\014nding)f(an)g
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Ft(h)p Fs(S)12 b Fu(,)38 b Fs(s)8 b Ft(i)p Fu(.)59 b(There)39
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%%Page: 34 44
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%%Page: 35 45
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%%Page: 40 50
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eop
%%Page: 41 51
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%%Page: 42 52
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%%Page: 43 53
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1030 y(ab)s(o)m(v)m(e)33 b(statemen)m(t)g(then)h(w)m(e)f(will)e(only)h
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244 1227 y Ft(h)p Fu(\()p Fr(while)g(true)h(do)f(skip)p
Fu(\))h Fr(or)f Fu(\()p Fr(x)f Fu(:=)h Fr(2)p Fu(;)g
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1424 y(T)-8 b(urning)29 b(to)g(the)h Fs(structur)-5 b(al)33
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1920 y Fn(2)358 1981 y(sos)453 1956 y Fu(])387 b Ft(h)p
Fs(S)973 1971 y Fn(1)1044 1956 y Fr(or)34 b Fs(S)1247
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2154 y Fu(F)-8 b(or)29 b(the)h(statemen)m(t)h Fr(x)f
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m(o)g(deriv)-5 b(ation)28 b(sequences:)244 2351 y Ft(h)p
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%%Page: 48 58
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1815 y(Using)43 b(these)h(rules)f(w)m(e)h(get)f(the)h(follo)m(wing)c
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y Ft(h)p Fs(S)360 4299 y Fn(1)399 4284 y Fu(,)f Fs(s)8
b Ft(i)33 b(!)f Fs(s)758 4247 y Fi(0)781 4284 y Fu(,)h
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254 4347 1158 4 v 396 4452 a Ft(h)p Fs(S)502 4467 y Fn(1)574
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254 4717 V 396 4822 a Ft(h)p Fs(S)502 4837 y Fn(1)574
4822 y Fr(par)h Fs(S)827 4837 y Fn(2)867 4822 y Fu(,)f
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%%Page: 50 60
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V 283 1553 3472 4 v 283 1569 V 283 1833 a Fw(Exercise)i(2.35)49
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2832 y Fr(x)h Fu(:=)g Fr(1)f(par)i(protect)g Fu(\()p
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3743 y(sions)42 b(where)h(the)f(individual)d(parts)j(of)g(an)f
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eop
%%Page: 51 61
51 60 bop 0 130 a Fw(2.5)112 b(Blo)s(c)m(ks)37 b(and)h(pro)s(cedures)
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2157 y Fr(begin)h(var)f(y)g Fu(:=)f Fr(1)p Fu(;)533 2325
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%%Page: 52 62
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b Fs(s)8 b Ft(i)33 b(!)1706 1462 y Fc(D)1803 1447 y Fs(s)p
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b(!)o Fs(s)8 b Fu(]\))33 b Fs(x)44 b Fu(=)1256 1815 y
Fg(\()1364 1900 y Fs(s)d(x)118 b Fu(if)31 b Fs(x)45 b
Ft(2)33 b Fs(X)1364 2020 y(s)1412 1984 y Fi(0)1468 2020
y Fs(x)95 b Fu(if)31 b Fs(x)45 b Ft(62)33 b Fs(X)283
2180 y Fu(This)c(op)s(eration)d(will)g(ensure)j(that)f(lo)s(cal)d(v)-5
b(ariables)27 b(are)h(restored)h(to)e(their)h(previous)g(v)-5
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2475 y Fw(Exercise)37 b(2.37)49 b Fu(Use)35 b(the)f(natural)g(seman)m
(tics)g(of)g(T)-8 b(able)34 b(2.3)f(to)h(sho)m(w)h(that)f(execution)h
(of)283 2595 y(the)e(statemen)m(t)527 2758 y Fr(begin)h(var)g(y)e
Fu(:=)h Fr(1)p Fu(;)816 2926 y(\()p Fr(x)g Fu(:=)f Fr(1)p
Fu(;)816 3093 y Fr(begin)i(var)f(x)g Fu(:=)g Fr(2)p Fu(;)f
Fr(y)h Fu(:=)g Fr(x)p Fu(+)p Fr(1)g(end)p Fu(;)816 3261
y Fr(x)g Fu(:=)f Fr(y)p Fu(+)p Fr(x)p Fu(\))527 3429
y Fr(end)283 3592 y Fu(will)f(lead)h(to)g(a)g(state)h(where)h
Fr(x)f Fu(has)g(the)g(v)-5 b(alue)32 b Fw(4)p Fu(.)1525
b Fh(2)430 3766 y Fu(It)32 b(is)f(somewhat)h(harder)g(to)f(sp)s(ecify)i
(a)e Fs(structur)-5 b(al)35 b(op)-5 b(er)g(ational)33
b(semantics)39 b Fu(for)31 b(the)i(ex-)283 3886 y(tended)c(language.)41
b(One)28 b(approac)m(h)g(is)f(to)g(replace)h(states)g(with)g(a)f
(structure)i(that)e(is)g(similar)283 4007 y(to)34 b(the)g(run-time)f
(stac)m(ks)i(used)h(in)d(the)h(implemen)m(tation)d(of)i(blo)s(c)m(k)h
(structured)h(languages.)283 4127 y(Another)43 b(is)f(to)g(extend)h
(the)g(statemen)m(ts)g(with)f(fragmen)m(ts)g(of)f(the)i(state.)73
b(Ho)m(w)m(ev)m(er,)47 b(w)m(e)283 4247 y(shall)32 b(not)g(go)g
(further)h(in)m(to)f(this.)283 4529 y Fp(Pro)t(cedures)283
4714 y Fu(W)-8 b(e)27 b(shall)f(no)m(w)h(extend)h(the)f(language)e
Fw(Blo)s(c)m(k)h Fu(with)g(pro)s(cedure)h(declarations.)41
b(The)27 b(syn)m(tax)283 4834 y(of)33 b(the)g(language)e
Fw(Pro)s(c)h Fu(is:)577 4989 y Fs(S)189 b Fu(::=)99 b
Fs(x)45 b Fu(:=)32 b Fs(a)40 b Ft(j)32 b Fr(skip)i Ft(j)e
Fs(S)1790 5004 y Fn(1)1862 4989 y Fu(;)g Fs(S)1988 5004
y Fn(2)2060 4989 y Ft(j)g Fr(if)h Fs(b)39 b Fr(then)33
b Fs(S)2643 5004 y Fn(1)2715 4989 y Fr(else)h Fs(S)3020
5004 y Fn(2)872 5156 y Ft(j)150 b Fr(while)34 b Fs(b)39
b Fr(do)33 b Fs(S)44 b Ft(j)32 b Fr(begin)i Fs(D)2089
5171 y Fc(V)2183 5156 y Fs(D)2266 5171 y Fc(P)2357 5156
y Fs(S)44 b Fr(end)33 b Ft(j)g Fr(call)g Fs(p)577 5324
y(D)660 5339 y Fc(V)821 5324 y Fu(::=)99 b Fr(var)34
b Fs(x)44 b Fu(:=)33 b Fs(a)7 b Fu(;)32 b Fs(D)1661 5339
y Fc(V)1755 5324 y Ft(j)g Fo(")577 5492 y Fs(D)660 5507
y Fc(P)821 5492 y Fu(::=)99 b Fr(proc)34 b Fs(p)k Fr(is)33
b Fs(S)12 b Fu(;)33 b Fs(D)1721 5507 y Fc(P)1812 5492
y Ft(j)f Fo(")p eop
%%Page: 53 63
53 62 bop 0 130 a Fw(2.5)112 b(Blo)s(c)m(ks)37 b(and)h(pro)s(cedures)
1998 b(53)p 0 193 3473 4 v 0 515 a Fu(Here)27 b Fs(p)33
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(syn)m(tactic)h(category)f Fw(Pname)f Fu(of)g(pro)s(cedure)0
636 y(names;)31 b(in)e(the)h(concrete)h(syn)m(tax)h(there)e(need)h(not)
f(b)s(e)g(an)m(y)g(di\013erence)h(b)s(et)m(w)m(een)g(pro)s(cedure)0
756 y(names)37 b(and)g(v)-5 b(ariable)36 b(names)h(but)g(in)g(the)g
(abstract)h(syn)m(tax)g(it)e(is)h(con)m(v)m(enien)m(t)i(to)e(b)s(e)g
(able)0 877 y(to)c(distinguish)f(b)s(et)m(w)m(een)j(the)f(t)m(w)m(o.)46
b(F)-8 b(urthermore,)33 b Fs(D)2061 892 y Fc(P)2152 877
y Fu(is)g(a)g(meta-v)-5 b(ariable)30 b(ranging)i(o)m(v)m(er)0
997 y(the)h(syn)m(tactic)g(category)g Fw(Dec)1160 1012
y Fn(P)1245 997 y Fu(of)f Fs(pr)-5 b(o)g(c)g(e)g(dur)g(e)34
b(de)-5 b(clar)g(ations)p Fu(.)146 1117 y(W)d(e)40 b(shall)d(giv)m(e)i
(three)h(di\013eren)m(t)f(seman)m(tics)g(of)f(this)h(language.)61
b(They)40 b(di\013er)f(in)f(their)0 1238 y(c)m(hoice)33
b(of)f(scop)s(e)h(rules)g(for)f(v)-5 b(ariables)31 b(and)i(pro)s
(cedures:)145 1436 y Ft(\017)49 b Fu(dynamic)32 b(scop)s(e)h(for)f(v)-5
b(ariables)31 b(as)i(w)m(ell)f(as)h(pro)s(cedures,)145
1637 y Ft(\017)49 b Fu(dynamic)32 b(scop)s(e)h(for)f(v)-5
b(ariables)31 b(but)i(static)f(scop)s(e)i(for)e(pro)s(cedures,)i(and)
145 1839 y Ft(\017)49 b Fu(static)32 b(scop)s(e)h(for)f(v)-5
b(ariables)32 b(as)g(w)m(ell)g(as)h(pro)s(cedures.)0
2037 y(T)-8 b(o)33 b(illustrate)d(the)j(di\013erence)g(consider)g(the)g
(statemen)m(t)244 2235 y Fr(begin)h(var)f(x)g Fu(:=)f
Fr(0)p Fu(;)533 2403 y Fr(proc)h(p)g(is)g(x)g Fu(:=)f
