A different view on Functional Programming

https://matiasmorant.wordpress.com/2017/12/25/a-different-view-on-functional-programming/

by wvlia5 • 9 years ago

116 94 9 years ago

matiasmorant.wordpress.com

thethirdone• 9 years ago

Minor typo

reduce(lambda b, b: ab, 1, positives)

Should be

reduce(lambda a, b: ab, 1, positives)

wvlia510• 9 years ago

Thanks, fixing it :)

ungzd• 9 years ago

attempts to reduce programs to equations

Logic programming is close to this. In functional programming, left side of equation always consists of dependent variable and nothing more. Logic programming allows to put any variables on both sides of equation.

jlg233• 9 years ago

I get the idea (doing fp for a living for 15 years) but the article lives in a bubble populated by mathematically pure unicorns: This strength/feature of fp can only weigh in where we have the mathematical formulas, arriving at those is the hard part in most programming jobs - most of the time those who "define" the product/spec cannot even do it in plain English (because they have to make up things as they go, no criticism, just acknowledgement of bizdev-reality).

maxxxxx2• 9 years ago

I always envy people who can work on something that can be expressed with math or some other kind of consistent logic. Most company problems are inherently messy and you just end up with a litany of convoluted code.

jjaredsimpson• 9 years ago

Example please? Because I'm tempted to respond that there are no inherently messy problems, only insufficient solutions.

What problem could possibly exist that only could be implemented in a convoluted way?

Sounds more like: me and my team made trade offs that were, in retrospect, bad and now we don't know how to transform our code into a new program will fulfills the same requirements but is easier to inspect and understand.

wvlia510• 9 years ago

Hi! I appreciate your honesty. Of course arriving at the Mathematical formula is the hard part, that's what it means to actually solve the problem. I consider the fact that you can't code your solution in this style until you have done so as a feature: you can't write code if you haven't really understood and solved the problem. (As opposed to imperative style which let's you implement a half done solution with hidden bugs, not covering all corner cases)

jlg233• 9 years ago

Understood. Just to be clear: I am saying that in most scenarios nobody understands the problem; people figure it out on the go.

Overall I really like the article because it spells what is an essential feature of fp for me much better than I could have. It is just that it is too far from reality of most programming jobs (unless you happen to be Peter Norvig, working on the Mars rover).

catnaroek2• 9 years ago

Of course arriving at the Mathematical formula is the hard part, that's what it means to actually solve the problem.

Most business problems can't be solved with a formula, or with a thousand formulas, or with a million formulas, especially if the problem is “our organization is an illogical clusterfuck” or “we don't even know what we should be doing”.

I consider the fact that you can't code your solution in this style until you have done so as a feature

It's a feature of programming discipline and intellectual honesty, not of functional programming.

As opposed to imperative style which (...)

Functional programming doesn't prevent you from implementing “half done solutions with hidden bugs, not covering all corner cases”.

kaeluka• 9 years ago

What's the mathematical formula that describes a text box GUI item? Languages that look like math might be great for... mathematical problems. But programs are much more than math.

HumanDrivenDev• 9 years ago

How do you mean?

I don't find myself scribbling down mathematical equations when doing things like chaining promises in javascript or transforming sequences with LINQ or marking fields as const. I realise functional programming can go in very different directions to things less mundane, but the general principle of avoiding side effects has been a huge win for me when programming in any language, even C++. It's just easier to debug or write something when you can fix some constraints, ie "this method is referentially transparent".

Those are pretty low hanging fruit, but they help a lot.

jlg233• 9 years ago

Yes, please pick those low hanging fruits wherever possible. If you do and I have to maintain your code later I'll send you a bottle of your favorite dram out of gratitude.

But the article (and my criticism) is about the rather high hanging fruit of mathematical purity - of which "side-effect free" programming is just a side-effect (pardon the pun).

skywhopper3• 9 years ago

Yeah as the other response said, side-effect free programming is great. And while it's a side effect of pure-functional programming, there's absolutely nothing that ties it to a functional approach.

skywhopper3• 9 years ago

It's not even always about "can we spec this?" or "do we even understand the problem?". But when you get into the real world on a non-isolated system, you have to deal with invalid data, unexpected input, network failures, hardware failures, software bugs, security probing, user errors, memory limitations, timing issues, remote system failures, corrupted data, network failures, data storage failures, network failures, network failures, and network failures.

