I think you're right--to do mathematical notation, you'd need mathematical
precedence and standard function notation. In addition, you'd need to use
conforming operators not #*, exponents denoted by graphic position not with
bogus operators such as #^, elided operators for multiplication, horizontal
lines for division, tall integrals, etc. etc. etc. That would be cool.

Short of that, though, and you are asking the users to learn a necessarily
incompatible (non-conforming) set of rules and you expect them to be able
to go back and forth between their computer notation and their math
notation. In that context, I don't see the relative precedence of #+ and #*
as particularly significant, and my sympathies lie with simplicity.

glenn

At 10:45 PM 1/26/99 -0500, Ian Bicking wrote:
>In message Tue, 26 Jan 1999 09:38:32 -0800,
>  glenn <krasner at objectshare.com>  writes:
>> 	c) cater to adults and children already computer-skilled who have
>> preconceived notions set by some other computer languages which have
>> multiple rules, one operator-based and the other left-to-right (or
>> right-to-left or some such).
>
>I'm not saying that the normal, mathematical rules of precedence are easier
>for children.  Quite the contrary -- Smalltalk's simple left-to-right rule
>is much more intuitive.  This is the problem.  A child who is introduced to
>Smalltalk's system would likely have their intuition reinforced, making it
>all the harder to learn the proper (mathematical notation) rules of
>precedence.
>
>The fact of the matter is, mathematics says that 3+4*5=23.  You can't change
>that -- the mathematical conventions of the world are not going to be
>changed because they are easier for the computer to parse.  In a practical
>matter, those conventions have been created because they *are* easier to
>parse (for humans) in real-world situations.  They lead to less parenthesis.
>They group factors.  They *are* aesthetic.
>
>Perhaps the real answer is to have a view of Squeak where the syntax is
>fully mathematical.  Where 3*sin(x^2+2) works.  In this view a child could
>learn mathematics.  But it seems that a better solution could be made, one
>that encompasses both needs (simplicity and conformity) instead of requiring
>a break-away syntax.
>
>I bring this up because I've been looking at Logo, and one of the big
>compromises they made in the syntax was to allow infix notation even though
>it wasn't part of the Lisp tradition and sullied the syntax quite a bit.
>
>Now, this is all assuming that a goal of Squeak (distinct from Smalltalk)
>is as a pedagogical tool.  This is by no means necessarily true... though
>it would be neat if Squeak could be used by children, that doesn't mean it
>needs to be created for them to learn from it (though, of course, it is
>impossible to seperate use from learning).  Pedagogically, introducing
>something that looks almost like proper mathematical expressions but isn't
>is a bad thing to do.  This is one reason (not necessarily a huge reason)
>that I don't think Squeak is ready for children.
>
>
>                                       -- Ian Bicking
>
>