Fr(x)h Fo(?)f Fr(2)p Fu(;)533 2570 y Fr(proc)h(q)g(is)g(call)h(p)p
Fu(;)533 2738 y Fr(begin)g(var)f(x)g Fu(:=)f Fr(5)p Fu(;)822
2905 y Fr(proc)h(p)g(is)g(x)g Fu(:=)f Fr(x)h Fu(+)f(1;)822
3073 y Fr(call)h(q)p Fu(;)g Fr(y)g Fu(:=)f Fr(x)533 3241
y(end)244 3408 y(end)0 3606 y Fu(If)39 b Fs(dynamic)i(sc)-5
b(op)g(e)46 b Fu(is)39 b(used)h(for)f(v)-5 b(ariables)38
b(as)i(w)m(ell)f(as)g(pro)s(cedures)i(then)f(the)g(\014nal)f(v)-5
b(alue)0 3727 y(of)42 b Fr(y)h Fu(is)f Fw(6)p Fu(.)74
b(The)44 b(reason)f(is)f(that)h Fr(call)g(q)g Fu(will)e(call)g(the)i
Fs(lo)-5 b(c)g(al)52 b Fu(pro)s(cedure)44 b Fr(p)e Fu(whic)m(h)i(will)0
3847 y(up)s(date)31 b(the)g Fs(lo)-5 b(c)g(al)40 b Fu(v)-5
b(ariable)29 b Fr(x)p Fu(.)43 b(If)30 b(w)m(e)i(use)f(dynamic)f(scop)s
(e)i(for)e(v)-5 b(ariables)29 b(but)i Fs(static)i(sc)-5
b(op)g(e)0 3967 y Fu(for)35 b(pro)s(cedures)i(then)f
Fr(y)g Fu(gets)g(the)g(v)-5 b(alue)35 b Fw(10)p Fu(.)52
b(The)37 b(reason)f(is)f(that)g(no)m(w)i Fr(call)f(q)g
Fu(will)d(call)0 4088 y(the)38 b Fs(glob)-5 b(al)47 b
Fu(pro)s(cedure)39 b Fr(p)f Fu(and)g(it)f(will)e(up)s(date)j(the)g
Fs(lo)-5 b(c)g(al)47 b Fu(v)-5 b(ariable)36 b Fr(x)p
Fu(.)60 b(Finally)-8 b(,)36 b(if)h(w)m(e)h(use)0 4208
y(static)28 b(scop)s(e)h(for)e(v)-5 b(ariables)27 b(as)h(w)m(ell)f(as)i
(pro)s(cedures)g(then)g Fr(y)f Fu(gets)h(the)f(v)-5 b(alue)28
b Fw(5)p Fu(.)42 b(The)29 b(reason)0 4329 y(is)39 b(that)g
Fr(call)h(q)g Fu(no)m(w)g(will)d(call)g(the)j Fs(glob)-5
b(al)49 b Fu(pro)s(cedure)40 b Fr(p)f Fu(whic)m(h)h(will)d(up)s(date)j
(the)f Fs(glob)-5 b(al)0 4449 y Fu(v)g(ariable)31 b Fr(x)i
Fu(so)f(the)h(lo)s(cal)e(v)-5 b(ariable)31 b Fr(x)h Fu(is)g(unc)m
(hanged.)0 4708 y Fw(Dynamic)37 b(scop)s(e)g(rules)g(for)h(v)-6
b(ariables)37 b(and)h(pro)s(cedures)0 4893 y Fu(The)44
b(general)f(idea)f(is)h(that)g(to)g(execute)i(the)e(statemen)m(t)h
Fr(call)g Fs(p)49 b Fu(w)m(e)44 b(shall)e(execute)j(the)0
5013 y(b)s(o)s(dy)34 b(of)f(the)i(pro)s(cedure.)48 b(This)34
b(means)g(that)g(w)m(e)g(ha)m(v)m(e)i(to)d(k)m(eep)j(trac)m(k)e(of)g
(the)g(asso)s(ciation)0 5133 y(of)k(pro)s(cedure)i(names)f(with)g(pro)s
(cedure)h(b)s(o)s(dies.)62 b(T)-8 b(o)39 b(facilitate)d(this)j(w)m(e)h
(shall)d(in)m(tro)s(duce)0 5254 y(the)42 b(notion)f(of)g(a)h
Fs(pr)-5 b(o)g(c)g(e)g(dur)g(e)42 b(envir)-5 b(onment)p
Fu(.)70 b(Giv)m(en)42 b(a)f(pro)s(cedure)i(name)e(the)h(pro)s(cedure)0
5374 y(en)m(vironmen)m(t)25 b Fs(env)709 5389 y Fc(P)792
5374 y Fu(will)d(return)k(the)f(statemen)m(t)g(that)g(is)f(its)g(b)s(o)
s(dy)-8 b(.)41 b(So)25 b Fs(env)2844 5389 y Fc(P)2927
5374 y Fu(is)f(an)h(elemen)m(t)0 5494 y(of)p eop
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54 63 bop 251 130 a Fw(54)2086 b(2)112 b(Op)s(erational)37
b(Seman)m(tics)p 251 193 3473 4 v 283 419 V 283 3862
4 3443 v 654 528 a Fu([ass)806 543 y Fn(ns)878 528 y
Fu(])372 b Fs(env)1433 543 y Fc(P)1523 528 y Ft(`)33
b(h)o Fs(x)45 b Fu(:=)32 b Fs(a)7 b Fu(,)33 b Fs(s)8
b Ft(i)32 b(!)g Fs(s)8 b Fu([)p Fs(x)k Ft(7!A)p Fu([)-17
b([)p Fs(a)7 b Fu(])-17 b(])q Fs(s)8 b Fu(])654 743 y([skip)852
758 y Fn(ns)923 743 y Fu(])327 b Fs(env)1433 758 y Fc(P)1523
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963 y Fc(P)2460 948 y Ft(`)f(h)p Fs(S)2659 963 y Fn(2)2698
948 y Fu(,)h Fs(s)2806 912 y Fi(0)2829 948 y Ft(i)g(!)f
Fs(s)3081 912 y Fi(00)p 1287 1012 1837 4 v 1695 1116
a Fs(env)1851 1131 y Fc(P)1942 1116 y Ft(`)g(h)p Fs(S)2141
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Fi(00)654 1397 y Fu([if)739 1361 y Fn(tt)739 1422 y(ns)809
1397 y Fu(])1703 1310 y Fs(env)1859 1325 y Fc(P)1949
1310 y Ft(`)h(h)p Fs(S)2149 1325 y Fn(1)2188 1310 y Fu(,)f
Fs(s)8 b Ft(i)33 b(!)f Fs(s)2547 1274 y Fi(0)p 1287 1374
1700 4 v 1287 1478 a Fs(env)1443 1493 y Fc(P)1533 1478
y Ft(`)h(h)o Fr(if)g Fs(b)39 b Fr(then)33 b Fs(S)2188
1493 y Fn(1)2260 1478 y Fr(else)h Fs(S)2565 1493 y Fn(2)2604
1478 y Fu(,)f Fs(s)8 b Ft(i)32 b(!)g Fs(s)2963 1442 y
Fi(0)1513 1635 y Fu(if)f Ft(B)t Fu([)-17 b([)p Fs(b)6
b Fu(])-17 b(])q Fs(s)41 b Fu(=)32 b Fw(tt)654 1927 y
Fu([if)739 1890 y Fn(\013)739 1951 y(ns)809 1927 y Fu(])1703
1840 y Fs(env)1859 1855 y Fc(P)1949 1840 y Ft(`)h(h)p
Fs(S)2149 1855 y Fn(2)2188 1840 y Fu(,)f Fs(s)8 b Ft(i)33
b(!)f Fs(s)2547 1804 y Fi(0)p 1287 1903 V 1287 2008 a
Fs(env)1443 2023 y Fc(P)1533 2008 y Ft(`)h(h)o Fr(if)g
Fs(b)39 b Fr(then)33 b Fs(S)2188 2023 y Fn(1)2260 2008
y Fr(else)h Fs(S)2565 2023 y Fn(2)2604 2008 y Fu(,)f
Fs(s)8 b Ft(i)32 b(!)g Fs(s)2963 1972 y Fi(0)1513 2165
y Fu(if)f Ft(B)t Fu([)-17 b([)p Fs(b)6 b Fu(])-17 b(])q
Fs(s)41 b Fu(=)32 b Fw(\013)654 2456 y Fu([while)904
2420 y Fn(tt)904 2481 y(ns)974 2456 y Fu(])1287 2370
y Fs(env)1443 2385 y Fc(P)1533 2370 y Ft(`)h(h)o Fs(S)12
b Fu(,)33 b Fs(s)8 b Ft(i)32 b(!)g Fs(s)2091 2334 y Fi(0)2115
2370 y Fu(,)g Fs(env)2330 2385 y Fc(P)2421 2370 y Ft(`)g(h)p
Fr(while)i Fs(b)k Fr(do)33 b Fs(S)12 b Fu(,)33 b Fs(s)3235
2334 y Fi(0)3258 2370 y Ft(i)f(!)g Fs(s)3509 2334 y Fi(00)p
1287 2433 2266 4 v 1742 2538 a Fs(env)1898 2553 y Fc(P)1989
2538 y Ft(`)g(h)p Fr(while)i Fs(b)k Fr(do)33 b Fs(S)12
b Fu(,)32 b Fs(s)8 b Ft(i)33 b(!)f Fs(s)3054 2502 y Fi(00)1513
2694 y Fu(if)f Ft(B)t Fu([)-17 b([)p Fs(b)6 b Fu(])-17
b(])q Fs(s)41 b Fu(=)32 b Fw(tt)654 2909 y Fu([while)904
2873 y Fn(\013)904 2934 y(ns)974 2909 y Fu(])276 b Fs(env)1433
2924 y Fc(P)1523 2909 y Ft(`)33 b(h)o Fr(while)h Fs(b)39
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b Fu(])-17 b(])q Fs(s)41 b Fu(=)32 b Fw(\013)654 3368
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3282 y Ft(h)p Fs(D)1532 3297 y Fc(V)1593 3282 y Fu(,)g
Fs(s)8 b Ft(i)33 b(!)1871 3297 y Fc(D)1968 3282 y Fs(s)2016
3246 y Fi(0)2039 3282 y Fu(,)g(up)s(d)2264 3297 y Fn(P)2316
3282 y Fu(\()p Fs(D)2437 3297 y Fc(P)2496 3282 y Fu(,)g
Fs(env)2712 3297 y Fc(P)2769 3282 y Fu(\))g Ft(`)f(h)p
Fs(S)12 b Fu(,)32 b Fs(s)3146 3246 y Fi(0)3170 3282 y
Ft(i)g(!)g Fs(s)3421 3246 y Fi(00)p 1287 3345 2301 4
v 1287 3450 a Fs(env)1443 3465 y Fc(P)1533 3450 y Ft(`)h(h)o
Fr(begin)h Fs(D)2037 3465 y Fc(V)2131 3450 y Fs(D)2214
3465 y Fc(P)2305 3450 y Fs(S)44 b Fr(end)p Fu(,)34 b
Fs(s)8 b Ft(i)32 b(!)g Fs(s)2917 3414 y Fi(00)2960 3450
y Fu([D)m(V\()p Fs(D)3253 3465 y Fc(V)3313 3450 y Fu(\))p
Ft(7\000)-16 b(!)p Fs(s)8 b Fu(])654 3731 y([call)829
3694 y Fn(rec)829 3755 y(ns)922 3731 y Fu(])1400 3644
y Fs(env)1556 3659 y Fc(P)1646 3644 y Ft(`)33 b(h)p Fs(S)12
b Fu(,)32 b Fs(s)8 b Ft(i)32 b(!)h Fs(s)2205 3608 y Fi(0)p
1287 3707 1055 4 v 1287 3812 a Fs(env)1443 3827 y Fc(P)1533
3812 y Ft(`)g(h)o Fr(call)h Fs(p)6 b Fu(,)32 b Fs(s)8
b Ft(i)33 b(!)f Fs(s)2318 3776 y Fi(0)2449 3731 y Fu(where)i
Fs(env)2887 3746 y Fc(P)2977 3731 y Fs(p)k Fu(=)33 b
Fs(S)p 3753 3862 4 3443 v 283 3865 3473 4 v 640 4026
a Fu(T)-8 b(able)32 b(2.5:)44 b(Natural)31 b(seman)m(tics)i(for)f
Fw(Pro)s(c)g Fu(with)g(dynamic)g(scop)s(e)h(rules)527
4322 y Fw(En)m(v)719 4337 y Fn(P)804 4322 y Fu(=)f Fw(Pname)h
Fo(,)-17 b Ft(!)32 b Fw(Stm)430 4552 y Fu(The)45 b(next)g(step)g(will)c
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(the)f(en)m(viron-)283 4672 y(men)m(t)35 b(in)m(to)f(accoun)m(t.)50
b(W)-8 b(e)35 b(shall)e(extend)j(the)f(transition)e(system)j(for)e
