NYCJUG/notationFAQ

Some frequently-asked questions regarding notation of APL and related languages.

Order of Operations

The following, from http://compilers.iecc.com/comparch/article/96-09-086, gives a couple of reasons why right-to-left evaluation makes more sense than evaluation in the other direction in the context of an array-processing language. A more complete list of the advantages of this direction are given here.

From: 	"Devon McCormick" <devon_mccormick@smb.com>
Newsgroups: 	comp.compilers
Date: 	17 Sep 1996 00:20:30 -0400
Organization: 	Compilers Central
References: 	96-09-021
Keywords: 	design


On 5 September 1996, Nils M. Holm asks:

> Given a language without any operator precedence, would you prefer
>
> 1) evaluation from the left to the right, like a sequence of identical
> Operations in C [a - b + c = (a - b) + c]
>
> or
>
> 2) evaluation from the right to the left, like in APL?
> [a - b + c = a - (b + c)]
>
> What are the reasons for your choice?

There are 2 related reasons APL chooses right to left precedence:

  1) the language supports the notion of applying a function across
     an array, e.g. +/1 2 3 <-> 1 + 2 + 3, or (for infix function f)
     f / 1 2 3 <-> 1 f 2 f 3;

  2) for a non-commutative function, such as minus, the result is much
     more interesting evaluated right to left, e.g. -/1 2 3 4 5
     becomes the alternating sum (((1 - 2) + 3) - 4) + 5; if evaluation
     were as in conventional mathematics, this would be equivalent
     to the less interesting 1 - (2 + 3 + 4 + 5).

     Similarly, division across a vector gives a continued fraction
     instead of the first number divided by the product of the remaining
     numbers.

I can find the citation of this if you are interested.
--
Devon McCormick
devon_mccormick@smb.com

Also, take a look at this small dissertation on the fallacy of "standard mathematical notation".