 1. (1 ). ip㢠 ii i  p祭i, p㣠 ip 直
pi i. H 㭪i (CALPA sentence letter).
Hp, (CALPHA "This is a house and this is an ass" s) p 3.


 2. (1 ).  ᯨ᮪ lst  n ᥫ (a1,a2,...,an). H 㭪i
(FINDN lst), 直 p ᯨ᮪ (b1,b2,...,bn),  b1 - 㬠  ᥫ,
b2 - 㬠 i  , b3 - 㬠 i  3,...,bn - 㬠 i
 n ( i᭮i bn  ⪮ i ᥫ)). ᫥ p p⠢
 ii pi   .
Hp, (FINDN '(1 2 3 4)) = (10 35 50 24), ⮬ 
10 = 1+2+3+4,
35 = 1*2+1*3+1*4+2*3+2*4+3*4
50 = 1*2*3 + 1*2*4 + 1*3*4 + 2*3*4
24 = 1*2*3*4

  i. 稬 p Sn1  n p ᥫ a1+...+an, p Snk - 
  i  k . i  i ᫨ S21 = a1 + a2,
S22 = a1*a2, S31 = S21 + a3, S32 = S22 + S21*a3, S33 = S22*a3 i i,
Sn1 = S(n-1)1 + an, Snk = S(n-1)k + Sn(k-1)*an ( 1<k<n), 
Snn = S(n-1)(n-1)*an.

  p⮢ 楩 p,  p'離 i  
1+2+...+(n-1) = n*(n-1)/2 pi   ⠪  ii .

  H p  p  ii, p㢠 i
᫥ 㯭 稭:
S11
 + *
S21  S22
 + *  +
S31  S32  S33
 + *  + *  + *
S41  S42  S43  S44
 i ⠪ i

   p i⪠ ᫥ 㢠⨬ :

1
3  2
6  11  6
10 35  50  24


 3. ( , 1,5 ). ஫  i᫠ ਬ쪮 
i i,  类 i ᫠, ᠭi ࠡ쪨 
ࠬ.  㭪i (INVERT lst),  lst - ᯨ᮪ p쪨 ᥫ, 
猪  i pi i 宬 ॢ i ᥫ 
 ਬ ⥬ ᫥. ( ii pi  i 
ii ᫠  ii  4000). 쪠 ⥬ ᫥ ᭮  
p⠭i 㯭 ᨬi  ⪮ ஧i:
     I   V   X    L    C    D    M
     1   5   10   50   100  500  1000

i: ࠫi ᫠,  ii  3999,   i ⥬i 
᫥   ७  .  쮬    
। i,   ii  i. ⠭ ࠢ ᮢ
  i p ७ i i i  . 
稭, I, X, C ⠢ ii । X,C,M  祭 ᥫ 9,90,900  
।  V,L,D  祭 ᥫ 4,40,400.   㤮i ᫠  ਬi 
⥬i ᫥   p ࠢ ii, ਭ ᫠ IX,XL, ...
  . 


 4. ( , 1,5 ). ᫠ ii U[1], U[2],  ...  
 ⪮ 祭ﬨ  ii襭ﬨ:
               U[1] = 1 ; U[2] = 2
               U[N] = U[N-1] + U[N-2]
  ﭥ ⥬ ᫥   ࠬ 0  1,  i  ii
i i ⥬    ⥯i i 1,2,4,8,16,...,  ᫠ 
ii 1,2,3,5,8,13...  .  i ⥬i ᫥   i ᫮
󤨭 稭 ।⠢  i p浪  㫥  , 猪
稭  1   i   , i  p.
   i p浪, i ।⠢ ᫠ A  B.  p冷, 直
।⠢ ᫮ A+B.  pi p ᠭ 㭪i
(ADD_FIBON A B).
  ਪ. ii p浪 "10101"  "100" ।⠢ ᫠ 8+3+1=12  3. 
ii  p冷 "100010", 直 ।⠢ ᫮ 13+2=15 = 12+3.
(ADD_FIBON "10101" "100") p "100010".

i:  祭:
     ) -᫮ 㤥  ᫮, ᠭ  ⥬i ᫥ 
᭮ ii;
     )  i ᫠  ip ,   -᫮;
     ) i-⨬ ஧冷 -᫠ 㤥  , i ii
 U [i].

