Folks,

I apologise for the length of this message. I hope there is
something of value in it. Cut mercilessly if you feel the
need to address some small point. Or cut all.

I try to expand here a bit on the proposed (shape b e ...)
specification. In the specification the bounds of each
dimension are simply arguments to a procedure, and the upper
bound is not a valid index.

Some are quick to point out that there are other possible
ways, and some other way even feels more natural or more
convenient to them. I trust that no one wants the interface
to cover every possible way. (At least, I feel the macro at
the end of this message is gross, and it is only half way
there.)

Let this message also serve to show what kind of thinking
made me do all the choices I made in the specification. I
do not say I have found the only reasonable way to do
things, but I have thought hard of it. (This was two years
ago. It has been dormant since up to now.)

Short summary: yes, it is inconvenient to always have to
provide the zero lower bounds, but not too inconvenient.
What we gain is, there is a single, simple, uniform way to
specify a shape, and the way is both right and consistent
with the rest of the specification and the rest of Scheme.

End of short summary: I want to choose one good way as
primitive; secondary ways need not be inside the primitive
- make them separate procedures, written when needed.

If it really feels too much to always type in the lower
bounds, and you end up doing it a lot, or it is a nuisance
in some other way, define a variant procedure with another
name, like so:

  (define (shape0 . es)
     (apply shape
        (apply append
           (map (lambda (e)
                   (list 0 e))
              es))))

Similarly, define shape1 for one-based work.

For specific purposes, like a package to match a linear
algebra text that always uses two dimensions and always
begins indexing at once, provide specific ways to default
to two dimensions and one based indexing:

   (define (tabulate-matrix m n proc) ...)
   ...
   (define a (tabulate-matrix 4 4 (lambda (r k) ...)))

If you need a lot of arrays with the same shape, define one
shape and cut all your arrays with it.

You get the drift: the primitive is simple and usable as
is; abstraction from it is allowed and encouraged; and even
convenience variants are easy to write according to taste.

I don't see how any procedure with a dispatch on argument
types would really be more convenient to use. It would make
the common case simpler, sure, but then it would make the
other cases pointlessly inconvenient.

Internal consistency of the array package carries a lot of
weight with me. Here is one point: (shape b e d f) is the
same as (array (shape 0 2 0 2) b e d f), and the arguments
are the same, if you see what I mean.

Consistency with Scheme carries equally lot of weight with
me. I'm glad Per Bothner saw what I meant when I pointed
out that the included lower bound, excluded upper bound
match substring. I'll expand on that: in the sensible
default case, when the lower bound is zero, the upper bound
is also the length of the dimension, matching make-vector
and make-string.

These are small points but they add up, to me at least.

I also believe, partly from programming experience, that
this indexing scheme is the best there is. It avoids an
amount of +1 or -1 correction terms, and a lot of thinking
at the boundaries: (- e b) is quite a lot simpler than any
of (+ (- e b) 1) or (- e b -1) or (- 1 b e) or so on. And
intervals add nicely: [a .. b) and [b .. c) form [a .. c).

(Stepping from last index to first requires correction,
since the upper bound is not a valid index. Conceded.)

The alternative of specifying a first index and length is
not much worse, I think, but it has no counterpart in the
rest of Scheme. (This is strenuous. Scheme is so small that
the only clearly relevant model there are strings.)
Consistency with other languages does not carry much weight
with me.

The alternative of specifying first and last index just
doesn't work as well. Look at the boundary case: an empty
dimension now is just an empty interval [b .. b). With the
last index less than the first, it is a monster. And
consistency with other languages does not carry much weight
with me. We are not adding to their libraries here.

One could remove the possibility of specifying arbitrary
lower bounds. I don't see any reason to do that. (It is
going beyond the model of the rest of Scheme, though.)

Anyway, one can write convenience procedures to extract
just what one wants. For dimension k = Integer[b .. e), let
us say, and let us even abstract away from the concept of a
shape as a thing:

    (array-length arr k) ==> e - b
    (array-begin arr k)  ==> b
    (array-past arr k)   ==> e
    (array-last arr k)   ==> e - 1

These are all simple to write. Only take a flick of the
wrist. Let us keep the primitives few and clean.

Oh well. Here is the gross macro I promised. It expands
into a call to shape and allows all kinds of combinations
of a default lower bound, defaulting to zero, with last
index or an excluded upper bound or dimension length. All
are expressions. The macro uses _ as a literal keyword,
like else in cond and case.

The following are then all equivalent (innit a mess?):

    (shape 0 4 0 4)
    (shape 0 (* 2 2) 0 (+ 2 2))
    (: 3 3)
    (: (0 3) (0 3))
    (: (0 _ 4) (0 _ 4))
    (: 0 _ (_ 4) (_ 4))
    (: 0 _ 3 3)
    (: #(4) #(4))
    (: (_ (* 2 2)) (_ (+ 2 2)))
    (: #((* 2 2)) #( (+ 2 2)))

You can see the expansions, with arguments evaluated, if you

    (define (shape . bounds)
      `(shape ,@ bounds)).

That breaks the array package, of course. Here goes.

;;; (: def _ dim ...)              library syntax
;;; (: dim ...)                    library syntax
;;; where each dim is one of
;;;   (b e)    e included
;;;   (b _ e)  e excluded
;;;   e        b default, e included
;;;   (_ e)    b default, e excluded
;;;   #(n)     length
;;; and def _ provides the default lower bound and
;;; defaults to 0.

(define-syntax :
  (syntax-rules (_)
    ((: bound _ . forms)
     (letrec-syntax
	 ((car (syntax-rules (_)
		 ((car d (_ e)) d)
		 ((car d (b e)) b)
		 ((car d (b _ e)) b)
		 ((car d #(n)) d)
		 ((car d e) d)))
	  (cdr (syntax-rules (_)
		 ((cdr d (_ e)) e)
		 ((cdr d (b e)) (+ e 1))
		 ((cdr d (b _ e)) e)
		 ((cdr d #(n)) (+ d n))
		 ((cdr d e) (+ e 1))))
	  (map (syntax-rules ()
		 ((map d () bs es)
		  (shuffle bs es))
		 ((map d (f . fs) bs es)
		  (map d fs
		       ((car d f) . bs)
		       ((cdr d f) . es)))))
	  (shuffle (syntax-rules ()
		     ((shuffle (a . bs) (d . es) . s)
		      (shuffle bs es a d . s))
		     ((shuffle () () . s)
		      (shape . s)))))
       (let ((b bound))
	 (map b forms () ()))))
    ((: . forms)
     (: 0 _ . forms))))
--
Jussi