That's exactly the problem: until you're used to it, it looks nothing like psuedocode. Contrast with Python. I'm not saying it's right, I just think this is the issue.
> Hint: if the first notation is so superior, why don't math papers use it.
Math papers usually use neither the first nor the second.
they use:
(a + b)(c + d)
in the example you propose, and, reversing the operators so that the first style would have:
(+ (* a b) (* b c))
and the second:
(a * b) + (c * d)
math papers would usually have:
ab + cd
So, I'm not sure "math papers do it differently" is the argument you want to use to advance your second syntax over the first.
Of course, since in lisp + and * are variadic rather than binary operators, they are a lot more like the pi and sigma operators applied to sets in mathematics than binary operators. Which are prefix, not infix. So, there's that.
Additionally there's more than one macro system out there to allow for infix math in Lisp... And for non-mathy things, in Clojure at least you're often using the threading macro -> or some variation of do/doto.
I do understand, but I'll also point out that that first expression will often (with longer variables or expressions in particular) be broken out like:
(* (+ a b)
(+ c d))
Which is readable, though not necessarily compact.
Also, * and + in the former, aren't strictly the same as in the latter. * and + take an arbitrary number of parameters in CL. From [0], `(* )` => `1`. I can't test, but I believe `(* 2)` => `2` (the spec doesn't describe the case of a single parameter, unless I'm missing it). `+` is the same, but `(+)` => `0` instead, it's identity value.
Order of operations is made more explicit, and, I've found, it's more useful to think of `+` and `*` as `sum` and `product` rather than `plus` and `times`.
Math does also have `sum` and `product` in the form of Sigma and Pi. Of course, not exactly the same thing (since they operate over a set, not discrete elements).
I would venture to say that the reason infix notation is naturally preferred is related to our psychology, the same way most human languages are SVO (Subject Verb Object) or SOV. VSO languages (Lisp like) are less prevalent.
In general my opinion is that when a majority vastly prefers one alternative, there is usually a strong reason for it (even if it may be irrational) and it's foolish to go against the grain.
I seem to recall that SOV (reverse Polish notation) is marginally more prevalent than SVO among the world's languages... though it is true that most creoles are SVO, which does at least seem to indicate that it's a default of sorts.
Infix is mostly used, in programming, within mathematical and logical expressions. But the majority of my code spends its time in some kind of chain of function calls, which has the verb first. Maybe if I did more with OO-languages I'd see it differently?
Interesting. OO syntax often is object.function(arguments), which is subject-verb-object order. I never thought of it that way before. You can throw some adverbs in among the arguments, too.
That's correspondent with how Java and especially Obj-C and super especially AppleScript programmers try to write code that reads like COBOL, er, English.
If you have Quicklisp[1] installed you can install the "infix" package and get infix notation in Common Lisp[2]:
$ sbcl
This is SBCL 1.2.4.debian, an implementation of ANSI Common Lisp.
More information about SBCL is available at <http://www.sbcl.org/>.
> (ql:quickload 'infix)
; Loading package
(INFIX)
> #i(1 + 1) ; addition
2
> #i(2^^128) ; exponentiation
340282366920938463463374607431768211456
> (defun factorial (x)
#i(if x == 0 then
1
else
x * factorial(x-1))) ; infix function call
FACTORIAL
> (factorial 5)
120
> #i(factorial(5) / factorial(6))
1/6
> '#i((a + b) * (c + d)) ; Put a ' before the #i() to see what code is generated
(* (+ A B)
(+ C D))
> Don't know if there is a similar package for Scheme.
I have to agree with others in the thread that infix in Lisp/Scheme is not the convention, and IMO an awkward fit. Don't recall encountering infix in any published/shared code I've seen, it may exist, but to learn Scheme becoming comfortable with s-expr notation is definitely necessary.
However, there is SRFI 105[0] which describes "curly infix expressions". It's implemented in Guile 2.x, possibly available in a few others but evidently not had a lot of uptake among Schemes.
