On Sat, Jul 19, 2008 at 8:09 AM, Roger Hui <[EMAIL PROTECTED]> wrote:
> http://www.jsoftware.com/jwiki/Doc/Elementary_Functions_An_Algorithmic_Treatment#evaluation_order
>
> by Ken Iverson, 1966.
in the interest of searchability, i copy the points on page 222 here:
The reasons for a right-to-left instead of a left-to-right convention are:
1. The usual mathematical convention of placing a monadic function to
the left of its argument leads to a right-to-left execution for
monadic functions; for example, F G x = F (G x) [0]
2. The notation F/ z for reduction (by any dyadic function F) tends to
require fewer parentheses with a right-to-left convention. For
example, expressions such as +/ (x * y) [1] or +/ (u/x) tend to occur
more frequently than (+/ x) * y and (+/ u) / x.
3. An expression /evaluated/ from right to left is easiest to /read/
from left-to-right. For example, the expression
a + x * b + x * c + x * d + x * e + x * f
(for the efficient evaluation of a polynomial) is read as a plus the
entire expression following, or as a plus x times the following
expression, or as a plus x times b plus the following expression, and
so on
4. In the definition
F/ x = x1 F x2 F x3 F ... F xn [0][2]
the right-to-left convention leads to a more useful definition for
nonassociative functions F than does the left-to-right convention. For
example, -/ x denotes the alternating sum of the components of x,
whereas in a left-to-right convention it would denote the first
component minus the sum of the remaining components. Thus if d is the
vector of decimal digits representing the number n, then the value of
the expression 0 = 9|+/ d determines the divisibility of n by 9; in
the right to left convention, the similar expression 0 = 11|-/
determines divisibility by 11.
[0] the symbol '=' here means congruence (triple horizontal lines in
the original)
[1] the symbol '*' here and later means multiplication ('x' in the original)
[2] the 'n' in xn is denoted {rho} x in the original
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