(statemen)m(ts)h(to)g(ha)m(v)m(e)283 4793 y(transitions)d(of)g(the)h
(form)527 5023 y Fs(env)683 5038 y Fc(P)774 5023 y Ft(`)f(h)p
Fs(S)12 b Fu(,)32 b Fs(s)8 b Ft(i)33 b(!)f Fs(s)1332
4987 y Fi(0)283 5254 y Fu(The)e(presence)g(of)e(the)h(en)m(vironmen)m
(t)f(means)h(that)f(w)m(e)h(can)g(alw)m(a)m(ys)g(access)h(it)d(and)h
(therefore)283 5374 y(get)36 b(hold)g(of)f(the)i(b)s(o)s(dies)e(of)h
(declared)g(pro)s(cedures.)55 b(The)37 b(result)f(of)f(mo)s(difying)f
(T)-8 b(able)35 b(2.1)283 5494 y(to)e(incorp)s(orate)e(this)h(extra)h
(information)d(is)i(sho)m(wn)i(in)e(T)-8 b(able)32 b(2.5.)p
eop
%%Page: 55 65
55 64 bop 0 130 a Fw(2.5)112 b(Blo)s(c)m(ks)37 b(and)h(pro)s(cedures)
1998 b(55)p 0 193 3473 4 v 146 515 a Fu(Concerning)39
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515 y Fs(D)1755 530 y Fc(P)1852 515 y Fs(S)50 b Fr(end)39
b Fu(the)f(idea)g(is)f(that)h(w)m(e)i(up)s(date)e(the)0
636 y(pro)s(cedure)44 b(en)m(vironmen)m(t)f(so)f(that)h(the)g(pro)s
(cedures)h(declared)f(in)f Fs(D)2666 651 y Fc(P)2767
636 y Fu(will)e(b)s(e)j(a)m(v)-5 b(ailable)0 756 y(when)41
b(executing)f Fs(S)12 b Fu(.)39 b(Giv)m(en)h(a)f(global)e(en)m
(vironmen)m(t)j Fs(env)2234 771 y Fc(P)2331 756 y Fu(and)g(a)f
(declaration)f Fs(D)3210 771 y Fc(P)3269 756 y Fu(,)j(the)0
877 y(up)s(dated)33 b(pro)s(cedure)h(en)m(vironmen)m(t,)f(up)s(d)1588
892 y Fn(P)1640 877 y Fu(\()p Fs(D)1761 892 y Fc(P)1820
877 y Fu(,)f Fs(env)2035 892 y Fc(P)2093 877 y Fu(\),)h(is)f(sp)s
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%%Page: 60 70
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%%Page: 76 86
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%%Page: 77 87
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b(all.)p eop
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Ft(?)h Fu(and)g(that)0 636 y Ft(?)k(v)g Fs(d)43 b Fu(for)32
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f(one)h(ma)m(y)f(sho)m(w)i(that)244 801 y Fs(f)295 765
y Fn(n)371 801 y Ft(?)f(v)g Fs(f)642 765 y Fn(n)717 801
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1716 y Fn(n)1351 1752 y Ft(?)p Fu(\))33 b Ft(j)f Fu(n)p
Ft(\025)q Fu(0)g Ft(g)357 b Fu(\(con)m(tin)m(uit)m(y)32
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1920 y Ft(f)32 b Fs(f)1186 1884 y Fn(n)1262 1920 y Ft(?)h(j)f
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b Fs(f)1186 2387 y Fn(n)1262 2423 y Ft(?)h(j)f Fu(n)p
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Fn(0)2340 2423 y Ft(?)33 b Fu(=)f Ft(?)q Fu(\))808 2591
y(=)100 b(FIX)32 b Fs(f)961 b Fu(\(de\014nition)31 b(of)h(FIX)h
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b Fu(giv)m(es)29 b Fs(f)2267 2833 y Fn(n)2339 2869 y
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%%Page: 106 116
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3735 3797 V 3752 3797 V 283 3800 3470 4 v 281 4049 4
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b(restrict)f(ourselv)m(es)i(to)e Fs(c)-5 b(ontinuous)35
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%%Page: 107 117
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%%Page: 114 124
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%%Page: 115 125
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958 y Fn(ds)2891 943 y Fu(and)g Ft(S)3149 907 y Fi(0)3149
967 y Fn(ds)3252 943 y Fu(satisfy)527 1144 y Ft(S)595
1159 y Fn(ds)666 1144 y Fu([)-17 b([)q Fs(S)12 b Fu(])-17
b(])33 b Ft(\016)f Fu(\(lo)s(okup)g Fs(env)1437 1159
y Fc(V)1497 1144 y Fu(\))g(=)h(\(lo)s(okup)f Fs(env)2190
1159 y Fc(V)2250 1144 y Fu(\))g Ft(\016)g Fu(\()p Ft(S)2508
1108 y Fi(0)2508 1169 y Fn(ds)2579 1144 y Fu([)-17 b([)q
Fs(S)12 b Fu(])-17 b(])p Fs(env)2877 1159 y Fc(V)2937
1144 y Fu(\))283 1346 y(for)44 b(all)e(statemen)m(ts)j
Fs(S)55 b Fu(of)44 b Fw(While)e Fu(and)i(for)g(all)d
Fs(env)2326 1361 y Fc(V)2430 1346 y Fu(suc)m(h)46 b(that)e
Fs(env)3041 1361 y Fc(V)3145 1346 y Fu(is)f(an)h(injectiv)m(e)283
1466 y(mapping.)3001 b Fh(2)283 1692 y Fw(Exercise)37
b(4.64)49 b Fu(Ha)m(ving)23 b(replaced)h(a)f(one)h(stage)g(mapping)f
(with)g(a)g(t)m(w)m(o)i(stage)f(mapping)e(w)m(e)283 1812
y(migh)m(t)j(consider)h(rede\014ning)g(the)g(seman)m(tic)g(functions)f
Ft(A)h Fu(and)f Ft(B)t Fu(.)41 b(The)27 b(new)g(functionalities)283
1933 y(of)33 b Ft(A)f Fu(and)g Ft(B)k Fu(migh)m(t)31
b(b)s(e)527 2134 y Ft(A)607 2098 y Fi(0)630 2134 y Fu(:)44
b Fw(Aexp)32 b Ft(!)g Fw(En)m(v)1314 2149 y Fn(V)1405
2134 y Ft(!)g Fu(\()p Fw(Store)g Ft(!)g Fw(Z)p Fu(\))527
2302 y Ft(B)596 2266 y Fi(0)619 2302 y Fu(:)44 b Fw(Bexp)32
b Ft(!)g Fw(En)m(v)1298 2317 y Fn(V)1389 2302 y Ft(!)g
Fu(\()p Fw(Store)g Ft(!)g Fw(T)p Fu(\))283 2504 y(and)h(the)g(in)m
(tended)g(relationship)e(is)h(that)527 2705 y Ft(A)607
2669 y Fi(0)630 2705 y Fu([)-17 b([)q Fs(a)7 b Fu(])-17
b(])q Fs(env)919 2720 y Fc(V)1011 2705 y Fu(=)33 b Ft(A)o
Fu([)-17 b([)q Fs(a)7 b Fu(])-17 b(])33 b Ft(\016)f Fu(\(lo)s(okup)g
Fs(env)1960 2720 y Fc(V)2020 2705 y Fu(\))527 2873 y
Ft(B)596 2837 y Fi(0)619 2873 y Fu([)-17 b([)q Fs(b)6
b Fu(])-17 b(])p Fs(env)901 2888 y Fc(V)994 2873 y Fu(=)32
b Ft(B)t Fu([)-17 b([)p Fs(b)6 b Fu(])-17 b(])33 b Ft(\016)g
Fu(\(lo)s(okup)e Fs(env)1925 2888 y Fc(V)1985 2873 y
Fu(\))283 3074 y(Giv)m(e)40 b(a)g(comp)s(ositional)c(de\014nition)j(of)
h(the)g(functions)g Ft(A)2479 3038 y Fi(0)2542 3074 y
Fu(and)g Ft(B)2808 3038 y Fi(0)2871 3074 y Fu(suc)m(h)h(that)f(this)g
(is)f(the)283 3195 y(case.)3198 b Fh(2)283 3454 y Fw(Up)s(dating)38
b(the)f(v)-6 b(ariable)37 b(en)m(vironmen)m(t)283 3639
y Fu(The)g(v)-5 b(ariable)34 b(en)m(vironmen)m(t)j(is)e(up)s(dated)h
(whenev)m(er)j(w)m(e)e(en)m(ter)f(a)g(blo)s(c)m(k)g(con)m(taining)e(lo)
s(cal)283 3759 y(declarations.)60 b(T)-8 b(o)38 b(express)i(this)e(w)m
(e)h(shall)e(in)m(tro)s(duce)h(a)g(seman)m(tic)f(function)h
Ft(D)3357 3723 y Fn(V)3357 3784 y(ds)3466 3759 y Fu(for)f(the)283
3880 y(syn)m(tactic)d(category)f(of)f(v)-5 b(ariable)31
b(declarations.)42 b(It)33 b(has)g(functionalit)m(y)527
4081 y Ft(D)607 4045 y Fn(V)607 4106 y(ds)678 4081 y
Fu(:)44 b Fw(Dec)936 4096 y Fn(V)1026 4081 y Ft(!)32
b Fw(En)m(v)1350 4096 y Fc(V)1443 4081 y Ft(\002)h Fw(Store)g
Ft(!)f Fw(En)m(v)2169 4096 y Fc(V)2262 4081 y Ft(\002)h
Fw(Store)283 4283 y Fu(The)i(function)f Ft(D)949 4246
y Fn(V)949 4307 y(ds)1020 4283 y Fu([)-17 b([)p Fs(D)1140
4298 y Fc(V)1201 4283 y Fu(])g(])35 b(will)c(tak)m(e)k(a)f(pair)f(as)h
(argumen)m(ts:)47 b(the)34 b(\014rst)h(comp)s(onen)m(t)f(of)f(that)283
4403 y(pair)22 b(will)e(b)s(e)i(the)h(curren)m(t)g(v)-5
b(ariable)21 b(en)m(vironmen)m(t)h(and)h(the)f(second)i(comp)s(onen)m
(t)e(the)h(curren)m(t)283 4523 y(store.)62 b(The)39 b(function)f(will)e
(return)j(the)g(up)s(dated)f(v)-5 b(ariable)37 b(en)m(vironmen)m(t)i
(as)f(w)m(ell)g(as)g(the)283 4644 y(up)s(dated)32 b(store.)44
b(The)32 b(function)f(is)g(de\014ned)h(b)m(y)h(the)e(seman)m(tic)g
(clauses)h(of)f(T)-8 b(able)31 b(4.3.)43 b(Note)283 4764
y(that)36 b(w)m(e)i(pro)s(cess)f(the)g(declarations)e(from)g(left)g(to)
h(righ)m(t)g(and)g(that)g(w)m(e)h(up)s(date)g(the)f(v)-5
b(alue)283 4885 y(of)33 b(the)g(tok)m(en)g(`next')h(in)e(the)h(store.)