I wouldn't recommend using infix libraries if you really want to get into Common Lisp though. They're a bit of a crutch for people coming from other languages, but that's it.
Pretty much the whole language is based on Polish notation. The sooner you realise that + - * / are just function names like any other, the better you'll do.
For example:
(+ 1 2 3)
in plain symbols is just:
(function parameter parameter parameter)
But if I were to write my own addition function:
(addition 1 2 3)
it would also be:
(function parameter parameter parameter)
and so is:
(http-request "http://www.google.com")
(function parameter)
If you use infix notation, you're writing half your code in a competely different semantic to the other half. I can't imagine it helping people really get a proper grasp of how Common Lisp works.
Nobody claimed Lisp syntax was optimal for math papers. Neither is C syntax. The Lisp syntax does have advantages for program source code. Sure, it has disadvantages too. Everything is a compromise.
The Lisp syntax is so incredibly controversial, and that fact itself is incredibly strange to me. I see it as a pragmatic engineering decision: let's represent source code as syntax trees, and then sophisticated editing modes become straightforward, macros become straightforward, and the syntax becomes very uniform.
This big thread indicates another reason Lisp isn't popular: because people keep arguing back and forth about the textual syntax, rather than discussing actual experiences with using it.
There are actual features which make Lisp a bit more difficult to understand and a few are related to syntax: especially the code as data feature. Some elements of the language have different purposes: both as code and as data. Symbols can be data and they can be identifiers. Lists can be data and they can group elements of the programming language. Others have only one purpose. For example an array is always data.
Symbols and lists behave differently depending on the context:
Examples for Lisp snippets:
(foo bar baz) ; it could be a macro, function or special operator form
(quote (foo bar baz)) ; here it is data
(defun do-something (foo bar baz) (a b c)) ; here it is an arglist
(defun do-something (a b c) (foo bar baz)) ; one element later it is a form
These context need to be learned and actual visual clues are a) the symbol in front and b) the structure of the expression.
This is puzzling for a lot of people. A few never really take that hurdle.
Yes, they learn the second syntax from birth. There have been arguments to teach the lisp syntax in mathematics due to it being easier to understand with multiple arguments:
(+ x y z a) instead of (x + y + z + a)
Also, there are no order of operations problems with the lisp syntax like there are with traditional mathematical notation (unless you use parens, which makes it look even more lispy).
So why don't we write all binary operations that way? eg. x f y instead of f(x,y). I've always felt more comfortable with prefix notation, especially because it easily generalizes to more than two arguments. I think infix notation is an accident of mathematical history.
because it preserves the "form" of the original expression and generalizes to more arguments. ie. it doesn't require liftAn for whatever n number of arguments my function takes.
Arithmetic is one place where infix notation is generally easier to read. If I were writing a program that basically just did a load of mathematics I may even consider using a different language.. However looking over the software I generally develop, I probably need to use arithmetic in about .01% of the code.
Something nobody has mentioned yet is that, in the C-style version, the precedence rules are eliminating some parentheses. You can't do that in Lisp (except maybe with a macro). But then, in Lisp, you don't have to remember precedence rules.
In this example, the advantage is on the C side, because pretty much everybody who knows any math knows that multiplication has precedence, and they can just read that syntax. If you have to go look at the precedence chart in K&R or Stroustrup before you know how to parse the expression correctly, well, then the Lisp approach is probably more efficient...
You are now arguing against parens. You can have mostly prefix syntax without parens, with blocks delimited with indentation only. Scheme's sweet-expressions[1] are one such example. Anyway, please take my example, remove the parens and check if your argument still applies.
If it does, then it's down to the function names and your (common) misconception that "+" or "^" is somehow more readable, easier to understand or something than "sum" or "sqr". Where I simply disagree. BTW: why do you insist on using infix syntax for a couple of operators, while you use every other possible operator in a prefix notation and are happy with it? What is the difference between "sqrt" and "-" which makes it ok to use sqrt in prefix form?
> Limiting the number of parentheses is also best when possible.
