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  1. %!PS-Adobe-2.0
  2. %%Creator: dvips 5.528 Copyright 1986, 1994 Radical Eye Software
  3. %%Title: Y.dvi
  4. %%CreationDate: Fri Jun 10 20:09:05 1994
  5. %%Pages: 10
  6. %%PageOrder: Ascend
  7. %%BoundingBox: 0 0 612 792
  8. %%EndComments
  9. %DVIPSCommandLine: dvips -oY2.ps -p2 -n10 Y.dvi
  10. %DVIPSParameters: dpi=300, comments removed
  11. %DVIPSSource: TeX output 1991.09.26:1012
  12. %%BeginProcSet: tex.pro
  13. /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N
  14. /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72
  15. mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1}
  16. ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale
  17. isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div
  18. hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul
  19. TR matrix currentmatrix dup dup 4 get round 4 exch put dup dup 5 get
  20. round 5 exch put setmatrix}N /@landscape{/isls true N}B /@manualfeed{
  21. statusdict /manualfeed true put}B /@copies{/#copies X}B /FMat[1 0 0 -1 0
  22. 0]N /FBB[0 0 0 0]N /nn 0 N /IE 0 N /ctr 0 N /df-tail{/nn 8 dict N nn
  23. begin /FontType 3 N /FontMatrix fntrx N /FontBBox FBB N string /base X
  24. array /BitMaps X /BuildChar{CharBuilder}N /Encoding IE N end dup{/foo
  25. setfont}2 array copy cvx N load 0 nn put /ctr 0 N[}B /df{/sf 1 N /fntrx
  26. FMat N df-tail}B /dfs{div /sf X /fntrx[sf 0 0 sf neg 0 0]N df-tail}B /E{
  27. pop nn dup definefont setfont}B /ch-width{ch-data dup length 5 sub get}
  28. B /ch-height{ch-data dup length 4 sub get}B /ch-xoff{128 ch-data dup
  29. length 3 sub get sub}B /ch-yoff{ch-data dup length 2 sub get 127 sub}B
  30. /ch-dx{ch-data dup length 1 sub get}B /ch-image{ch-data dup type
  31. /stringtype ne{ctr get /ctr ctr 1 add N}if}B /id 0 N /rw 0 N /rc 0 N /gp
  32. 0 N /cp 0 N /G 0 N /sf 0 N /CharBuilder{save 3 1 roll S dup /base get 2
  33. index get S /BitMaps get S get /ch-data X pop /ctr 0 N ch-dx 0 ch-xoff
  34. ch-yoff ch-height sub ch-xoff ch-width add ch-yoff setcachedevice
  35. ch-width ch-height true[1 0 0 -1 -.1 ch-xoff sub ch-yoff .1 add]{
  36. ch-image}imagemask restore}B /D{/cc X dup type /stringtype ne{]}if nn
  37. /base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{dup dup length 1
  38. sub dup 2 index S get sf div put}if put /ctr ctr 1 add N}B /I{cc 1 add D
  39. }B /bop{userdict /bop-hook known{bop-hook}if /SI save N @rigin 0 0
  40. moveto /V matrix currentmatrix dup 1 get dup mul exch 0 get dup mul add
  41. .99 lt{/QV}{/RV}ifelse load def pop pop}N /eop{SI restore showpage