  㤥    ᫠  ⮢稪.  쮣 i i
 쮣 ᫠  p  쮣. ஡  쮣 ,
直  ᫠  ⥬i ᫥ ii  U [n]= 10...(n-1 㫥). 
 i  ii ii ⥬i ᫥,  i襭 类 
   ࠢ  ᫠ (ਪ,  i  10),  
p ⥬ ७i.  pi,   ⥬i ᫥ 猪
p鸞, i  ࠢ ७:
     U [n] + U [n-1] --> U [n+1] -  ࠢ ७
     2 * U [n]       --> U [n+1] + U [n-2] - p㣥 ࠢ
  ⠭  i ⮬  
     2 * U [n] = U [n]  +  U  [n-1]  +  U[n-2] = U [n+1] + U [n-2].
   稭, ७  i㢠   訩 ஧, ⠪ i  
訩, i ⠪   i ७.

ﭥ pi p.
  10101
+   100
 p㣥 p  p쮣 pp:
  10001
+  1001
 p㣥 p  p讣 pp  p p  ⢥p⮣ 
 '⮣ ppi:
 100010
 i  ii.

   ⠭:
  1)  ७ த i ७,   i祭   
?
  2) ﭥ  ....10 + 10 (  ....1 + 1).
i 㢠 p㭥 ࠢ, i쪨 ७i   ஭ 
i᭨ .  pi  ᫠  ii  ࠬ -1  0:
U[0]=1  U[-1]=0.  ७i  쮢 ஧   ७ᮬ 
 訩,  ७i  i 訩 ஧ ip㢠.

,  p   i祭 ( 横).


 5. ( , 1,5 ) ५i i ii  n i
ᥫ 1..k  ⠪ 浪, 鮡  㯭 ipi﫠 i p
 󤨭i i, 箬  i, i  1.

  i: ﭥ אַ  ਭ n   k.  i
⨪i 㤥  誠.  稭,  襪 ii
i i ᥫ  1..k  n (s- 童 ii ii
i 誨  s-i ਧ⠫i).  i i  i,
猪   ࠢ p  .  i 誨 ⠢  
ਧ⠫ i p. i p 誨  ⠪ ࠢ:  ᠬ
ࠢ ,   p  שׁ (쮢  i) ii, 
p    i⨭  쮬 שׁ,  i 誨,   pi
i  ( i諨  ) ஧p  180 pi.
  pi,    pi   誠 㢠, ⮡  童
ii i  1.  ii  n,  室 i 
ii i ᥫ 1...k. 
   n = 1 祢. H堩 n > 1. i p i  i,  p
⠭ 誠, i i,  p  ⠭.  p㣮  ⠭ 誠
  i, i   , ⠪    p p㣮 ⨯
i k-1 pi 讣 ⨯,   直 ⠭ 誠 㢠  i i⨭.
  ⥯ 㤥 p ⠭ ,  p  n-1  p饭
ii ஡i i ii  n-1   ࠧ; p
⠭ 誨 i  ii  n-1 p k i⥩
 n.
   ணࠬi pi ii x[1]...x[n],  ⢮p ᨢ d[1]...d[n]
i ᥫ +1  -1 (+1 ii ii p, -1 - i ).
⪮ ⠭: x[1] =...= x[n] = 1; d[1] =...= d[n] = 1.

   i⥩ 㫥    i訩 ஧'燐, 直 
㤥 p⮢㢠 i ⥬. ( i ' i 
" ".)
  襬 i i ᫠ i 0  (2  ⥯i n) - 1  ii ⥬i.
ਪ,  n = 3 襬:
            000 001 010 011 100 101 110 111
i  i ᥫ i ⢮p, i  , i ,
    p  ( 㫥 2).  ᫮
     a[1], a[2],...,a[n]  ⢮p 
     a[1], a[1] + a[2], a[2] + a[3],...,a[n-1] + a[n]
(㬠  㫥 2).  n=3 p:
            000 001 011 010  110  111 101 100.
   ॢi,  ᠭ ⢮p ᥫ  p (i ⨬ ᠬ 
p i ii   ࠧ). pi ⮣, ii  ii
ᥫ ipi i i 011...1  i 100...0,   -  i
⢮p - ਢ  i 󤨭 .