No. It's only best if it aids readability. This is something that Lisp does rather well actually - there are many examples of equivalent Java and Clojure expressions where Clojure version has half as many parens. Getting rid of parens for the sake of getting rid of parens is counterproductive.
Because your version takes up 6 lines! A simple one line expression!
And yes you can remove the parentheses, but not only does no one do that, it still takes up 6 lines. And then you have significant whitespace too.
>why do you insist on using infix syntax for a couple of operators, while you use every other possible operator in a prefix notation and are happy with it? What is the difference between "sqrt" and "-" which makes it ok to use sqrt in prefix form?
Because that's universal and standard for math notation. But also sqrt only takes one argument. If it took two arguments, then it would be perfectly reasonable to add an infix operator for it too. Many languages do add infix operators for everything from combining strings to ANDing booleans, etc, because they are so much more readable.
I think the thing about lisp isn't the fact that it's functions start with a paren. It's the fact it uses function composition to write everything that makes it harder to keep track of. Most languages don't define their functions like this:
c = sqrt(a^2+b^2)
vs.
define(c, sqrt(sum(sqr(a),sqr(b))))
def getMaxValue(numbers):
answer = numbers.first()
for (i in xrange(numbers.length)):
if (numbers[i] > answer):
answer = numbers[i]
return answer
vs.
(defun get-max-value (list)
(let ((answer (first list)))
(do ((i 1 (1+ i)))
((>= i (length list)) answer)
(when (> (nth i list) answer)
(setf answer (nth i list))))))
if you could only use python functions:
defun(get-max-value, [list],
let(answer,first(list)),
do( (i,1,(1+ i)),
(>=(i, length(list)), ans),
when( >(nth(i,list),answer),
setf(answer,nth(i,list)))))
defun(get-max-value, [list], let(answer,first(list)), do( (i,1,(1+ i)), (>=(i, length(list)), ans), when( >(nth(i,list),answer), setf(answer,nth(i,list)))))
Not really. We are demonstrating how multiline statements become hard to read in lisp because in practice you can only use function calls to write everything.
Any language where you write an entire function as a huge one liner expression with functionality in nested function calls is hard to read. It's the behavior, not the syntax per say.
What the actual behavior is doesn't matter as much, even if you can reduce both of them to one liners in many languages.
Not really, since Lisp does not only have function calls, but special forms and macros.
In actual Lisp practice, one uses macros, special forms and function calls.
You seem to have failed to understand the difference.
There are two REAL reasons why Lisp is harder to read than some other languages:
* the syntax looks and works slightly different and most programmers have been trained to other programmning language syntax. With training, this is less a problem.
* Lisp uses a data syntax as the base layer of the programming languages and encodes programs as data. So the syntax of Lisp comes on top of s-expressions. Very few other programming languages are doing that and as a consequence it complicates a few things. The user of Lisp has to understand the effects of code as data. This is something you don't have to understand in Java or Python. It can be learned, but it has to be learned.
At the same time, this code as data principle of Lisp gives a lot of power, flexibility and new capabilities. It makes Lisp different and in some way more powerful than Java or Python. The added power comes from easy syntactic meta programming in Lisp, which neither Java nor Python provide. This has also consequences for interactive programming, since programs can be written and manipulated by programs under user control.
I already mentioned sweet-expressions in another comment. And also, there's one important thing we're forgetting when discussing syntaxes, which is the fact that we very rarely read the code without syntax highlighting, so the examples you posted actually look like this: http://pygments.org/demo/3781004/
I'm not sure if this is what you're talking about but there actually is a Lisp where you can call Python functions. It's called Hy[1] and I encourage you to take a look, it borrows some good solutions from Clojure, but generally is quite an acceptable Lisp :)
Why do mathematicians not use s-exps but syntax that is much more similar to C? Reading "sum" "mul" etc. takes longer than if you have visual anchors like * +. And infix is an advantage for simple expressions, because they split arguments, where as with sexps you have to parse from left to right and count parens.
Please tell me why should I care. No, really - I'm a programmer, not a mathematician.
> Reading "sum" "mul" etc. takes longer than if you have visual anchors like * +.
