Why do you need a header in a table like that on page 214
of SICP?

The list  ((a . 1) (b . 2) (c . 3))  would seem to be adequate
for using assq  -- indeed, the list that is actually used,

 (*table* (a . 1) (b . 2) (c . 3)) seems to have a redundant
header... if you look at "lookup"

all it does is check for (assq key (cdr table))  , so why have *table*
there?

The answer is in insert!:  If we have a particular table TTT in mind
all the time, then insertion could be done by

(set! TTT (cons (cons key value) TTT)

but if we do not know the NAME of the table, but only want to modify
some value given to us we cannot do

(set!   <whatgoeshere???> newtable)

If we modify the table in the middle,  we can "splice"  "b" into the
list after the first element...

L =     (a c d)

by  (set-cdr! L (cons b (cdr L)))

now L = (a b c d)

but how can we splice into L before the FIRST element?

how can we change L to be  (z a b c) ?

The answer is, not easily.

(set-car! L 'z)  changes L to  (z a b c).

If we produce a new table by (cons 'z ..)
we don't have L's name, just it's value  (a b c), so we can't use
set!...

So the usual way of doing this insertion nicely is to have a
HEADER, and insert after it.


(Here's a non-recommended way of inserting in front of a header-less
first value in a list, in a way that mutates the list.  Can you
see what it is doing?  Do you understand its limitations?  Hint:
is there a minimum length for l ?)

(define (bash1 l item)
  ;; change l =( a b c)  to  (item a b c) by mutation
  (set-cdr! l (cons (car l) (cdr l)))
  (set-car! l item)
  l)