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From: barmar@mit-eddie.UUCP (Barry Margolin)
Newsgroups: net.lang
Subject: Re: Operator Precedence
Message-ID: <5257@mit-eddie.UUCP>
Date: Sun, 8-Sep-85 04:33:37 EDT
Article-I.D.: mit-eddi.5257
Posted: Sun Sep  8 04:33:37 1985
Date-Received: Mon, 9-Sep-85 04:32:44 EDT
References: <262@pedsgd.UUCP>
Reply-To: barmar@mit-eddie.UUCP (Barry Margolin)
Organization: MIT, Cambridge, MA
Lines: 52

In article <262@pedsgd.UUCP> bob@pedsgd.UUCP (Robert A. Weiler) writes:
>

Well, we have Fortran to thank for operator precedence in programming
languages, I suspect.  As for how it got there in the first place, here
is my hypothesis.  It is an attempt to emulate the precedence inherent
in mathematical notation.  In mathematics, one does not normally write
the multiplication operator, one writes A*B as AB.  So, when one sees
the expression A+BC in mathematics, it is implicitly parsed as A+(BC).
A similar argument accounts for the higher precedence of exponentiation
(** or ^ in most Fortran-descendents):  N is generally interpreted as
                                      AB
   N
A(B ).  As for the higher precedence of division, that may be because of
                                    N
fractions being written as N/D when - is not convenient, or it might be
                                    D
because division is to subtraction as multiplication is to addition, so
the corresponding operations have similar precedence.  Also, division is
almost associative with multiplication, i.e. A*B/C can be interpreted as
(A*B)/C or A*(B/C) without affecting the mathematical answer (although
the computer answers might be different, due to the problems of computer
representations of numbers).

The "founding fathers" of high-level languages probably didn't
anticipate the confusion that would ensue when their simple rule of
operator precedence (* and / higher than + and - [= was not considered
part of an expression, it was part of the syntax of an assignment
statement, and the original Fortran didn't even have comparison
operators (remember arithmetical IF?)]) got extended to handle a dozens
of operators.  Even after comparison operators came around, their
results could usually be used only in boolean expresions, and A+(B==C)
is not valid in many languages, so it was very natural that A+B==C
should be forced to mean (A+B)==C.

The only operator precedence I can ever remember is that ^ is higher
than * and /, which are higher than + and -, and that comparison
operators are the lowest.  And, in the case of languages in which
assignments are expressions (are there any other commonly-used ones
besides C [not counting functional languages, in which everything is an
expression by definition]?), assignments are usually even lower.  These
last two are easy to remember because they match the common use: one
usually uses comparisons and assignments at the highest possible levels,
rather than using them as subexpresions; the C expression
		a*b==c+d
almost always is intended to compare the two outer expressions, rather
than to involve the result of the inner comparison in the arithmetic
expression.
-- 
    Barry Margolin
    ARPA: barmar@MIT-Multics
    UUCP: ..!genrad!mit-eddie!barmar