430 5005 y(In)28 b(the)h(case)g(where)g(there)g(are)f
Fs(no)34 b Fu(pro)s(cedure)29 b(declarations)e(in)h(a)g(blo)s(c)m(k)g
(w)m(e)h(can)f(extend)283 5125 y(the)33 b(seman)m(tic)g(function)f
Ft(S)1306 5089 y Fi(0)1306 5150 y Fn(ds)1409 5125 y Fu(of)g(T)-8
b(able)33 b(4.2)f(with)g(a)g(clause)h(lik)m(e)527 5327
y Ft(S)595 5291 y Fi(0)595 5351 y Fn(ds)666 5327 y Fu([)-17
b([)q Fr(begin)34 b Fs(D)1076 5342 y Fc(V)1169 5327 y
Fs(S)45 b Fr(end)p Fu(])-17 b(])q Fs(env)1616 5342 y
Fc(V)1709 5327 y Fs(sto)38 b Fu(=)33 b Ft(S)2045 5291
y Fi(0)2045 5351 y Fn(ds)2117 5327 y Fu([)-17 b([)p Fs(S)12
b Fu(])-17 b(])q Fs(env)2415 5291 y Fi(0)2415 5351 y
Fc(V)2507 5327 y Fs(sto)2635 5291 y Fi(0)796 5494 y Fu(where)34
b Ft(D)1158 5458 y Fn(V)1158 5519 y(ds)1229 5494 y Fu([)-17
b([)p Fs(D)1349 5509 y Fc(V)1410 5494 y Fu(])g(])q(\()p
Fs(env)1642 5509 y Fc(V)1702 5494 y Fu(,)32 b Fs(sto)6
b Fu(\))33 b(=)f(\()p Fs(env)2262 5458 y Fi(0)2262 5519
y Fc(V)2322 5494 y Fu(,)h Fs(sto)2510 5458 y Fi(0)2534
5494 y Fu(\))p eop
%%Page: 121 131
121 130 bop 0 130 a Fw(4.5)112 b(Extensions)37 b(of)h(While)2063
b(121)p 0 193 3473 4 v 0 419 V 0 1102 4 683 v 382 526
a Ft(D)462 489 y Fn(V)462 550 y(ds)533 526 y Fu([)-17
b([)p Fr(var)34 b Fs(x)44 b Fu(:=)33 b Fs(a)7 b Fu(;)32
b Fs(D)1181 541 y Fc(V)1242 526 y Fu(])-17 b(])q(\()p
Fs(env)1474 541 y Fc(V)1534 526 y Fu(,)33 b Fs(sto)6
b Fu(\))32 b(=)651 693 y Ft(D)730 657 y Fn(V)730 718
y(ds)802 693 y Fu([)-17 b([)p Fs(D)922 708 y Fc(V)983
693 y Fu(])g(])q(\()p Fs(env)1215 708 y Fc(V)1275 693
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b Fu([)p Fs(l)k Ft(7!)p Fs(v)h Fu(][next)p Ft(7!)q Fu(new)33
b Fs(l)10 b Fu(]\))651 861 y(where)34 b Fs(l)42 b Fu(=)33
b Fs(sto)38 b Fu(next)c(and)f Fs(v)43 b Fu(=)32 b Ft(A)p
Fu([)-17 b([)p Fs(a)7 b Fu(])-17 b(])q(\(lo)s(okup)32
b Fs(env)2601 876 y Fc(V)2693 861 y Fs(sto)6 b Fu(\))382
1052 y Ft(D)462 1016 y Fn(V)462 1077 y(ds)533 1052 y
Fu([)-17 b([)p Fo(")p Fu(])g(])33 b(=)g(id)p 3469 1102
V 0 1105 3473 4 v 479 1266 a(T)-8 b(able)32 b(4.3:)43
b(Denotational)30 b(seman)m(tics)j(for)f(v)-5 b(ariable)31
b(declarations)0 1536 y(Th)m(us)g(w)m(e)e(ev)-5 b(aluate)29
b(the)g(b)s(o)s(dy)g Fs(S)41 b Fu(in)28 b(an)h(up)s(dated)g(v)-5
b(ariable)28 b(en)m(vironmen)m(t)h(and)g(an)g(up)s(dated)0
1657 y(store.)55 b(W)-8 b(e)36 b(shall)f(later)g(mo)s(dify)g(the)h(ab)s
(o)m(v)m(e)i(clause)e(to)g(tak)m(e)h(the)f(pro)s(cedure)h(declarations)
0 1777 y(in)m(to)32 b(accoun)m(t.)0 2025 y Fw(Exercise)k(4.65)49
b Fu(Consider)33 b(the)g(follo)m(wing)d(statemen)m(t)j(of)f
Fw(Pro)s(c)p Fu(:)244 2241 y Fr(begin)i(var)f(y)g Fu(:=)f
Fr(0)p Fu(;)h Fr(var)h(x)e Fu(:=)h Fr(1)p Fu(;)533 2409
y Fr(begin)h(var)f(x)g Fu(:=)f Fr(7)p Fu(;)h Fr(x)g Fu(:=)f
Fr(x)p Fu(+)p Fr(1)h(end)p Fu(;)533 2576 y Fr(y)g Fu(:=)f
Fr(x)244 2744 y(end)0 2960 y Fu(Use)g(the)f(seman)m(tic)f(equations)h
(to)f(sho)m(w)i(that)f(the)g(lo)s(cation)d(for)i Fr(y)h
Fu(is)f(assigned)h(the)g(v)-5 b(alue)30 b Fw(1)0 3080
y Fu(in)i(the)h(\014nal)f(store.)2666 b Fh(2)0 3355 y
Fw(Pro)s(cedure)37 b(en)m(vironmen)m(ts)0 3545 y Fu(T)-8
b(o)32 b(cater)g(for)g(pro)s(cedures)h(w)m(e)g(shall)e(in)m(tro)s(duce)
h(the)g(notion)f(of)h(a)g Fs(pr)-5 b(o)g(c)g(e)g(dur)g(e)34
b(envir)-5 b(onment)p Fu(.)0 3666 y(It)43 b(will)e(b)s(e)j(a)f(total)e
(function)i(that)g(will)e(asso)s(ciate)i(eac)m(h)h(pro)s(cedure)g(with)
f(the)h(e\013ect)g(of)0 3786 y(executing)38 b(its)g(b)s(o)s(dy)-8
b(.)59 b(This)38 b(means)g(that)f(a)h(pro)s(cedure)g(en)m(vironmen)m
(t,)i Fs(env)2918 3801 y Fc(P)2976 3786 y Fu(,)f(will)c(b)s(e)j(an)0
3906 y(elemen)m(t)32 b(of)244 4122 y Fw(En)m(v)436 4137
y Fn(P)520 4122 y Fu(=)h Fw(Pname)f Ft(!)g Fu(\()p Fw(Store)h
Fo(,)-17 b Ft(!)32 b Fw(Store)p Fu(\))0 4338 y Fw(Remark)24
b Fu(This)h(notion)e(of)h(pro)s(cedure)h(en)m(vironmen)m(t)g(di\013ers)
f(from)g(that)g(of)g(the)h(op)s(erational)0 4458 y(approac)m(h.)2984
b Fh(2)146 4581 y Fu(The)46 b(pro)s(cedure)g(en)m(vironmen)m(t)f(is)f
(up)s(dated)i(using)e(the)h(seman)m(tic)g(function)f
Ft(D)3240 4545 y Fn(P)3240 4606 y(ds)3356 4581 y Fu(for)0
4702 y(pro)s(cedure)34 b(declarations.)42 b(It)33 b(has)g(functionalit)
m(y)244 4917 y Ft(D)323 4881 y Fn(P)323 4942 y(ds)395
4917 y Fu(:)43 b Fw(Dec)652 4932 y Fn(P)737 4917 y Ft(!)32
b Fw(En)m(v)1061 4932 y Fn(V)1151 4917 y Ft(!)g Fw(En)m(v)1475
4932 y Fn(P)1560 4917 y Ft(!)g Fw(En)m(v)1884 4932 y
Fn(P)0 5133 y Fu(So)e(giv)m(en)f(the)i(curren)m(t)g(v)-5
b(ariable)27 b(en)m(vironmen)m(t)k(and)e(the)i(curren)m(t)f(pro)s
(cedure)h(en)m(vironmen)m(t)0 5254 y(the)k(function)e
Ft(D)633 5218 y Fn(P)633 5278 y(ds)704 5254 y Fu([)-17
b([)q Fs(D)825 5269 y Fc(P)883 5254 y Fu(])g(])35 b(will)d(up)s(date)i
(the)h(pro)s(cedure)g(en)m(vironmen)m(t.)48 b(The)35
b(v)-5 b(ariable)33 b(en)m(vi-)0 5374 y(ronmen)m(t)e(m)m(ust)g(b)s(e)h
(a)m(v)-5 b(ailable)29 b(b)s(ecause)j(pro)s(cedures)h(m)m(ust)e(kno)m
(w)h(the)g(v)-5 b(ariables)30 b(that)h(ha)m(v)m(e)0 5494
y(b)s(een)i(declared)g(so)g(far.)43 b(An)33 b(example)f(is)g(the)h
(statemen)m(t)p eop
%%Page: 122 132
122 131 bop 251 130 a Fw(122)1978 b(4)112 b(Denotational)36
b(Seman)m(tics)p 251 193 3473 4 v 283 419 V 283 934 4
516 v 666 526 a Ft(D)745 489 y Fn(P)745 550 y(ds)816
526 y Fu([)-17 b([)q Fr(proc)34 b Fs(p)k Fr(is)33 b Fs(S)12
b Fu(;)32 b Fs(D)1524 541 y Fc(P)1583 526 y Fu(])-17
b(])q Fs(env)1777 541 y Fc(V)1869 526 y Fs(env)2025 541
y Fc(P)2116 526 y Fu(=)32 b Ft(D)2304 489 y Fn(P)2304
550 y(ds)2375 526 y Fu([)-17 b([)q Fs(D)2496 541 y Fc(P)2554
526 y Fu(])g(])q Fs(env)2748 541 y Fc(V)2840 526 y Fu(\()p
Fs(env)3034 541 y Fc(P)3092 526 y Fu([)p Fs(p)6 b Ft(7!)p
Fs(g)j Fu(]\))934 693 y(where)34 b Fs(g)41 b Fu(=)33
b Ft(S)1478 708 y Fn(ds)1550 693 y Fu([)-17 b([)p Fs(S)12
b Fu(])-17 b(])q Fs(env)1848 708 y Fc(V)1940 693 y Fs(env)2096
708 y Fc(P)666 884 y Ft(D)745 848 y Fn(P)745 909 y(ds)816
884 y Fu([)g([)q Fo(")p Fu(])g(])p Fs(env)1093 899 y