Citation for this?
IMO it's exactly the opposite, but I may be wrong. Some kind of reference would be nice.
> And infix is an advantage for simple expressions, because they split arguments, where as with sexps you have to parse from left to right and count parens.
Ok, so 2 ("sum" vs. "+", 3 vs. 1 char) additional characters are bad, because they take longer to read, but for example 3 additional characters here:
(+ a b c d)
vs.
a + b + c + d
are good, because they take longer to read. That's interesting.
>> Reading "sum" "mul" etc. takes longer than if you have visual anchors like * +.
> Citation for this? IMO it's exactly the opposite, but I may be wrong. Some kind of reference would be nice.
I know it from myself and don't think I have to to provide evidence that by large most people work like this. Reading and interpreting text is just WAY more complex a process and thus much slower than associating a shape with a meaning.
For example, application designers have known for a long time that it's important to build a symbolic language (icons etc) because that's just way faster (once you have learned what the symbol means, for example with the help of a tooltip).
> I know it from myself and don't think I have to to provide evidence that by large most people work like this. Reading and interpreting text is just WAY more complex a process and thus much slower than associating a shape with a meaning.
I don't think there is a difference in speed between reading "sum" and "+". You don't read the word "sum" letter by letter: you see it as a whole token and your brain recognizes it instantly.
> For example, application designers have known for a long time that it's important to build a symbolic language (icons etc) because that's just way faster (once you have learned what the symbol means, for example with the help of a tooltip).
You're talking GUI, which is different than writing and reading code. There are, for instance, much less GUI elements visible on the screen than there are identifiers even in a short snippet of code and there is much more context available for deduction in the code than in the GUI. I don't think the two situations - recognizing GUI features and recognizing and understanding identifiers in the code - are comparable.
Come on. It's totally obvious that the shapes of * and + are much simpler and much more distinct than "sum" and "mul" (which by the way are relatively short and simple examples for words).
Humans have excellent shape recognition -- recognizing (and differentiating) a tree and a person happens subconsciously, effortlessly. Interpreting the words "person" and "tree" takes way more effort.
Similarly, humans have usually very good spatial sense. If there are persons to the left and to the right of a tree, it is effortless to recognize that they are "separated".
> You're talking GUI, which is different than writing and reading code.
No. I'm talking perception.
> There are, for instance, much less GUI elements visible on the screen than there are identifiers
That depends. There are very complex GUIs out there. But let's assume it for a moment.
(By the way that typically that means the code is not good (weak cohesion)).
> there is much more context available for deduction in the code than in the GUI.
That is not supportive of your previous argument: The more identifiers, the less context per identifier.
> I don't think the two situations - recognizing GUI features and recognizing and understanding identifiers in the code - are comparable.
It's both about perception. It's very, very important that programmers can focus on their work instead of wasting energy building parse trees in their minds, incurring severe "cache misses". Again, take this simple commonplace example:
(sum (mul a (minus (b c)) d)
a*(b-c) + d
If you don't think there's a huge difference I can't help you. I'm sure I need about three seconds to parse the sexp as a tree and figure out what goes with what. Then I have to go back and interpret the operators.
Conversely, the infix/symbol operators example I can map out with minimal, and linear, movement of the eyes. In most cases I don't even need to parse it as a tree -- it's almost a sequence. On a good day, it costs me maybe a second to parse the thing and extract the information I need.
Another advantage of symbols for arithmetic is that they give a sense of security, because one can intuitively infer that they have "static" meaning. While usually words are reserved for things that change, i.e. mutable variables. Being able to infer non-mutability based on shape alone gives a huge advantage.
> Come on. It's totally obvious that the shapes of * and + are much simpler and much more distinct than "sum" and "mul"
I disagree that it's obvious. Moreover, I don't believe there is a measurable difference between the speed of recognizing "sum" and "+", once you're equally familiar with both.
> The more identifiers, the less context per identifier.
I don't believe it's that simple, but we're starting to go into semantics (which are part of comprehensibility of code, but not part of it's readability I think).
