Re: number syntax

[David Bartley <Bartley%TI-CSL.CSNET@CSNET-RELAY.ARPA>]

> Date: Thu, 10 Jul 86 12:09 EDT
> From: Jonathan A Rees <JAR%ai.ai.mit.edu@CSNET-RELAY.ARPA>
>
>    Date: Tue 17 Jun 86 16:00:31-CDT
>    From: David Bartley <Bartley%ti-csl.csnet at CSNET-RELAY.ARPA>
>    
>    One irritant in the Report that we have neglected to comment on until
>    now (sorry!) is the syntax of numbers.  We believe that Scheme numbers
>    are essentially equivalent to Common Lisp numbers except for the new
>    notion of exactness.  To the extent that that is so, it seems to be a
>    (shudder!) ``gratuitous difference'' from Common Lisp to have an
>    incompatible syntax.      [...]
>    
>    What we'd like to see is an essential syntax for numbers which is
>    compatible with Common Lisp's.  Additional features, including
>    exactness, would be optional extensions.  Even so, they should not
>    conflict with Common Lisp.  For example, the use of `#s' and the order
>    of <sign> and <prefix> are different in the two languages.     [...]
>    
>    Does anyone agree with us?  Is there time to make such a change before
>    R^3RS goes to press?
>
>I think everyone agrees with you, and that there is time.  Could you
>please write a concrete proposal, preferably something close to being
>suitable for inclusion in the report.  Also please provide BNF.  Thanks.
>
>Jonathan

Here's a stab at it---we expect and welcome debate over the details.

The major differences between the syntax of numbers in Common Lisp (CL)
and heretofore in Scheme (R^3RS) are:

(1) CL has the prefix denoting base precede the sign; R^3RS has the sign
precede the prefix, which includes the base specifier.  I see no reason to
differ from CL.

(2) CL uses several exponent markers to specify levels of precision for
floating point numbers; R^3RS specifies precision levels (S and L) in the
prefix.  Again, why differ from CL?

(3) CL does not provide for the use of `#' to indicate insignificant
digits.  Making this a non-essential feature in R^3RS seems reasonable.

(4) CL provides only the #C(real real) notation for complex numbers; R^3RS
provides infix notations for both polar and rectangular forms.  For
compatibility with CL, R^3RS should support the #C notation and the infix
forms should be non-essential extensions.

(5) CL integers may optionally terminate in a decimal point; R^3RS permits
such a number to be treated as floating point and it is debated whether it
is to be considered exact.  This is a serious problem, since many
procedures are defined to accept only integer values.  Is the call
(INTEGER->CHAR 55.) valid?  We propose that this be a non-essential
feature in R^3RS.

(6) CL integers and ratios are not permitted to have exponent markers.
This feature should be a non-essential extension to Scheme.

(7) CL does not have the concept of exactness.  Most (all?) existing
implementations of Scheme do not support this feature, so it should be
non-essential.

We propose the following syntax for numbers in Scheme.  (Recall that
letter case is insignificant in the grammar and that the rules for <ureal
R>, <prefix R>, etc., should be replicated for R = 2, 8, 10, and 16.)

<number>  -->  <real>  |  #c( <real>  <real> )

<real>  -->  <prefix R> <sign> <ureal R>

<prefix R>  -->  <exactness> <radix R>
  
<exactness>  -->  <empty>  |  #i  |  #e

<radix 2>  -->  #b
<radix 8>  -->  #o
<radix 10>  -->  <empty>  |  #d
<radix 16>  -->  #x

<sign>  -->  <empty>  |  +  |  -

<ureal R>  -->  <integer R>  |  <ratio R>  |  <flonum R>

<integer R>  -->  <digit R>+ #* 

<ratio R>  -->  <digit R>+ #* / <digit R>+ #*

<flonum R>  -->  . <digit R>+ #* <expon>
   |  <digit R>+ . <digit R>* #* <expon>
   |  <digit R>+ #* . #* <expon>

<expon>  -->  <empty>  |  <expon-marker> <sign> <digit>+

<expon-marker>  -->  e  |  f  |  d  |  l  |  s

<digit 2>  -->  0  |  1
<digit 8>  -->  0  |  1  |  2  |  3  |  4  |  5  |  6  |  7
<digit 10>  -->   <digit 8>  |  8  |  9
<digit 16>  -->  <digit 10>  |  a  |  b  |  c  |  d  |  e  |  f


Although we have incorporated <exactness> and the use of `#' above, they
should be stated to be non-essential features of Scheme.  

Nonessential feature: integers with optional decimal points.  

<integer R>  -->  <digit R>+ #* .

Nonessential feature:  integers and ratios with exponents.

<integer R>  -->  <digit R>+ #* <expon>
<ratio R>  -->  <digit R>+ #* <expon> / <digit R>+ #* <expon>

Nonessential number productions representing complex numbers.  We worry
that the forms <real>+<ureal>i and <real>-<ureal>i can be hard to parse.
Perhaps combining the suffix `i' with the infix `+' or `-' would be
palatable to those who want this feature.

<number>  -->  <real> +i <ureal>
   |   <real> -i <ureal>
   |   <real> @ <real>

Regards,
David Bartley
Mark Meyer
-------