Did I mention network failures? Also, as beautiful as side-effect-free programming is, any non-trivial program will have side-effects outside the program itself. And your beautiful functional code must account for that.

avmich8• 9 years ago

((+/) % #) &. ^.

is the same as

(+/ % #) &. ^.

because adverb (/ in this case) binds with + before three verbs +/ , % and # are grouped into the fork. So some parentheses aren't necessary. It would be cleaner to show three expressions which share the common part as similar in letters as well.

wvlia510• 9 years ago

Thanks, fixing it

kowdermeister• 9 years ago

Is this software? What does it do?

skybrian3• 9 years ago

Have you considered that many people aren't particularly fond of deciphering complicated math equations?

For them, your argument is in favor of avoiding functional languages. Too math-like! A step-by-step procedure might be simpler to understand.

wvlia510• 9 years ago

A good analogy would be music notation (pentagram) I could describe a piece of music in English prose, telling you were to put your fingers and for how long. The language itself would be easier to understand, but the efficiency of information transmission would be very low.

Chinese looks complicated, unless you know Chinese.

The ultimate criteria to judge a language should be how efficiently (concisely) it expresses the concepts of the subject matter.

At most, I will concede you: Goodness_of_language = conciseness × parsing_speed_of_an_experienced_user

Arainach2• 9 years ago

Understandability is more important than conciseness in a team environment. In a team, you're not writing code for you - you're writing code to be reviewed by other people, integrated with other people's code, and maintained by other people in the future.

In the example from this article, all developers I've ever worked with would understand what the "good old C" example is doing within seconds. Most would understand the Python example. Most of them still working in the industry today would be able to figure out what the functional python code was doing without much excessive effort - it would take them longer, which is bad, but if they were working in it every day I'm willing to believe that they'd parse simple examples like that readily enough.

None of them would understand APL. J is even worse. I stared at the J code for a full minute without any comprehension of the language syntax or what was being accomplished. That code isn't readable or maintainable. It is bad code.

dvt• 9 years ago

The ultimate criteria to judge a language should be how efficiently (concisely) it expresses the concepts of the subject matter.

Some might say that the ultimate criteria to judge a language should be how quickly an inexperienced user starts to be fluent in it.

I studied math (so the syntax isn't really an issue), but I think functional programming is completely inappropriate for general purpose programming tasks (e.g. writing a website, writing an iPhone app, etc.).

skybrian3• 9 years ago

But if you don't know Chinese, it would take quite a compelling argument to convince you to give it a serious try, no? If you're not in China, why not continue in English?

Of course leaning more math isn't nearly as hard as Chinese (for the non-Chinese), but this analogy isn't working in your favor.

crdb• 9 years ago

Interesting examples to pick.

I trained as a classical musician and when I picked up the guitar, I was too lazy to learn the notation and learnt the songs by ear and feel instead (this may be why my guitar is collecting dust in a corner). Conversely I know a lot of "amateur" musicians, some pretty advanced, who have learnt songs by ear and can't decipher musical notation of any kind, or understand any music theory.

Chinese looks complicated even to the Chinese, hence Simplified Chinese arriving in the 1950s (and according to Wikipedia, they've started another round of simplification in 2013). Without an alphabet, there are thousands of characters to learn (8,000 in the 2013 version). Ask any Western-born Chinese how fluent they feel and how easily they can read it...

AlexCoventry2• 9 years ago

Yeah, this was a strange post, and it's strange that it's risen so high on HN. I'm not even sure what argument it's trying to make.

mikebenfield4• 9 years ago

aren't particularly fond of deciphering complicated math equations?

But it's not complicated. One of the great things about mathematical expressions is that they are simple. But two of the other great things are that they are concise and unambiguous, and it's those two that unfortunately lead many students to think they are complicated.

mrob• 9 years ago

Mathematical notation is highly ambiguous. See recent discussion of the alleged proof of the ABC conjecture (https://news.ycombinator.com/item?id=15971802 ). If it was really unambiguous then we could parse it like computer code and decide if it is correct or not without all the controversy about what it really means.

