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+Fi(const1)23 b(\(1/0\))15 b Fp(also)g(ev)m(aluates)h(prop)q(erly)g(to)e +Fi(1)p Fp(.)71 1400 y(Non-strict)h(functions)i(are)f(extremely)g(useful)h(in) +g(a)e(v)m(ariet)o(y)h(of)g(con)o(texts.)21 b(The)16 b(main)g(adv)m(an)o(tage) +f(is)i(that)0 1456 y(they)d(free)f(the)h(programmer)f(from)f(man)o(y)i +(concerns)g(ab)q(out)f(ev)m(aluation)i(order.)k(Computationally)14 +b(exp)q(ensiv)o(e)0 1513 y(v)m(alues)j(ma)o(y)f(b)q(e)h(passed)g(as)e +(argumen)o(ts)h(to)g(functions)h(without)f(fear)g(of)g(them)g(b)q(eing)h +(computed)g(if)g(they)f(are)0 1569 y(not)f(needed.)21 b(An)15 +b(imp)q(ortan)o(t)g(example)h(of)f(this)h(is)f(a)g(p)q(ossibly)i +Fo(in\014nite)d Fp(data)g(structure.)0 1714 y Fg(3.4)56 b(\\In\014nite")17 +b(Data)i(Structures)0 1824 y Fp(One)13 b(adv)m(an)o(tage)f(of)g(the)g +(non-strict)h(nature)f(of)g(Hask)o(ell)h(is)g(that)f(data)g(constructors)f +(are)h(non-strict,)h(to)q(o.)18 b(This)0 1880 y(should)h(not)e(b)q(e)i +(surprising,)g(since)g(constructors)e(are)g(really)i(just)e(a)h(sp)q(ecial)h +(kind)g(of)e(function)i(\(the)e(distin-)0 1937 y(guishing)h(feature)e(b)q +(eing)i(that)e(they)g(can)h(b)q(e)g(used)g(in)g(pattern)f(matc)o(hing\).)24 +b(F)l(or)16 b(example,)h(the)g(constructor)0 1993 y(for)e(lists,)g +Fi(\(:\))p Fp(,)g(is)g(non-strict.)71 2073 y(Non-strict)g(constructors)f(p)q +(ermit)h(the)g(de\014nition)i(of)e(\(conceptually\))h Fo(in\014nite)d +Fp(data)i(structures.)k(Here)c(is)0 2130 y(an)g(in\014nite)i(list)f(of)f +(ones:)71 2230 y Fi(ones)476 b(=)24 b(1)g(:)f(ones)0 2339 y +Fp(P)o(erhaps)15 b(more)g(in)o(teresting)h(is)f(the)h(function)g +Fi(numsFrom)o Fp(:)71 2448 y Fi(numsFrom)22 b(n)334 b(=)24 +b(n)g(:)f(numsFrom)g(\(n+1\))0 2557 y Fp(Th)o(us)10 b Fi(numsFrom)23 +b(n)11 b Fp(is)g(the)f(in\014nite)j(list)e(of)f(successiv)o(e)i(in)o(tegers)e +(b)q(eginning)j(with)e Fi(n)p Fp(.)18 b(F)l(rom)10 b(it)g(w)o(e)h(can)f +(construct)0 2614 y(an)15 b(in\014nite)i(list)f(of)f(squares:)p +eop +%%Page: 14 14 +bop 0 -40 a Fp(T-14)1513 b Fj(3)45 b(FUNCTIONS)71 160 y Fi(squares)404 +b(=)24 b(map)f(\(^2\))h(\(numsfrom)e(0\))0 271 y Fp(\(Note)15 +b(the)g(use)g(of)g(a)g(section;)g Fi(^)g Fp(is)h(the)f(in\014x)i(exp)q(onen)o +(tiation)f(op)q(erator.\))71 353 y(Of)c(course,)h(ev)o(en)o(tually)g(w)o(e)f +(exp)q(ect)i(to)d(extract)h(some)g(\014nite)i(p)q(ortion)e(of)g(the)h(list)g +(for)f(actual)g(computation,)0 409 y(and)17 b(there)f(are)h(lots)f(of)g +(prede\014ned)j(functions)e(in)h(Hask)o(ell)f(that)f(do)g(this)i(sort)d(of)h +(thing:)24 b Fi(take)o Fp(,)17 b Fi(takeWhile)n Fp(,)0 466 +y Fi(filter)o Fp(,)g(and)h(others)f(\(see)g(the)g(p)q(ortion)h(of)e(the)i +(Standard)f(Prelude)h(called)h Fi(PreludeList)n Fp(\).)26 b(F)l(or)16 +b(example,)0 522 y Fi(take)f Fp(remo)o(v)o(es)f(the)h(\014rst)g +Fi(n)g Fp(elemen)o(ts)h(from)e(a)h(list:)569 625 y Fi(take)23 +b(5)h(squares)72 b Fn(\))i Fi([0,1,4,9,16])71 753 y Fp(The)14 +b(de\014nition)i(of)d Fi(ones)g Fp(ab)q(o)o(v)o(e)h(is)h(an)e(example)i(of)f +(a)f Fo(cir)n(cular)j(list)p Fp(.)i(In)d(most)e(circumstances)i(this)f(has)g +(an)0 809 y(imp)q(ortan)o(t)h(impact)h(on)g(e\016ciency)l(,)h(since)g(an)f +(implemen)o(tation)h(can)f(b)q(e)h(exp)q(ected)g(to)e(implemen)o(t)i(the)f +(list)g(as)0 866 y(a)f(true)g(circular)h(structure,)f(th)o(us)g(sa)o(ving)g +(space.)71 947 y(F)l(or)10 b(another)h(example)i(of)e(the)g(use)h(of)f +(circularit)o(y)l(,)i(the)f(Fib)q(onacci)h(sequence)f(can)g(b)q(e)g(computed) +g(e\016cien)o(tly)0 1004 y(as)j(the)g(follo)o(wing)h(in\014nite)h(sequence:) +71 1113 y Fi(fib)309 b(=)24 b(1)g(:)g(1)f(:)h([)g(a+b)f(|)h(\(a,b\))f(<-)h +(zip)f(fib)h(\(tail)f(fib\))g(])0 1222 y Fp(where)e Fi(zip)g +Fp(is)g(a)g(Standard)g(Prelude)h(function)g(that)e(returns)h(the)g(pairwise)h +(in)o(terlea)o(ving)g(of)e(its)i(t)o(w)o(o)d(list)0 1278 y(argumen)o(ts:)71 +1387 y Fi(zip)k(\(x:xs\))g(\(y:ys\))166 b(=)24 b(\(x,y\))f(:)h(zip)f(xs)h(ys) +71 1444 y(zip)47 b(xs)119 b(ys)238 b(=)24 b([])0 1553 y Fp(Note)16 +b(ho)o(w)g Fi(fib)o Fp(,)g(an)h(in\014nite)h(list,)f(is)f(de\014ned)i(in)f +(terms)f(of)g(itself,)h(as)e(if)i(it)g(w)o(ere)f(\\c)o(hasing)g(its)g(tail.") +24 b(Indeed,)0 1609 y(w)o(e)15 b(can)g(dra)o(w)g(a)g(picture)h(of)f(this)g +(computation)g(as)g(sho)o(wn)g(in)h(Figure)g(1a.)71 1691 y(F)l(or)e(another)h +(application)i(of)e(in\014nite)i(lists,)e(see)h(Section)g(4.4.)0 +1839 y Fg(3.5)56 b(The)18 b(Error)g(F)-5 b(unction)0 1950 y +Fp(Hask)o(ell)20 b(has)f(a)g(built-in)i(function)f(called)h +Fi(error)d Fp(whose)h(t)o(yp)q(e)g(is)h Fi(String->a)o Fp(.)31 +b(This)20 b(is)f(a)g(somewhat)g(o)q(dd)0 2007 y(function:)k(F)l(rom)15 +b(its)h(t)o(yp)q(e)g(it)h(lo)q(oks)f(as)g(if)h(it)f(is)h(returning)f(a)g(v)m +(alue)h(of)f(a)g(p)q(olymorphic)i(t)o(yp)q(e)e(ab)q(out)g(whic)o(h)h(it)0 +2063 y(kno)o(ws)e(nothing,)g(since)h(it)g(nev)o(er)f(receiv)o(es)h(a)f(v)m +(alue)h(of)f(that)g(t)o(yp)q(e)g(as)g(an)g(argumen)o(t!)71 +2145 y(In)h(fact,)f(there)h Fo(is)g Fp(one)g(v)m(alue)h(\\shared")e(b)o(y)h +(all)h(t)o(yp)q(es:)k Fn(?)p Fp(.)h(Indeed,)c(seman)o(tically)f(that)e(is)h +(exactly)h(what)0 2201 y(v)m(alue)c(is)g(alw)o(a)o(ys)e(returned)h(b)o(y)g +Fi(error)f Fp(\(recall)i(that)e(all)i(errors)e(ha)o(v)o(e)h(v)m(alue)h +Fn(?)p Fp(\).)19 b(Ho)o(w)o(ev)o(er,)11 b(w)o(e)h(can)g(exp)q(ect)h(that)0 +2258 y(a)g(reasonable)g(implemen)o(tation)i(will)g(prin)o(t)e(the)g(string)h +(argumen)o(t)e(to)g Fi(error)h Fp(for)f(diagnostic)i(purp)q(oses.)20 +b(Th)o(us)0 2314 y(this)e(function)g(is)g(useful)g(when)g(w)o(e)f(wish)h(to)f +(terminate)g(a)g(program)g(when)h(something)f(has)g(\\gone)g(wrong.")0 +2371 y(F)l(or)e(example,)g(the)h(actual)f(de\014nition)i(of)e +Fi(head)f Fp(tak)o(en)h(from)f(the)i(Standard)f(Prelude)h(is:)71 +2480 y Fi(head)23 b(\(x:xs\))309 b(=)48 b(x)71 2536 y(head)f([])381 +b(=)48 b(error)23 b("head{PreludeList}:)e(head)j([]")p eop +%%Page: 15 15 +bop 1857 -40 a Fp(T-15)33 869 y @beginspecial 5.156800 @llx +435.382507 @lly 327.294495 @urx 781.187195 @ury 1800 @rwi @setspecial +%%BeginDocument: fib.eps +/FHIODict 30 dict def +FHIODict begin +/bdf{bind def}bind def +/d{setdash}bdf +/h{closepath}bdf +/H{}bdf +/J{setlinecap}bdf +/j{setlinejoin}bdf +/M{setmiterlimit}bdf +/n{newpath}bdf +/N{newpath}bdf +/q{gsave}bdf +/Q{grestore}bdf +/w{setlinewidth}bdf +/u{}bdf +/U{}bdf +/sepdef{ +dup where not +{ +FreeHandSepDict +} +if +3 1 roll exch put +}bdf +/` +{end %. FreeHandDict +/-save0- save def +pop pop pop pop pop +concat +userdict begin +/showpage {} def +0 setgray 0 setlinecap 1 setlinewidth +0 setlinejoin 10 setmiterlimit [] 0 setdash newpath +/languagelevel where {pop languagelevel 1 ne{false setstrokeadjust false setoverprint}if}if +} bdf +/~ +{end +-save0- restore +FreeHandDict begin +}bdf +/FreeHandDict 190 dict def +FreeHandDict begin +/currentpacking where{pop true setpacking}if +/xdf{exch def}bdf +/ndf{1 index where{pop pop pop}{dup xcheck{bind}if def}ifelse}bdf +/min{2 copy gt{exch}if pop}bdf +/max{2 copy lt{exch}if pop}bdf +/isLino statusdict /product get (Lino) anchorsearch{pop pop true}{pop false}ifelse def +/dr{transform .25 sub round .25 add +exch .25 sub round .25 add exch itransform}bdf +/C{dr curveto}bdf +/L{dr lineto}bdf +/m{dr moveto}bdf +/printerRes +gsave +matrix defaultmatrix setmatrix +72 72 dtransform +abs exch abs +max +grestore +def +/maxsteps 256 def +/calcgraysteps { +currentscreen pop exch +printerRes exch div exch +2 copy +sin mul round dup mul +3 1 roll +cos mul round dup mul +add 1 add +dup maxsteps gt {pop maxsteps} if +} bdf +/bottom -0 def +/delta -0 def +/frac -0 def +/left -0 def +/numsteps -0 def +/numsteps1 -0 def +/radius -0 def +/right -0 def +/top -0 def +/xt -0 def +/yt -0 def +/df currentflat def +/tempstr 1 string def +/clipflatness currentflat def +/inverted? +0 currenttransfer exec .5 ge def +/colorexists +systemdict/setcmykcolor known def +/tc1 [0 0 0 1] def +/tc2 [0 0 0 1] def +/fc [0 0 0 1] def +/sc [0 0 0 1] def +/concatprocs{ +/proc2 exch cvlit def/proc1 exch cvlit def +/newproc proc1 length proc2 length add array def +newproc 0 proc1 putinterval newproc proc1 length proc2 putinterval +newproc cvx}bdf +/storerect{/top xdf/right xdf/bottom xdf/left xdf}bdf +/rectpath{newpath left bottom m left