4 ms·

> you can even make your own syntactic extensions, so if infix math is necessary, then you can have it ...in what Lisp and how can one do this?

by nnq 14y ago

betterunix 14y ago
In pretty much any Lisp by using macros. It is a 10 minute exercise in writing a simple parser, or you can just use one of the parser generators out there (plenty for Common Lisp, probably plenty for other Lisps).
serichsen 14y ago
Define a function that transforms an infix form to a prefix form. Write a reader macro that understands some special character to mean that the following form is an infix form and uses the function above to transform it. Done.
fogus 14y ago
You could do it in ~15 lines with Clojure: http://www.fogus.me/fun/unfix/infix-src.html http://www.fogus.me/fun/unfix/infix-src.html I suspect most Lisps would require about the same.
fusiongyro 14y ago
Any Lisp, but it turns out to reveal a bunch of Lisp warts. The most obvious one being that no Lisp out there ships with a built-in macro to do this. The subtle truth, though, is that most people who use Lisp start out wanting this and then either give up before they become proficient enough to implement it, or else get acclimated to prefix math and once they are proficient, they don't care anymore. If you were to set out to do this, the first thing you'd have to accept is that the macro is going to look a little weird. For instance: (infixmath 2 + 3 * 4 * (2 + 1)) You're going to want to put spaces between all the terms, every time, because you'd rather have separate atoms for numbers and functions. The next problem you're going to run into is that Lisp doesn't ship with any context-free grammar support akin to Parsec or Yacc. This is the corollary to the point above, that once Lispers become proficient enough to do this they don't want to anymore. Once you're fully enamored with prefix notation, you never find yourself wishing for the kinds of grammar that necessitate this kind of work. (This has a lot to do with why most Lispers hate loop and format too). In other words, you'll be writing your own recursive descent parser from scratch. Once you've written your recursive descent parser to handle infix math, you'll face the next challenge: what to do with the parse tree. The simplest thing to do is just evaluate it. If you were really clever you might be building a Lisp prefix expression as you went and you can just let Lisp evaluate that directly with eval. A part of you will wonder if you should instead generate a compiled function, but then you have to capture the variables properly and it will be a lot more work, but it could become more efficient, since the Lisp compiler would have access to that information and could do better things with it... Anyway, my point is that this is sort of a will-o-the-wisp or mermaid example, because it's intended to capture the imaginations of non-Lispers, but actual Lispers have never actually gotten serious enough about it to make a robust implementation and ship it with the system, because the mindset that values infix math is incompatible with the mindset that produces good Lisp programmers.
- betterunix 14y ago
  The macro will not necessarily look weird, nor will you necessarily need to put spaces between the terms; in Common Lisp you have reader macros, and you can make this as simple as using [] to delimit regions of infix notations. As for why you do not see it done in practice, I would say it is mainly because it is not terribly useful in practice. Infix notation is just what most people are comfortable with, because they learned it in school; it has no real technical advantage, and the need for precedence rules is something of a disadvantage (though not a terribly major issue).
  - fusiongyro 14y ago
    How many projects do you see promoting reader macros? The only package I ever used that came with one was CL-SQL, and it was really unpleasant to get everything working. Reader macros are another example of a feature that Lispers haul out when discussing the benefits of Lisp but never use in practice, because they're almost always more trouble than they're worth. The reason you perceive this as not terribly useful in practice is my overall point: once you're good enough with Lisp to develop this, you think in terms of s-exps and don't see the point. The primary technical advantage of infix notation is that the book you're getting the formula from used it, so it's easier to see if you transcribed it correctly. A secondary advantage is that it's what you use in your head and on paper. If the advantages of Lisp syntax outweigh the advantages of a lifetime of schooling and compatibility with the world at large, you are, at last, a Lisper. :)
    - lispm 14y ago
      Reader macros are there to extend s-expressions. Lisp developers who think in s-expressions use reader macros to implement new data structure syntax (sets, tables, JSON, ...), new code syntax (infix, SQL, Objective-C, ...), ...
    - betterunix 14y ago
      Actually I stopped seeing the point of infix notation long before I started programming in Lisp; infix notation stopped seeming like the cat's meow when I had to actually spend time thinking about how to parse it. I have yet to encounter a good argument for infix notation; all anyone seems to offer is, "Well it's what everyone knows and what we teach in schools!" I am not even sure that infix notation being taught in schools should be pointed to as a positive thing, given that "Please Excuse My Dear Aunt Sally" does nothing to improve anyone's understanding of math (when was the last time you saw PEMDAS written in a proof?). I'm sure there would be endless complaints from parents who were unable to help their children with their arithmetic homework if we suddenly switched to postfix notation in elementary school. I don't think mindlessly transcribing formulas from textbooks is a strong argument for infix notation, and it is definitely not a technical advantage. I am not entirely sure that infix is what people naturally use internally, either, as it is not unusual to hear people say things like, "subtract 3 from x" or "divide the sum of the numbers by the count" -- those look more like something you would see in Lisp than infix notation to me.
muuh-gnu 14y ago
CL-USER> (ql:quickload "infix") ("infix") CL-USER> #I(abs(-4)+5^^2-6) -23

