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invertmatrix matrix concatmatrix matrix invertmatrix put %%EndSetup %%Page: (0,1) 1 userdict/PStoPSsaved save put PStoPSmatrix setmatrix 595.000000 0.271378 translate 90 rotate 0.706651 dup scale userdict/PStoPSmatrix matrix currentmatrix put userdict/PStoPSclip{0 0 moveto 595.000000 0 rlineto 0 842.000000 rlineto -595.000000 0 rlineto closepath}put initclip /showpage{}def/copypage{}def/erasepage{}def PStoPSxform concat 1 0 bop Fn 281 370 a(Cleaner) p 570 370 a(seman) n(tics) p 927 370 a(for) p 1047 370 a(Ob) t(jectiv) n(e) p 1404 370 a(Lab) r(el) p Fm 717 518 a(Jacques) p 934 518 a(Garrigue) 719 634 y(Octob) r(er) p 945 634 a(26,) p 1040 634 a(1999) p Fl 11 836 a(Credits) p Fk 11 929 a(This) p 122 929 a(prop) q(osal) p 319 929 a(con) o(tains) p 510 929 a(ideas) p 632 929 a(from) p 747 929 a(Damien) p 928 929 a(Doligez) p 1101 929 a(and) p 1196 929 a(Pierre) p 1340 929 a(W) l(eis.) p Fl 11 1073 a(Lab) r(els) p 221 1073 a(and) p 351 1073 a(optionals) p Fk 11 1165 a(Lab) q(els) p 165 1165 a(and) p 259 1165 a(optional) p 449 1165 a(argumen) o(ts) p 687 1165 a(had) p 781 1165 a(t) o(w) o(o) p 873 1165 a(problems) p 1082 1165 a(in) p 1139 1165 a(Ob) s(jectiv) o(e) p 1360 1165 a(Lab) q(el.) p Fj 83 1280 a(\017) p Fk 133 1280 a(They) p 259 1280 a(w) o(ere) p 372 1280 a(not) p 459 1280 a(fully) p 570 1280 a(coheren) o(t) p 767 1280 a(with) p 878 1280 a(the) p 963 1280 a(original) p 1139 1280 a(call-b) o(y-v) m (alue) p 1423 1280 a(seman) o(tics) p 1644 1280 a(of) p 1700 1280 a(the) p 1784 1280 a(lan-) 133 1340 y(guage.) p 303 1340 a(In) p 368 1340 a(some) p 495 1340 a(\(subtle\)) p 681 1340 a(cases,) p 823 1340 a(a) p 868 1340 a(side-e\013ect) p 1099 1340 a(migh) o(t) p 1243 1340 a(get) p 1329 1340 a(dela) o(y) o(ed) p 1508 1340 a(more) p 1635 1340 a(than) p 1753 1340 a(in) p 1814 1340 a(an) 133 1400 y(un) o(t) o(yp) q(ed) p 322 1400 a(seman) o(tics.) p Fj 83 1502 a(\017) p Fk 133 1502 a(F) l(or) p 220 1502 a(optional) p 410 1502 a(argumen) o(ts,) p 660 1502 a(no) p 728 1502 a(un) o(t) o(yp) q(ed) p 918 1502 a(seman) o(tics) p 1139 1502 a(existed.) 84 1616 y(This) p 195 1616 a(new) p 295 1616 a(prop) q(osal) p 492 1616 a(corrects) p 674 1616 a(these) p 799 1616 a(t) o(w) o(o) p 891 1616 a(\015a) o(ws.) p Fi 11 1746 a(Syn) n(tax) p Fk 11 1838 a(W) l(e) p 95 1838 a(k) o(eep) p 206 1838 a(Ob) s(jectiv) o(e) p 426 1838 a(Lab) q(el's) p 594 1838 a(syn) o(tax,) p 764 1838 a(except) p 917 1838 a(for) p 991 1838 a(default) p 1155 1838 a(v) m(alues) p 1301 1838 a(in) p 1357 1838 a(optional) p 1547 1838 a(argumen) o(ts.) p Fh 329 1944 a(typ) n(expr) p Fk 528 1944 a(::=) p Fg 634 1944 a(:) p 656 1944 a(:) p 678 1944 a(:) p Fj 579 2004 a(j) p Fh 634 2004 a(typ) n(expr) p Fj 806 2004 a(!) p Fh 870 2004 a(typ) n(expr) p Fj 579 2064 a(j) p Fk 634 2064 a([?]) p Fi(lab) r(el) p Fk 801 2064 a(:) p Fh(typ) n(expr) p Fj 987 2064 a(!) p Fh 1050 2064 a(typ) n(expr) 391 2124 y(expr) p Fk 528 2124 a(::=) p Fg 634 2124 a(:) p 656 2124 a(:) p 678 2124 a(:) p Fj 579 2185 a(j) p Fh 634 2185 a(expr) p 746 2185 a(lab) n(ele) n(d-expr) p Ff 991 2163 a(+) p Fj 579 2245 a(j) p Fe 634 2245 a(fun) p Fj 728 2245 a(f) p Fh(lab) n(ele) n(d-simple-p) n(attern) p Fj 1209 2245 a(g) p Ff 1234 2227 a(+) p Fk 1280 2245 a([) p Fe(when) p Fh 1412 2245 a(expr) p Fk 1507 2245 a(]) p Fj 1535 2245 a(!) p Fh 1599 2245 a(expr) p Fj 579 2305 a(j) p Fe 634 2305 a(function) p Fh 856 2305 a(lab) n(ele) n(d-p) n(attern) p Fk 1177 2305 a([) p Fe(when) p Fh 1309 2305 a(expr) p Fk 1404 2305 a(]) p Fj 1432 2305 a(!) p Fh 1496 2305 a(expr) p Fj 785 2365 a(f) p Fe(|) p Fh 851 2365 a(lab) n(ele) n(d-p) n(attern) p Fk 1172 2365 a([) p Fe(when) p Fg 1305 2365 a(expr) p Fk 1403 2365 a(]) p Fj 1430 2365 a(!) p Fh 1494 2365 a(expr) p Fj 1589 2365 a(g) p Fd 1614 2347 a(\003) p Fh 242 2425 a(lab) n(ele) n(d-expr) p Fk 528 2425 a(::=) p 634 2425 a([?]) p Fh(expr) p Fj 579 2486 a(j) p Fk 634 2486 a([?]) p Fi(lab) r(el) p Fk 801 2486 a(:) p Fh(expr) 182 2546 y(lab) n(ele) n(d-p) n(attern) p Fk 528 2546 a(::=) p Fh 634 2546 a(p) n(attern) p Fj 579 2606 a(j) p Fi 634 2606 a(lab) r(el) p Fk 751 2606 a(:) p Fh(p) n(attern) p Fj 579 2666 a(j) p Fk 634 2666 a(?