// 
// So we accidentally created a monster:
// 

>(cons 'cat1 '(cons 'cat2 nil ) )

(CAT1 CONS 'CAT2 NIL)

>(setq l (cons 'cat1 '(cons 'cat2 nil ) ))

(CAT1 CONS 'CAT2 NIL)

// Let's dissect it.

>(length l)

4

>(cadr l)

CONS

>(cddr l)

('CAT2 NIL)

>(caddr l)

'CAT2

// 'CAT2 is (quote CAT2), i.e., a list of its own, with its own cons cell:

>(caaddr l)

QUOTE

>(caddr l)

'CAT2

>(cdaddr l)

(CAT2)

>(cadaddr l)

Error:
Fast links are on: do (si::use-fast-links nil) for debugging
Signalled by EVAL.
Condition in EVAL [or a callee]: INTERNAL-SIMPLE-UNDEFINED-FUNCTION: Cell error on CADADDR: Undefined function:

Broken at EVAL.  Type :H for Help.
    1  Return to top level.
>>1

Top level.

// OK then, not all combinations of A and D are available as built-in functions :) 

>(car (cdaddr l))

CAT2

// Finally, let's get to the NIL, too:

>(cdddr l)

(NIL)

>(cadddr l)

NIL