Fc(V)1186 884 y Fu(=)32 b(id)p 3753 934 V 283 937 3473
4 v 421 1098 a(T)-8 b(able)32 b(4.4:)43 b(Denotational)30
b(seman)m(tics)j(for)f(non-recursiv)m(e)h(pro)s(cedure)h(declarations)
527 1360 y Fr(begin)g(var)g(x)e Fu(:=)h Fr(7)p Fu(;)g
Fr(proc)g(p)g(is)g(x)g Fu(:=)f Fr(0)p Fu(;)816 1527 y
Fr(begin)i(var)f(x)g Fu(:=)g Fr(5)p Fu(;)f Fr(call)i(p)f(end)527
1695 y(end)283 1864 y Fu(where)k(the)f(b)s(o)s(dy)g(of)f
Fr(p)h Fu(m)m(ust)g(kno)m(w)h(that)e(a)h(v)-5 b(ariable)34
b Fr(x)h Fu(has)h(b)s(een)h(declared)f(in)f(the)h(outer)283
1984 y(blo)s(c)m(k.)430 2104 y(The)h(seman)m(tic)g(clauses)g
(de\014ning)g Ft(D)1826 2068 y Fn(P)1826 2129 y(ds)1933
2104 y Fu(in)f(the)h(case)h(of)e Fs(non-r)-5 b(e)g(cursive)38
b(pr)-5 b(o)g(c)g(e)g(dur)g(es)36 b Fu(are)283 2225 y(giv)m(en)i(in)e
(T)-8 b(able)37 b(4.4.)56 b(In)37 b(the)h(clause)f(for)g(pro)s(cedure)h
(declarations)e(w)m(e)i(use)g(the)f(seman)m(tic)283 2345
y(function)30 b Ft(S)730 2360 y Fn(ds)831 2345 y Fu(for)f(statemen)m
(ts)i(\(de\014ned)g(b)s(elo)m(w\))e(to)g(determine)g(the)h(meaning)f
(of)g(the)h(b)s(o)s(dy)283 2465 y(of)35 b(the)h(pro)s(cedure)g(using)f
(that)h Fs(env)1652 2480 y Fc(V)1747 2465 y Fu(and)g
Fs(env)2096 2480 y Fc(P)2189 2465 y Fu(are)f(the)h(en)m(vironmen)m(ts)g
(at)f(the)h(p)s(oin)m(t)e(of)283 2586 y(declaration.)41
b(The)30 b(v)-5 b(ariables)28 b(o)s(ccurring)h(in)f(the)h(b)s(o)s(dy)h
Fs(S)40 b Fu(of)29 b Fs(p)35 b Fu(will)27 b(therefore)j(b)s(e)f(b)s
(ound)g(to)283 2706 y(the)37 b(lo)s(cations)e(of)h(the)h(v)-5
b(ariables)35 b(as)h(kno)m(wn)i(at)e(the)h(time)e(of)h(declaration)e
(but)j(the)g(v)-5 b(alues)283 2827 y(of)39 b(the)g(lo)s(cations)e(will)
f(not)j(b)s(e)g(kno)m(wn)h(un)m(til)d(the)i(time)f(of)g(call.)60
b(In)39 b(this)g(w)m(a)m(y)h(w)m(e)f(ensure)283 2947
y(that)j(w)m(e)g(obtain)f(static)g(scop)s(e)h(for)f(v)-5
b(ariables.)69 b(Also)41 b(an)g(o)s(ccurrence)i(of)e
Fr(call)i Fs(p)3433 2911 y Fi(0)3498 2947 y Fu(in)d(the)283
3067 y(b)s(o)s(dy)g(of)e(the)i(pro)s(cedure)g(will)d(refer)i(to)g(a)g
(pro)s(cedure)h Fs(p)2439 3031 y Fi(0)2502 3067 y Fu(men)m(tioned)e(in)
h Fs(env)3259 3082 y Fc(P)3317 3067 y Fu(,)h(that)f(is)g(a)283
3188 y(pro)s(cedure)k(declared)g(in)e(an)h(outer)g(blo)s(c)m(k)g(or)g
(in)f(the)i(curren)m(t)g(blo)s(c)m(k)f(but)g(preceding)g(the)283
3308 y(presen)m(t)32 b(pro)s(cedure.)44 b(In)30 b(this)g(w)m(a)m(y)h(w)
m(e)g(obtain)e(static)h(scop)s(e)h(for)f(pro)s(cedures.)44
b(This)30 b(will)e(b)s(e)283 3429 y(illustrated)j(in)h(Exercise)i(4.67)
e(b)s(elo)m(w.)283 3682 y Fw(The)38 b(seman)m(tic)e(function)h
Ft(S)1483 3697 y Fn(ds)1592 3682 y Fw(for)g(Pro)s(c)283
3867 y Fu(The)j(meaning)c(of)i(a)g(statemen)m(t)g(dep)s(ends)i(on)e
(the)h(v)-5 b(ariables)37 b(and)h(pro)s(cedures)i(that)e(ha)m(v)m(e)283
3987 y(b)s(een)i(declared.)63 b(Therefore)40 b(the)f(seman)m(tic)g
(function)f Ft(S)2451 4002 y Fn(ds)2561 3987 y Fu(for)g(statemen)m(ts)i
(in)e Fw(Pro)s(c)g Fu(will)283 4108 y(ha)m(v)m(e)c(functionalit)m(y)527
4276 y Ft(S)595 4291 y Fn(ds)666 4276 y Fu(:)44 b Fw(Stm)32
b Ft(!)g Fw(En)m(v)1293 4291 y Fn(V)1383 4276 y Ft(!)g
Fw(En)m(v)1707 4291 y Fn(P)1792 4276 y Ft(!)g Fu(\()p
Fw(Store)g Fo(,)-17 b Ft(!)33 b Fw(Store)p Fu(\))283
4445 y(The)f(function)d(is)h(de\014ned)i(b)m(y)f(the)f(clauses)h(of)f
(T)-8 b(able)30 b(4.5.)42 b(In)30 b(most)g(cases)i(the)e(de\014nition)f
(of)283 4565 y Ft(S)351 4580 y Fn(ds)453 4565 y Fu(is)h(a)g(straigh)m
(tforw)m(ard)h(mo)s(di\014cation)d(of)i(the)h(clauses)g(of)f
Ft(S)2648 4529 y Fi(0)2648 4590 y Fn(ds)2719 4565 y Fu(.)43
b(Note)31 b(that)f(the)h(meaning)283 4686 y(of)i(a)f(pro)s(cedure)h
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%%Page: 123 133
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%%Page: 124 134
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%%Page: 125 135
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%%Page: 166 176
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%%Page: 167 177
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%%Page: 173 183
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%%Page: 188 198
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eop
%%Page: 189 199
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b(A)35 b(Hoare-lik)m(e)f(pro)s(of)f(system)j(for)e(run-time)g(analysis)
g(of)g(programs,)201 5494 y Fs(Scienc)-5 b(e)33 b(of)i(Computer)f(Pr)-5
b(o)g(gr)g(amming)p Fu(,)32 b(v)m(ol)g(9)g(\(1987\).)1663
5849 y(233)p eop
%%Page: 234 244
234 243 bop 251 130 a Fw(234)2676 b(Bibliograph)m(y)p
251 193 3473 4 v 283 515 a Fu([13])49 b(F.)29 b(Nielson,)g(H.)g(R.)h
(Nielson:)40 b(Tw)m(o-lev)m(el)30 b(seman)m(tics)f(and)h(co)s(de)f
(generation,)g Fs(The)-5 b(or)g(et-)484 636 y(ic)g(al)34
b(Computer)h(Scienc)-5 b(e)p Fu(,)31 b(v)m(ol)h(56)h(\(1988\).)283
839 y([14])49 b(G.)22 b(D.)f(Plotkin:)38 b Fs(A)25 b(Structur)-5
b(al)27 b(appr)-5 b(o)g(ach)24 b(to)h(Op)-5 b(er)g(ational)25
b(Semantics)p Fu(,)e(Lecture)g(notes,)484 960 y(D)m(AIMI)33
b(FN-19,)f(Aarh)m(us)h(Univ)m(ersit)m(y)-8 b(,)33 b(Denmark)f(\(1981,)g
(reprin)m(ted)h(1991\).)283 1163 y([15])49 b(G.)34 b(D.)f(Plotkin:)45
b(An)35 b(op)s(erational)c(seman)m(tics)k(for)e(CSP)-8
b(,)35 b(in:)46 b Fs(F)-7 b(ormal)34 b(Description)h(of)484
1283 y(Pr)-5 b(o)g(gr)g(amming)28 b(Conc)-5 b(epts)29
b(II)p Fu(,)d(Pro)s(ceedings)i(of)e(TC-2)h(W)-8 b(ork.)28
b(Conf.)f(\(ed.)g(D.)g(Bj\034rner\),)484 1404 y(North{Holland)k
(\(1982\).)283 1607 y([16])49 b(D.)32 b(A.)h(Sc)m(hmidt:)44
b Fs(Denotational)33 b(Semantics:)44 b(a)35 b(Metho)-5
b(dolo)g(gy)35 b(for)g(L)-5 b(anguage)34 b(Devel-)484
1727 y(opment)p Fu(,)e(Allyn)f(&)i(Bacon,)g(Inc.)g(\(1986\).)283
1931 y([17])49 b(J.)42 b(E.)h(Sto)m(y:)63 b Fs(Denotational)42
b(Semantics:)62 b(The)43 b(Sc)-5 b(ott{Str)g(achey)43
b(Appr)-5 b(o)g(ach)43 b(to)h(Pr)-5 b(o-)484 2051 y(gr)g(amming)34
b(L)-5 b(anguage)34 b(The)-5 b(ory)p Fu(,)32 b(MIT)i(Press)g(\(1977\).)