[) p Fe(\() p Fh(expr) p Fe(\)) p Fk(]) p Fi(lab) r(el) p Fk 943 2666 a(:) p Fh 956 2666 a(p) n(attern) p Fk 926 2937 a(1) p eop PStoPSsaved restore userdict/PStoPSsaved save put PStoPSmatrix setmatrix 595.000000 421.271378 translate 90 rotate 0.706651 dup scale userdict/PStoPSmatrix matrix currentmatrix put userdict/PStoPSclip{0 0 moveto 595.000000 0 rlineto 0 842.000000 rlineto -595.000000 0 rlineto closepath}put initclip PStoPSxform concat 2 1 bop Fi 11 168 a(Dynamic) p 247 168 a(seman) n(tics) p Fj 11 261 a(;) p Fk 52 261 a(is) p 101 261 a(a) p 141 261 a(notation) p 337 261 a(for) p 411 261 a(the) p 495 261 a(empt) o(y) p 644 261 a(lab) q(el.) 86 366 y(\() p Fe(fun) p Fi 198 366 a(l) p Fc 214 373 a(i) p Fk 227 366 a(:) p Fg(x) p Fj 282 366 a(!) p Fg 346 366 a(e) p Fk(\)) p Fi 404 366 a(l) p Fc 420 373 a(1) p Fk 442 366 a(:) p Fg 455 366 a(e) p Ff 478 373 a(1) p Fg 506 366 a(:) p 528 366 a(:) p 550 366 a(:) p Fi 571 366 a(l) p Fc 587 373 a(n) p Fk 612 366 a(:) p Fg 625 366 a(e) p Fb 648 373 a(n) p Fj 515 427 a(!) p Fk 579 427 a(\() p Fg(e) p Fk([) p Fg(e) p Fb 658 434 a(i) p Fg 671 427 a(=x) p Fk(]) p Fi 752 427 a(l) p Fc 768 434 a(1) p Fk 790 427 a(:) p Fg(e) p Ff 827 434 a(1) p Fg 855 427 a(:) p 877 427 a(:) p 899 427 a(:) p Fi 920 427 a(l) p Fc 936 434 a(i) p Fd(\000) p Fc(1) p Fk 997 427 a(:) p Fg 1010 427 a(e) p Fb 1033 434 a(i) p Fd(\000) p Ff(1) p Fi 1108 427 a(l) p Fc 1124 434 a(i) p Ff(+) p Fc(1) p Fk 1185 427 a(:) p Fg(e) p Fb 1222 434 a(i) p Ff(+1) p Fg 1289 427 a(:) p 1311 427 a(:) p 1333 427 a(:) p Fi 1354 427 a(l) p Fc 1370 434 a(n) p Fk 1395 427 a(:) p Fg 1408 427 a(e) p Fb 1431 434 a(n) p Fk 86 487 a(\() p Fe(fun) p Fk 198 487 a(?) p Fi(l) p Fc 237 494 a(i) p Fk 250 487 a(:) p Fg(x) p Fj 305 487 a(!) p Fg 369 487 a(e) p Fk(\)) p Fi 427 487 a(l) p Fc 443 494 a(1) p Fk 465 487 a(:) p Fg 478 487 a(e) p Ff 501 494 a(1) p Fg 529 487 a(:) p 551 487 a(:) p 573 487 a(:) p Fi 594 487 a(l) p Fc 610 494 a(n) p Fk 635 487 a(:) p Fg 648 487 a(e) p Fb 671 494 a(n) p Fj 515 547 a(!) p Fg 579 547 a(e) p Fk([) p Fe(Some) p Fk 717 547 a(\() p Fg(e) p Fb 759 554 a(i) p Fk 773 547 a(\)) p Fg(=x) p Fk(]) p Fi 874 547 a(l) p Fc 890 554 a(1) p Fk 912 547 a(:) p Fg 925 547 a(e) p Ff 948 554 a(1) p Fg 976 547 a(:) p 998 547 a(:) p 1020 547 a(:) p Fi 1042 547 a(l) p Fc 1058 554 a(i) p Fd(\000) p Fc(1) p Fk 1118 547 a(:) p Fg(e) p Fb 1155 554 a(i) p Fd(\000) p Ff(1) p Fi 1230 547 a(l) p Fc 1246 554 a(i) p Ff(+) p Fc(1) p Fk 1307 547 a(:) p Fg 1320 547 a(e) p Fb 1343 554 a(i) p Ff(+1) p Fg 1410 547 a(:) p 1432 547 a(:) p 1454 547 a(:) p Fi 1476 547 a(l) p Fc 1492 554 a(n) p Fk 1516 547 a(:) p Fg(e) p Fb 1553 554 a(n) p Fk 86 607 a(\() p Fe(fun) p Fk 198 607 a(?) p Fi(l) p Fk(:) p Fg 250 607 a(x) p Fj 292 607 a(!) p Fg 356 607 a(e) p Fk(\)) p Fi 413 607 a(l) p Fc 429 614 a(1) p Fk 451 607 a(:) p Fg(e) p Ff 488 614 a(1) p Fg 516 607 a(:) p 538 607 a(:) p 560 607 a(:) p Fi 581 607 a(l) p Fc 597 614 a(n) p Fk 621 607 a(:) p Fg(e) p Fb 658 614 a(n) p Fk 1154 607 a(when) p Fi 1281 607 a(l) p Fc 1297 614 a(i) p Fk 1324 607 a(=) p Fj 1376 607 a(;) p Fk 1417 607 a(and) p Fg 1512 607 a(l) p Fj 1541 607 a(62) p 1588 607 a(f) p Fi(l) p Fc 1629 614 a(1) p Fg 1660 607 a(:) p 1682 607 