top L +right top L right bottom L closepath}bdf +/i{dup 0 eq +{pop df dup} +{dup} ifelse +/clipflatness xdf setflat +}bdf +version cvr 38.0 le +{/setrgbcolor{ +currenttransfer exec 3 1 roll +currenttransfer exec 3 1 roll +currenttransfer exec 3 1 roll +setrgbcolor}bdf}if +/gettint{0 get}bdf +/puttint{0 exch put}bdf +/vms {/vmsv save def} bdf +/vmr {vmsv restore} bdf +/vmrs{vmsv restore /vmsv save def}bdf +/eomode{ +{/filler /eofill load def /clipper /eoclip load def} +{/filler /fill load def /clipper /clip load def} +ifelse +}bdf +/CD{/NF exch def{exch dup/FID ne 1 index/UniqueID ne and{exch NF 3 1 roll put} +{pop pop}ifelse}forall NF}bdf +/MN{1 index length/Len exch def +dup length Len add string dup +Len 4 -1 roll putinterval dup 0 4 -1 roll putinterval}bdf +/RC{4 -1 roll /ourvec xdf 256 string cvs(|______)anchorsearch +{1 index MN cvn/NewN exch def cvn +findfont dup maxlength dict CD dup/FontName NewN put dup +/Encoding ourvec put NewN exch definefont pop}{pop}ifelse}bdf +/RF{dup FontDirectory exch known{pop 3 -1 roll pop}{RC}ifelse}bdf +/FF{dup 256 string cvs(|______)exch MN cvn dup FontDirectory exch known +{exch pop findfont 3 -1 roll pop}{pop dup findfont dup maxlength dict CD dup dup +/Encoding exch /Encoding get 256 array copy 7 -1 roll {3 -1 roll dup 4 -2 roll put}forall put definefont}ifelse}bdf +userdict begin /BDFontDict 20 dict def end +BDFontDict begin +/bu{}def +/bn{}def +/setTxMode{av 70 ge{pop}if pop}def +/gm{m}def +/show{pop}def +/gr{pop}def +/fnt{pop pop pop}def +/fs{pop}def +/fz{pop}def +/lin{pop pop}def +end +/MacVec 256 array def +MacVec 0 /Helvetica findfont +/Encoding get 0 128 getinterval putinterval +MacVec 127 /DEL put MacVec 16#27 /quotesingle put MacVec 16#60 /grave put +/NUL/SOH/STX/ETX/EOT/ENQ/ACK/BEL/BS/HT/LF/VT/FF/CR/SO/SI +/DLE/DC1/DC2/DC3/DC4/NAK/SYN/ETB/CAN/EM/SUB/ESC/FS/GS/RS/US +MacVec 0 32 getinterval astore pop +/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute +/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave +/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute +/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis +/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls +/register/copyright/trademark/acute/dieresis/notequal/AE/Oslash +/infinity/plusminus/lessequal/greaterequal/yen/mu/partialdiff/summation +/product/pi/integral/ordfeminine/ordmasculine/Omega/ae/oslash +/questiondown/exclamdown/logicalnot/radical/florin/approxequal/Delta/guillemotleft +/guillemotright/ellipsis/nbspace/Agrave/Atilde/Otilde/OE/oe +/endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide/lozenge +/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright/fi/fl +/daggerdbl/periodcentered/quotesinglbase/quotedblbase +/perthousand/Acircumflex/Ecircumflex/Aacute +/Edieresis/Egrave/Iacute/Icircumflex/Idieresis/Igrave/Oacute/Ocircumflex +/apple/Ograve/Uacute/Ucircumflex/Ugrave/dotlessi/circumflex/tilde +/macron/breve/dotaccent/ring/cedilla/hungarumlaut/ogonek/caron +MacVec 128 128 getinterval astore pop +/fps{ +currentflat +exch +dup 0 le{pop 1}if +{ +dup setflat 3 index stopped +{1.3 mul dup 3 index gt{pop setflat pop pop stop}if} +{exit} +ifelse +}loop +pop setflat pop pop +}bdf +/fp{100 currentflat fps}bdf +/clipper{clip}bdf +/W{/clipper load 100 clipflatness fps}bdf +/fixtrans1 { +dup{ic mul ic sub 1 add}concatprocs exch +dup{im mul im sub 1 add}concatprocs exch +dup{iy mul iy sub 1 add}concatprocs exch +{ik mul ik sub 1 add}concatprocs +}bdf +/fixtrans2 { +currentcolortransfer +5 -1 roll exch concatprocs 7 1 roll +4 -1 roll exch concatprocs 6 1 roll +3 -1 roll exch concatprocs 5 1 roll +concatprocs 4 1 roll +setcolortransfer +}bdf +end%. FreeHandDict +end%. FHIODict +FHIODict begin +FreeHandDict begin +5.1568 435.3825 327.2945 781.1872 storerect rectpath clip newpath +/onlyk{false}ndf +/ccmyk{dup 5 -1 roll sub 0 max exch}ndf +/setcmykcolor{1 exch sub ccmyk ccmyk ccmyk pop setrgbcolor}ndf +/setcmykcoloroverprint{4{dup -1 eq{pop 0}if 4 1 roll}repeat setcmykcolor}ndf +/findcmykcustomcolor{5 /packedarray where{pop packedarray}{array astore readonly}ifelse}ndf +/setcustomcolor{exch