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?

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.

Could you get most of the same mileage out of capitalization conventions? foo vs Foo vs FOO...

I tried to argue elsewhere that math matters more than you're suggesting: http://arclanguage.org/item?id=2412

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.

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*

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)

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.

  (sort (fn (sm gr) (sm < gr)) somelist)

What are those plans for numbers in the functional position? pg's comments in the arc1 source are completely compatible with eds's system:

Comment 1 is about literal numbers as functions: (1) evaluates to 1

But that is not incompatible with comment two, which is about swapping first and second positions: (1 + 1) evaluates to 2

  (1 + x/y        ;expanded: x / y
   + (w/bar func) ;not expanded, function call

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

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)

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"

This is about syntactic sugar only. Everything is still s-expressions underneath.

I don't know the right way to do this yet (mathematica is the best way I've seen so far) but one thing I'd like to implore Paul to do:

Forbid all special characters in symbol names. Nice as they are, they will be more valuable as syntactic sugar.

(Parting thought:

  x*2+7 - f(5/2,y+8)

  (- (+ (* x 2) 7) (f (/ 5 2) (+ y 8)))

)

(For some background on the rpn example, see http://arclanguage.org/item?id=2115 )

And note that if I remove those error checks, my code is this:

  rpn[lst_] := rpn[lst, {}]
  rpn[{}, {x_,___}] := x
  rpn[{a_Symbol, b___}, {x_, y_, r___}] := rpn[{b}, {a[y,x], r}]
  rpn[{a_, b___}, {s___}] := rpn[{b}, {a,s}]

  (defpat rpn
    (lst)          (rpn lst ())
    (() (x . xs))  x
    ((x . xs) (a b . s))
                   (if (isa x 'fn)
                      (rpn xs (cons (x a b) s))
                      (rpn xs `(,x ,a ,b ,@s)) )
    ((x . xs) s)
                   (if (isa x 'fn)
                      (ero "Too few parameters")
                      (rpn xs `(,x ,@s))))

  f[{{a_,{b_,c_,{{d_},e_}}}}] := g[a,b,c,d,e]

  (defpat foo
    (x (isa x 'sym))
        (list x isa))

  (defpat cmd
    ('niaw)   "cat"
    ('arf)    "dog"
    ('squeek) "mouse"
    (x)       (ero "unknown sound!"))

  ([cons _ (cddr __)] 1 2 3) => (1 3)

(#1 - #2 - #3)&[3,2,1]

with # equivalent to #1.