> If you don't think there's a huge difference I can't help you.
I think you can help yourself: just go and train yourself in reading prefix notation, like I did. Then get back to this example and then tell me again that there is a huge difference.
> I'm sure I need about three seconds to parse the sexp
I don't even know how to measure the time I needed to read the sexp, it was that short. And I even instantly realized that you've put parens around "b c" in the "minus" call, which would cause an error in most lisps.
> Conversely, the infix/symbol operators example I can map out with minimal, and linear, movement of the eyes.
That's why I used newlines and indentation in my example above. To take your example:
(sum (mul a (minus b c))
d)
This also reads linearly, just in a different order than you expect. This doesn't make it objectively harder or slower to read, it's just unfamiliar to you.
I'm not interested in differentiating between readability and comprehensability. If I want to work on some code I need to comprehend it. That starts "in the small" with the mechanical aspects of "readability", if you will. Where to draw lines is not relevant. Every aspect to the process of comprehension is important. The "small" aspects are more important than you might think: Because they affect every line of code. Whereas there are fewer instances of the more global aspects to comprehension.
Like in a binary tree, where half of the elements are in the lowest level.
> you've put parens around "b c" in the "minus" call
You have a point. One pair of Irritating Superfluous Parentheses less.
> (sum (mul a (minus b c))
> d)
Even the consideration to sprinkle such a trivial expression over multiple lines hints at the superiority of a * (b-c) + d. It's just the most straightforward thing to do. No far-fetched argument can change that.
I'd love to see eye-tracking data which show the tradeoffs between various syntaxes.
The regularity and the simplicty of sexps is of course good for computers, because these can barely associate. Because they can't learn new tricks (they have fixed wiring). But humans have streamlined their languages (which also includes syntax; again, I'm not differentiating here) to their environments since forever.
Sexps are also good for abstraction and meta programming. But as we all know abstraction has a cost and there is no point in abstracting an arithmetic expression. And most code, for that matter.
> I'm not interested in differentiating between readability and comprehensability.
Fair enough, but then please stop using single letter variable names, add type annotations where applicable, provide docstrings and contracts for functions. Comprehensibility is so much more than syntax that I think mixing the two will make for even more interesting, but even less fact-based discussion.
> I'd love to see eye-tracking data which show the tradeoffs between various syntaxes.
Yeah, that would be very interesting. The thing is, there is no such data available, but you still are convinced that one kind of syntax is better than the other. I'm not - from where I stand the differences and tradeoffs in readability of syntaxes, once you know them equally well, seem too minor to measure.
> Even the consideration to sprinkle such a trivial expression over multiple lines
No. It's just different way of getting to the same effect. I don't see why would one be worse than the other (splitting things using infix operators vs. splitting things using horizontal and vertical whitespace).
Other than that, you completely avoided the familiarity issue. Do you think that we're genetically programmed for reading infix syntax? If not, then it means we need to learn infix syntax just like any other. My question was, would someone not yet exposed to infix propaganda have a harder time learning infix (with precedence rules and resolving ambiguities) or prefix?
You also ignored my question about the difference in readability when you are equally well trained in both syntaxes. You can't compare readability of two syntaxes fairly unless you have about equal amount of skill in both. And the fact that readability is influenced by skill is undeniable. So, in other words, are you sure you're as skilled with sexps - that you wrote comparable amount of code - as with infix? Honestly asking.
> No. It's just different way of getting to the same effect. I don't see why would one be worse than the other (splitting things using infix operators vs. splitting things using horizontal and vertical whitespace).
It's very important since size matters. Efficiency of encoding and cost of decoding (~ perception) matters. But if you don't think it makes a difference -- fine, you are free to read braille instead of plain text even if you have perfect eyesight. You can also add three layers of parens around each expression if you think that's more regular.
> Do you think that we're genetically programmed for reading infix syntax?
