Other useful functions

Obs: a simple list always ends with nil;

- caar, cadr, cdar, cddr, caaar, ...
(caadr x) <=> (car (car (cdr x)))
caddr: the third element in the list

- list-length: 
> (list-length '(a (b c) d))
3

- nth n xs: returns the n-th element in list xs (0-indexed)

- first, second, third, ..., tenth, rest
(third x) <=> (nth 2 x)
> (first '(1 2 3))
1
> (rest '(1 2 3))
(2 3)

- last: returns the last cons cell of the list 
> (last '(a b c d))
(d)
> (last '(a b c . d))
(c . d)
> (last '(a b c d) 3)
(b c d)
 

Predicates
- listp: returns true if its argument is a list
> (listp '(a b c))
T

-endp: returns true if the given list is null (usually used to check if the end of a list has been reached)
> (endp nil)
T
> (endp '(a b c))
NIL

- null
> (null nil)
T

- atom: returns true if the argument is an atom
> (atom 'abc)
T
> (atom '(a b))
nil

- equal: returns true if the two arguments are structurally similar 
> (equal '(a (b c)) '(a (b c)))
T
> (equal '(a (b c)) '(a b c))
nil

-eq: returns true if the two arguments are identical
> (setq x '(a b c) y (cdr x))
(b c)
> (equal y '(b c))
T
> (eq y '(b c))
NIL
> (eq y (cdr x))
T

- member: looks for an element in a list and returns the corresponding cons cell
> (member 'b '(a b c))
(b c)
> (member 'a '(f (a g) b c a d a e))
(a d a e)
(member '(c d) '(a b (c d) e))
NIL
> (member '(c d) '(a b (c d) e) :test #'equal)
((c d) e)
See also: member-if, member-if-not


Logical operators
- and: if all arguments evaluate to true, it returns the last of them; 
       if any of the arguments evaluates to false, none of the following ones are evaluated
> (and t (+ 5 4))
9

- or
> (or t (+ 5 4))
T


Conditional expressions
- if: 
> (if (listp 5)
  (+ 5 4)
  (- 5 3))
2

Obs: Anything except nil is evaluated as true
> (if 5 1 2)
1

- cond
(cond 
      (test-1 expr-1)
      (test-2 expr-2)
      ...
)
evaluates the tests until it finds one which is not nil, which is evaluated and returned
> (setq x 0)
0
> (setq valx (cond
      ((< x 0) '(x is less than zero))
      ((= x 0) '(x is equal to zero))
      (t '(x is greater than zero))))
(x is equal to zero)


Recursive functions
Example: length of a list.
(defun len (ls)
  (if (null ls)
      0
      (+ (len (cdr ls)) 1)))