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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 31 "Functional Programming in
 Maple" }}}{PARA 3 "" 0 "" {TEXT -1 32 "Lists and higher-order functio
ns" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "n := 7:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "L := [1,2,3,4,5,6,7];" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"LG7)\"\"\"\"\"#\"\"$\"\"%\"\"&\"\"'\"\"(" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "L2 := Array(1..n):\nfor i f
rom 1 to n do\n    L2[i] := L[i]^2;\nend do:\nL2;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%'RTABLEG6%\")O-_5-%'VECTORG6#7)\"\"\"\"\"%\"\"*\"#;\"
#D\"#O\"#\\%&ArrayG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "map(
 x->x^2, L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7)\"\"\"\"\"%\"\"*\"#;
\"#D\"#O\"#\\" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "map( x->10
*x, L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7)\"#5\"#?\"#I\"#S\"#]\"#g
\"#q" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "map( `*`, L, 10);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#7)\"#5\"#?\"#I\"#S\"#]\"#g\"#q" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "g := x -> (y -> x*y);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGf*6#%\"xG6\"6$%)operatorG%&arrow
GF(f*6#%\"yGF(F)F(*&T$\"\"\"9$F1F(F(6$F'F2F(F(F(" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 5 "g(5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#f*6#%
\"yG6\"6$%)operatorG%&arrowGF&*&T$\"\"\"9$F,F&F&6$%\"xG\"\"&" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "map( g(a), L);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#7)%\"aG,$*&\"\"#\"\"\"F$F(F(,$*&\"\"$F(F$F(F(,$*
&\"\"%F(F$F(F(,$*&\"\"&F(F$F(F(,$*&\"\"'F(F$F(F(,$*&\"\"(F(F$F(F(" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "h := x -> y -> exp(I*Pi/2*x*
y) + x^y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hGf*6#%\"xG6\"6$%)ope
ratorG%&arrowGF(f*6#%\"yGF(F)F(,&-%$expG6#**^##\"\"\"\"\"#F6%#PiGF6T$F
69$F6F6)F9F:F6F(F(6$F'F:F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 5 "h(3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#f*6#%\"yG6\"6$%)operat
orG%&arrowGF&,&-%$expG6#**^##\"\"\"\"\"#F1%#PiGF1T$F19$F1F1)F4F5F1F&F&
6$%\"xG\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "map(h(2), L
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7)\"\"\"\"\"&\"\"(\"#<\"#J\"#l\"
$F\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "assume(a,posint);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "expand(h(3)(a));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,&)!\"\",$*(\"\"$\"\"\"\"\"#F%%#a|irGF
)F)F))F(F+F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 
3 "" 0 "" {TEXT -1 18 "Generating objects" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "L := [ seq(i, i=1..n) ];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"LG7)\"\"\"\"\"#\"\"$\"\"%\"\"&\"\"'\"\"(" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "S := \{ seq(i, i=1..n) \};" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"SG<)\"\"\"\"\"#\"\"$\"\"%\"\"&\"
\"'\"\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "L2 := [ seq( i^
2, i=L ) ];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#L2G7)\"\"\"\"\"%\"\"
*\"#;\"#D\"#O\"#\\" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "L3 :=
 [ seq(i, i=1..100) ];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#L3G7`q\"
\"\"\"\"#\"\"$\"\"%\"\"&\"\"'\"\"(\"\")\"\"*\"#5\"#6\"#7\"#8\"#9\"#:\"
#;\"#<\"#=\"#>\"#?\"#@\"#A\"#B\"#C\"#D\"#E\"#F\"#G\"#H\"#I\"#J\"#K\"#L
\"#M\"#N\"#O\"#P\"#Q\"#R\"#S\"#T\"#U\"#V\"#W\"#X\"#Y\"#Z\"#[\"#\\\"#]
\"#^\"#_\"#`\"#a\"#b\"#c\"#d\"#e\"#f\"#g\"#h\"#i\"#j\"#k\"#l\"#m\"#n\"
#o\"#p\"#q\"#r\"#s\"#t\"#u\"#v\"#w\"#x\"#y\"#z\"#!)\"#\")\"##)\"#$)\"#
%)\"#&)\"#')\"#()\"#))\"#*)\"#!*\"#\"*\"##*\"#$*\"#%*\"#&*\"#'*\"#(*\"
#)*\"#**\"$+\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "add( x, x
=L3 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"%]]" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 23 "add( x^2-10*x+5, x=L3);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"']$)G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "p
 := add( (i-5)*y^i, i=L );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG,.
*&\"\"%\"\"\"%\"yGF(!\"\"*&\"\"$F()F)\"\"#F(F**&F.F()F)F,F(F**$)F)F'F(
F**$)F)\"\"'F(F(*&F.F()F)\"\"(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "map( g(4), p );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,.