  42. userdict /eop-hook known{eop-hook}if}N /@start{userdict /start-hook
  43. known{start-hook}if pop /VResolution X /Resolution X 1000 div /DVImag X
  44. /IE 256 array N 0 1 255{IE S 1 string dup 0 3 index put cvn put}for
  45. 65781.76 div /vsize X 65781.76 div /hsize X}N /p{show}N /RMat[1 0 0 -1 0
  46. 0]N /BDot 260 string N /rulex 0 N /ruley 0 N /v{/ruley X /rulex X V}B /V
  47. {}B /RV statusdict begin /product where{pop product dup length 7 ge{0 7
  48. getinterval dup(Display)eq exch 0 4 getinterval(NeXT)eq or}{pop false}
  49. ifelse}{false}ifelse end{{gsave TR -.1 -.1 TR 1 1 scale rulex ruley
  50. false RMat{BDot}imagemask grestore}}{{gsave TR -.1 -.1 TR rulex ruley
  51. scale 1 1 false RMat{BDot}imagemask grestore}}ifelse B /QV{gsave
  52. transform round exch round exch itransform moveto rulex 0 rlineto 0
  53. ruley neg rlineto rulex neg 0 rlineto fill grestore}B /a{moveto}B /delta
  54. 0 N /tail{dup /delta X 0 rmoveto}B /M{S p delta add tail}B /b{S p tail}
  55. B /c{-4 M}B /d{-3 M}B /e{-2 M}B /f{-1 M}B /g{0 M}B /h{1 M}B /i{2 M}B /j{
  56. 3 M}B /k{4 M}B /w{0 rmoveto}B /l{p -4 w}B /m{p -3 w}B /n{p -2 w}B /o{p
  57. -1 w}B /q{p 1 w}B /r{p 2 w}B /s{p 3 w}B /t{p 4 w}B /x{0 S rmoveto}B /y{
  58. 3 2 roll p a}B /bos{/SS save N}B /eos{SS restore}B end
  59. %%EndProcSet
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  675. (for)h(this)g(function?)195 b(What)13 b(ab)q(out)h Fe(mk-length)j
  676. Fi(for)d(\\mak)o(e)e Fe(length)s Fi("?)p 75 1783 V 75
  677. 1784 V 75 1871 a(Ok,)i(do)f(this)h(to)g Fe(length)451
  678. 1877 y Fb(0)470 1871 y Fi(.)493 b(No)14 b(problem.)p
  679. 975 1910 821 2 v 975 2250 2 341 v 993 1966 a(\(\()p Fd(lam)o(b)q(da)e
  680. Fi(\()p Fe(mk-length)s Fi(\))1055 2015 y(\()p Fe(mk-length)17
  681. b(hukairs)s Fi(\)\))1016 2065 y(\()p Fd(lam)o(b)q(da)12
  682. b Fi(\()p Fe(length)s Fi(\))1055 2115 y(\()p Fd(lam)o(b)q(da)h
  683. Fi(\()p Fe(l)t Fi(\))1094 2165 y(\()p Fd(if)g Fi(\()p
  684. Fe(nul)r(l?)24 b(l)t Fi(\))14 b Fc(0)1152 2215 y Fi(\()p
  685. Fe(add1)21 b Fi(\()p Fe(length)c Fi(\()p Fe(c)n(dr)h(l)t
  686. Fi(\)\)\)\)\)\)\))p 1795 2250 V 975 2251 821 2 v 75 2312
  687. 1725 2 v eop
  688. %%Page: 7 6
  689. 7 5 bop 75 275 a Ff(0.1.)31 b(\()p Fe(Y)22 b(Y)8 b Ff(\))14
  690. b(W)o(ORKS!)1297 b Fi(7)p 75 391 1725 2 v 75 472 a(Is)14
  691. b(this)g Fe(length)308 478 y Fb(1)327 472 y Fi(?)p 75
  692. 510 821 2 v 75 900 2 391 v 93 566 a(\(\()p Fd(lam)o(b)q(da)e
  693. Fi(\()p Fe(mk-length)s Fi(\))155 616 y(\()p Fe(mk-length)171
  694. 666 y Fi(\()p Fe(mk-length)17 b(hukairs)s Fi(\)\)\))116
  695. 716 y(\()p Fd(lam)o(b)q(da)12 b Fi(\()p Fe(length)s Fi(\))155
  696. 765 y(\()p Fd(lam)o(b)q(da)h Fi(\()p Fe(l)t Fi(\))194