a(:) p 1704 607 a(:) p Fi 1725 607 a(l) p Fc 1741 614 a(n) p Fj 1765 607 a(g) 515 667 y(!) p Fg 579 667 a(e) p Fk([) p Fe(None) p Fg 717 667 a(=x) p Fk(]) p Fi 799 667 a(l) p Fc 815 674 a(1) p Fk 837 667 a(:) p Fg(e) p Ff 874 674 a(1) p Fg 901 667 a(:) p 923 667 a(:) p 945 667 a(:) p Fi 967 667 a(l) p Fc 983 674 a(n) p Fk 1007 667 a(:) p Fg(e) p Fb 1044 674 a(n) p Fk 86 728 a(\(\() p Fe(fun) p Fi 217 728 a(l) p Fk(:) p Fg 246 728 a(x) p Fj 288 728 a(!) p Fg 352 728 a(e) p Fk(\)) p Fi 409 728 a(l) p Fc 425 735 a(1) p Fk 447 728 a(:) p Fg(e) p Ff 484 735 a(1) p Fg 511 728 a(:) p 533 728 a(:) p 555 728 a(:) p Fi 577 728 a(l) p Fc 593 735 a(m) p Fk 629 728 a(:) p Fg 642 728 a(e) p Fb 665 735 a(m) p Fk 698 728 a(\)) p Fi 733 728 a(l) p Fc 749 735 a(m) p Ff(+) p Fc(1) p Fk 833 728 a(:) p Fg 846 728 a(e) p Fb 869 735 a(m) p Ff(+1) p Fg 955 728 a(:) p 977 728 a(:) p 999 728 a(:) p Fi 1021 728 a(l) p Fc 1037 735 a(n) p Fk 1061 728 a(:) p Fg(e) p Fb 1098 735 a(n) p Fk 1373 728 a(when) p Fi 1501 728 a(l) p Fj 1530 728 a(62) p 1577 728 a(f) p Fi(l) p Fc 1618 735 a(1) p Fg 1648 728 a(:) p 1670 728 a(:) p 1692 728 a(:) p Fi 1714 728 a(l) p Fc 1730 735 a(m) p Fj 1765 728 a(g) 515 788 y(!) p Fk 579 788 a(\() p Fe(fun) p Fi 691 788 a(l) p Fk(:) p Fg 720 788 a(x) p Fj 761 788 a(!) p Fg 825 788 a(e) p Fk(\)) p Fi 883 788 a(l) p Fc 899 795 a(1) p Fk 921 788 a(:) p Fg 934 788 a(e) p Ff 957 795 a(1) p Fg 985 788 a(:) p 1007 788 a(:) p 1029 788 a(:) p Fi 1051 788 a(l) p Fc 1067 795 a(n) p Fk 1091 788 a(:) p Fg 1104 788 a(e) p Fb 1127 795 a(n) p Fk 86 848 a(\(\() p Fe(fun) p Fk 217 848 a(?) p Fi(l) p Fk(:) p Fg 269 848 a(x) p Fj 311 848 a(!) p Fg 375 848 a(e) p Fk(\)) p Fi 432 848 a(l) p Fc 448 855 a(1) p Fk 470 848 a(:) p Fg(e) p Ff 507 855 a(1) p Fg 535 848 a(:) p 557 848 a(:) p 579 848 a(:) p Fi 600 848 a(l) p Fc 616 855 a(m) p Fk 652 848 a(:) p Fg 665 848 a(e) p Fb 688 855 a(m) p Fk 721 848 a(\)) p Fi 756 848 a(l) p Fc 772 855 a(m) p Ff(+) p Fc(1) p Fk 856 848 a(:) p Fg 869 848 a(e) p Fb 892 855 a(m) p Ff(+1) p Fg 978 848 a(:) p 1000 848 a(:) p 1022 848 a(:) p Fi 1044 848 a(l) p Fc 1060 855 a(n) p Fk 1084 848 a(:) p Fg(e) p Fb 1121 855 a(n) p Fk 1261 848 a(when) p Fj 1388 848 a(f) p Fi(l) p Fg(;) p Fj 1451 848 a(;g) p 1530 848 a(6) m(\\) p 1577 848 a(f) p Fi(l) p Fc 1618 855 a(1) p Fg 1648 848 a(:) p 1670 848 a(:) p 1692 848 a(:) p Fi 1714 848 a(l) p Fc 1730 855 a(m) p Fj 1765 848 a(g) 515 908 y(!) p Fk 579 908 a(\() p Fe(fun) p Fk 691 908 a(?) p Fi(l) p Fk(:) p Fg 743 908 a(x) p Fj 785 908 a(!) p Fg 848 908 a(e) p Fk(\)) p Fi 906 908 a(l) p Fc 922 915 a(1) p Fk 944 908 a(:) p Fg(e) p Ff 981 915 a(1) p Fg 1008 908 a(:) p 1030 908 a(:) p 1052 908 a(:) p Fi 1074 908 a(l) p Fc 1090 915 a(n) p Fk 1114 908 a(:) p Fg 1127 908 a(e) p Fb 1150 915 a(n) p Fi 11 1035 a(T) n(yping) p Fk 11 1127 a(Seman) o(tics) p 240 1127 a(are) p 321 1127 a(k) o(ept) p 430 1127 a(throughout) p 685 1127 a(compilation) p 950 1127 a(b) o(y) p 1018 1127 a(disallo) o(wing) p 1269 1127 a(lab) q(el) p 1387 1127 a(comm) o(utation) p 1684 1127 a(for) p 1759 1127 a(func-) 11 1187 y(tion) p 116 1187 a(t) o(yp) q(es.) p 278 1187 a(Ho) o(w) o(ev) o(er,) p 494 1187 a(the) p 583 1187 a(original) p 764 1187 a(comfort) p 949 1187 a(of) p 1009 1187 a(out-of-order) p 1283 1187 a(application) p 1540 1187 a(is) p 1594 1187 a(reco) o(v) o(ered) p 1814 1187 a(b) o(y) 11 1247 y(allo) o(wing) p 207 1247 a(argumen) o(t) p 431 1247 a(reordering) p 670 1247 a(in) p 732 1247 a(application,) p 1005 1247 a(when) p 1138 1247 a(the) p 1227 1247 a(function's) p 1457 1247 a(t) o(yp) q(e) p 1572 1247 a(is) p Fh 1626 1247 a(wel) r(l) p 1731 1247 a(known) p Fk 11 1308 a(\() p Fh(c.f.) p Fk 118 1308 a(p) q(olymorphic) p 400 1308 