 6. ( , 1,5 )  ࠫi ᫠ N  K. Hi 
 ࠧ, 直  K^N.  p㢠 iﬨ *   
^ (iᥭ  ⥯), 㣫 㦪  i K. p 
 pi ii.    i, iᥭ  
⥯ Q  Q-1 i.  ii ii i  
 N.
  Hp:  N=5 -  i: (K*K)^2*K
H 㭪i (OP N) - ii쭠 ii i  iᥭ 
N- ⥯i.

  i:  iᥭ   ⥯i ᠣ 0 i (p  
 K), ⮬ OP(1)=0. 稭  N=2, 㤥   i訬 
童 ii OP(N), pi i  ip客i 祭  ᯨ.
   ᫥i ࠧ,   N- ⥯i ᫠ K, 䬥i i
ᮢ  i ii ii  ਮ ( ^ 
࠭i, i * ) ஧⠢ 㦮. ﭥ  ⠭ i.
  ) .   ࠫi ⥯i ᫠ K, i  i   N.
⥯i  i i   N i  i   ii 
ii i   p. ⦥  ⠭ i  ,
K^N  ᫨ ii 
      OP1(N) = min {  i p: 1<=p<N: OP(p)+OP(N-p)+1 }
i.
  )   iᥭ  ⥯i,  i ࠭  猪 ⥯i ᫠ K,
猪  i  ࠢ ࠭ - ࠫ쭥 ᫮,  N. ⦥ 
⠭i i iᥭ  ⥯i, K^N  ᫨ ii 
    OP2(N) = min {  i r<>1 i쭨i N: OP(N/r)+r-1 }
i.
    OP(N) = min { OP1(N), OP2(N) }.



  ⨦ ᠬi p ( p'離i)

1. (3 ). 㭪i f 祭  i i ⭨ ᥫ  i
㯭 㬮:
  f(1)=1, f(3)=3, f(2*n) = f(n),
  f(4*n+1) = 2*f(2*n+1) - f(n),
  f(4*n+3) = 3*f(2*n+1) - 2*f(n).
H 㭪i (FTASK n), 猪 室 ⠪ ii 祭 k, 1<=k<=n,
 直 f(k)=k   ᮢ i. ᫨  i.

2. (3 ). p㢠 i ⠭ ᥫ 1..n ⠪, 鮡  㯭
p㢠 i p ⠭ (࠭ᯮi)  ii ᥫ.
ਪ,  n = 3  ⠪ 冷: 
3.2 1 -> 2 3.1 -> 2.1 3 -> 1 2.3 -> -> 1.3 2 -> 3 1 2 
(i ᫠  p⠢, ⠢i p).

  i: p⠩ ⥮pi i p (.  5).



த i୨ 'i.

1. 㢠 i ii  n   0,1. (P1 n).

㭪i P1    㬥⮬ n, 㬥 lst - i.

(DEFUN p1 (n lst)				(DEFUN p3 (n lst)
((ZEROP n) (PRIN1 lst) (TERPRI))		((ZEROP n) (PRN3 lst) (TERPRI))
(P1 (- n 1) (CONS 0 lst))			(P3 (- n 1) (CONS 0 lst))
(P1 (- n 1) (CONS 1 lst))  )			(P3 (- n 1) (CONS 1 lst))  )


2. 㢠 i ii  k  ᥫ 1..n. (P2 k n).
㢠⨬ ii  ᨪi筮 浪.   㭪i 
(GEN1 n)  ᯨ᮪  n i,   直 i 1. ᮪ lst
i⨬  ⠭. 㭪i (NEXT lst n) 室 ⠭, 
猪 㤥 㯭 i lst. 㭪i P2BEST  騬 ४ᨢ 
஧'離 i i.

(DEFUN GEN1 n)			(DEFUN NEXT (lst n)
((ZEROP n) NIL)			((< (CAR lst) n) (CONS (+ (CAR lst) 1) (CDR lst)))
(CONS 1 (GEN1 (- n 1)))  )	((NULL (CDR lst)) NIL)
				(CONS 1 (NEXT (CDR lst) n))

㪠 㭪i  :		(DEFUN P2BEST (n k lst c)
(DEFUN P2 k n)				((ZEROP n) (PRIN1 lst) (TERPRI))
(SETQ lst (GEN1 k))			(PUSH 1 c)
(LOOP					(LOOP
   ((< (LENGTH lst) k))				((> (CAR c) k))
   (PRIN1 lst) (TERPRI)				(P2BEST (- n 1) k (CONS (CAR c) lst) c)
   (SETQ lst (NEXT lst n))			(SETQ c (CONS (+ 1 (CAR c)) (CDR c)))
)  )					) (POP c)  )


3. 㢠 i i  {1..n}.  (P3 n).

i쪨 i i -类  {1..n} ॡ㢠  󬭮 
i iii i i iﬨ  0  1  n,   
   i 1. 㭪i (P3 n)  . i쪨 i 
 ᯨ  0  1 i   i i ᯨ, i 
i 1. 㭪i (PRN3 lst)  ii  i.

