Thanks for writing this. I think it would be a lot better if we didn't have to intersperse all that whitespace, like (a+b) vs (a + b). To allow that, arc needs to disallow special characters in variable names. I think the benefits from tricks like this and other syntactic sugar is much more valuable than being able to have symbol names like foo* or w/bar or even set-car.
Think what an awful idea it would be to modify the language of math so that + and - were valid parts of variable names. We treat those specially for a reason.
Old-time lispers rather enjoy our punctuated names and get great mileage out of (especially) using it to flag special variables thus: foo.
Meanwhile, this is all fun, but exactly how often does one put formulas into code, especially formulas one is forever revising meaning we need the editing to be a breeze?
I doubt I code one formula a year, and I write a lot of code. Maybe the engineers out there should just toss off a w/infix macro within which the highly optimized language of math is understood. A starting point might be a Common Lisp infix package, ask on comp.lang.lisp for recommendations.
Personally I don't think the whitespace is that much of a problem. Certainly I don't think whitespace makes infix less readable; it probably makes it more readable if anything. And it don't think there is a terribly appreciable difference in typing or reading time because of the extra characters. (Arguably the space bar is the easiest key to hit on the entire keyboard.)
While I wouldn't necessarily miss punctuation characters that much, I don't really think it is worth it just to remove the whitespace from infix expressions. You could interpret +-/* as separate in infix expressions only, but I think that creates unnecessary uniformities in the language.
And I do think that math matters. Maybe there are a lot of areas in which you wouldn't really gain much with the infix notation, but exactly the opposite can be said for other fields. I've been working on simple 2D game in CL, and all the math expressions were getting a bit annoying. I would love to try rewriting it in Arc if Arc ever got bindings to any good game libraries.
Sorry for my repetitiveness (said the same elsewhere) but The Lisp Way when you need a domain-specific syntax is to implement that with a macro and then use the syntax wrapped by the macro. Then Peter does not need to rob Paul (in this case by impoverishing the Arc naming syntax to get math syntax).
If you will simply go without not having whitespace between operators, then you doesn't need to disallow cool characters in symbols or add macro calls in front of all the infix expressions in your code. Honestly, all you save in whitespace you probably spend immediately in having to make the call explicit. I like that the current system integrates infix math seamlessly with s-expressions, that's why I spent my time writing that code. (Admittedly, the infix parts aren't perfect, but the integration itself is fairly seamless.)
I did look at some of the CL infix packages. And if I didn't have programming assignments to work on I might consider porting one.
Yeah, I saw that about the foo getting italicized. I guess I'll use octothorpes for asterisks from now one. :)
The coolest hackery has beautiful mathematical gems at the core or in the cleverest bits.
I guess I am not emitting the coolest hackery. :) I know I never put math formulas in my code because it is such a PITA when I do. :) I thought about challenging math infix proponents to post one or two examples from their code, no cheating and contest closed to scientists and engineers.
I do not see it as religious, just a simple question: how often does this come up? And I tried to make another point: this is a Lisp with an intelligible macro mechanism, do what at least one CL project did: write an infix-eating macro! Then you do not need whitespace either, you can have any syntax you want inside the macro. If the task sounds daunting, well that is why I suggested asking on c.l.lisp for the recommended infix package -- just port it to Arc.
First, disallowing arithmetic operators in symbol names, so that (a+b/c) is interpreted like (a + b / c). All the replies to that, up till now, can be summed up like this:
eds: *I don't really think it is worth it*
kennytilton: *impoverishing the Arc naming syntax*
cadaver: *seems not such a good idea after all*
Secondly, whether or not to have some language support for infix. As can be seen in previous discussion, with eds's system, you only need swapped positions where a literal-in-functional-position is encountered for infix support. Paul Graham said that literals in functional position are valuable real estate, nevertheless a comment regarding such an idea can be found in the arc1 source.
One good point of having support is brevity for math-infix users. The only bad point that I see is that we use up the valuable number-in-functional-position real estate, which could have been used for something else.
Supporting infix may not only be good for math. Consider the following:
(sort (fn (sm gr) (sm < gr)) somelist)
I'm sorry that I can't supply any good examples of heavy maths in real world programs, though I don't doubt that such exist (ciphers?). On the other side, if in a program there isn't any heavy use of maths at all, except for a single mathematical formula that the programmer would like to write in infix, then using a separate macro package would introduce a dependency, and that might make the programmer grudgingly write out the formula in prefix. Another good case for lisp-infix is that when, like me, you tend to copy other's non-lisp formulae then, in eds's infix system, it would look more like its original form.