a(metho) q(ds\).) p Fl 11 1452 a(V) p 56 1452 a(arian) n(ts) p Fk 11 1544 a(V) l(arian) o(t) p 187 1544 a(t) o(yping,) p 355 1544 a(as) p 417 1544 a(it) p 468 1544 a(is) p 519 1544 a(presen) o(ted) p 739 1544 a(in) p 798 1544 a(the) p 884 1544 a(user's) p 1022 1544 a(man) o(ual,) p 1210 1544 a(is) p 1261 1544 a(not) p 1350 1544 a(principal:) p 1576 1544 a(in) p 1635 1544 a(some) p 1760 1544 a(cases) 11 1605 y(t) o(ypabilit) o(y) p 239 1605 a(of) p 301 1605 a(an) p 375 1605 a(expression) p 616 1605 a(ma) o(y) p 728 1605 a(dep) q(end) p 904 1605 a(on) p 978 1605 a(the) p 1069 1605 a(order) p 1202 1605 a(in) p 1265 1605 a(whic) o(h) p 1411 1605 a(the) p 1502 1605 a(t) o(yping) p 1660 1605 a(algorithm) 11 1665 y(pro) q(ceeds.) p Fe 133 1779 a(#) p 184 1779 a(let) p 286 1779 a(f1) p 363 1779 a(\(x) p 440 1779 a(:) p 491 1779 a([<) p 568 1779 a(a) p 620 1779 a(b\(int\)]\)) p 850 1779 a(=) p 902 1779 a(\(\)) 184 1839 y(let) p 286 1839 a(f2) p 363 1839 a(\(x) p 440 1839 a(:) p 491 1839 a([<) p 568 1839 a(a]\)) p 671 1839 a(=) p 722 1839 a(\(\)) 184 1899 y(let) p 286 1899 a(f3) p 363 1899 a(\(x) p 440 1899 a(:) p 491 1899 a([<) p 568 1899 a(a) p 620 1899 a(b\(bool\)]\)) p 876 1899 a(=) p 927 1899 a(\(\);;) 133 1960 y(val) p 235 1960 a(f1) p 312 1960 a(:) p 363 1960 a([<) p 440 1960 a(a) p 491 1960 a(b\(int\)]) p 696 1960 a(->) p 773 1960 a(unit) p 902 1960 a(=) p 953 1960 a() 133 2020 y(val) p 235 2020 a(f2) p 312 2020 a(:) p 363 2020 a([<) p 440 2020 a(a]) p 517 2020 a(->) p 594 2020 a(unit) p 722 2020 a(=) p 773 2020 a() 133 2080 y(val) p 235 2080 a(f3) p 312 2080 a(:) p 363 2080 a([<) p 440 2080 a(a) p 491 2080 a(b\(bool\)]) p 722 2080 a(->) p 799 2080 a(unit) p 927 2080 a(=) p 978 2080 a() 133 2140 y(#) p 184 2140 a(fun) p 286 2140 a(x) p 338 2140 a(->) p 414 2140 a(f1) p 491 2140 a(x;) p 568 2140 a(f2) p 645 2140 a(x;) p 722 2140 a(f3) p 799 2140 a(x;;) 133 2200 y(-) p 184 2200 a(:) p 235 2200 a([<) p 312 2200 a(a]) p 389 2200 a(->) p 466 2200 a(unit) p 594 2200 a(=) p 645 2200 a() 133 2260 y(#) p 184 2260 a(fun) p 286 2260 a(x) p 338 2260 a(->) p 414 2260 a(f1) p 491 2260 a(x;) p 568 2260 a(f3) p 645 2260 a(x;;) 133 2321 y(Character) o(s) p 414 2321 a(18-19:) 133 2381 y(This) p 261 2381 a(expressio) o(n) p 543 2381 a(has) p 645 2381 a(type) p 773 2381 a([<) p 850 2381 a(a) p 902 2381 a(b\(int\)]) p 1107 2381 a(but) p 1209 2381 a(is) p 1286 2381 a(here) p 1414 2381 a(used) p 1542 2381 a(with) p 1670 2381 a(type) 184 2441 y([<) p 261 2441 a(a) p 312 2441 a(b\(bool\)]) p Fk 84 2555 a(Here) p 204 2555 a(the) p 292 2555 a(constrain) o(t) p 526 2555 a(in) o(tro) q(duced) p 775 2555 a(b) o(y) p Fe 848 2555 a(f2) p Fk 920 2555 a(hides) p 1049 2555 a(the) p 1138 2555 a(constructor) p Fe 1401 2555 a(b) p Fk(,) p 1462 2555 a(and) p 1562 2555 a(a) o(v) o(oids) p 1714 2555 a(a) p 1760 2555 a(clash) 11 2615 y(b) q(et) o(w) o(een) p Fe 199 2615 a(int) p Fk 292 2615 a(and) p Fe 387 2615 a(bool) p Fk(.) 84 2676 y(An) p 163 2676 a(easy) p 270 2676 a(w) o(a) o(y) p 369 2676 a(to) p 428 2676 a(solv) o(e) p 547 2676 a(this) p 642 2676 a(w) o(ould) p 784 2676 a(b) q(e) p 850 2676 a(to) p 909 2676 a(restrict) p 1077 2676 a(hiding) p 1226 2676 a(absen) o(t) p 1379 2676 a(lab) q(els) p 1515 2676 a(to) p 1575 2676 a(generic) p 1739 2676 a(t) o(yp) q(es.) 11 2736 y(This) p 124 2736 a(w) o(a) o(y) p 224 2736 a(the) p 310 2736 a(second) p 469 2736 a(case) p 574 2736 a(w) o(ould) p 718 2736 a(still) p 814 2736 a(fail,) p 913 2736 a(since) p Fe 1034 2736 a(x) p Fk 1077 2736 a(has) p 1166 2736 a(a) p 1208 2736 a(monorphic) p 1451 2736 a(t) o(yp) q(e.) p 1584 2736 a(This) p 1697 2736 a(solution) 11 2796 y(w) o(ould) p 153 2796 a(b) q(e) p 219 2796 a(correct) p 382 2796 a(and) p 477 2796 a(principal.) 