  697. 815 y(\()p Fd(if)g Fi(\()p Fe(nul)r(l?)24 b(l)t Fi(\))14
  698. b Fc(0)252 865 y Fi(\()p Fe(add1)21 b Fi(\()p Fe(length)c
  699. Fi(\()p Fe(c)n(dr)h(l)t Fi(\)\)\)\)\)\)\))p 895 900 V
  700. 75 901 821 2 v 975 472 a(It)c(sure)h(is.)j(And)c(this)g(is)g
  701. Fe(length)1487 478 y Fb(2)1505 472 y Fi(.)p 975 510 V
  702. 975 950 2 441 v 993 566 a(\(\()p Fd(lam)o(b)q(da)e Fi(\()p
  703. Fe(mk-length)s Fi(\))1055 616 y(\()p Fe(mk-length)1071
  704. 666 y Fi(\()p Fe(mk-length)1087 716 y Fi(\()p Fe(mk-length)18
  705. b(hukairs)s Fi(\)\)\)\))1016 765 y(\()p Fd(lam)o(b)q(da)12
  706. b Fi(\()p Fe(length)s Fi(\))1055 815 y(\()p Fd(lam)o(b)q(da)h
  707. Fi(\()p Fe(l)t Fi(\))1094 865 y(\()p Fd(if)g Fi(\()p
  708. Fe(nul)r(l?)24 b(l)t Fi(\))14 b Fc(0)1152 915 y Fi(\()p
  709. Fe(add1)21 b Fi(\()p Fe(length)c Fi(\()p Fe(c)n(dr)h(l)t
  710. Fi(\)\)\)\)\)\)\))p 1795 950 V 975 951 821 2 v 75 1005
  711. 1725 2 v 75 1006 V 75 1086 a(Can)c(y)o(ou)f(do)h Fe(length)409
  712. 1092 y Fb(3)428 1086 y Fi(?)527 b(Here)15 b(w)o(e)f(go.)p
  713. 975 1124 821 2 v 975 1614 2 490 v 993 1180 a(\(\()p Fd(lam)o(b)q(da)e
  714. Fi(\()p Fe(mk-length)s Fi(\))1055 1230 y(\()p Fe(mk-length)1071
  715. 1280 y Fi(\()p Fe(mk-length)1087 1329 y Fi(\()p Fe(mk-length)1103
  716. 1379 y Fi(\()p Fe(mk-length)18 b(hukairs)s Fi(\)\)\)\)\))1016
  717. 1429 y(\()p Fd(lam)o(b)q(da)12 b Fi(\()p Fe(length)s
  718. Fi(\))1055 1479 y(\()p Fd(lam)o(b)q(da)h Fi(\()p Fe(l)t
  719. Fi(\))1094 1529 y(\()p Fd(if)g Fi(\()p Fe(nul)r(l?)24
  720. b(l)t Fi(\))14 b Fc(0)1152 1579 y Fi(\()p Fe(add1)21
  721. b Fi(\()p Fe(length)c Fi(\()p Fe(c)n(dr)h(l)t Fi(\)\)\)\)\)\)\))p
  722. 1795 1614 V 975 1615 821 2 v 75 1668 1725 2 v 75 1669
  723. V 75 1750 a(So)c(what)f(is)h(recursion?)514 b(It)14 b(is)g(lik)o(e)f
  724. (an)g(in\014nite)h(to)o(w)o(er)g(of)g(applications)e(of)975
  725. 1800 y Fe(mk-length)17 b Fi(to)d(an)f(arbitrary)h(function.)p
  726. 75 1861 V 75 1862 V 75 1943 a(Do)f(w)o(e)h(really)g(need)h(an)e
  727. (in\014nite)h(to)o(w)o(er?)244 b(Not)14 b(really)f(of)g(course.)19
  728. b(Ev)o(erytime)13 b(w)o(e)g(use)i Fe(length)975 1993
  729. y Fi(w)o(e)f(only)f(need)i(a)f(\014nite)g(n)o(um)o(b)q(er,)e(but)j(w)o
  730. (e)f(nev)o(er)975 2042 y(kno)o(w)f(ho)o(w)h(man)o(y)m(.)p
  731. 75 2104 V 75 2105 V 75 2186 a(Could)f(w)o(e)h(guess)h(ho)o(w)f(man)o(y)
  732. e(w)o(e)i(need?)245 b(Sure,)14 b(but)g(w)o(e)g(ma)o(y)e(not)i(guess)h
  733. (a)f(large)f(enough)975 2235 y(n)o(um)o(b)q(er.)p 75
  734. 2289 V 75 2290 V 75 2370 a(When)h(do)g(w)o(e)g(\014nd)g(out)g(that)g(w)
  735. o(e)g(didn't)f(guess)i(a)75 2420 y(large)f(enough)g(n)o(um)o(b)q(er?)