p eop
%%Page: 235 245
235 244 bop 0 974 a Fv(Index)77 b(of)h(Sym)-6 b(b)6 b(ols)0
1446 y Fu(\()p Fw(P)p Fu(,)32 b Ft(v)251 1461 y Fn(P)304
1446 y Fu(\),)g(136)0 1567 y(\()p Fw(PState)p Fu(,)g
Ft(v)506 1582 y Fn(PS)598 1567 y Fu(\),)h(140)0 1687
y(\()p Fw(PState)f Ft(!)g Fw(PState)p Fu(,)g Ft(v)p Fu(\),)i(148)0
1807 y(\()p Fw(State)f Fo(,)-17 b Ft(!)32 b Fw(State)p
Fu(,)h Ft(v)p Fu(\),)g(93)0 1928 y(\()p Fs(D)9 b Fu(,)33
b Ft(v)258 1943 y Fc(D)322 1928 y Fu(\),)g(95)0 2124
y Ft(\001)17 b(\001)g(\001)n Fu([)p Ft(\001)g(\001)g(\001)o(7\000)-17
b(!\001)17 b(\001)g(\001)n Fu(],)33 b(51)0 2244 y Ft(\001)17
b(\001)g(\001)n Fu([)p Ft(\001)g(\001)g(\001)o(7!\001)g(\001)g(\001)m
Fu(],)33 b(16,)f(17,)g(177,)g(214)0 2365 y Ft(\001)17
b(\001)g(\001)n(\021)33 b(\001)17 b(\001)g(\001)n Fu(rel)p
342 2378 109 4 v 32 w Ft(\001)g(\001)g(\001)o Fu(,)32
b(137,)g(138)0 2485 y Ft(\001)17 b(\001)g(\001)n(`)33
b(\001)17 b(\001)g(\001)n(!)32 b(\001)17 b(\001)g(\001)n
Fu(,)33 b(54,)f(58)0 2605 y Ft(\016)p Fu(,)g(214)0 2726
y Ft(\005)p Fu(,)f(215)0 2846 y Fo(,)-17 b Ft(!)p Fu(,)33
b(213)0 2966 y Ft(!)p Fu(,)f(213)0 3087 y Fh(\003)p Fu(,)h(64)0
3207 y Ft(\))p Fu(,)f(32)0 3328 y Ft(!)p Fu(,)g(20)0
3448 y Ft(!)100 3412 y Fc(t)129 3448 y Fu(,)h(202)0 3568
y Ft(!)100 3583 y Fc(D)164 3568 y Fu(,)f(51,)g(58)0 3689
y Ft(!)100 3704 y Fn(Aexp)264 3689 y Fu(,)h(31)0 3809
y Ft(!)100 3824 y Fn(Bexp)262 3809 y Fu(,)f(32)0 3930
y Ft(t)p Fu(,)h(136)0 3983 y Fg(F)69 4050 y Fu(,)g(97,)f(99,)g(136,)g
(140,)g(148)0 4170 y Ft(?)p Fu(,)h(95)0 4291 y Ft(v)p
Fu(,)g(95,)f(136,)g(140,)g(148)0 4411 y Ft(w)p Fu(,)h(95)0
4531 y Ft(`)p Fu(,)f(180,)g(192,)g(203)0 4652 y Ft(j)-17
b Fu(=,)33 b(184,)e(191,)h(203)0 4772 y Ft(:)p Fu(,)h(177)0
4893 y Ft(_)p Fu(,)g(177)0 5013 y Ft(^)p Fu(,)g(177)0
5133 y Ft(\))p Fu(,)f(177)0 5254 y Ft(f)g Fs(P)43 b Ft(g)33
b Fs(S)44 b Ft(f)32 b Fs(Q)42 b Ft(g)p Fu(,)32 b(176)0
5374 y Ft(f)g Fs(P)43 b Ft(g)33 b Fs(S)44 b Ft(f)32 b(+)h
Fs(Q)41 b Ft(g)p Fu(,)33 b(191)0 5494 y Ft(f)f Fs(P)43
b Ft(g)33 b Fs(S)44 b Ft(f)32 b Fs(e)40 b Ft(+)32 b Fs(Q)42
b Ft(g)p Fu(,)33 b(202)1882 1446 y Fs(f)1932 1410 y Fn(n)1976
1446 y Fu(,)f(104)1882 1567 y Fs(R)1957 1531 y Fi(\003)1996
1567 y Fu(,)h(215)1882 1688 y Fs(R)1957 1652 y Fn(+)2016
1688 y Fu(,)f(215)1882 1899 y Ft(A)o Fu(,)h(12)1882 2020
y Ft(B)s Fu(,)g(14)1882 2141 y Ft(C)6 b(A)o Fu(,)33 b(70)1882
2262 y Ft(C)6 b(B)s Fu(,)33 b(70)1882 2383 y Ft(C)6 b(S)i
Fu(,)32 b(71)1882 2504 y Ft(D)1961 2467 y Fn(P)1961 2528
y(ds)2032 2504 y Fu(,)h(121)1882 2624 y Ft(D)1961 2588
y Fn(V)1961 2649 y(ds)2032 2624 y Fu(,)g(120)1882 2745
y Ft(M)o Fu(,)g(68)1882 2866 y Ft(N)14 b Fu(,)33 b(9)1882
2987 y Ft(O)s Fu(\()p Fs(g)9 b Fu(\),)32 b(214)1882 3108
y Ft(P)8 b Fu(,)33 b(213)1882 3229 y Ft(P)8 b(A)p Fu(,)32
b(142)1882 3349 y Ft(P)8 b(A)2039 3364 y Fc(X)2106 3349
y Fu(,)33 b(161)1882 3470 y Ft(P)8 b(B)s Fu(,)33 b(142)1882
3591 y Ft(P)8 b(B)2027 3606 y Fc(X)2095 3591 y Fu(,)32
b(161)1882 3712 y Ft(P)8 b(S)g Fu(,)32 b(144)1882 3833
y Ft(P)8 b(S)2027 3848 y Fc(X)2094 3833 y Fu(,)33 b(161)1882
3954 y Ft(S)1949 3969 y Fn(am)2048 3954 y Fu(,)f(72)1882
4075 y Ft(S)1949 4090 y Fn(cs)2013 4075 y Fu(,)g(130)1882
4195 y Ft(S)1949 4159 y Fi(0)1949 4220 y Fn(cs)2013 4195
y Fu(,)g(128)1882 4316 y Ft(S)1949 4331 y Fn(ds)2021
4316 y Fu(,)g(85,)g(122)1882 4437 y Ft(S)1949 4401 y
Fi(0)1949 4462 y Fn(ds)2021 4437 y Fu(,)g(119)1882 4558
y Ft(S)1949 4573 y Fn(ns)2021 4558 y Fu(,)g(31)1882 4679
y Ft(S)1949 4694 y Fn(sos)2044 4679 y Fu(,)h(39)1882
4800 y Ft(T)25 b(A)p Fu(,)32 b(201)1882 4920 y Ft(T)25
b(B)t Fu(,)32 b(201)1882 5132 y Fw(AM)p Fu(,)g(63)1882
5253 y Fw(Aexp)p Fu(,)g(7)1882 5374 y Fw(Aexp)2139 5389
y Fc(X)2206 5374 y Fu(,)h(161)1882 5494 y Fw(Bexp)p Fu(,)f(7)1663
5849 y(235)p eop
%%Page: 236 246
236 245 bop 251 130 a Fw(236)2454 b(Index)38 b(of)g(Sym)m(b)s(ols)p
251 193 3473 4 v 283 515 a(Bexp)535 530 y Fc(X)603 515
y Fu(,)33 b(161)283 636 y Fw(Blo)s(c)m(k)p Fu(,)f(51)283
756 y Fw(Co)s(de)p Fu(,)i(64)283 877 y Fw(Con)m(t)p Fu(,)f(127)283
997 y Fw(Dec)470 1012 y Fn(P)522 997 y Fu(,)g(53,)f(117)283
1117 y Fw(Dec)470 1132 y Fn(V)528 1117 y Fu(,)h(51,)f(117)283
1238 y Fw(En)m(v)475 1253 y Fn(E)527 1238 y Fu(,)h(130)283
1358 y Fw(En)m(v)475 1373 y Fn(P)527 1358 y Fu(,)g(54,)f(56,)g(58,)h
(121)283 1478 y Fw(En)m(v)475 1493 y Fn(V)533 1478 y
Fu(,)g(57,)f(118)283 1599 y Fw(Exc)p Fu(,)h(126)283 1719
y Fw(Exception)p Fu(,)f(126)283 1840 y Fw(\013)p Fu(,)h(213)283
1960 y Fw(Lo)s(c)p Fu(,)g(57,)g(118)283 2080 y Fw(N)p
Fu(,)g(213)283 2201 y Fw(Num)p Fu(,)f(7)283 2321 y Fw(P)p
Fu(,)h(136)283 2441 y Fw(PState)p Fu(,)g(137)283 2562
y Fw(Pname)p Fu(,)g(53,)f(117)283 2682 y Fw(Pro)s(c)p
Fu(,)g(52,)h(117)283 2803 y Fw(Stac)m(k)p Fu(,)g(64)283
2923 y Fw(State)p Fu(,)g(12)283 3043 y Fw(State)538 3058
y Fc(X)606 3043 y Fu(,)g(161)283 3164 y Fw(Stm)p Fu(,)f(7)283
3284 y Fw(Stm)483 3299 y Fc(X)550 3284 y Fu(,)h(161)283
3405 y Fw(Store)p Fu(,)g(57,)f(118)283 3525 y Fw(T)p
Fu(,)h(213)283 3645 y Fw(tt)p Fu(,)f(213)283 3766 y Fw(V)-9
b(ar)p Fu(,)33 b(7)283 3886 y Fw(While)p Fu(,)f(6)283
4006 y Fw(Z)p Fu(,)i(213)283 4210 y Fs(a)7 b Fu(,)33
b(7)283 4330 y Fs(b)6 b Fu(,)33 b(7)283 4451 y Fs(c)6
b Fu(,)33 b(64,)f(127)283 4571 y Fs(D)366 4586 y Fc(P)425
4571 y Fu(,)h(53,)f(117)283 4691 y Fs(D)366 4706 y Fc(V)427
4691 y Fu(,)h(51,)f(117)283 4812 y Fs(e)7 b Fu(,)33 b(64,)g(126)283
4932 y Fs(env)439 4947 y Fc(E)498 4932 y Fu(,)g(130)283
5053 y Fs(env)439 5068 y Fc(P)497 5053 y Fu(,)g(54,)f(121)2165
515 y Fs(env)2321 530 y Fc(V)2381 515 y Fu(,)h(57,)f(118)2165
636 y Fs(n)7 b Fu(,)33 b(7)2165 756 y Fs(P)10 b Fu(,)33
b(176)2165 877 y Fs(p)6 b Fu(,)33 b(53,)f(117,)g(136)2165