(DEFUN PRN3 (lst)
(SETQ i 0)
(LOOP
   ((NULL lst))
   (INCQ i)
   (IF (= 1 (POP lst)) (PROGN (PRIN1 i) (SPACES 1)))
)  )

4.  ⠭ (1 2 3 ... n )  i ਬ ⠭ (n ... 2 1) 
  ii பi. ப 㤥  i iﬨ i쭨 
 ii ᥫ. ਪ,  ⠭ (1 3 4 2)  ਬ   
㯭: (3 1 4 2), (1 4 3 2), (1 3 2 4). 
堩 lst - 筠 ⠭. 襬 ,  直 㤥 室 
㯭 ⠭.  쮣, ॣ鸞 ᯨ᮪ lst i ࠢ, 
 ⠪i  ᫠  室 ,     㣥. 
i  iﬨ  祬 ४ᨢ 㭪i move_per  ਬ 
ᯨ᪮.

(defun move_per (lst)
(prin1 lst) (terpri 1)
(SETQ cur NIL)
(LOOP
  ((ATOM (CDR lst)))
  ((< (CAR lst) (CADR lst)) (SETQ a (POP lst))
                            (SETQ b (POP lst))
                            (PUSH a lst)
                            (PUSH b lst)
                            (SETQ lst (APPEND (REVERSE cur) lst))
                            (move_per lst)  )
  (PUSH (POP lst) cur)
)   )



i 㭪i

᫥ ࠧi  ୥  㭪i i㢠 ⮬筮 
i஬ muLisp. i 㭪i ii     
i । ᫨ ࠧ    㭪i. 祭 
㭪i  ᯨ᮪, 直 ᪫   ⨭: ii ⨯ 㭪i, 
ଠ쭨 ࠬi  i 㭪i.
CAR-⮬ 祭 㭪i  i' ⨯ i - LAMBDA, NLAMBDA  MACRO. 
 㭪i  i஢i iଠi  ,  ⮢㢠  
㭪i.

祭 㭪i   ᫥  ii ᭮  ﬡ-᫥i . 
ﬡ ࠧ, 直   ﬡ ᫥,   堭i  
ணࠬ㢠i.  ﬡ ᫥i  㭪i   i:
lambda (x1, x2, ..., xn) . f

 ii ﬡ ࠧ  :
(LAMBDA (x1 x2 ... xn) f)

 LAMBDA    祭 㭪i.  xi -  ଠi 
ࠬ, f - i 㭪i. i 㭪i   i쭠 ଠ, 祭 
类  ᫨ i iᯠ. 㭪i, 猪   i 
 ᥫ,   ⠪:
(LAMBDA (x y) (+ (* x x) (* y y)) )

ଠi ࠬi   ,    i   ii ᨬ,
 i 쮣  i i ᫥ 㭪i.
ﬡ ࠧ -  祭 ᫥  ࠬi 㭪i  ⮬ i
 䠪筨 ࠬi  㬥i.  㢠 ⠪ 㭪i  
 㬥i, i ⠢ ﬡ ࠧ  i ii 㭪i:
(ﬡ-ࠧ a1 a2 ... an)
 ai - ନ,   䠪i ࠬ. ਪ,  (* 3 4) 
   ⠭ ﬡ :

$ ((LAMBDA (x y) (* x y)) 3 4)
12

㯭   ᯨ᮪   㬥i:
$ ((LAMBDA (x y) (CONS x (CONS y NIL))) 'dog 'cat)
(dog cat)

    ﬡ . ᫥ ﬡ  
i㢠   ⠯.   祭 䠪筨 ࠬi 
 iii ଠi ࠬ '  ਬ 祭ﬨ.  
㣮 ⠯i  ଠ, 猪  i ﬡ ࠧ. ਬ 祭 
  类i 祭 ﬡ .  襭 ᫥ 
ଠ쭨 ࠬࠬ  '離 , i i㢠  ﬡ . 
 楩   ﬡ ⢮७.