  736. 975 2370 y(When)g(w)o(e)g(apply)f(the)i(function)e Fe(hukairs)18
  737. b Fi(that)c(is)975 2420 y(passed)h(to)f(the)g(\014rst)h
  738. Fe(mk-length)s Fi(.)p 75 2482 V 75 2483 V 75 2563 a(What)e(if)h(w)o(e)g
  739. (could)f(create)j(another)e(application)75 2613 y(of)f
  740. Fe(mk-length)k Fi(to)d Fe(huhairs)j Fi(at)d(this)g(p)q(oin)o(t?)975
  741. 2563 y(That)g(w)o(ould)f(p)q(ostp)q(one)i(the)f(problem)f(b)o(y)g(one,)
  742. 975 2613 y(and)h(b)q(esides,)h(ho)o(w)e(could)h(w)o(e)g(do)f(that?)p
  743. 75 2675 V eop
  744. %%Page: 8 7
  745. 8 6 bop 75 275 a Fi(8)p 75 391 1725 2 v 75 477 a(W)m(ell,)12
  746. b(since)j(nob)q(o)q(dy)f(cares)h(what)e(function)h(w)o(e)75
  747. 526 y(pass)g(to)g Fe(mk-length)s Fi(,)g(w)o(e)g(could)g(pass)g(it)f
  748. Fe(mk-length)75 576 y Fi(initially)m(.)975 477 y(That's)h(the)g(righ)o
  749. (t)g(idea.)j(And)d(then)h(w)o(e)f(in)o(v)o(ok)o(e)975
  750. 526 y Fe(mk-length)j Fi(on)d Fe(huhairs)j Fi(and)d(the)g(result)h(of)e
  751. (this)975 576 y(on)h(the)g Fe(c)n(dr)k Fi(so)c(that)g(w)o(e)g(get)g
  752. (one)g(more)f(piece)i(of)975 626 y(the)f(to)o(w)o(er.)p
  753. 75 684 V 75 685 V 75 770 a(Then)g(this)g(is)g(still)f
  754. Fe(length)497 776 y Fb(0)516 770 y Fi(?)p 75 808 821
  755. 2 v 75 1149 2 341 v 93 864 a(\(\()p Fd(lam)o(b)q(da)f
  756. Fi(\()p Fe(mk-length)s Fi(\))155 914 y(\()p Fe(mk-length)17
  757. b(mk-length)s Fi(\)\))116 964 y(\()p Fd(lam)o(b)q(da)12
  758. b Fi(\()p Fe(mk-length)s Fi(\))155 1014 y(\()p Fd(lam)o(b)q(da)h
  759. Fi(\()p Fe(l)t Fi(\))194 1064 y(\()p Fd(if)g Fi(\()p
  760. Fe(nul)r(l?)24 b(l)t Fi(\))14 b Fc(0)252 1113 y Fi(\()p
  761. Fe(add1)21 b Fi(\()p Fe(mk-length)c Fi(\()p Fe(c)n(dr)h(l)t
  762. Fi(\)\)\)\)\)\)\))p 895 1149 V 75 1150 821 2 v 975 770
  763. a(Y)m(es.)g(And)d(when)f(w)o(e)g(apply)f Fe(mk-length)k
  764. Fi(once,)d(w)o(e)975 820 y(get)g Fe(length)1151 826 y
  765. Fb(1)1170 820 y Fi(.)p 975 858 V 975 1248 2 391 v 993
  766. 914 a(\(\()p Fd(lam)o(b)q(da)e Fi(\()p Fe(mk-length)s
  767. Fi(\))1055 964 y(\()p Fe(mk-length)17 b(mk-length)s Fi(\)\))1016
  768. 1014 y(\()p Fd(lam)o(b)q(da)12 b Fi(\()p Fe(mk-length)s
  769. Fi(\))1055 1064 y(\()p Fd(lam)o(b)q(da)h Fi(\()p Fe(l)t