997 y Fs(ps)8 b Fu(,)32 b(137)2165 1117 y Fs(S)12 b Fu(,)32
b(7)2165 1238 y Fs(s)8 b Fu(,)33 b(12)2165 1358 y Fs(sto)6
b Fu(,)33 b(57,)f(118)2165 1478 y Fs(Q)9 b Fu(,)33 b(176)2165
1599 y Fs(x)12 b Fu(,)32 b(7)2165 1802 y Fb(d)p Fu(?,)h(135,)f(136)2165
1923 y Fb(init)p Fu(,)h(141)2165 2043 y Fb(init)2345
2058 y Fc(X)2413 2043 y Fu(,)f(163)2165 2163 y Fb(lost)p
Fu(,)h(141)2165 2284 y Fb(ok)p Fu(,)g(135)2165 2487 y(cond,)g(87,)f
(119)2165 2608 y(cond)2365 2623 y Fn(P)2418 2608 y Fu(,)g(145)2165
2728 y(D)m(V,)h(51)2165 2848 y(extend)2448 2863 y Fc(X)2517
2848 y Fu(,)f(161)2165 2969 y(FIX,)h(88,)f(97,)g(104,)g(146)2165
3089 y(FV,)g(15,)h(16,)f(160)2165 3209 y(graph,)g(214)2165
3330 y(I,)h(215)2165 3450 y(I)2200 3465 y Fc(p)2240 3450
y Fu(,)f(215)2165 3571 y(I)2200 3586 y Fc(X)2268 3571
y Fu(,)g(215)2165 3691 y(id,)g(214)2165 3811 y(lo)s(okup,)g(118)2165
3932 y(new,)i(57,)e(118)2165 4052 y(next,)i(57,)e(118)2165
4172 y(OK,)g(137)2165 4293 y(on-trac)m(k,)h(137)2165
4413 y(up)s(d)2330 4428 y Fn(P)2382 4413 y Fu(,)g(54,)f(56,)g(58)2165
4534 y(wlp,)g(186)2165 4737 y(rel)p 2165 4750 109 4 v
-1 w(,)h(136{138)2165 4857 y(undef)p 2165 4870 236 4
v 1 w(,)f(214)p eop
%%Page: 237 247
237 246 bop 0 974 a Fv(Index)0 1406 y Fr(abort)p Fu(-construct,)35
b(44)0 1529 y(abstract)e(mac)m(hine,)f(63)0 1653 y(abstract)h(syn)m
(tax,)h(7)0 1776 y(additiv)m(e)e(function,)g(163)0 1900
y(admissible)f(predicate,)h(173)0 2023 y(an)m(ti-symmetric)f(relation,)
f(95)0 2146 y(arithmetic)g(expression,)k(7)166 2270 y(analysis,)e(142)
166 2393 y(execution)h(time,)f(201)166 2517 y(seman)m(tics,)h(12)166
2640 y(translation,)e(70)0 2763 y Fr(assert)p Fu(-construct,)k(46)0
2887 y(assertion,)e(175)0 3010 y(axiom,)e(20)0 3133 y(axiomatic)f
(seman)m(tics,)j(178)0 3390 y(basis)g(elemen)m(t,)f(7)0
3513 y Fr(begin)p Fu(-construct,)j(51,)d(117,)g(126)0
3637 y(bisim)m(ulation)d(relation,)i(81)0 3760 y(b)s(o)s(olean)g
(expression,)j(7)166 3884 y(analysis,)e(142)166 4007
y(execution)h(time,)f(201)166 4130 y(seman)m(tics,)h(14)166
4254 y(translation,)e(70)0 4510 y Fr(call)p Fu(-construct,)j(53,)f
(117,)e(197)0 4634 y(call-b)m(y-v)-5 b(alue)30 b(parameter,)i(60,)h
(126)0 4757 y(ccp)s(o,)g(99)0 4881 y(c)m(hain,)g(97)0
5004 y(c)m(hain)40 b(complete)f(partially)e(ordered)k(set,)332
5124 y(99)0 5248 y(co)s(de)33 b(generation,)f(69)0 5371
y(complete)g(lattice,)f(99)0 5494 y(completeness,)i(183)2048
1406 y(of)21 b(partial)e(correctness)24 b(inference)e(sys-)2214
1526 y(tem,)32 b(187)2048 1648 y(of)i(total)g(correctness)k(inference)d
(sys-)2214 1768 y(tem,)d(196)1882 1890 y(comp)s(osite)f(elemen)m(t,)h
(7)1882 2011 y(comp)s(ositional)d(de\014nition,)i(11)1882
2133 y(computation)g(sequence,)k(66)1882 2254 y(concrete)e(syn)m(tax,)i
(7)1882 2376 y(con\014guration,)c(216)2048 2497 y(\014nal,)g(216)2048
2619 y(stuc)m(k,)j(216)2048 2740 y(terminal,)c(216)1882
2862 y(constan)m(t)j(propagation,)e(133)1882 2983 y(con)m(tin)m
(uation,)g(127)1882 3105 y(con)m(tin)m(uation)g(st)m(yle)i(seman)m
(tics,)g(127)1882 3226 y(con)m(tin)m(uous)g(function,)f(103)1882
3348 y(correct)h(implemen)m(tation,)c(73)1882 3571 y(declared)j(v)-5
b(ariable,)31 b(51)1882 3692 y(denotational)f(seman)m(tics,)j(85)2048
3814 y(con)m(tin)m(uation)e(st)m(yle,)i(127)2048 3935
y(direct)f(st)m(yle,)h(85)1882 4057 y(dep)s(endency)i(analysis,)d(134)
1882 4178 y(deriv)-5 b(ation)30 b(sequence,)36 b(33)1882
4300 y(deriv)-5 b(ation)30 b(tree,)k(22)1882 4421 y(detection)e(of)g
(signs)h(analysis,)f(133)1882 4543 y(deterministic)e(seman)m(tics,)j
(28,)f(38,)h(68)1882 4664 y(direct)f(st)m(yle)h(seman)m(tics,)g(85)1882
4786 y(dubious,)f(135)1882 4907 y(dynamic)f(scop)s(e,)j(53)1882
5130 y(equiv)-5 b(alence)32 b(relation,)f(141)1882 5252
y(ev)-5 b(aluation)30 b(stac)m(k,)k(64)1882 5373 y(exception,)f(126)
1882 5494 y(exception)g(en)m(vironmen)m(t,)g(130)1663
5849 y(237)p eop
%%Page: 238 248
238 247 bop 251 130 a Fw(238)3028 b(Index)p 251 193 3473
4 v 283 515 a Fu(expressiv)m(eness,)37 b(191)283 636
y(extensional)c(approac)m(h,)g(177)283 837 y(\014xed)h(p)s(oin)m(t,)e
(87)450 957 y(least,)g(97,)g(104)450 1078 y(requiremen)m(ts,)h(92,)f
(97)283 1198 y(\014xed)i(p)s(oin)m(t)e(induction,)g(173)283
1319 y(\014xed)i(p)s(oin)m(t)e(theory)-8 b(,)33 b(106)283
1439 y(\015o)m(w)h(of)e(con)m(trol,)g(137)283 1559 y
Fr(for)p Fu(-construct,)26 b(28,)d(36,)h(43,)f(72,)h(111,)f(117,)616
1680 y(151,)31 b(182)283 1800 y(free)i(v)-5 b(ariable,)31
b(15,)i(16,)f(160)283 1920 y(function)h(comp)s(osition,)d(214)283
2041 y(functional)h(dep)s(endency)-8 b(,)35 b(134)283
2242 y(graph)e(of)f(a)g(function,)g(214)283 2443 y Fr(handle)p
Fu(-construct,)j(126)283 2645 y(iden)m(tit)m(y)e(function,)f(214)283
2765 y(iden)m(tit)m(y)h(relation,)e(215)283 2886 y(induction,)h(10)450
3006 y(\014xed)h(p)s(oin)m(t,)f(173)450 3126 y(on)38
b(the)h(length)e(of)h(computation)f(se-)616 3247 y(quences,)e(67)450
3367 y(on)21 b(the)h(length)g(of)f(deriv)-5 b(ation)20
b(sequences,)616 3487 y(37)450 3608 y(on)42 b(the)h(shap)s(e)g(of)f
(deriv)-5 b(ation)41 b(trees,)616 3728 y(28)450 3849
y(on)52 b(the)g(shap)s(e)h(of)f(inference)h(trees,)616
3969 y(183)450 4089 y(structural,)32 b(11)283 4210 y(inference)i
(system,)f(178)450 4330 y(for)f(execution)h(time,)e(200)450
4451 y(for)h(partial)e(correctness,)35 b(178)450 4571
y(for)d(total)f(correctness,)j(191)283 4691 y(inference)g(tree,)f(180)
283 4812 y(injectiv)m(e)g(function,)f(214)283 4932 y(input)h(v)-5
b(ariable,)31 b(134)283 5052 y(instructions,)i(64)283
5173 y(in)m(tensional)e(approac)m(h,)j(177,)e(190)283
5293 y(in)m(v)-5 b(arian)m(t,)32 b(179,)g(192)283 5494
y(Kripk)m(e-relation,)f(141)2165 515 y(least)h(elemen)m(t,)h(95)2165
636 y(least)f(\014xed)i(p)s(oin)m(t,)e(97,)g(104)2165