'⠩,  ﬡ ࠧ  䠪筨 ࠬi   祭,   
ଠ,   ᫨.   ᮡi ﬡ ࠧ i஬  
਩.   : (LAMBDA (x y) (CONS x (CONS y NIL))),  
i i  i  .

ﬡ ࠧ    ࠪ⭨ 堭i  祭   
᫥, ⠪ i 堭i  '㢠 ଠ쭨  䠪筨 
ࠬi i   ᫥. ﬡ ࠧ  㭪i  ii.

  ਫ  ,    㭪i -   i᭨  
 㭪i DEFUN. 祭 㭪i  ⠪:

(DEFUN <i'> <ﬡ ࠧ>)

 饭 ⨬ ii 㦪  ﬡ ࠧi  ᠬ ⮬ LAMBDA. i
 ਬ   祭 㭪i. 㯭i 祭 ii:

(DEFUN list2 (LAMBDA (x y) (CONS x (CONS y NIL))))
 
(DEFUN list2         (x y) (CONS x (CONS y NIL)))

㭪i DEFUN ' ᨬ  ﬡ ࠧ, i 箣 ᨬ 稭 
i㢠 ᫥, 瘟  ﬡ ࠧ. 祭 㭪i 
DEFUN  i'  㭪i.

   LET, 猪 祭  common.lsp,  ⢮ 
쭨 '. 祭 i ନ LET ᢮ ᭮.  
  㯭 :

(LET ((m1 a1) (m2 a2) ... (mN aN)) <ଠ1> <ଠ2> ... <ଠN>),
猪  i᭮i  ﬡ ,  ଠi  䠪i ࠬ 
室 ࠧ   :

((LAMBDA (m1 m2 ... mN) <ଠ1> <ଠ2> ... <ଠN>) a1 a2 ... aN)

㯭i  ii:

$ (LET ((x 4)(y 2))(+ x y))	$ ((LAMBDA (x y) (+ x y)) 4 2)
6				6

㭪i ⨯ NLAMBDA  .   
 㭪i,   㬥 ।  ᫥ - ⠪,  
   浪 . ᭨   ਪi. 稬 i 㭪i f1 
 f2, i  訩  i:

(DEFUN f1 (LAMBDA (x y)		(DEFUN f2 (NLAMBDA (x y)
(+ x y)) )			(+ x y)) )

   (f1 5 6)  (f2 5 6),  १ 㤥  - 11.
堩 i k  l ᢮i i 祭: (SETQ k 5 l 6). i

$ (f1 k l)	$ (f2 k l)
11		: (+ k l)  /   (+ 5 6), i쪨 ।i 㬥  ᫥i /

㭪i ⨯ MACRO  -㭪i.   㦭 ஡稬 
i㬥⮬ ணࠬ㢠. ⠪ 祭  鸞 ⠪  
稭  ᨭ⠪ 祭 㭪i ନ DEFUN:
(DEFMACRO <i'> <ﬡ ᯨ᮪> <i>)

  i  ମ   㭪,   ᫥ 
ii i ᫥  㭪i.  i   
㬥. ᫥   ᪫   i ⠯i. 
 i㢠 ᫥ i  㬥⠬ ( i  㭪i).  
⠯  ஧७  ஧ .  㣮 ⠯i 
 ஧ ଠ, 祭 类   类i 祭 
쮣 ஢. 稬  PUSH1, 直   i  㭪i 
PUSH ( i᭮i PUSH  ⮢  । i ᮬ).

$ (DEFMACRO PUSH1 (x y)			$ (SETQ 'a '(1 2 3)) (PUSH1 6 'a)
(LIST 'SETQ y (LIST 'CONS x y)))	i 箣 a = (6 1 2 3)

稬  㭪i P, i 类   PUSH1:

(DEFUN p (x y)
(PUSH1 x y))

    (GETD p)  , 直   㭪 p:
(LAMBDA (X Y) (SETQ Y (CONS X Y)))

 ணࠬ㢠i ஧⮣    , ⮬   㢠 
i ᯥi쭠 㭪i - MACROEXPAND, 猪 i i쪨 ஧ . 
 ஧७ , 瘟  .