  770. Fi(\))1094 1113 y(\()p Fd(if)g Fi(\()p Fe(nul)r(l?)24
  771. b(l)t Fi(\))14 b Fc(0)1152 1163 y Fi(\()p Fe(add1)21
  772. b Fi(\(\()p Fe(mk-length)c(hukairs)s Fi(\))1289 1213
  773. y(\()p Fe(c)n(dr)h(l)t Fi(\)\)\)\)\)\)\))p 1795 1248
  774. V 975 1249 821 2 v 75 1307 1725 2 v 75 1308 V 75 1393
  775. a(Could)13 b(w)o(e)h(do)g(this)g(more)f(than)h(once?)277
  776. b(Y)m(es,)14 b(just)g(k)o(eep)h(passing)e Fe(mk-length)k
  777. Fi(to)d(itself,)975 1443 y(and)g(w)o(e)g(can)g(do)g(this)g(as)g(often)f
  778. (as)h(w)o(e)h(need)f(to!)p 75 1501 V 75 1502 V 75 1587
  779. a(What)f(w)o(ould)h(y)o(ou)f(call)g Fe(this)k Fi(function?)p
  780. 75 1625 821 2 v 75 2016 2 391 v 93 1681 a(\(\()p Fd(lam)o(b)q(da)12
  781. b Fi(\()p Fe(mk-length)s Fi(\))155 1731 y(\()p Fe(mk-length)17
  782. b(mk-length)s Fi(\)\))116 1781 y(\()p Fd(lam)o(b)q(da)12
  783. b Fi(\()p Fe(mk-length)s Fi(\))155 1831 y(\()p Fd(lam)o(b)q(da)h
  784. Fi(\()p Fe(l)t Fi(\))194 1881 y(\()p Fd(if)g Fi(\()p
  785. Fe(nul)r(l?)24 b(l)t Fi(\))14 b Fc(0)252 1931 y Fi(\()p
  786. Fe(add1)21 b Fi(\(\()p Fe(mk-length)c(mk-length)s Fi(\))389
  787. 1980 y(\()p Fe(c)n(dr)h(l)t Fi(\)\)\)\)\)\)\))p 895 2016
  788. V 75 2017 821 2 v 975 1587 a(It)c(is)g Fe(length)s Fi(,)f(of)h(course.)
  789. p 75 2075 1725 2 v 75 2076 V 75 2161 a(Except)h(that)f(it)g(no)f
  790. (longer)h(con)o(tains)g(the)75 2211 y(function)g(that)g(lo)q(oks)f(lik)
  791. o(e)g Fe(length)s Fi(.)18 b(Can)c(w)o(e)g(\014x)75 2260
  792. y(that?)975 2161 y(W)m(e)f(could)h(extract)h(the)g(self-application)d
  793. (of)975 2211 y Fe(mk-length)17 b Fi(and)d(call)f(it)g
  794. Fe(length)s Fi(.)p 75 2318 V 75 2319 V 75 2404 a(Wh)o(y?)793
  795. b(Because)16 b(it)d(really)h(mak)o(es)e(the)j(function)e
  796. Fe(length)s Fi(.)p 75 2471 V 75 2472 V 75 2559 a(But)h(\()p
  797. Fe(mk-length)h(mk-length)p Fi(\))f(is)g(not)g(a)g(function.)75
  798. 2609 y(It)g(only)f(returns)j(a)d(function.)975 2557 y(So)h(what)f(do)h
  799. (w)o(e)g(do?)p 75 2675 V eop
  800. %%Page: 9 8
  801. 9 7 bop 75 275 a Ff(0.1.)31 b(\()p Fe(Y)22 b(Y)8 b Ff(\))14
  802. b(W)o(ORKS!)1297 b Fi(9)p 75 391 1725 2 v 75 479 a(Mak)o(e)14
  803. b(the)g(self-application)f(of)g Fe(mk-length)k Fi(in)o(to)c(a)75