926 2937 y(2) p eop PStoPSsaved restore %%Page: (2,3) 2 userdict/PStoPSsaved save put PStoPSmatrix setmatrix 595.000000 0.271378 translate 90 rotate 0.706651 dup scale userdict/PStoPSmatrix matrix currentmatrix put userdict/PStoPSclip{0 0 moveto 595.000000 0 rlineto 0 842.000000 rlineto -595.000000 0 rlineto closepath}put initclip /showpage{}def/copypage{}def/erasepage{}def PStoPSxform concat 3 2 bop Fk 84 168 a(Ho) o(w) o(ev) o(er,) p 293 168 a(one) p 382 168 a(can) p 472 168 a(easily) p 606 168 a(see) p 684 168 a(that) p 789 168 a(this) p 884 168 a(solution) p 1068 168 a(is) p 1117 168 a(coun) o(ter-in) o(tuitiv) o(e.) p 1504 168 a(F) l(or) p 1591 168 a(the) p 1675 168 a(user,) p Fe 1791 168 a(b) p Fk 1833 168 a(is) 11 229 y(already) p 183 229 a(an) p 250 229 a(imp) q(ossible) p 488 229 a(constructor,) p 759 229 a(and) p 854 229 a(ha) o(ving) p 1011 229 a(a) p 1052 229 a(clash) p 1174 229 a(on) p 1242 229 a(it) p 1291 229 a(is) p 1340 229 a(hard) p 1453 229 a(to) p 1513 229 a(understand.) 84 289 y(Another) p 277 289 a(solution) p 463 289 a(is) p 514 289 a(to) p 575 289 a(go) p 642 289 a(the) p 728 289 a(opp) q(osite) p 924 289 a(w) o(a) o(y) l(.) p 1044 289 a(T) l(o) p 1117 289 a(accept) p 1271 289 a(more) p 1395 289 a(programs.) p 1634 289 a(This) p 1747 289 a(is) p 1798 289 a(the) 11 349 y(w) o(a) o(y) p 109 349 a(w) o(e) p 181 349 a(explore) p 351 349 a(here,) p 470 349 a(with) p 581 349 a(an) p 649 349 a(unc) o(hanged) p 891 349 a(syn) o(tax.) p Fi 11 479 a(T) n(yping) p Fk 11 571 a(The) p 114 571 a(idea) p 220 571 a(is) p 273 571 a(to) p 336 571 a(dela) o(y) p 466 571 a(uni\014cation) p 711 571 a(on) p 782 571 a(constructor) p 1043 571 a(un) o(til) p 1161 571 a(they) p 1274 571 a(are) p 1359 571 a(explicitely) p 1595 571 a(kno) o(wn) p 1753 571 a(to) p 1816 571 a(b) q(e) 11 631 y(presen) o(t.) p 199 631 a(W) l(e) p 280 631 a(k) o(eep) p 390 631 a(the) p 472 631 a(\() p Fg(T) t(;) p 546 631 a(U;) p 601 631 a(L) p Fk(\)) p 666 631 a(represen) o(tation) p 983 631 a(of) p 1036 631 a(v) m(arian) o(t) p 1200 631 a(t) o(yp) q(es,) p 1341 631 a(but) p Fg 1428 631 a(T) p Fk 1478 631 a(is) p 1525 631 a(no) p 1591 631 a(longer) p 1735 631 a(a) p 1774 631 a(map) 11 692 y(from) p 126 692 a(constructors) p 403 692 a(to) p 462 692 a(t) o(yp) q(es,) p 605 692 a(but) p 694 692 a(from) p 809 692 a(constructors) p 1086 692 a(to) p 1146 692 a(sets) p 1241 692 a(of) p 1297 692 a(t) o(yp) q(es.) 84 752 y(When) p 230 752 a(w) o(e) p 307 752 a(unify) p 436 752 a(t) o(w) o(o) p 532 752 a(v) m(arian) o(t) p 702 752 a(t) o(yp) q(es,) p 850 752 a(the) p 938 752 a(\014rst) p 1043 752 a(step) p 1150 752 a(is) p 1204 752 a(just) p 1305 752 a(to) p 1369 752 a(tak) o(e) p 1479 752 a(the) p 1567 752 a(union) p 1707 752 a(of) p 1767 752 a(b) q(oth) 11 812 y(t) o(yping) p 162 812 a(en) o(vironmen) o (ts,) p 476 812 a(dropping) p 682 812 a(unnecessary) p 952 812 a(t) o(yp) q(es.) 204 932 y(\() p Fg(T) p Ff 252 939 a(1) p Fg 272 932 a(;) p 294 932 a(U) p Ff 327 939 a(1) p Fg 346 932 a(;) p 368 932 a(L) p Ff 401 939 a(1) p Fk 421 932 a(\)) p Fj 451 932 a(^) p Fk 495 932 a(\() p Fg(T) p Ff 543 939 a(2) p Fg 563 932 a(;) p 585 932 a(U) p Ff 618 939 a(2) p Fg 637 932 a(;) p 659 932 a(L) p Ff 692 939 a(2) p Fk 712 932 a(\)) p 745 932 a(=) p 797 932 a(\(\() p Fg(T) p Ff 864 939 a(1) p Fj 883 932 a(j) p Fb 897 939 a(U) p Fa 921 944 a(1) p Fd 938 939 a(\\) p Fb(U) p Fa 986 944 a(2) p Fk 1005 932 a(\)) p Fj 1035 932 a([) p Fk 1079 932 a(\() p Fg(T) p Ff 1127 939 a(2) p Fj 1146 932 a(j) p Fb 1160 939 a(U) p Fa 1184 944 a(1) p Fd 1201 939 a(\\) p Fb(U) p Fa 1249 944 a(2) p Fk 1268 932 a(\)) p Fg(;) p 1309 932 a(U) p Ff 1342 939 a(1) p Fj 1373 932 a(\\) p Fg 1417 932 