$ (MACROEXPAND '(PUSH1 6 s))
(SETQ S (CONS 6 S))

CADR-⮬ 祭 㭪i   ᯨ᮪ ଠ쭨 㬥i,  i' 
ଠ쭮 㬥. 㭪i, 猪 祭   ᯨ ଠ쭨 
㬥i,  ⮬ i i ஦쮣,  ஧.   
⠪ 㭪i 䠪i 㬥 ਢ' ii  ଠ쭨 
㬥i.

㭪i, 猪 祭   ii ଠ쭮 㬥,  
஧.   ⠪ 㭪i, ᯨ᮪ 䠪筨 㬥i 
'  i ଠ쭮 㬥. ⦥ ஧i 㭪i 
᪠ -i i 䠪筨 㬥i.

CDDR-⮬ 祭 㭪i  ᯨ᮪ , 直  i 
㭪i. i ⮣  ଠi 㬥 㭪i 㫨 ਢ'易i   
䠪筨, 稭   㭪i PROGN, 猪  i 㭪i.
i ᫥ i 㭪i ଠi 㬥  ਩ ᢮ ii 
祭,  १ ᫥ i 㭪i   祭 㭪i.


1. FUNCALL (<㭪i> <arg1> <arg2> ... <argN>)
 i 㭪i <㭪i>  㬥⠬   १. 
<㭪i>    i  㭪i,  i LAMBDA. 
 <㭪i> -  i'   祭 㭪i,  ਢ 
 i <祭 㭪i>.

$ (FUNCALL 'CONS 'a '(b c d))           $ (FUNCALL '(LAMBDA (n) (* n n)) 5)
(a b c d)                               25


2. EVAL <'>

I iᯠ  EVAL,    i ii 㭪i   
ணࠬ.  砩i ஡i i    ॡ, i쪨 
   i .   i   䥪 
㢠 (QUOTE),    祭 ࠧ. EVAL -  
iᠫ쭠 㭪i iᯠ, 猪  ᫨ i쭨 ࠢ쭮 㤮 
iᯮ쪨 ࠧ.

 ' - ⮬, 㭪i  i iન 祭 '. 

 CAR- '  i  㭪i  LAMBDA, 㭪i 
   CDR-⨭ ' i  CAR- '  
ᯨ १i. 

 CAR- '  i  㭪i, EVAL  
CAR- '  CDR- '  ᫥ ⠭쮣.

 CAR- '  㭪i, EVAL ४ᨢ  १ 
 CAR- '   CDR-.

 CAR- '   㭪i, EVAL   "祭
㭪i"   ਢ  i.

$ (SETQ a 'b b 'c)	$ (EVAL '(CONS 'A '(B C)))	 $ (EVAL '(PRIN1 '(a b c)))
$ (EVAL a)		(A B C)			  	 (a b c) (a b c)
c

$ (DEFUN a (n)		$ (EVAL '(a 3))		$ (EVAL (LAMBDA (n) (* n n)) 7)
(+ n 2)  )		5			49

i  i஬ iᯠ  쮬 () ii   
⨬ 横:

(SETQ e (READ))		 ࠧ
(SETQ v (EVAL e))	᫥ ࠧ
(PRINT v)		 १

 i i 쭮 㭪i    㭪i 
EVAL  ᫥ 㬥i.

(DEFUN f3 (NLAMBDA (x y)		(SETQ k 5 l 6)	(f3 k l)
(+ (EVAL x) (EVAL y))) )				11


3. CONSTANTP <'>

'  ⠭ ⮤i i i쪨 ⮤i,  (EVAL <'>)  <'>.
 NIL, ᫠  ᯨ᪨,  直 CAR-  ᨬ QUOTE,  muLisp  
⠭⠬.  <'> - ⠭, 㭪i CONSTANTP  , 
i - NIL.

$ (CONSTANTP ())	$ (CONSTANTP 23.543)	(DEFUN CONSTANTP (obj)
T			T			((NULL obj))
$ (CONSTANTP 'v)	$ (CONSTANTP '(a b c))	((NUMBERP obj))
NIL			NIL			((ATOM obj) NIL)
$ (CONSTANTP '(QUOTE (a b c)))			(EQ (CAR obj) 'QUOTE)  )
T


4. APPLY <㭪i> <1> <2> ... <-ᯨ᮪>

ᮢ 㭪i  ᯨ 㬥i. (APPLY f x1 x2 ... xN) i⭮ 
(f  x1 x2 ... xN). ⠭ 㭪i APPLY  i 窨  iﭭi  
ﬨ  㭪i. i  i 㭪i FUNCALL, i쪨 㬥 㭪i 
਩  ६,  ᯨ᪮.