  804. 529 y(function.)975 479 y(No)h(problem,)e(w)o(e)i(just)g(use)h(the)f
  805. (old)f(tric)o(k)h(of)975 529 y(wrapping)f(a)h Fd(lam)o(b)q(da)e
  806. Fi(around)i(the)h(application.)975 579 y(After)g(all,)d(the)i
  807. (self-application)f(do)q(es)h(return)h(a)975 629 y(function!)p
  808. 75 689 V 75 690 V 75 778 a(Whic)o(h)e(function?)600 b(The)14
  809. b(function)g Fe(length)s Fi(.)k(Remem)o(b)q(er?)p 75
  810. 847 V 75 848 V 75 936 a(Ok,)c(do)f(it!)p 975 908 821
  811. 2 v 975 1398 2 490 v 993 964 a(\(\()p Fd(lam)o(b)q(da)f
  812. Fi(\()p Fe(mk-length)s Fi(\))1055 1014 y(\()p Fe(mk-length)17
  813. b(mk-length)s Fi(\)\))1016 1063 y(\()p Fd(lam)o(b)q(da)12
  814. b Fi(\()p Fe(mk-length)s Fi(\))1055 1113 y(\()p Fd(lam)o(b)q(da)h
  815. Fi(\()p Fe(l)t Fi(\))1094 1163 y(\()p Fd(if)g Fi(\()p
  816. Fe(nul)r(l?)24 b(l)t Fi(\))14 b Fc(0)1152 1213 y Fi(\()p
  817. Fe(add1)1191 1263 y Fi(\(\()p Fd(lam)o(b)q(da)f Fi(\()p
  818. Fe(x)5 b Fi(\))1247 1313 y(\(\()p Fe(mk-length)17 b(mk-length)s
  819. Fi(\))d Fe(x)5 b Fi(\)\))1207 1362 y(\()p Fe(c)n(dr)19
  820. b(l)t Fi(\)\)\)\)\)\)\))p 1795 1398 V 975 1399 821 2
  821. v 75 1468 1725 2 v 75 1469 V 75 1556 a(Mo)o(v)o(e)14
  822. b(out)f(the)i(new)f(function)g(so)g(that)g(w)o(e)g(get)75
  823. 1606 y Fe(length)j Fi(bac)o(k.)p 975 1529 821 2 v 975
  824. 2018 2 490 v 993 1585 a(\(\()p Fd(lam)o(b)q(da)12 b Fi(\()p
  825. Fe(mk-length)s Fi(\))1055 1634 y(\()p Fe(mk-length)17
  826. b(mk-length)s Fi(\)\))1016 1684 y(\()p Fd(lam)o(b)q(da)12
  827. b Fi(\()p Fe(mk-length)s Fi(\))1055 1734 y(\(\()p Fd(lam)o(b)q(da)h
  828. Fi(\()p Fe(length)s Fi(\))1110 1784 y(\()p Fd(lam)o(b)q(da)g
  829. Fi(\()p Fe(l)t Fi(\))1150 1834 y(\()p Fd(if)f Fi(\()p
  830. Fe(nul)r(l?)24 b(l)t Fi(\))14 b Fc(0)1207 1884 y Fi(\()p
  831. Fe(add1)21 b Fi(\()p Fe(length)c Fi(\()p Fe(c)n(dr)h(l)t
  832. Fi(\)\)\)\)\)\))1071 1933 y(\()p Fd(lam)o(b)q(da)13 b
  833. Fi(\()p Fe(x)5 b Fi(\))1110 1983 y(\(\()p Fe(mk-length)18
  834. b(mk-length)s Fi(\))c Fe(x)5 b Fi(\)\)\)\)\))p 1795 2018
  835. V 975 2019 821 2 v 75 2088 1725 2 v 75 2089 V 75 2177
  836. a(Is)14 b(this)g(ok)g(to)f(do?)603 b(Y)m(es.)18 b(Think)c(ab)q(out)g