*&\"#;\"\"\"%\"yGF&!\"\"*&\"#7F&)F'\"\"#F&F(*&\"\")F&)F'\"\"$F&F(*&\"
\"%F&)F'F2F&F(*&F2F&)F'\"\"'F&F&*&F.F&)F'\"\"(F&F&" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 45 "mygen := (f, len) -> [ seq(f(i), i=1..len) \+
];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&mygenGf*6$%\"fG%$lenG6\"6$%)o
peratorG%&arrowGF)7#-%$seqG6$-9$6#%\"iG/F4;\"\"\"9%F)F)F)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "mygen( x->max((x-5)^2,x), 10);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#7,\"#;\"\"*\"\"%F&\"\"&\"\"'\"\"(F%F$
\"#D" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 0 "" }}}{PARA 3 "" 0 "" 
{TEXT -1 19 "Map and its friends" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 18 "map( isprime, L3);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7`q%&fal
seG%%trueGF%F$F%F$F%F$F$F$F%F$F%F$F$F$F%F$F%F$F$F$F%F$F$F$F$F$F%F$F%F$
F$F$F$F$F%F$F$F$F%F$F%F$F$F$F%F$F$F$F$F$F%F$F$F$F$F$F%F$F%F$F$F$F$F$F%
F$F$F$F%F$F%F$F$F$F$F$F%F$F$F$F%F$F$F$F$F$F%F$F$F$F$F$F$F$F%F$F$F$" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "select(isprime, L3);" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#7;\"\"#\"\"$\"\"&\"\"(\"#6\"#8\"#<\"#>
\"#B\"#H\"#J\"#P\"#T\"#V\"#Z\"#`\"#f\"#h\"#n\"#r\"#t\"#z\"#$)\"#*)\"#(
*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "L3[85..100];" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#72\"#&)\"#')\"#()\"#))\"#*)\"#!*\"#\"*\"##*
\"#$*\"#%*\"#&*\"#'*\"#(*\"#)*\"#**\"$+\"" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 51 "Complicated programs without assignment, nor loops:" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "map(ifactor, remove(isprime, [seq(i
, i=85..100)]));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#70*&-%!G6#\"\"&\"
\"\"-F&6#\"#<F)*&-F&6#\"\"#F)-F&6#\"#VF)*&-F&6#\"\"$F)-F&6#\"#HF)*&)F.
F7F)-F&6#\"#6F)*(F.F))F5F0F)F%F)*&-F&6#\"\"(F)-F&6#\"#8F)*&)F.F0F)-F&6
#\"#BF)*&F5F)-F&6#\"#JF)*&F.F)-F&6#\"#ZF)*&F%F)-F&6#\"#>F)*&)F.F(F)F5F
)*&F.F))FCF0F)*&FAF)F=F)*&FJF))F%F0F)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 42 "map( x -> `if`(isprime(x), x+1, x-1), L3);" }}{PARA 
12 "" 1 "" {XPPMATH 20 "6#7`q\"\"!\"\"$\"\"%F%\"\"'\"\"&\"\")\"\"(F)\"
\"*\"#7\"#6\"#9\"#8F.\"#:\"#=\"#<\"#?\"#>F3\"#@\"#C\"#BF6\"#D\"#E\"#F
\"#I\"#H\"#K\"#JF=\"#L\"#M\"#N\"#Q\"#PFB\"#R\"#U\"#T\"#W\"#VFG\"#X\"#[
\"#ZFJ\"#\\\"#]\"#^\"#a\"#`FO\"#b\"#c\"#d\"#g\"#f\"#i\"#hFV\"#j\"#k\"#
l\"#o\"#nFen\"#p\"#s\"#r\"#u\"#tFjn\"#v\"#w\"#x\"#!)\"#zF_o\"#\")\"#%)
\"#$)Fbo\"#&)\"#')\"#()\"#!*\"#*)Fgo\"#\"*\"##*\"#$*\"#%*\"#&*\"#)*\"#
(*F^p\"#**" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "Twin primes" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "select(x->isprime(x+2),select(ispri
me,L3));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7*\"\"$\"\"&\"#6\"#<\"#H\"
#T\"#f\"#r" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "L4 := mygen(g
(2),10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#L4G7,\"\"#\"\"%\"\"'\"
\")\"#5\"#7\"#9\"#;\"#=\"#?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
25 "L5 := mygen(x->2*x-1,10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#L5
G7,\"\"\"\"\"$\"\"&\"\"(\"\"*\"#6\"#8\"#:\"#<\"#>" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 25 "add(i,i=L4), add(i,i=L5);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6$\"$5\"\"$+\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 26 "zip( (x,y)->x-y, L4, L5 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7,
\"\"\"F$F$F$F$F$F$F$F$F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 
"L6 := zip(`*`, L4, L5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#L6G7,\"