758 y(least)g(upp)s(er)h(b)s(ound,)g(97)2165 879 y(lo)s(cal)d(v)-5
b(ariable,)31 b(51)2165 1000 y(lo)s(cation,)f(57,)i(118)2165
1121 y(logical)d(v)-5 b(ariable,)31 b(176)2165 1242 y(lo)s(oping)f
(computation)h(sequence,)36 b(66)2165 1363 y(lo)s(oping)30
b(execution,)j(25,)g(36)2165 1579 y(monotone)f(function,)g(100)2165
1700 y(m)m(utual)f(recursiv)m(e)j(pro)s(cedure,)g(60)2165
1916 y(natural)d(seman)m(tics,)i(20)2165 2037 y(non-determinism,)d(46,)
j(197)2165 2158 y(non-recursiv)m(e)h(pro)s(cedure,)f(56,)f(122,)g(197)
2165 2279 y(n)m(um)m(b)s(er,)h(9)2165 2400 y(n)m(umeral,)f(7,)g(11)2165
2616 y Fr(or)p Fu(-construct,)i(46,)e(197)2165 2737 y(order)h(of)f
(magnitude,)f(214)2165 2858 y(order)d(of)g(magnitude)f(of)h(execution)h
(time,)2497 2979 y(200)2165 3100 y(ordering,)j(93)2331
3221 y(an)m(ti-symmetry)-8 b(,)32 b(95)2331 3342 y(on)h
Fw(P)p Fu(,)f(136)2331 3463 y(on)h Fw(PState)p Fu(,)f(140)2331
3584 y(on)h Fw(PState)f Ft(!)g Fw(PState)p Fu(,)g(148)2331
3705 y(on)h Fw(State)f Fo(,)-17 b Ft(!)33 b Fw(State)p
Fu(,)f(93)2331 3826 y(re\015exivit)m(y)-8 b(,)33 b(95,)f(141)2331
3947 y(symmetry)-8 b(,)33 b(141)2331 4068 y(transitivit)m(y)-8
b(,)31 b(95,)h(141)2165 4190 y(output)h(v)-5 b(ariable,)31
b(134)2165 4405 y Fr(par)p Fu(-construct,)j(48)2165 4526
y(parallelism,)29 b(48)2165 4648 y(parameterized)j(relation,)f(141)2165
4769 y(partial)f(correctness,)35 b(169,)d(175)2331 4890
y(axiomatic)e(seman)m(tics,)j(178)2331 5011 y(denotational)e(seman)m
(tics,)i(172)2331 5132 y(natural)e(seman)m(tics,)i(169)2331
5253 y(structural)45 b(op)s(erational)e(seman)m(tics,)2497
5373 y(172)2165 5494 y(partial)30 b(function,)i(213)p
eop
%%Page: 239 249
239 248 bop 0 130 a Fw(Index)3028 b(239)p 0 193 3473
4 v 0 515 a Fu(partially)30 b(ordered)j(set,)h(95)0 636
y(p)s(ostcondition,)d(176)0 756 y(precondition,)h(176)0
877 y(predicate,)h(215)0 997 y Fr(proc)p Fu(-construct,)h(53,)f(117,)e
(197)0 1117 y(pro)s(cedure)j(declaration,)d(53,)h(117,)g(121)0
1238 y(pro)s(cedure)23 b(en)m(vironmen)m(t,)h(54,)g(56,)f(58,)g(121)0
1358 y(pro)s(cedure)34 b(name,)e(53,)g(117)0 1478 y(program)f(v)-5
b(ariable,)31 b(176)0 1599 y(prop)s(ert)m(y)-8 b(,)33
b(135)0 1719 y(prop)s(ert)m(y)g(state,)g(137)166 1840
y(improp)s(er,)e(138)166 1960 y(prop)s(er,)i(138)0 2080
y Fr(protect)p Fu(-construct,)i(50)0 2201 y(pro)m(v)-5
b(abilit)m(y)d(,)31 b(180)166 2321 y(in)21 b(execution)h(time)f
(inference)h(system,)332 2441 y(203)166 2562 y(in)f(partial)f
(correctness)j(inference)g(sys-)332 2682 y(tem,)32 b(180)166
2803 y(in)i(total)f(correctness)k(inference)e(sys-)332
2923 y(tem,)d(192)0 3043 y(pro)m(v)-5 b(ably)32 b(equiv)-5
b(alence,)33 b(182)0 3246 y Fr(raise)p Fu(-construct,)i(126)0
3366 y Fr(random)p Fu(-construct,)g(48)0 3486 y(recurrence)f(equation,)
f(205,)f(207)0 3607 y(recursiv)m(e)i(pro)s(cedure,)g(54,)e(56,)g(125,)g
(198)0 3727 y(re\015exiv)m(e)i(ordering,)e(141)0 3848
y(re\015exiv)m(e)i(relation,)d(95)0 3968 y(re\015exiv)m(e)j(transitiv)m
(e)e(closure,)h(215)0 4088 y(relation,)e(215)0 4209 y(relation)g(comp)s
(osition,)f(215)0 4329 y Fr(repeat)p Fu(-construct,)43
b(28,)e(30,)f(36,)h(39,)f(43,)332 4450 y(72,)24 b(81,)f(111,)g(112,)h
(117,)f(129,)g(151,)332 4570 y(160,)43 b(182,)g(183,)g(186,)g(190,)h
(194,)332 4690 y(196,)32 b(208)0 4811 y(rule,)g(20)0
4931 y(rule)g(of)g(consequence,)k(180)0 5133 y(safet)m(y)e(of)e(static)
g(analysis,)g(153,)g(159)0 5254 y(seman)m(tic)g(clause,)h(9)0
5374 y(seman)m(tic)f(equation,)h(9)0 5494 y(seman)m(tic)f(equiv)-5
b(alence,)33 b(26,)f(39,)h(112)1882 515 y(seman)m(tic)f(function,)g(9)
1882 638 y(soundness,)i(183)2048 760 y(of)21 b(execution)h(time)f
(inference)h(system,)2214 880 y(208)2048 1003 y(of)f(partial)e
(correctness)24 b(inference)e(sys-)2214 1123 y(tem,)32
b(184)2048 1245 y(of)i(total)g(correctness)k(inference)d(sys-)2214
1366 y(tem,)d(194)1882 1488 y(state,)h(12)1882 1610 y(statemen)m(t,)g
(7)2048 1732 y(analysis,)f(144)2048 1855 y(execution)h(time,)e(202)2048
1977 y(seman)m(tics,)h(31,)h(39,)f(85)2048 2099 y(translation,)e(71)
1882 2221 y(static)i(scop)s(e,)h(53,)f(117)1882 2344
y(storage,)g(64)1882 2466 y(store,)h(57,)f(118)1882 2588
y(strict)g(function,)g(103)1882 2710 y(strongest)h(p)s(ostcondition,)e
(187,)h(190)1882 2833 y(structural)g(induction,)g(11)1882
2955 y(structural)g(op)s(erational)e(seman)m(tics,)j(32)1882
3077 y(stuc)m(k)h(con\014guration,)e(216)1882 3199 y(substitution,)g
(16,)g(17,)g(51)1882 3322 y(symmetric)f(ordering,)h(141)1882
3558 y(terminating)19 b(computation)h(sequence,)27 b(66)1882
3680 y(terminating)j(execution,)j(25,)f(36)1882 3803
y(total)f(correctness,)j(169)2048 3925 y(axiomatic)c(seman)m(tics,)j
(191)1882 4047 y(total)e(function,)h(213)1882 4169 y(transition)e
(relation,)h(216)1882 4292 y(transition)f(system,)k(216)1882
4414 y(transitiv)m(e)e(ordering,)f(141)1882 4536 y(transitiv)m(e)h
(relation,)e(95)1882 4773 y(upp)s(er)j(b)s(ound,)f(97)1882
5009 y(v)-5 b(alidit)m(y)d(,)30 b(184)2048 5131 y(in)21
b(execution)h(time)e(inference)j(system,)2214 5252 y(203)2048
5374 y(in)e(partial)e(correctness)24 b(inference)e(sys-)2214
5494 y(tem,)32 b(184)p eop
%%Page: 240 250
240 249 bop 251 130 a Fw(240)3028 b(Index)p 251 193 3473
4 v 450 515 a Fu(in)33 b(total)g(correctness)k(inference)e(sys-)616
636 y(tem,)d(191)283 756 y Fr(var)p Fu(-construct,)j(51,)d(117)283
877 y(v)-5 b(ariable,)31 b(7)283 997 y(v)-5 b(ariable)31
b(declaration,)g(51,)i(117,)e(120)283 1117 y(v)-5 b(ariable)31
b(en)m(vironmen)m(t,)i(57,)f(118)283 1321 y(w)m(eak)m(est)j(lib)s(eral)
30 b(precondition,)i(187)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF
generated by cgit v1.2.3 (git 2.39.1) at 2025-03-14 19:26:39 +0000