> you can even make your own syntactic extensions, so if infix math is necessary, then you can have it ...in what Lisp and how can one do this?

by nnq 14y ago

> you can even make your own syntactic extensions, so if infix math is necessary, then you can have it ...in what Lisp and how can one do this?

betterunix 14y ago

In pretty much any Lisp by using macros. It is a 10 minute exercise in writing a simple parser, or you can just use one of the parser generators out there (plenty for Common Lisp, probably plenty for other Lisps).

serichsen 14y ago

Define a function that transforms an infix form to a prefix form. Write a reader macro that understands some special character to mean that the following form is an infix form and uses the function above to transform it. Done.

fogus 14y ago

You could do it in ~15 lines with Clojure: http://www.fogus.me/fun/unfix/infix-src.html http://www.fogus.me/fun/unfix/infix-src.html I suspect most Lisps would require about the same.

fusiongyro 14y ago

Any Lisp, but it turns out to reveal a bunch of Lisp warts. The most obvious one being that no Lisp out there ships with a built-in macro to do this. The subtle truth, though, is that most people who use Lisp start out wanting this and then either give up before they become proficient enough to implement it, or else get acclimated to prefix math and once they are proficient, they don't care anymore. If you were to set out to do this, the first thing you'd have to accept is that the macro is going to look a little weird. For instance: (infixmath 2 + 3 * 4 * (2 + 1)) You're going to want to put spaces between all the terms, every time, because you'd rather have separate atoms for numbers and functions. The next problem you're going to run into is that Lisp doesn't ship with any context-free grammar support akin to Parsec or Yacc. This is the corollary to the point above, that once Lispers become proficient enough to do this they don't want to anymore. Once you're fully enamored with prefix notation, you never find yourself wishing for the kinds of grammar that necessitate this kind of work. (This has a lot to do with why most Lispers hate loop and format too). In other words, you'll be writing your own recursive descent parser from scratch. Once you've written your recursive descent parser to handle infix math, you'll face the next challenge: what to do with the parse tree. The simplest thing to do is just evaluate it. If you were really clever you might be building a Lisp prefix expression as you went and you can just let Lisp evaluate that directly with eval. A part of you will wonder if you should instead generate a compiled function, but then you have to capture the variables properly and it will be a lot more work, but it could become more efficient, since the Lisp compiler would have access to that information and could do better things with it... Anyway, my point is that this is sort of a will-o-the-wisp or mermaid example, because it's intended to capture the imaginations of non-Lispers, but actual Lispers have never actually gotten serious enough about it to make a robust implementation and ship it with the system, because the mindset that values infix math is incompatible with the mindset that produces good Lisp programmers.

betterunix 14y ago
The macro will not necessarily look weird, nor will you necessarily need to put spaces between the terms; in Common Lisp you have reader macros, and you can make this as simple as using [] to delimit regions of infix notations. As for why you do not see it done in practice, I would say it is mainly because it is not terribly useful in practice. Infix notation is just what most people are comfortable with, because they learned it in school; it has no real technical advantage, and the need for precedence rules is something of a disadvantage (though not a terribly major issue).
- fusiongyro 14y ago
  How many projects do you see promoting reader macros? The only package I ever used that came with one was CL-SQL, and it was really unpleasant to get everything working. Reader macros are another example of a feature that Lispers haul out when discussing the benefits of Lisp but never use in practice, because they're almost always more trouble than they're worth. The reason you perceive this as not terribly useful in practice is my overall point: once you're good enough with Lisp to develop this, you think in terms of s-exps and don't see the point. The primary technical advantage of infix notation is that the book you're getting the formula from used it, so it's easier to see if you transcribed it correctly. A secondary advantage is that it's what you use in your head and on paper. If the advantages of Lisp syntax outweigh the advantages of a lifetime of schooling and compatibility with the world at large, you are, at last, a Lisper. :)
  - lispm 14y ago
    Reader macros are there to extend s-expressions. Lisp developers who think in s-expressions use reader macros to implement new data structure syntax (sets, tables, JSON, ...), new code syntax (infix, SQL, Objective-C, ...), ...
  - betterunix 14y ago
    Actually I stopped seeing the point of infix notation long before I started programming in Lisp; infix notation stopped seeming like the cat's meow when I had to actually spend time thinking about how to parse it. I have yet to encounter a good argument for infix notation; all anyone seems to offer is, "Well it's what everyone knows and what we teach in schools!" I am not even sure that infix notation being taught in schools should be pointed to as a positive thing, given that "Please Excuse My Dear Aunt Sally" does nothing to improve anyone's understanding of math (when was the last time you saw PEMDAS written in a proof?). I'm sure there would be endless complaints from parents who were unable to help their children with their arithmetic homework if we suddenly switched to postfix notation in elementary school. I don't think mindlessly transcribing formulas from textbooks is a strong argument for infix notation, and it is definitely not a technical advantage. I am not entirely sure that infix is what people naturally use internally, either, as it is not unusual to hear people say things like, "subtract 3 from x" or "divide the sum of the numbers by the count" -- those look more like something you would see in Lisp than infix notation to me.

muuh-gnu 14y ago

CL-USER> (ql:quickload "infix") ("infix") CL-USER> #I(abs(-4)+5^^2-6) -23