Arc Forum | Infix Math

 ; another possibility: constant in functional pos means it gets
 ; passed to the first arg, i.e. ('kids item) means (item 'kids).

 item!kids ; Should really be item.'kids
 'kids.item ; Huh? It's the same?

You could combine it with the dot operator of course but I wouldn't really see a reason for it. (Why would you use 3.+.4 instead of (3 + 4)?)

And actually, the example you gave doesn't quite work (because of quote, you can't actually put a symbol in the functional position using the . operator).

 arc> (= item (table))
 #hash()
 arc> item!kids
 nil
 arc> 'kids.item
 kids.item

But I'm not quite clear on your point about defining precedence in the definitions of +-*/. Perhaps you could elaborate.

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infix-eval is like an implicit function that gets added before every number-in-functional-position. If, like the arc1 comment suggests, a literal-in-functional-position gets applied to its first argument (swapped positions), then every infix expression that would have been handled with infix-eval could be handled by the first infix function:

 (1 + 2 * 3)

 ([infix-eval] 1 + 2 * 3)

 (+ 1 2 * 3)

EDIT: This would also take care of the case where you use infix notation within a prefix expression, e.g. (+ 1 2 * 3), which infix-eval would not get the opportunity to handle. Not sure whether that's important though.

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 (def + args
 (infix-eval
 (cons (car args)
 (cons + (cdr args)))))

It seems a little strange to me to mix infix and prefix. But I don't see any reason to disallow it.

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 (def % args
 (if (some [isa _ 'fn] args)
 (infix-eval (cons (car args) (cons % (cdr args))))
 (apply mod args)))

I'm still trying to work out what is the best way to allow user-defined precedence. In the above case, (3 % 4 + 5) will evaluate as (% 3 (+ 4 5)) not (+ (% 3 4) 5), because by default it is lowest precedence. I wrote a little set-precedence function that can be called to do the job:

 (set-precedence % 2)

 (set-precedence % *)

But this method of setting precedence seems a little like a hack. And it doesn't play nicely with =. Any suggestions would be welcome.

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I was really glad when cadaver suggested this solution to infix syntax. I just don't like the look of expressions like

 +[*[2; f[x/3]]; y]

 2*f[x/3]+y

I also added setter forms so the user can now define precedence of an operator as such:

 (= (precedence %) 2)

 (= (precedence %) /)

 [3] ; always evaluates to 3
 (3 + 4) ; same as (+ 3 4)
 (3 + 4 * 5 - 6) ; when using my infix library

The code can be obtained at the following url:

http://blackthorncentral.net/files/infix.arc

Changes to ac.scm required to make this work:

 (define (literal? x)
 ; ...
 (procedure? x) ; to allow (eval `(,+ 3 4))
 (define (ar-apply fn args)
 ; ...
 ((or (number? fn) (symbol? fn)) ; (3 + 4) means (+ 3 4)
 (if (pair? args) (apply (car args) fn (cdr args)) fn))

This means that infix.arc now gets loaded by default when arc starts. Since infix.arc redefines the existing +-/* operators, if you don't want this to happen when arc loads, you can remove it from the list in libs.arc, then load it or not at your leisure.

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 (0 + x * y * scale)

 (= somelist '(1 2))
 ...
 (somelist 1)

 ('(1 2) 1)

As to your second argument, the +-*/ operators are passed as first-class functions, so, there shouldn't be any optimization happening. Worst thing that can happen is that the compiler doesn't understand literal numbers in functional position, or arithmetic operators applied to first-class functions, and signals an error.

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 (x * y * scale)

 (x * y * (sqrt z))

 (x * Y * (sqrt (t * u + v)))

Everyone feel free to make improvements as you see fit.

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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.

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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.

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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.

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Has anyone looked at the CL infix packages?

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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.

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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

I guess this is kind of a religious thing though. :)

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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.

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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.

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...

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 (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

In fact, math-infix can only benefit if both were added to the language.

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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.

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 (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.

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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"