 㭪i - i' 祭 㢠祬 㭪i  i LAMBDA, APPLY 
' ଠi 㬥 㭪i  䠪筨 㬥⠬,  i 
㭪i, i⢮ ii 祭 ଠ쭨 㬥i i  祭 
᫥ i 㭪i.

 㭪i -  i' 㭪i i  i LAMBDA, APPLY  ਢ  
i "祭 㭪i".

$ (APPLY 'CONS '(a (b c d)))		$ (SETQ z '(LAMBDA (n) (* n n)))
(a b c d)				$ (APPLY z '(4))
16


5. UNDEFINED <ᨬ> <ଠ1> ... <ଠN>

 㭪i iii ਢ  i "祭 㭪i".  㭪i 
㢠  ⮢ ⮤i,   ᫨ , 
CAR- 类  ᨬ, 直   祭 㭪i.





1. (PL1 lst1 lst2),  lst1 - ᯨ᮪  n ᥫ, lst2 - ᯨ᮪  n - 1 i 
   䬥筨 i. (PL '(3 6 4 1) '(+ * - ))  -  (3 + 6) * 4 - 1 = 35.

2. 㢠 i ii  k ࠫ쭨 ᥫ,  直 i- 童  
   ॢ i.

3. 㢠 i ஧⠭ 㦮   i. 冷 i  
   i, 㦪 筮  冷 i. 
   ਪ, n=4: ((a b) c) d  (a (b c)) d  a ((b c) d)  (a b)(c d)  
                    a (b (c d)).

4.  ணࠬ:
) (INTEGRATE f a b n) - i⥣㢠 㭪i f i a  b; ii [a; b] 
			஧  n ⨭.
) (HALFDIV f a b e) - 	 i iﭭ f(x)=0, 直   iࢠi
			[a; b] ⮤  i  娡 e.
) (SQRT2  n  ) - ᫨ ⭨ i ⮤ ii  娡 .
) (DIFF f  x) - ᫨ 祭 i 㭪i f  i x.



iii

1. $ (defun PL1 (lst1 lst2)
      ((NULL lst2) (car lst1))
      (PL1 (cons (funcall (car lst2) (car lst1) (cadr lst1)) (CDDR lst1)) (CDR lst2))  )

2. $ (DEFUN cl (i)
      (SETQ list nil)
      (calc i)  )

   $ (DEFUN calc (i)
       ((ZEROP i) (RETURN (PRINT list)))
       (PUSH i list)
       (LOOP ((> 1 (CAR list)) (RETURN (POP list)))
       (calc (- i 1))
       (PUSH (- (POP list) 1) list)
      )  )

4. ) $  (DEFUN INTEGRATE (function a b n)		(defun f (x)
            (SETQ step (/ (- b a) n) intsumma 0)	(* x x)
            (LOOP					)
     ((= a b) (* intsumma step))
     (INCQ intsumma (FUNCALL function a))	: (INTEGRATE f 0 1 100)
     (INCQ a step)
)   )

) (DEFUN HALFDIV (function a b eps)
     (SETQ middle (/ (+ a b) 2) res (FUNCALL function middle))
     ((< (- b a) eps) middle)
     (IF (MINUSP (* res (FUNCALL function a)))
(HALFDIV function a middle eps) (HALFDIV function middle b eps))
   )

) $ (DEFUN SQRT2 (n eps) 		) $ (DEFUN DIFF (function x)
       (SETQ s (/ n 2))				       (SETQ delta 0.01)
       (LOOP					       (/ (- (FUNCALL function (+ x delta))
	(SETQ snew (/ (+ s (/ n s)) 2))	 		(FUNCALL function x)) delta)
	((< (ABS(- s snew)) eps) snew) 	     )
	      (SETQ s snew)					
      )   )
i: x1 = n/2, xi = (xi-1 + n/xi-1) / 2.	f'(x) =  (f(x + dx) - f(x)) / dx,  dx = 0.001.