aload pop pop 4{4 index mul 4 1 roll}repeat setcmykcolor pop}ndf +/setseparationgray{1 exch sub dup dup dup setcmykcolor}ndf +/setoverprint{pop}ndf +/currentoverprint false ndf +/colorimage{pop pop +[5 -1 roll/exec cvx 6 -1 roll/exec cvx 7 -1 roll/exec cvx 8 -1 roll/exec cvx +/cmykbufs2gray cvx]cvx image} +version cvr 47.1 le isLino and{userdict begin bdf end}{ndf}ifelse +/cci1 { +currentcolortransfer +{ik mul ik sub 1 add}concatprocs 4 1 roll +{iy mul iy sub 1 add}concatprocs 4 1 roll +{im mul im sub 1 add}concatprocs 4 1 roll +{ic mul ic sub 1 add}concatprocs 4 1 roll +setcolortransfer +}ndf +/cci2 { +{invbuf dup length magentabuf length ne +{dup length dup dup +/magentabuf exch string def +/yellowbuf exch string def +/blackbuf exch string def}if +dup magentabuf copy yellowbuf copy blackbuf copy pop}concatprocs +}ndf +/customcolorimage{colorexists{ +aload pop pop 4 array astore +setimagecmyk +cci1 +/magentabuf 0 string def +/yellowbuf 0 string def +/blackbuf 0 string def +cci2 {magentabuf}{yellowbuf}{blackbuf}true 4 colorimage} +{pop image}ifelse}ndf +/separationimage{image}ndf +/newcmykcustomcolor{6 /packedarray where{pop packedarray}{array astore readonly}ifelse}ndf +/inkoverprint false ndf +/setinkoverprint{pop}ndf +/overprintprocess{pop}ndf +/setspotcolor +{spots exch get 0 5 getinterval exch setcustomcolor}ndf +/currentcolortransfer{currenttransfer dup dup dup}ndf +/setcolortransfer{systemdict begin settransfer end pop pop pop}ndf +/getcmyk { +dup length 4 eq +{aload pop} +{aload pop spots exch get 0 4 getinterval aload pop 4 +{4 index mul 4 1 roll}repeat 5 -1 roll pop} ifelse +}bdf +/setimagecmyk{ +getcmyk/ik xdf /iy xdf /im xdf /ic xdf +}ndf +/autospread{pop}ndf +/fhsetspreadsize{pop}ndf +/strokeopf false def +/fillopf false def +/R{0 ne /strokeopf xdf}bdf +/O{0 ne /fillopf xdf}bdf +/filler{fill}bdf +/F{fc fhsetcolor fillopf setoverprint false autospread +gsave /filler load fp grestore false setoverprint}bdf +/f{closepath F}bdf +/S{sc fhsetcolor strokeopf setoverprint true autospread {stroke}fp false setoverprint}bdf +/s{closepath S}bdf +/B{fc fhsetcolor fillopf setoverprint gsave /filler load fp grestore +sc fhsetcolor strokeopf setoverprint true autospread {stroke}fp false setoverprint}bdf +/b{closepath B}bdf +colorexists not{/setcolorscreen {setscreen pop pop pop pop pop pop pop pop pop}bdf}if +/fhsetcolor{dup length 4 eq +{aload overprintprocess setcmykcolor} +{aload 1 get spots exch get 5 get setinkoverprint setspotcolor} +ifelse +}ndf +/settextcolor{dup fhsetcolor dup length 4 eq +{onlyk{3 get 1.0 eq{true setinkoverprint}if}{pop}ifelse} +{pop} +ifelse +}ndf +/ka{/fc xdf}bdf +/Ka{/sc xdf}bdf +/xa{/fc xdf} bdf +/Xa{/sc xdf} bdf +/bc2[0 0]def +/bc4[0 0 0 0]def +/absmax{2 copy abs exch abs gt{exch}if pop}bdf +/calcstep +{ colorexists not and{calcgraysteps}{maxsteps}ifelse +tc1 length 4 eq +{ +0 1 3 +{tc1 1 index get +tc2 3 -1 roll get +sub +}for +absmax absmax absmax +} +{ +bc2 tc1 1 get 1 exch put +tc1 gettint tc2 gettint +sub abs +} +ifelse +mul abs round dup 0 eq{pop 1}if +dup /numsteps xdf 1 sub dup 0 eq{pop 1}if /numsteps1 xdf +}bdf +/cblend{ +tc1 length 4 eq +{ +0 1 3 +{bc4 exch +tc1 1 index get +tc2 2 index get +1 index sub +frac mul add put +}for bc4 +} +{ +bc2 +tc1 gettint +tc2 gettint +1 index sub +frac mul add +puttint bc2 +} +ifelse +fhsetcolor +}bdf +/logtaper{/frac frac 9 mul 1 add log def}bdf +FHIODict begin +/origmtx matrix currentmatrix def +/iminv false def +/invbuf{0 1 2 index length 1 sub{dup 2 index exch get 255 exch sub 2 index 3 1 roll put}for}bdf +/cyanrp{currentfile cyanbuf readhexstring pop iminv{invbuf}if}def +/magentarp{cyanbuf magentabuf copy}bdf +/yellowrp{cyanbuf yellowbuf copy}bdf +/blackrp{cyanbuf blackbuf copy}bdf +/fixtransfer{ +colorexists +{fixtrans1 fixtrans2} +{{dup 1 exch sub currentgray mul add}concatprocs +currenttransfer exch concatprocs +systemdict begin settransfer end}ifelse +}ndf +/cmykbufs2gray{ +dup length 0 1 3 -1 roll 1 sub +{4 index 1 index get +4 index 2 index get +4 index 3 index get +4 index 4 index get +255 exch sub ccmyk ccmyk ccmyk pop 5 mul