\"#\"#7\"#I\"#c\"#!*\"$K\"\"$#=\"$S#\"$1$\"$!Q" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 38 "zip( `-`, L6, mygen(x->4*x^2-2*x,10));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#7,\"\"!F$F$F$F$F$F$F$F$F$" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "p;" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#,.*&\"\"%\"\"\"%\"yGF&!\"\"*&\"\"$F&)F'\"\"#F&F(*&F,F&)F'F*F&F(*$)F'
F%F&F(*$)F'\"\"'F&F&*&F,F&)F'\"\"(F&F&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "expand( p^3 );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,H*
&\"\"'\"\"\")%\"yG\"#>F&F&*&\"#7F&)F(\"#?F&F&*&\"#kF&)F(\"\"$F&!\"\"*&
\"$W\"F&)F(\"\"%F&F2*&\"$/#F&)F(\"\"&F&F2*&\"$>#F&)F(F%F&F2*&\"$u\"F&)
F(\"\"(F&F2*&\"#jF&)F(\"\")F&F2*&\"$7\"F&)F(\"\"*F&F&*&\"$)>F&)F(\"#5F
&F&*&F8F&)F(\"#6F&F&*&\"$\\\"F&)F(F+F&F&*&\"#gF&)F(\"#8F&F&*&\"#IF&)F(
\"#9F&F2*&\"#%)F&)F(\"#:F&F2*&FCF&)F(\"#;F&F2*&\"#OF&)F(\"#<F&F2*&FPF&
)F(\"#=F&F2*&FEF&)F(\"#@F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 8 "nops(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#>" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "f1 := unapply( p, y );" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%#f1Gf*6#%\"yG6\"6$%)operatorG%&arrowGF(,.*&\"
\"%\"\"\"9$F/!\"\"*&\"\"$F/)F0\"\"#F/F1*&F5F/)F0F3F/F1*$)F0F.F/F1*$)F0
\"\"'F/F/*&F5F/)F0\"\"(F/F/F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 35 "f2 := unapply( expand( p^21 ), y ):" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 12 "nops(f2(y));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"$F\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "f2(
0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 6 "f2(1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!32SG$3
keae&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "f1(5)^21-f2(5);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 44 "h := unapply(mygen(x->mygen(z->y^z,x),5),y);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hGf*6#%\"yG6\"6$%)operatorG%&arrow
GF(7'7#9$7$F.*$)F.\"\"#\"\"\"7%F.F0*$)F.\"\"$F37&F.F0F5*$)F.\"\"%F37'F
.F0F5F9*$)F.\"\"&F3F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 
"h(3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7'7#\"\"$7$F%\"\"*7%F%F'\"#F
7&F%F'F)\"#\")7'F%F'F)F+\"$V#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 24 "map(x->add(i,i=x),h(3));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7'\"
\"$\"#7\"#R\"$?\"\"$j$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "Of cour
se it doesn't have to be that complicated:" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 38 "(y->[seq(add(y^j,j=1..i),i=1..5)])(3);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#7'\"\"$\"#7\"#R\"$?\"\"$j$" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 48 "sel_gen := f -> g -> n -> select(f, mygen(g,n
));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(sel_genGf*6#%\"fG6\"6$%)oper
atorG%&arrowGF(f*6#%\"gGF(F)F(f*6#%\"nGF(F)F(-%'selectG6$T$-%&mygenG6$
T&9$F(F(6&F'F5F.F:F(F(6$F'F:F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 31 "sel_gen(isprime)(x->2*x-1)(20);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7-\"\"$\"\"&\"\"(\"#6\"#8\"#<\"#>\"#B\"#H\"#J\"#P" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "map(unapply, map2( `^`, x, %
 ), x );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7-f*6#%\"xG6\"6$%)operator
G%&arrowGF'*$)9$\"\"$\"\"\"F'F'F'f*F%F'F(F'*$)F-\"\"&F/F'F'F'f*F%F'F(F
'*$)F-\"\"(F/F'F'F'f*F%F'F(F'*$)F-\"#6F/F'F'F'f*F%F'F(F'*$)F-\"#8F/F'F
'F'f*F%F'F(F'*$)F-\"#<F/F'F'F'f*F%F'F(F'*$)F-\"#>F/F'F'F'f*F%F'F(F'*$)
F-\"#BF/F'F'F'f*F%F'F(F'*$)F-\"#HF/F'F'F'f*F%F'F(F'*$)F-\"#JF/F'F'F'f*
F%F'F(F'*$)F-\"#PF/F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 
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