Supporting infix may not only be good for math. Consider the following: (sort (fn (sm gr) (sm < gr)) somelist)
Consider: (sort < somelist)
And if (sort (fn (x y) (< x y)) somelist) looks awkward then maybe the issue is prefix altogether? I think anyone trying Arc who is new to Lisp might try Just Lisping (in Arc, of course) for a few weeks before even thinking about changing the language. These things take time and until one has done enough coding to get fluent (or throw up ones hands and say it has been three weeks and I still hate this!) one cannot even form an opinion about the whatever that thing might be. It is like an editor or IDE -- I hated the IDE I love now but made myself wait a month before ripping the vendor a new one. Now people accuse me of being on their sales team.
Case in point: Arc. It is hard judging the brevity/parens stuff because I am in pain anyway without a decent IDE, without a debugger, without a standard library... but I slogged my way thru a port of Cells from Lisp to Arc and some of the brevity is growing on me (I deliberately stopped doing a transliteration and reinvented over the keyboard so I could feel the language better) and at this point I think I can say I would not kick Arc out of bed. Something like that.
btw, if we are just talking about one math formula in a blue moon, why bother? I mean, it would be fun if it had no cost, sure, but apparently pg has plans for numbers in the functional position. Anyway...
Although literals in functional position may be valuable real estate, I think that infix math is valuable enough to justify using it (at least until we think of something more important).
The only other thing that was suggested in the comment in ar-apply was that literals in functional position might be constant functions. I think infix syntax gives the programmer far more expressive power than being able to denote constant functions.
Since a number-in-functional-position introduces a context for its own s-expression (not for any of its sub-expressions), it would be possible to expand intrasymbol arithmetic, much like with the . and ! notations, only in infix-context.
(1 + x/y ;expanded: x / y
+ (w/bar func) ;not expanded, function call
This would effectively keep you from referring to any symbols that contain arithmetic operators from infix-context, but maybe this is not really such a problem.
For this to work you'd need truly first-class macros, since it is not possible to definitely detect infix-context at compile-time:
(1 + x/y) ;infix, but may be subject to macro expansion
((sqrt 16)*4 + x/y) ;need to decide at runtime
Being able to work with symbols, instead of the functions they are bound to, would also be better for precedence analysis, since infix is essentially a visual thing.
Possibly. But you still need whitespace in the first position in the call or Arc will try to evaluate the variable a+b rather than the expression (+ a b).
As for precedence analysis, you need some evaluation to happen in order to know that the object in the functional position is a number, after which all your symbols representing functions have been evaluated too.
But even if you did manage to get a hold of the symbols, you would have to make arbitrary decisions about what is an operator and what is a function. (Unless you start evaluating stuff, which gets us back to where we started.) For example, even though expt isn't defined as an operator in the current version, this expression still works:
(2 expt 3)
You might not get proper precedence when using it like this, but at least it is interpreted correctly as a function.
True, (a+b) has no infix context, havn't thought about that; seems not such a good idea after all.
--
Regarding symbol precedence
Getting hold of the symbols: it's the same with macros, you need some evaluation to happen to know that the object in the functional position is a macro. That's why I said truly first-class macros; the functional position is evaluated first and only then a decision is made to either evaluate the already compiled form in the case of a function call, or to macro-expand the uncompiled form in case of a macro expansion.
Arbitrary decisions about operator/function: macros have all the power, you can handle precedence exactly like in your current system, but get the precedence information by looking up a table with the symbols as keys. This will work exactly the same for functions and yield more predictable precedence for operators.
On the other hand, I'd prefer that functions with undefined precedence were forbidden wherever precedence matters, because it's very easy to unwittingly redefine a function that has precedence defined for it. By itself, (2 expt 3) is fine; no precedence handling necessary.
Think of it as: infix-functions make precedence invisible (masked through the binding, you see the symbol not the function); infix-symbols make precedence obvious.
EDIT: Actually, you wouldn't need first-class macros, if you could redefine "fn" and "set" to handle specially all functions that get bound/assigned to symbols that have some precedence defined for them.
There seems to be some difficulty doing this in arc1; "fn" and "set" are kind of special:
arc> set
Error: "reference to undefined identifier: _set"
arc> fn
Error: "reference to undefined identifier: _fn"