a(U) p Ff 1450 939 a(2) p Fg 1470 932 a(;) p 1492 932 a(L) p Ff 1525 939 a(1) p Fj 1556 932 a([) p Fg 1600 932 a(L) p Ff 1633 939 a(2) p Fk 1653 932 a(\)) 84 1042 y(Here) p 203 1042 a(the) p 291 1042 a(union) p 431 1042 a(of) p 490 1042 a(t) o(w) o(o) p 587 1042 a(t) o(yping) p 742 1042 a(en) o(vironmen) o (ts) p 1046 1042 a(is) p 1099 1042 a(the) p 1187 1042 a(p) q(oin) o(t) o(wise) p 1407 1042 a(union) p 1547 1042 a(of) p 1606 1042 a(their) p 1727 1042 a(sets) p 1826 1042 a(of) 11 1102 y(t) o(yp) q(es) p 140 1102 a(for) p 214 1102 a(eac) o(h) p 324 1102 a(constructor.) 84 1162 y(This) p 195 1162 a(\014rst) p 296 1162 a(step) p 399 1162 a(nev) o(er) p 529 1162 a(fails.) 84 1222 y(In) p 145 1222 a(a) p 186 1222 a(second) p 343 1222 a(step,) p 460 1222 a(structural) p 685 1222 a(constrain) o(ts) p 934 1222 a(are) p 1015 1222 a(enforced) p 1209 1222 a(on) p 1277 1222 a(the) p 1361 1222 a(resulting) p 1562 1222 a(t) o(yp) q(e) p 1672 1222 a(\() p Fg(T) t(;) p 1746 1222 a(U;) p 1801 1222 a(L) p Fk(\).) 11 1282 y(First,) p Fg 144 1282 a(L) p Fk 195 1282 a(should) p 351 1282 a(b) q(e) p 418 1282 a(included) p 614 1282 a(in) p Fg 672 1282 a(U) p Fk 710 1282 a(.) p 749 1282 a(Then,) p 892 1282 a(for) p 967 1282 a(all) p 1036 1282 a(constructors) p 1314 1282 a(app) q(earing) p 1542 1282 a(in) p Fg 1600 1282 a(L) p Fk(,) p 1664 1282 a(the) p 1749 1282 a(set) p 1826 1282 a(of) 11 1343 y(t) o(yp) q(es) p 136 1343 a(asso) q(ciated) p 365 1343 a(with) p 472 1343 a(eac) o(h) p 578 1343 a(constructor) p 833 1343 a(is) p 878 1343 a(collapsed) p 1084 1343 a(b) o(y) p 1148 1343 a(uni\014cation.) p 1407 1343 a(This) p 1515 1343 a(can) p 1600 1343 a(b) q(e) p 1663 1343 a(expressed) 11 1403 y(b) o(y) p 78 1403 a(rewriting) p 287 1403 a(rules,) p 417 1403 a(where) p Fg 558 1403 a(e) p Fk 597 1403 a(is) p 646 1403 a(a) p 687 1403 a(m) o(ulti-equation) p 1015 1403 a(and) p Fg 1109 1403 a(\036) p Fk 1155 1403 a(a) p 1195 1403 a(set) p 1271 1403 a(of) p 1327 1403 a(m) o(ultiequations) 249 1509 y(if) p Fg 294 1509 a(L) p Fj 341 1509 a(6\032) p Fg 393 1509 a(U) p Fk 448 1509 a(then) p 559 1509 a(\() p Fg(T) t(;) p 633 1509 a(U;) p 688 1509 a(L) p Fk(\)) p 753 1509 a(=) p Fg 805 1509 a(e) p Fj 839 1509 a(^) p Fg 883 1509 a(\036) p Fj 926 1509 a(\000) p 956 1509 a(!) p 1020 1509 a(?) p Fk 249 1629 a(if) p Fg 294 1629 a(l) p Fj 323 1629 a(2) p Fg 370 1629 a(L) p Fk 420 1629 a(and) p Fg 515 1629 a(T) p Fk 551 1629 a(\() p Fg(l) p Fk 586 1629 a(\)) p 617 1629 a(=) p Fj 669 1629 a(f) p Fg(\034) p Ff 715 1636 a(1) p Fg 735 1629 a(;) p 757 1629 a(:) p 779 1629 a(:) p 801 1629 a(:) p 822 1629 a(;) p 844 1629 a(\034) p Fb 865 1636 a(n) p Fj 889 1629 a(g) p Fk 930 1629 a(then) 298 1689 y(\() p Fg(T) t(;) p 372 1689 a(U;) p 427 1689 a(L) p Fk(\)) p 492 1689 a(=) p Fg 544 1689 a(e) p Fj 577 1689 a(^) p Fg 622 1689 a(\036) p Fj 664 1689 a(\000) p 695 1689 a(!) p Fk 759 1689 a(\() p Fg(T) p Fj 814 1689 a(f) p Fg(l) p Fj 867 1689 a(7!) p Fg 931 1689 a(\034) p Ff 952 1696 a(1) p Fj 972 1689 a(g) p Fg(;) p 1019 1689 a(U;) p 1074 1689 a(L) p Fk(\)) p 1139 1689 a(=) p Fg 1191 1689 a(e) p Fj 1225 1689 a(^) p Fg 1269 1689 a(\034) p Ff 1290 1696 a(1) p Fk 1324 1689 a(=) p Fg 1376 1689 a(:) p 1398 1689 a(:) p 1420 1689 a(:) p Fk 1447 1689 a(=) p Fg 1498 1689 a(\034) p Fb 1519 1696 a(n) p Fj 1554 1689 a(^) p Fg 1598 1689 a(\036) p Fk 84 1796 a(Optionally) p 331 1796 a(one) p 425 1796 a(can) p 519 1796 a(add) p 619 1796 a(rules) p 740 1796 a(that) p 850 1796 a(remo) o(v) o(e) p 1022 1796 a(a) p 1067 1796 a(constructor) p Fg 1329 1796 a(l) p Fk 1366 1796 a(from) p Fg 1486 1796 a(U) p Fk 1545 1796 a(if) p 1594 1796 a(the) p 1683 1796 a(equation) 11 1856 y(obtained) p 211 1856 a(from) p Fg 326 1856 