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From: am@cl.cam.ac.uk (Alan Mycroft)
Newsgroups: comp.lang.c
Subject: Re: Paying attention to parentheses
Message-ID: <697@jenny.cl.cam.ac.uk>
Date: Mon, 27-Apr-87 05:48:51 EDT
Article-I.D.: jenny.697
Posted: Mon Apr 27 05:48:51 1987
Date-Received: Sun, 3-May-87 00:50:58 EDT
References: <15958@sun.uucp> <5716@brl-smoke.ARPA> <532@omepd> <2094@mmintl.UUCP>
Reply-To: am@cl.cam.ac.uk (Alan Mycroft)
Organization: U of Cambridge Comp Lab, UK
Lines: 26

Consider the following examples from an article by Jim Valerio (532@omepd):
>>Here are some examples of parenthesized expressions, pulled from the
>>Elefunt tests, which want the order of evaluation guaranteed by the
>>parentheses:
>>		x = ((one + x * a) - one) * 16.0;
>>		y = x / ((half + x * half) *((half - x) + half));
>>		x = (x + eight) - eight;
>>		while (((b+one)-b)-one == zero);
>>		if ((a+betam1)-a != zero)
Frank Adams (Ashton Tate) then suggests that these need to be:
>	x = +(+(one + x * a) - one) * 16.0;
(etc - lots of unary '+'s)
Now, by my understanding of the ANSI draft, none of the above 4 expressions
may be re-arranged so that none of the unary '+'s are required here:
The only rearrangements that are allowed are ASSOCIATIVITY AND COMMUTATIVITY.
So, by the mathematical definition, the only changes allowed are
(a+b)+c <-> a+(b+c) and a+b <-> b+a and the analogues for '*'.
None of the above expressions contain a+b+c or a*b*c and unary plus
cannot be used anyway to stop a+b being re-arranged as b+a.
Therefore using unary plus cannot affect the allowable compilations of the
above expressions.

As I have remarked before, the re-arrangements only apply to the above 4
cases.    a+b-c CANNOT be rearranged as a-c+b or even a+(b-c)
since '-' is not an associative commutative operator.
Similar reasoning forbids any other rearrangement.