exch 45 mul add exch 14 mul add -6 bitshift +2 index 3 1 roll put}for +4 1 roll pop pop pop +}bdf +end +/textopf false def +/curtextmtx{}def +/otw .25 def +/msf{dup/curtextmtx xdf makefont setfont}bdf +/makesetfont/msf load def +/curtextheight{.707104 .707104 curtextmtx dtransform +dup mul exch dup mul add sqrt}bdf +/ta{1 index +{tempstr 0 2 index put tempstr 2 index +gsave exec grestore +tempstr stringwidth rmoveto +5 index eq{6 index 6 index rmoveto}if +3 index 3 index rmoveto +}forall 7{pop}repeat}bdf +/sts{settextcolor textopf setoverprint/ts{awidthshow}def exec false setoverprint}bdf +/stol{setlinewidth settextcolor textopf setoverprint newpath +/ts{{false charpath stroke}ta}def exec false setoverprint}bdf +/currentpacking where{pop false setpacking}if +/spots[1 0 0 0 (Process Cyan) false newcmykcustomcolor +0 1 0 0 (Process Magenta) false newcmykcustomcolor +0 0 1 0 (Process Yellow) false newcmykcustomcolor +0 0 0 1 (Process Black) false newcmykcustomcolor +0 0 0 0 (White) false +newcmykcustomcolor +]def +0 dict dup begin +end +/f0 /Symbol FF def +[] 0 d +3.863708 M +1 w +0 j +0 J +0 O +0 R +0 i +false eomode +[0 0 0 1] Ka +[0 0 0 1] ka +vms +u +vmrs +MacVec 256 array copy +/f1 /|______Helvetica-Bold dup RF findfont def +{ +f1 [18 0 0 18 0 0] makesetfont +9.656845 613.020248 m +0 0 32 0 0 (1) ts +} +[0 0 0 1] +sts +78.6568 699.0202 m +78.6568 745.0202 L +2 J +S +78.6568 745.0202 m +83.6568 745.0202 L +78.6568 757.0202 L +73.6568 745.0202 L 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+240.6568 515.0202 L +f +n +U +vmrs +MacVec 256 array copy +/f1 /|______Helvetica-Bold dup RF findfont def +{ +f1 [18 0 0 18 0 0] makesetfont +76.656845 538.020248 m +0 0 32 0 0 (1) ts +} +[0 0 0 1] +sts +vmrs +MacVec 256 array copy +/f1 /|______Helvetica-Bold dup RF findfont def +{ +f1 [18 0 0 18 0 0] makesetfont +126.656845 724.020248 m +0 0 32 0 0 (1,1,2,3,5,...) ts +} +[0 0 0 1] +sts +vmrs +MacVec 256 array copy +/f1 /|______Helvetica-Bold dup RF findfont def +{ +f1 [18 0 0 18 0 0] makesetfont +164.656845 655.020248 m +0 0 32 0 0 (1,2,3,5,8,...) ts +} +[0 0 0 1] +sts +vmrs +MacVec 256 array copy +/f3 /|______Times-BoldItalic dup RF findfont def +{ +f3 [18 0 0 18 0 0] makesetfont +69.656845 763.020248 m +0 0 32 0 0 (fib) ts +} +[0 0 0 1] +sts +U +vmr +end % FreeHandDict +end % FHIODict +%%EndDocument + @endspecial 1134 w @beginspecial 14.258400 @llx 620.398376 +@lly 377.258392 @urx 783.398376 @ury 1800 @rwi @setspecial +%%BeginDocument: io.eps +/FHIODict 30 dict def +FHIODict begin +/bdf{bind def}bind def +/d{setdash}bdf +/h{closepath}bdf +/H{}bdf +/J{setlinecap}bdf +/j{setlinejoin}bdf +/M{setmiterlimit}bdf +/n{newpath}bdf +/N{newpath}bdf +/q{gsave}bdf +/Q{grestore}bdf +/w{setlinewidth}bdf +/u{}bdf +/U{}bdf +/sepdef{ +dup where not +{ +FreeHandSepDict +} +if +3 1 roll exch put +}bdf +/` +{end %. FreeHandDict +/-save0- save def +pop pop pop pop pop +concat +userdict begin +/showpage {} def +0 setgray 0 setlinecap 1 setlinewidth +0 setlinejoin 10 setmiterlimit [] 0 setdash newpath +/languagelevel where {pop languagelevel 1 ne{false setstrokeadjust false setoverprint}if}if +} bdf +/~ +{end +-save0- restore +FreeHandDict begin +}bdf +/FreeHandDict 190 dict def +FreeHandDict begin +/currentpacking where{pop true setpacking}if +/xdf{exch def}bdf +/ndf{1 index where{pop pop pop}{dup xcheck{bind}if def}ifelse}bdf +/min{2 copy gt{exch}if pop}bdf +/max{2 copy lt{exch}if pop}bdf +/isLino statusdict /product get (Lino) anchorsearch{pop pop true}{pop false}ifelse def +/dr{transform .25 sub round .25 add +exch .25 sub round .25 add exch itransform}bdf +/C{dr curveto}bdf +/L{dr lineto}bdf +/m{dr moveto}bdf +/printerRes +gsave +matrix defaultmatrix setmatrix +72 72 dtransform +abs exch abs +max +grestore +def +/maxsteps 256 def +/calcgraysteps { +currentscreen pop exch +printerRes exch div exch +2 copy +sin mul round dup mul +3 1 roll +cos mul round dup mul +add 1 add +dup maxsteps gt {pop maxsteps} if +} bdf +/bottom -0 def +/delta -0 def +/frac -0 def +/left -0 def +/numsteps -0 def +/numsteps1 -0 def +/radius -0 def +/right -0 def +/top -0 def +/xt -0 def +/yt -0 def +/df currentflat def +/tempstr 1 string def +/clipflatness currentflat def +/inverted? +0 currenttransfer exec .5 ge def +/colorexists +systemdict/setcmykcolor known def +/tc1 [0 0 0 1] def +/tc2 [0 0 0 1] def +/fc [0 0 0 1] def +/sc [0 0 0 1] def +/concatprocs{ +/proc2 exch cvlit def/proc1 exch cvlit def +/newproc proc1 length proc2 length add array def +newproc 0 proc1 putinterval newproc proc1 length proc2 putinterval +newproc cvx}bdf +/storerect{/top xdf/right xdf/bottom xdf/left xdf}bdf +/rectpath{newpath left bottom m left top L +right top L right bottom L closepath}bdf +/i{dup 0 eq +{pop df dup} +{dup} ifelse +/clipflatness xdf setflat +}bdf +version cvr 38.0 le +{/setrgbcolor{ +currenttransfer exec 3 1 roll +currenttransfer exec 3 1 roll +currenttransfer exec 3 1 roll +setrgbcolor}bdf}if +/gettint{0 get}bdf +/puttint{0 exch put}bdf +/vms {/vmsv save def} bdf +/vmr {vmsv restore} bdf +/vmrs{vmsv restore /vmsv save def}bdf +/eomode{ +{/filler /eofill load def /clipper /eoclip load def} +{/filler /fill load def /clipper /clip load def} +ifelse +}bdf +/CD{/NF exch def{exch dup/FID ne 1 index/UniqueID ne and{exch NF 3 1 roll put} +{pop pop}ifelse}forall NF}bdf +/MN{1 index length/Len exch def +dup length Len add string dup +Len 4 -1 roll putinterval dup 0 4 -1 roll putinterval}bdf +/RC{4 -1 roll /ourvec xdf 256 string cvs(|______)anchorsearch +{1 index MN cvn/NewN exch def cvn +findfont dup maxlength dict CD dup/FontName NewN put dup +/Encoding ourvec put NewN exch definefont pop}{pop}ifelse}bdf +/RF{dup FontDirectory exch known{pop 3 -1 roll pop}{RC}ifelse}bdf +/FF{dup 256 string cvs(|______)exch MN cvn dup FontDirectory exch known +{exch pop findfont 3 -1 roll pop}{pop dup findfont dup maxlength dict CD dup dup +/Encoding exch /Encoding get 256 array copy 7 -1 roll {3 -1 roll dup 4 -2 roll put}forall put definefont}ifelse}bdf +userdict begin /BDFontDict 20 dict def end +BDFontDict begin +/bu{}def +/bn{}def +/setTxMode{av 70 ge{pop}if pop}def +/gm{m}def +/show{pop}def +/gr{pop}def +/fnt{pop pop pop}def +/fs{pop}def +/fz{pop}def +/lin{pop pop}def +end +/MacVec 256 array def +MacVec 0 /Helvetica findfont +/Encoding get 0 128 getinterval putinterval +MacVec 127 /DEL put MacVec 16#27 /quotesingle put MacVec 16#60 /grave put +/NUL/SOH/STX/ETX/EOT/ENQ/ACK/BEL/BS/HT/LF/VT/FF/CR/SO/SI +/DLE/DC1/DC2/DC3/DC4/NAK/SYN/ETB/CAN/EM/SUB/ESC/FS/GS/RS/US +MacVec 0 32 getinterval astore pop +/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute +/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave +/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute +/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis +/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls +/register/copyright/trademark/acute/dieresis/notequal/AE/Oslash +/infinity/plusminus/lessequal/greaterequal/yen/mu/partialdiff/summation +/product/pi/integral/ordfeminine/ordmasculine/Omega/ae/oslash +/questiondown/exclamdown/logicalnot/radical/florin/approxequal/Delta/guillemotleft +/guillemotright/ellipsis/nbspace/Agrave/Atilde/Otilde/OE/oe +/endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide/lozenge +/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright/fi/fl +/daggerdbl/periodcentered/quotesinglbase/quotedblbase +/perthousand/Acircumflex/Ecircumflex/Aacute +/Edieresis/Egrave/Iacute/Icircumflex/Idieresis/Igrave/Oacute/Ocircumflex +/apple/Ograve/Uacute/Ucircumflex/Ugrave/dotlessi/circumflex/tilde +/macron/breve/dotaccent/ring/cedilla/hungarumlaut/ogonek/caron +MacVec 128 128 getinterval astore pop +/fps{ +currentflat +exch +dup 0 le{pop 1}if +{ +dup setflat 3 index stopped +{1.3 mul dup 3 index gt{pop setflat pop pop stop}if} +{exit} +ifelse +}loop +pop setflat pop pop +}bdf +/fp{100 currentflat fps}bdf +/clipper{clip}bdf +/W{/clipper load 100 clipflatness fps}bdf +/fixtrans1 { +dup{ic mul ic sub 1 add}concatprocs exch +dup{im mul im sub 1 add}concatprocs exch +dup{iy mul iy sub 1 add}concatprocs exch +{ik mul ik sub 1 add}concatprocs +}bdf +/fixtrans2 { +currentcolortransfer +5 -1 roll exch concatprocs 7 1 roll +4 -1 roll exch concatprocs 6 1 roll +3 -1 roll exch concatprocs 5 1 roll +concatprocs 4 1 roll +setcolortransfer +}bdf +end%. FreeHandDict +end%. FHIODict +FHIODict begin +FreeHandDict begin +14.2584 620.3984 377.2584 783.3984 storerect rectpath clip newpath +/onlyk{false}ndf +/ccmyk{dup 5 -1 roll sub 0 max exch}ndf +/setcmykcolor{1 exch sub ccmyk ccmyk ccmyk pop setrgbcolor}ndf +/setcmykcoloroverprint{4{dup -1 eq{pop 0}if 4 1 roll}repeat setcmykcolor}ndf +/findcmykcustomcolor{5 /packedarray where{pop packedarray}{array astore readonly}ifelse}ndf +/setcustomcolor{exch aload pop pop 4{4 index mul 4 1 roll}repeat setcmykcolor pop}ndf +/setseparationgray{1 exch sub dup dup dup setcmykcolor}ndf +/setoverprint{pop}ndf +/currentoverprint false ndf +/colorimage{pop pop +[5 -1 roll/exec cvx 6 -1 roll/exec cvx 7 -1 roll/exec cvx 8 -1 roll/exec cvx +/cmykbufs2gray cvx]cvx image} +version cvr 47.1 le isLino and{userdict begin bdf end}{ndf}ifelse +/cci1 { +currentcolortransfer +{ik mul ik sub 1 add}concatprocs 4 1 roll +{iy mul iy sub 1 add}concatprocs 4 1 roll +{im mul im sub 1 add}concatprocs 4 1 roll +{ic mul ic sub 1 add}concatprocs 4 1 roll +setcolortransfer +}ndf +/cci2 { +{invbuf dup length magentabuf length ne +{dup length dup dup +/magentabuf exch string def +/yellowbuf exch string def +/blackbuf exch string def}if +dup magentabuf copy yellowbuf copy blackbuf copy pop}concatprocs +}ndf +/customcolorimage{colorexists{ +aload pop pop 4 array astore +setimagecmyk +cci1 +/magentabuf 0 string def +/yellowbuf 0 string def +/blackbuf 0 string def +cci2 {magentabuf}{yellowbuf}{blackbuf}true 4 colorimage} +{pop image}ifelse}ndf +/separationimage{image}ndf +/newcmykcustomcolor{6 /packedarray where{pop packedarray}{array astore readonly}ifelse}ndf +/inkoverprint false ndf +/setinkoverprint{pop}ndf +/overprintprocess{pop}ndf +/setspotcolor +{spots exch get 0 5 getinterval exch setcustomcolor}ndf +/currentcolortransfer{currenttransfer dup dup dup}ndf +/setcolortransfer{systemdict begin settransfer end pop pop pop}ndf +/getcmyk { +dup length 4 eq +{aload pop} +{aload pop spots exch get 0 4 getinterval aload pop 4 +{4 index mul 4 1 roll}repeat 5 -1 roll pop} ifelse +}bdf +/setimagecmyk{ +getcmyk/ik xdf /iy xdf /im xdf /ic xdf +}ndf +/autospread{pop}ndf +/fhsetspreadsize{pop}ndf +/strokeopf false def +/fillopf false def +/R{0 ne /strokeopf xdf}bdf +/O{0 ne /fillopf xdf}bdf +/filler{fill}bdf +/F{fc fhsetcolor fillopf setoverprint false autospread +gsave /filler load fp grestore false setoverprint}bdf +/f{closepath F}bdf +/S{sc fhsetcolor strokeopf setoverprint true autospread {stroke}fp false setoverprint}bdf +/s{closepath S}bdf +/B{fc fhsetcolor fillopf setoverprint gsave /filler load fp grestore +sc fhsetcolor strokeopf setoverprint true autospread {stroke}fp false setoverprint}bdf +/b{closepath B}bdf +colorexists not{/setcolorscreen {setscreen pop pop pop pop pop pop pop pop pop}bdf}if +/fhsetcolor{dup length 4 eq +{aload overprintprocess setcmykcolor} +{aload 1 get spots exch get 5 get setinkoverprint setspotcolor} +ifelse +}ndf +/settextcolor{dup fhsetcolor dup length 4 eq +{onlyk{3 get 1.0 eq{true setinkoverprint}if}{pop}ifelse} +{pop} +ifelse +}ndf +/ka{/fc xdf}bdf +/Ka{/sc xdf}bdf +/xa{/fc xdf} bdf +/Xa{/sc xdf} bdf +/bc2[0 0]def +/bc4[0 0 0 0]def +/absmax{2 copy abs exch abs gt{exch}if pop}bdf +/calcstep +{ colorexists not and{calcgraysteps}{maxsteps}ifelse +tc1 length 4 eq +{ +0 1 3 +{tc1 1 index get +tc2 3 -1 roll get +sub +}for +absmax absmax absmax +} +{ +bc2 tc1 1 get 1 exch put +tc1 gettint tc2 gettint +sub abs +} +ifelse +mul abs round dup 0 eq{pop 1}if +dup /numsteps xdf 1 sub dup 0 eq{pop 1}if /numsteps1 xdf +}bdf +/cblend{ +tc1 length 4 eq +{ +0 1 3 +{bc4 exch +tc1 1 index get +tc2 2 index get +1 index sub +frac mul add put +}for bc4 +} +{ +bc2 +tc1 gettint +tc2 gettint +1 index sub +frac mul add +puttint bc2 +} +ifelse +fhsetcolor +}bdf +/logtaper{/frac frac 9 mul 1 add log def}bdf +FHIODict begin +/origmtx matrix currentmatrix def +/iminv false def +/invbuf{0 1 2 index length 1 sub{dup 2 index exch get 255 exch sub 