a(T) p Fk 362 1856 a(\() p Fg(l) p Fk 397 1856 a(\)) p 431 1856 a(has) p 518 1856 a(no) p 586 1856 a(solution.) p 790 1856 a(Suc) o(h) p 908 1856 a(rules) p 1024 1856 a(w) o(ould) p 1167 1856 a(b) q(e) p 1233 1856 a(sound) p 1374 1856 a(and) p 1469 1856 a(complete.) p Fi 11 1986 a(Syn) n(tax) p 198 1986 a(of) p 262 1986 a(t) n(yp) r(es) p Fk 11 2078 a(Thanks) p 188 2078 a(to) p 250 2078 a(the) p 336 2078 a(go) q(o) q(d) p 458 2078 a(prop) q(erties) p 689 2078 a(of) p 747 2078 a(these) p 874 2078 a(constrain) o(ts,) p 1139 2078 a(the) p 1226 2078 a(surface) p 1392 2078 a(syn) o(tax) p 1551 2078 a(of) p 1608 2078 a(t) o(yp) q(es) p 1740 2078 a(w) o(ould) 11 2138 y(only) p 118 2138 a(ha) o(v) o(e) p 230 2138 a(to) p 290 2138 a(b) q(e) p 356 2138 a(sligh) o(tly) p 527 2138 a(extended.) p Fh 590 2244 a(tag-typ) n(e) p Fk 798 2244 a(::=) p Fh 904 2244 a(ident) p Fj 849 2304 a(j) p Fh 904 2304 a(ident) p Fe 1031 2304 a(\() p Fh(typ) n(expr-list) p Fe(\)) p Fh 523 2365 a(typ) n(expr-list) p Fk 798 2365 a(::=) p Fh 904 2365 a(typ) n(expr) p Fj 849 2425 a(j) p Fh 904 2425 a(typ) n(expr) p Fe 1078 2425 a(&) p Fh 1120 2425 a(typ) n(expr-list) p Fk 84 2531 a(Notice) p 234 2531 a(that) p 336 2531 a(a) p 373 2531 a(0-ary) p 496 2531 a(constructor) p 751 2531 a(and) p 842 2531 a(an) p 907 2531 a(1-ary) p 1030 2531 a(construtor) p 1262 2531 a(are) p 1340 2531 a(con) o(tradictory) l(,) p 1648 2531 a(and) p 1740 2531 a(w) o(ould) 11 2592 y(result) p 146 2592 a(in) p 203 2592 a(the) p 287 2592 a(absence) p 466 2592 a(of) p 522 2592 a(this) p 617 2592 a(constructor.) 926 2937 y(3) p eop PStoPSsaved restore userdict/PStoPSsaved save put PStoPSmatrix setmatrix 595.000000 421.271378 translate 90 rotate 0.706651 dup scale userdict/PStoPSmatrix matrix currentmatrix put userdict/PStoPSclip{0 0 moveto 595.000000 0 rlineto 0 842.000000 rlineto -595.000000 0 rlineto closepath}put initclip PStoPSxform concat 4 3 bop Fi 11 168 a(Discussion) p Fk 11 261 a(Suc) o(h) p 133 261 a(a) p 179 261 a(c) o(hange) p 345 261 a(has) p 436 261 a(the) p 525 261 a(ma) s(jor) p 672 261 a(adv) m(an) o(tage) p 907 261 a(of) p 967 261 a(b) q(oth) p 1087 261 a(reco) o(v) o(ering) p 1324 261 a(principalit) o(y) p 1589 261 a(and) p 1688 261 a(a) o(v) o(oiding) 11 321 y(unin) o(tuitiv) o(e) p 266 321 a(error) p 392 321 a(messages.) p 640 321 a(Constrain) o(ts) p 909 321 a(created) p 1087 321 a(in) p 1152 321 a(suc) o(h) p 1269 321 a(a) p 1317 321 a(w) o(a) o(y) p 1423 321 a(are) p 1512 321 a(v) o(ery) p 1626 321 a(ligh) o(t:) p 1772 321 a(they) 11 381 y(alw) o(a) o(ys) p 165 381 a(app) q(ear) p 325 381 a(inside) p 463 381 a(a) p 502 381 a(v) m(arian) o(t) p 666 381 a(t) o(yp) q(e,) p 788 381 a(and) p 882 381 a(if) p 926 381 a(the) p 1008 381 a(v) m(arian) o(t) p 1172 381 a(t) o(yp) q(e) p 1281 381 a(do) q(es) p 1390 381 a(not) p 1475 381 a(app) q(ear) p 1635 381 a(in) p 1691 381 a(the) p 1774 381 a(\014nal) 11 441 y(t) o(yp) q(e) p 120 441 a(sc) o(heme,) p 301 441 a(then) p 412 441 a(the) p 496 441 a(constrain) o(t) p 725 441 a(can) p 815 441 a(b) q(e) p 881 441 a(discarded) p 1098 441 a(safely) l(.) 84 501 y(On) p 165 501 a(the) p 249 501 a(other) p 376 501 a(hand,) p 512 501 a(there) p 637 501 a(are) p 718 501 a(t) o(w) o(o) p 810 501 a(dra) o(wbac) o(ks.) p Fj 83 616 a(\017) p Fk 133 616 a(Some) p 259 616 a(errors) p 393 616 a(will) p 482 616 a(b) q(e) p 544 616 a(dela) o(y) o(ed) p 715 616 a(longer) p 858 616 a(than) p 968 616 a(no) o(w,) p 1080 616 a(un) o(til) p 1191 616 a(a) p 1228 616 a(construtor) p 1460 616 a(is) p 1505 616 a(actually) p 1687 616 a(included) 133 676 y(in) p Fg 189 676 a(L) p Fk(.) p 258 676 a(It) p 311 676 a(is) p 360 676 a(not) p 446 676 a(clear) p 563 676 a(ho) o(w) p 665 676 