  837. (it.)j(W)m(e)d(alw)o(a)o(ys)f(did)g(the)975 2227 y(rev)o(erse:)20
  838. b(When)14 b(w)o(e)g(knew)g(what)g(the)h(argumen)o(t)975
  839. 2277 y(to)f(a)f(function)h(w)o(as,)f(w)o(e)h(pro)q(ceeded)i(with)e(the)
  840. 975 2327 y(function)g(b)q(o)q(dy)g(and)f(used)i(the)g(argumen)o(t)d(v)n
  841. (alue)975 2376 y(whenev)o(er)j(w)o(e)f(sa)o(w)g(the)h(parameter)e
  842. (name.)p 75 2445 V 75 2446 V 75 2534 a(Can)h(w)o(e)g(extract)h(the)f
  843. (function)g(that)g(lo)q(oks)f(lik)o(e)75 2584 y Fe(length)k
  844. Fi(and)d(giv)o(e)f(it)h(a)f(name?)975 2534 y(Y)m(es,)h(it)f(do)q(es)i
  845. (not)f(dep)q(end)h(on)f Fe(mk-length)j Fi(at)c(all!)p
  846. 75 2653 V eop
  847. %%Page: 10 9
  848. 10 8 bop 75 275 a Fi(10)p 75 391 1725 2 v 75 479 a(Is)14
  849. b(this)g(the)h(righ)o(t)e(function?)p 75 517 821 2 v
  850. 75 1057 2 540 v 93 573 a(\(\()p Fd(lam)o(b)q(da)f Fi(\()p
  851. Fe(le)s Fi(\))155 623 y(\(\()p Fd(lam)o(b)q(da)h Fi(\()p
  852. Fe(mk-length)s Fi(\))210 673 y(\()p Fe(mk-length)18 b(mk-length)s
  853. Fi(\)\))171 723 y(\()p Fd(lam)o(b)q(da)13 b Fi(\()p Fe(mk-length)s
  854. Fi(\))210 773 y(\()p Fe(le)k Fi(\()p Fd(lam)o(b)q(da)c
  855. Fi(\()p Fe(x)5 b Fi(\))312 822 y(\(\()p Fe(mk-length)18
  856. b(mk-length)s Fi(\))c Fe(x)5 b Fi(\)\)\)\)\)\))116 872
  857. y(\()p Fd(lam)o(b)q(da)12 b Fi(\()p Fe(length)s Fi(\))155
  858. 922 y(\()p Fd(lam)o(b)q(da)h Fi(\()p Fe(l)t Fi(\))194
  859. 972 y(\()p Fd(if)g Fi(\()p Fe(nul)r(l?)24 b(l)t Fi(\))14
  860. b Fc(0)252 1022 y Fi(\()p Fe(add1)21 b Fi(\()p Fe(length)c
  861. Fi(\()p Fe(c)n(dr)h(l)t Fi(\)\)\)\)\)\)\))p 895 1057
  862. V 75 1058 821 2 v 975 479 a(Y)m(es.)p 75 1119 1725 2
  863. v 75 1120 V 75 1207 a(What)13 b(did)h(w)o(e)g(actually)f(get)h(bac)o
  864. (k?)321 b(W)m(e)13 b(extracted)j(the)e Fe(old)19 b Fi(function)13
  865. b Fe(mk-length)s Fi(!)p 75 1276 V 75 1277 V 75 1365 a(Let's)h(separate)
  866. h(the)g(function)e(that)h(mak)o(es)f Fe(length)75 1415
  867. y Fi(from)f(the)j(function)e(that)h(lo)q(oks)f(lik)o(e)h
  868. Fe(length)s Fi(.)975 1365 y(That's)g(easy)m(.)p 975 1403
  869. 821 2 v 975 1744 2 341 v 993 1459 a(\()p Fd(lam)o(b)q(da)e
  870. Fi(\()p Fe(le)s Fi(\))1039 1509 y(\(\()p Fd(lam)o(b)q(da)h
