Why choose a left-to-right convention?

Question

On the subject of associativity when all operators have equal precendence, Ken Iverson writes in Conventions Governing Order of Evaluation that

The reasons for choosing 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) .
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) or +/(u/x) tend to occur more frequently than (+/x)×y and (+/u)/x .
3. An expression evaluated from right to left is the 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 x⍴x
   

   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|-/d determines divisibility by 11 .

What would be the reasons for choosing a left-to-right convention?

Answer 1

Consistency with pure OO

In Smalltalk, everything is a method (even operators), and all methods that take more arguments than just self use infix syntax. Using a simple left-to-right rule solidifies this consistency, and avoids having to implement precedence for regular methods.

Obviously, this has the drawback of running counter to mathematical convention, when 1 + 2 * 3 is 9 rather than 7.

Answer 2

Easier writing

In my experience writing APL programs, I constantly have to press the left arrow key to type in the next part of my program. A left-to-right evaluation would would effectively reverse that, allowing for a more natural flow of program writing. Note that this would apply more to symbolic languages like APL and golfing languages, instead of conventional C derivatives.