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*To*: scheme@mc.lcs.mit.edu*Subject*: R3RS number syntax*From*: Pavel.pa@Xerox.COM*Date*: Wed ,27 Apr 88 20:30:37 EDT

I have a few questions about the syntax of numbers in R3RS Scheme: 1. The sequence of characters ``#x3e4'' has two very different parses. The question is whether or not the ``e'' is a digit or the exponent marker. What is intended here? 2. What is the meaning of the exponent part when the radix is not 10? My guess was that ``#O3E4'' meant 3 times 8 to the 4th, but C-Scheme, at least, treats this as 3 times 10 to the 4th. I can guess from the syntax that the digits of the exponent are always in radix 10 (since the base 10 digits are all that's allowed there), but what is the base for the exponentiation? I thought it would be more useful if the exponentiation base was the same as the number radix (so that, for example, I could say #b1E20 to make a mask that has only bit 20 turned on). 3. Does ``3/4e5'' mean the same as ``75000'' or ``.0000075''? That is, is the exponent intended to apply to the entire rational ``3/4'' or just to the denominator? 4. Does ``123##.##'' mean anything different from ``12300'' when read? Or does it really mean the same as ``#i12300''? 5. I assume that the syntax ``3@4'' is meant to denote the complex number with magnitude 3 and angle 4, but this isn't actually said anywhere in the document. The same goes for the (assumed rectangular) notation ``3+4i'', though it's more clear in that case. I had to infer the meaning from an example in the description of number-printing formats. It would really be nice if R4RS were to include a formal semantics for the syntax of numbers. I realize that some issues (such as whether or not such a literal is exact) are intended to be implementation-dependent, but I think that there could be a semantics that defined the mathematical number that each input syntax is intending to represent (perhaps the semantic function should return an interval of the reals for each expansion of the <real> nonterminal in the grammar). Pavel

**Follow-Ups**:**Re: R3RS number syntax***From:*spar!freeman@decwrl.dec.com (Jay Freeman)

**Re: R3RS number syntax***From:*spar!freeman@decwrl.dec.com (Jay Freeman)

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