  871. Fi(\()p Fe(mk-length)s Fi(\))1094 1559 y(\()p Fe(mk-length)k(mk-length)
  872. s Fi(\)\))1055 1609 y(\()p Fd(lam)o(b)q(da)c Fi(\()p
  873. Fe(mk-length)s Fi(\))1094 1658 y(\()p Fe(le)k Fi(\()p
  874. Fd(lam)o(b)q(da)c Fi(\()p Fe(x)5 b Fi(\))1196 1708 y(\(\()p
  875. Fe(mk-length)18 b(mk-length)s Fi(\))c Fe(x)5 b Fi(\)\)\)\)\)\))p
  876. 1795 1744 V 975 1745 821 2 v 75 1805 1725 2 v 75 1806
  877. V 75 1894 a(Do)q(es)14 b(this)g(function)g(ha)o(v)o(e)g(a)f(name?)306
  878. b(Y)m(es,)14 b(it)f(is)h(called)g(the)g(applicativ)o(e-order)g
  879. Fe(Y)975 1944 y Fi(com)o(binator.)i(A)o(t)e(least,)g(when)g(w)o(e)g
  880. (rewrite)h(it)f(a)975 1994 y(little)f(bit.)p 975 2024
  881. 821 2 v 975 2364 2 341 v 993 2080 a(\()p Fd(de\014ne)f
  882. Fe(Y)1039 2130 y Fi(\()p Fd(lam)o(b)q(da)g Fi(\()p Fe(le)s
  883. Fi(\))1078 2179 y(\(\()p Fd(lam)o(b)q(da)h Fi(\()p Fe(f)8
  884. b Fi(\))1133 2229 y(\()p Fe(le)17 b Fi(\()p Fd(lam)o(b)q(da)c
  885. Fi(\()p Fe(x)5 b Fi(\))14 b(\(\()p Fe(f)23 b(f)8 b Fi(\))14
  886. b Fe(x)5 b Fi(\)\)\)\))1094 2279 y(\()p Fd(lam)o(b)q(da)13
  887. b Fi(\()p Fe(f)8 b Fi(\))1133 2329 y(\()p Fe(le)17 b
  888. Fi(\()p Fd(lam)o(b)q(da)c Fi(\()p Fe(x)5 b Fi(\))14 b(\(\()p
  889. Fe(f)23 b(f)8 b Fi(\))14 b Fe(x)5 b Fi(\)\)\)\)\)\)\))p
  890. 1795 2364 V 975 2365 821 2 v 75 2426 1725 2 v 75 2427
  891. V 75 2517 a(Do)q(es)14 b(\()p Fd(de\014ne)f Fi(.)7 b(.)g(.)19
  892. b(.)7 b(.)g(.)e(\))14 b(w)o(ork)g(again?)975 2515 y(Sure,)g(no)o(w)g
  893. (that)g(w)o(e)g(kno)o(w)f(what)h(recursion)h(is.)p 75
  894. 2588 V eop
  895. %%Page: 11 10
  896. 11 9 bop 75 275 a Ff(0.1.)31 b(\()p Fe(Y)22 b(Y)8 b Ff(\))14
  897. b(W)o(ORKS!)1276 b Fi(11)p 75 391 1725 2 v 75 479 a(Do)13
  898. b(y)o(ou)h(no)o(w)f(kno)o(w)h(wh)o(y)f Fe(Y)22 b Fi(w)o(orks?)296
  899. b(Read)14 b(this)g(c)o(hapter)g(one)h(more)d(time)h(and)h(y)o(ou)975
  900. 529 y(will.)p 75 590 V 75 591 V 75 681 a(Do)q(es)g(\()p
  901. Fe(Y)22 b(Y)8 b Fi(\))14 b(w)o(ork,)f(to)q(o?)975 678
  902. y(And)h(ho)o(w)g(it)f(w)o(orks!!!)p 75 752 V eop
  903. %%Trailer
  904. end
  905. userdict /end-hook known{end-hook}if
  906. %%EOF
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