(defun singletonp (the-list)
	(cond
		((null the-list)
			nil)
		((null (cdr the-list))
			T)
		(T
  			nil)
	)
)

Demo:

Break 2 [7]> (singletonp '(a))
T
Break 2 [7]> (singletonp '(1 2))
NIL
Break 2 [7]> (singletonp '(a b c 2 3 4 1))
NIL


(defun rac (the-list)
	(cond
		((singletonp the-list)
			(car the-list)
		)
		(T
			(rac(cdr the-list))
		)
	)
)

Demo:

Break 2 [7]> (rac '(1))
1. Trace: (RAC '(1))
1. Trace: RAC ==> 1
1
Break 2 [7]> (rac '(1 2 3 4))
1. Trace: (RAC '(1 2 3 4))
2. Trace: (RAC '(2 3 4))
3. Trace: (RAC '(3 4))
4. Trace: (RAC '(4))
4. Trace: RAC ==> 4
3. Trace: RAC ==> 4
2. Trace: RAC ==> 4
1. Trace: RAC ==> 4
4



(defun rdc (the-list)

	(cond
		((singletonp the-list)
			nil
		)
		(T
			(cons (car the-list) (rdc (cdr the-list)))
		)
	)
)


Demo:

[11]> (rdc '(1))
1. Trace: (RDC '(1))
1. Trace: RDC ==> NIL
NIL
[12]> (rdc '(1 2 3 4 5))
1. Trace: (RDC '(1 2 3 4 5))
2. Trace: (RDC '(2 3 4 5))
3. Trace: (RDC '(3 4 5))
4. Trace: (RDC '(4 5))
5. Trace: (RDC '(5))
5. Trace: RDC ==> NIL
4. Trace: RDC ==> (4)
3. Trace: RDC ==> (3 4)
2. Trace: RDC ==> (2 3 4)
1. Trace: RDC ==> (1 2 3 4)
(1 2 3 4)




(defun snoc (x the-list)
	(cond
		((null the-list)
			(list x)
		)
		(T
			(cons (car the-list) (snoc x (cdr the-list)))
		)
	)
)

Demo:

[25]> (snoc 'blue ())
1. Trace: (SNOC 'BLUE 'NIL)
1. Trace: SNOC ==> (BLUE)
(BLUE)
[26]> (snoc 'blue '(red))
1. Trace: (SNOC 'BLUE '(RED))
2. Trace: (SNOC 'BLUE 'NIL)
2. Trace: SNOC ==> (BLUE)
1. Trace: SNOC ==> (RED BLUE)
(RED BLUE)
[27]> (snoc 'blue '(dark-blue light-blue sky-blue purple))
1. Trace: (SNOC 'BLUE '(DARK-BLUE LIGHT-BLUE SKY-BLUE PURPLE))
2. Trace: (SNOC 'BLUE '(LIGHT-BLUE SKY-BLUE PURPLE))
3. Trace: (SNOC 'BLUE '(SKY-BLUE PURPLE))
4. Trace: (SNOC 'BLUE '(PURPLE))
5. Trace: (SNOC 'BLUE 'NIL)
5. Trace: SNOC ==> (BLUE)
4. Trace: SNOC ==> (PURPLE BLUE)
3. Trace: SNOC ==> (SKY-BLUE PURPLE BLUE)
2. Trace: SNOC ==> (LIGHT-BLUE SKY-BLUE PURPLE BLUE)
1. Trace: SNOC ==> (DARK-BLUE LIGHT-BLUE SKY-BLUE PURPLE BLUE)
(DARK-BLUE LIGHT-BLUE SKY-BLUE PURPLE BLUE)



(defun palindromep (the-list)
	(cond
		((null the-list)
			T
		)
		((singletonp the-list)
			T
		)
		((eq (car the-list) (rac the-list))
			(palindromep (cdr (rdc the-list)))
		)

	)
)


Demo:


[29]> (palindromep ())
1. Trace: (PALINDROMEP 'NIL)
1. Trace: PALINDROMEP ==> T
T
Break 1 [31]> (palindromep '(palindrome))
1. Trace: (PALINDROMEP '(PALINDROME))
1. Trace: PALINDROMEP ==> T
T
Break 1 [31]> (palindromep '(clos sloc))
1. Trace: (PALINDROMEP '(CLOS SLOC))
1. Trace: PALINDROMEP ==> NIL
NIL
Break 1 [31]> (palindromep '(food drink food))
1. Trace: (PALINDROMEP '(FOOD DRINK FOOD))
2. Trace: (PALINDROMEP '(DRINK))
2. Trace: PALINDROMEP ==> T
1. Trace: PALINDROMEP ==> T
T
Break 1 [31]> (palindromep '(1 2 3 4 5 4 3 2 1))
1. Trace: (PALINDROMEP '(1 2 3 4 5 4 3 2 1))
2. Trace: (PALINDROMEP '(2 3 4 5 4 3 2))
3. Trace: (PALINDROMEP '(3 4 5 4 3))
4. Trace: (PALINDROMEP '(4 5 4))
5. Trace: (PALINDROMEP '(5))
5. Trace: PALINDROMEP ==> T
4. Trace: PALINDROMEP ==> T
3. Trace: PALINDROMEP ==> T
2. Trace: PALINDROMEP ==> T
1. Trace: PALINDROMEP ==> T
T
Break 1 [31]> (palindromep '(hey hey my my my my hey hey))
1. Trace: (PALINDROMEP '(HEY HEY MY MY MY MY HEY HEY))
2. Trace: (PALINDROMEP '(HEY MY MY MY MY HEY))
3. Trace: (PALINDROMEP '(MY MY MY MY))
4. Trace: (PALINDROMEP '(MY MY))
5. Trace: (PALINDROMEP 'NIL)
5. Trace: PALINDROMEP ==> T
4. Trace: PALINDROMEP ==> T
3. Trace: PALINDROMEP ==> T
2. Trace: PALINDROMEP ==> T
1. Trace: PALINDROMEP ==> T
T