Degenerate array axes

[Guy Steele <gls@THINK.ARPA>]

    Date: 06 Jun 85  0543 PDT
    From: Jon White <JLW@SU-AI.ARPA@think>

    What does one mean by (make-array '(0 5)) ?  How should it print?
    (assuming that *print-array* is non-null)

    The description of array printing on page 369 presumes that the array
    is either single-dimensional, or else it has some (i.e., not 0) elements.
    Notice how the looping part of the algorithm resets an index to 0 (not -1)
    in order to try to access the "element" at index <i1 i2 ... 0 ...>.

Eeee-yuk!  This boner is completely my fault, and I feel very bad about it,
inasmuch as I put a lot of study into how APL hackers solved this problem.
(Essentially what they do is to exhibit a NON-empty array showing typical
components, and then say "the array I'm talking about is just like this
one except that thus-and-so axes are zero".  I'm not crazy about this solution,
since we don't have the same problem of prototypes [their technical term for
what you get when you take the "CAR" of an empty array] that APL does.)

    I've looked a several CL implementations, and all fail to print such
    objects in a readable manner.  Furthermore, they all print the above
    array exactly the same as they do (make-array '(0 10)), even though the 
    two arrays are not equalp [with *print-array* set to non-null].

    It seems clear to me that the algorithm of page 369 does not
    provide for a way to distinguish these two arrays, since the
    #nA syntax deduces the contents of th dimensions list from
    the :initial-contents -- but for arrays of array-total-size equal to
    zero, they all have the same "initial contents" even though their
    dimensions lists may assume infinitely may values.

    Three possible solutions come to mind:
      1) simply rule out degenerate axes as being somehow wrong -- the
	 only zero-element arrays must then be vectors
      2) coerce all such beasts into one with all dimensions zero -- e.g.,
	 treat the '(0 5) and '(0 10) as if they were '(0 0); then a NIL
	 for the :initial-contents would be acceptable.
      3) extend the print syntax of #nA so that it can specify the dimension
	 list exactly, and independently of the :initial-contents field.
    Anyone have any ideas on this one?

    -- JonL --

Under option (3), how about
	#A<dimension-list><initial-element>
?  This would provide a notation for empty arrays, as well as a concise
notation for arrays with all elements the same (EQL).  For empty arrays
the initial element doesn't especially matter, so use ().
So one would have
	(make-array '(0 5)) => #A(0 5)()
	(make-array '(0 10)) => #A(0 10)()

Of course, this is a non-trivial extension to the language.

--Guy