No. There's this fact that all combinations of basic grammar are represented in natural languages: SVO, SOV, VSO, VOS, OSV, OVS. And then there are some programming languages which don't differentiate between subjects and objects, but go for (OVO), VO, VOO, VOOO... (or concatenative style OV, OOV, OOOV...). Which is great since the goal of formalism is to be "objective". (Note that Object-oriented programming is actually subject-oriented programming from this standpoint. It's not "objective")
Instead I say that it is more efficient if syntax is optimized for the common cases. Shorter is better, if the decoding won't produce more cache misses. Infix and symbols don't produce cache misses for the vast majority of humans, in the case of arithmetic (read: mostly sequential, barely tree-shaped) expressions.
Sexps are inherently unoptimized for the common cases. They are "optimized for abstraction": for regularity. It is an explicit design goal to not differentiate things which are different "only" on a very concrete level. Instead of content, form is accentuated. This is not suitable for the > 95% of real life software that is just super-concrete and where abstraction has no benefits.
I'm sure I have now given 5 to 10 quite plausible examples which support the standpoint that symbols-and-infix arithmetics is good for humans, based on how their mind works. You haven't provided any counter-arguments but just shrunk off everything. But thanks anyway for that. I think I'm satisfied now with the examples that came out.
> are you sure you're as skilled with sexps [..] as with infix?
No. Never will be.
Are you? Show me a Lisp program with more than casual usage of arithmetics and tell my why you consider it readable. By the way, the first google hit I just got for "lisp arithmetic readability" is http://www.dwheeler.com/readable/
As a mathematician, sum(whatever) or product(whatever), reads just fine. There are in fact, a lot of uses of sums and products, so after a while, they are pretty naturally.
Yes, sum(whatever) is fine. What is "whatever"? If it's the common case of two operands, then I don't think you're making a point against a + b.
And you don't think (sum (mul a (minus b c)) d), or (+ (* a (- b c)) d) for that matter, is more readable than a * (b-c) + d, do you?
> There are in fact, a lot of uses of sums and products, so after a while, they are pretty naturally.
I think you are talking about summing up a collection (like, an array, a matrix, etc.) as opposed to building an expression tree. Of course, sum(myIntList) is just fine. That's a whole different story.
There are also the rare cases where you have to sum, like 6 integers. (sum a b c d e f) might not be worse than a + b + c + d + e + f. But that's by far not the common case in most problem domains. The common case is like a*(b-c) + d.
I already admitted that it was a guess. But I still think I can defend it.
Starting in elementary school, everyone learns to read math notation. By high school, everyone knows what
c = sqrt(a*a + b*b)
means. The Lisp version may be easier to read for those who have spent enough time using Lisp. That's not the majority of programmers, though, and it's only a tiny minority of the general population.
Do you think that, to a non-Lisp programmer, the Lisp version is easier to read? Do you think it is easier to read to a non-programmer who has had high school math? Or is it just easier to read for you?
> Starting in elementary school, everyone learns to read math notation. By high school, everyone knows what
We're either talking about objective readability or personal familiarity. What you say is that, after extensive training for many years, it is easier for people to read notation they were trained to read. This is both true and utterly uninteresting.
What is interesting, though, is how much training you need to read prefix and how much training you need to read infix. It's obvious that infix takes more time to learn: operator precedence and things like using "-" in both infix and prefix forms make it objectively more complex than prefix notation. You just forgot how much time you spent learning it.
> Do you think that, to a non-Lisp programmer, the Lisp version is easier to read? Do you think it is easier to read to a non-programmer who has had high school math?
Again, this is not interesting at all. You're talking familiarity, not readability. Of course, it's easier to read something you've been taught to read. To make this more objective, take an elementary school kid - who wasn't exposed to years long infix propaganda - and check both notations' readability with them.
Personally, I learned to read just about any kind of notation used in programming. From my observations, there are only minor differences between the speed of comprehension when using different notations - once you've trained enough. The difference is how much training you need. I can tell you that reading J - an infix language, it's an APL descendant - took me much, much longer to master than reading Lisp.
Learning lisp syntax requires just a very short introduction.
In SICP, it is said that they never formally taught lisp at class. The students just pick Lisp up in a matter of weeks.