a(damageable) p 930 676 a(it) p 979 676 a(is.) p Fj 83 777 a(\017) p Fk 133 777 a(While) p 272 777 a(t) o(yp) q(e) p 378 777 a(inference) p 579 777 a(is) p 625 777 a(simple) p 774 777 a(and) p 865 777 a(costless) p 1036 777 a(for) p 1108 777 a(this) p 1200 777 a(extension,) p 1426 777 a(simpli\014cation) p 1724 777 a(of) p 1776 777 a(con-) 133 838 y(strain) o(ts) p 310 838 a(|marking) p 551 838 a(constructors) p 830 838 a(with) p 943 838 a(unsolv) m(able) p 1182 838 a(constrain) o(ts) p 1432 838 a(as) p 1494 838 a(absen) o(t,) p 1663 838 a(and) p 1760 838 a(elim-) 133 898 y(inating) p 300 898 a(redundan) o(t) p 536 898 a(t) o(yp) q(es) p 667 898 a(in) p 726 898 a(constrain) o(ts|) p 1025 898 a(is) p 1076 898 a(a) p 1119 898 a(bit) p 1197 898 a(more) p 1320 898 a(exp) q(ensiv) o(e.) p 1565 898 a(Also,) p 1691 898 a(allo) o(wing) 133 958 y(suc) o(h) p 244 958 a(constrained) p 506 958 a(t) o(yp) q(es) p 637 958 a(inside) p 777 958 a(signatures) p 1010 958 a(w) o(ould) p 1154 958 a(mean) p 1286 958 a(ha) o(ving) p 1444 958 a(to) p 1506 958 a(solv) o(e) p 1627 958 a(a) p 1669 958 a(matc) o(hing) 133 1018 y(problem,) p 333 1018 a(whic) o(h) p 469 1018 a(is) p 514 1018 a(exp) q(onen) o(tial) p 772 1018 a(in) p 825 1018 a(the) p 906 1018 a(n) o(um) o(b) q(er) p 1080 1018 a(of) p 1132 1018 a(connected) p 1356 1018 a(constrain) o(ts) p 1600 1018 a(inside) p 1735 1018 a(a) p 1772 1018 a(t) o(yp) q(e) 133 1078 y(sc) o(heme.) 84 1193 y(Reasonably) p 340 1193 a(e\016cien) o(t) p 516 1193 a(algorithms) p 754 1193 a(exist) p 866 1193 a(to) p 922 1193 a(solv) o(e) p 1038 1193 a(these) p 1159 1193 a(problems,) p 1379 1193 a(so) p 1435 1193 a(the) p 1515 1193 a(di\016cult) o(y) p 1715 1193 a(is) p 1760 1193 a(more) 11 1253 y(in) p 67 1253 a(the) p 151 1253 a(increased) p 363 1253 a(complexit) o(y) p 611 1253 a(of) p 667 1253 a(the) p 751 1253 a(t) o(yp) q(e-c) o(hec) o(k) o(er) p 1031 1253 a(than) p 1145 1253 a(in) p 1202 1253 a(run-time) p 1402 1253 a(cost.) p Fl 11 1397 a(Other) p 205 1397 a(features) p Fk 11 1490 a(Ob) s(jectiv) o(e) p 238 1490 a(Lab) q(el) p 380 1490 a(con) o(tains) p 579 1490 a(t) o(w) o(o) p 678 1490 a(other) p 812 1490 a(features:) p 1029 1490 a(p) q(olymorphic) p 1318 1490 a(metho) q(ds) p 1521 1490 a(and) p 1623 1490 a(t) o(yp) q(e-driv) o(en) 11 1550 y(access) p 153 1550 a(of) p 208 1550 a(records.) p 394 1550 a(Both) p 514 1550 a(of) p 568 1550 a(them) p 692 1550 a(use) p 775 1550 a(the) p 857 1550 a(same) p 978 1550 a(metho) q(d) p 1154 1550 a(of) p 1209 1550 a(enforcing) p 1417 1550 a(principalit) o(y) p 1676 1550 a(of) p 1730 1550 a(t) o(yping) 11 1610 y(through) p 191 1610 a(tracing) p 351 1610 a(user) p 450 1610 a(pro) o(vided) p 647 1610 a(t) o(yp) q(e) p 752 1610 a(information.) p 1034 1610 a(With) p 1155 1610 a(this) p 1246 1610 a(tracing,) p 1422 1610 a(their) p 1534 1610 a(implem) o(en) n(tation) 11 1670 y(is) p 60 1670 a(v) o(ery) p 167 1670 a(easy) l(,) p 283 1670 a(but) p 373 1670 a(without) p 554 1670 a(it) p 603 1670 a(they) p 713 1670 a(lo) q(ose) p 834 1670 a(principalit) o(y) l(.) 84 1730 y(While) p 229 1730 a(these) p 357 1730 a(features) p 543 1730 a(pro) o(vide) p 720 1730 a(some) p 845 1730 a(comfort) p 1029 1730 a(in) p 1089 1730 a(writing) p 1260 1730 a(user) p 1366 1730 a(programs,) p 1598 1730 a(they) p 1711 1730 a(are) p 1795 1730 a(not) 11 1791 y(strictly) p 182 1791 a(necessary) p 403 1791 a(for) p 482 1791 a(the) p 571 1791 a(v) m(arious) p 742 1791 a(libraries) p 934 1791 a(coming) p 1107 1791 a(with) p 1223 1791 a(O'Labl) p 1391 1791 a(\(LablTk,) p 1602 1791 a(LablGL) p 1787 1791 a(and) 11 1851 y(LablGTK\).) 926 2937 y(4) p eop PStoPSsaved restore %%Trailer end userdict /end-hook known{end-hook}if %%EOF