2 index 3 1 roll put}for}bdf +/cyanrp{currentfile cyanbuf readhexstring pop iminv{invbuf}if}def +/magentarp{cyanbuf magentabuf copy}bdf +/yellowrp{cyanbuf yellowbuf copy}bdf +/blackrp{cyanbuf blackbuf copy}bdf +/fixtransfer{ +colorexists +{fixtrans1 fixtrans2} +{{dup 1 exch sub currentgray mul add}concatprocs +currenttransfer exch concatprocs +systemdict begin settransfer end}ifelse +}ndf +/cmykbufs2gray{ +dup length 0 1 3 -1 roll 1 sub +{4 index 1 index get +4 index 2 index get +4 index 3 index get +4 index 4 index get +255 exch sub ccmyk ccmyk ccmyk pop 5 mul exch 45 mul add exch 14 mul add -6 bitshift +2 index 3 1 roll put}for +4 1 roll pop pop pop +}bdf +end +/textopf false def +/curtextmtx{}def +/otw .25 def +/msf{dup/curtextmtx xdf makefont setfont}bdf +/makesetfont/msf load def +/curtextheight{.707104 .707104 curtextmtx dtransform +dup mul exch dup mul add sqrt}bdf +/ta{1 index +{tempstr 0 2 index put tempstr 2 index +gsave exec grestore +tempstr stringwidth rmoveto +5 index eq{6 index 6 index rmoveto}if +3 index 3 index rmoveto +}forall 7{pop}repeat}bdf +/sts{settextcolor textopf setoverprint/ts{awidthshow}def exec false setoverprint}bdf +/stol{setlinewidth settextcolor textopf setoverprint newpath +/ts{{false charpath stroke}ta}def exec false setoverprint}bdf +/currentpacking where{pop false setpacking}if +/spots[1 0 0 0 (Process Cyan) false newcmykcustomcolor +0 1 0 0 (Process Magenta) false newcmykcustomcolor +0 0 1 0 (Process Yellow) false newcmykcustomcolor +0 0 0 1 (Process Black) false newcmykcustomcolor +0 0 0 0 (White) false +newcmykcustomcolor +]def +0 dict dup begin +end +/f0 /Symbol FF def +[] 0 d +3.863708 M +1 w +0 j +0 J +0 O +0 R +0 i +false eomode +[0 0 0 1] Ka +[0 0 0 1] ka +vms +u +u +u +u +u +14.7584 767.5217 m +119.7584 767.5217 L +119.7584 710.5217 L +14.7584 710.5217 L +14.7584 767.5217 L +[0 0 0 0] ka +2 J +b +U +vmrs +MacVec 256 array copy +/f1 /|______Helvetica-Bold dup RF findfont def +{ +f1 [24 0 0 24 0 0] makesetfont +34.258438 731.021698 m +0 0 32 0 0 (client) ts +} +[0 0 0 1] +sts +U +u +271.7584 767.5217 m +376.7584 767.5217 L +376.7584 710.5217 L +271.7584 710.5217 L +271.7584 767.5217 L +[0 0 0 0] ka +2 J +b +U +vmrs +MacVec 256 array copy +/f1 /|______Helvetica-Bold dup RF findfont def +{ +f1 [24 0 0 24 0 0] makesetfont +286.258438 732.021698 m +0 0 32 0 0 (server) ts +} +[0 0 0 1] +sts +u +119.2584 756.0217 m +254.2584 756.0217 L +2 J +S +254.2584 756.0217 m +254.2584 751.0217 L +266.2584 756.0217 L +254.2584 761.0217 L +254.2584 756.0217 L +f +n +U +u +271.2584 721.0217 m +135.2584 721.0217 L +S +135.2584 721.0217 m +135.2584 726.0217 L +123.2584 721.0217 L +135.2584 716.0217 L +135.2584 721.0217 L +f +n +U +u +65.2584 653.0217 m +65.2584 694.0217 L +S +65.2584 694.0217 m +70.2584 694.0217 L +65.2584 706.0217 L +60.2584 694.0217 L +65.2584 694.0217 L +f +n +U +vmrs +MacVec 256 array copy +/f2 /|______Courier-Bold dup RF findfont def +{ +f2 [24 0 0 24 0 0] makesetfont +163.258438 760.021698 m +0 0 32 0 0 (reqs) ts +} +[0 0 0 1] +sts +vmrs +MacVec 256 array copy +/f2 /|______Courier-Bold dup RF findfont def +{ +f2 [24 0 0 24 0 0] makesetfont +158.258438 705.021698 m +0 0 32 0 0 (resps) ts +} +[0 0 0 1] +sts +vmrs +MacVec 256 array copy +/f2 /|______Courier-Bold dup RF findfont def +{ +f2 [24 0 0 24 0 0] makesetfont +38.258438 633.021698 m +0 0 32 0 0 (init) ts +} +[0 0 0 1] +sts +U +U +U +vmr +end % FreeHandDict +end % FHIODict +%%EndDocument + @endspecial 106 967 a(Figure)15 b(1:)20 b(\(a\))14 b(Circular)i(Fib)q +(onacci)h(Sequence)331 b(\(b\))15 b(Serv)o(er/Clien)o(t)h(Sim)o(ulation)0 +1093 y Fq(4)69 b(Case)23 b(Expressions)g(and)h(P)n(attern)f(Matc)n(hing)0 +1215 y Fp(Earlier)c(w)o(e)e(ga)o(v)o(e)g(sev)o(eral)h(examples)h(of)e +(pattern)h(matc)o(hing)g(in)g(de\014ning)i(functions|for)e(example)h +Fi(length)0 1271 y Fp(and)f Fi(fringe)o Fp(.)28 b(In)19 b(this)f(section)g(w) +o(e)g(will)h(lo)q(ok)f(at)g(the)g(pattern-matc)o(hing)f(pro)q(cess)h(in)h(m)o +(uc)o(h)f(greater)f(detail)0 1328 y(\()p Fn(x)p Fp(3.14\).)151 +1311 y 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