marssaxman• 9 years ago

Mathematical notation is not one thing; it is a whole poorly-specified family of context-dependent micro-notations. While I have spent my entire career enthusiastically educating myself on a wide variety of topics beyond anything I was exposed to in school, I have found it essentially impossible to learn any new mathematical notation beyond that which was taught formally. I am capable of understanding novel computer-science concepts perfectly well once they have been translated into a more accessible notation, and of putting those concepts into practice in my own engineering work; but as long as I am struggling through papers which express those concepts in mathematical notation, I understand little and get only as far as I can by inferring what the underlying abstractions must be from the surrounding English text. It very much is complicated, if you aren't already part of an academic system capable of passing it along to you, and so far as my experience has gone there is basically no other way to bootstrap yourself into it. I have spent rather more of my life educating myself outside any academic system than I ever did within one, so the value of a notation with such limited learnability strikes me as being considerably lower than what people who have made a career inside academia might naturally assume.

naasking2• 9 years ago

Too math-like! A step-by-step procedure might be simpler to understand.

A step by step procedure is exactly a mathematical process. Mathematical notation is just a shorthand for some procedures so you don't have to spell out every single step every time. You'd be well served by learning them!

skybrian3• 9 years ago

Mathematically equivalence has little to do with readability. Readability is both important and subjective. Sadly, few people investigate what their audience actually finds easy to read.

oh-kumudo3• 9 years ago

True. I think some FP people, especially the new converts, seem to hold a weird view that simple == shorter code, which is SIMPLY not true.

avmich8• 9 years ago

Size often correlates with complexity. I suspect a size of certain kind can serve as a definition of complexity.

In programming it's often the case that a shorter program is preferred to a longer.

gt_2• 9 years ago

I am something like an intermediate programmer and this is useful.

I want to understand how FP replaces OOP in a similarly concise example. I have a sense that it involves a reconsideration of why OOP is useful, and solving that issue with a widely new approach, but I am not there yet myself. I’d love to see something like these Python comparisons but involving the demolition of an OOP implementation.

wvlia510• 9 years ago

I'll keep that in mind, thanks

AlexCoventry2• 9 years ago

Try this: https://www.braveclojure.com/multimethods-records-protocols/

gt_2• 9 years ago

Thanks. OK. This gave me a good outline. These ideas were somewhat right under my nose, in some of the Python concepts like closures and decorators. I don't know the languages here quite the same but the possibilities are convincing nonetheless. Hmmm... I could see myself getting carried away with this if I put some time into it.

im3w1l• 9 years ago

Python with numpy has a pretty concise solution

np.exp(np.mean(np.log(a[a>0])))

wvlia510• 9 years ago

That's what the J sample is doing (minus the filtering)

xixixao• 9 years ago

I wrote my own functional, Haskell-like, language, and after a couple of years and seeing a couple more code bases in various languages, I am now starting to firmly believe that currying should be strictly avoided (or at least highly discouraged). Obscure symbol operators with operator precedence are also a clear readability problem.

But unlike what this article suggests, these traits are not essential to functional programming. As long as you stick to functions which given values return other values, and your language has support for passing functions to other functions as well, you can reap most of the benefits of functional programming.

naasking2• 9 years ago

I'm mixed on currying. It really increases expressiveness, but it does allow obscure point-free composition styles that can look like line noise.

theoh• 9 years ago

And, quick, what's the type of (.) (.) (.) (.) (.)

How about (.) (.) (.) (.) (.) (.)

tzahola2• 9 years ago

Most of us spend 90% of our time reading other people’s code. So even though writing a concise and elegant formula in J might be a satisfying puzzle, I personally don’t want to deal with the cognitive burden of point-free style when sifting through my colleagues’ pull requests.

dllthomas2• 9 years ago

When it's appropriate, point free style doesn't increase cognitive burden. It's often inappropriate.

tzahola2• 9 years ago

Well said.

pimmen• 9 years ago

In the author's example of the geometric mean, shouldn't the function return an error if any of the numbers were negative? Because the program shouldn't be sending negative numbers to that function to begin with so he/she should maybe get some hint that one of those functions producing said numbers isn't working properly. And if there are no positives, I sure as hell don't want a divide by zero error bringing the program to a complete stop when I could just simply display "Could not calculate geometric mean, check the inputs" to the user.

wvlia510• 9 years ago

The functions in the article are not the geometric_mean. They are functions which first filter the list and then take the geometric mean. I only misnamed them that way for the sake of exposition. The only true geometric_mean in there is the J version

quicksnap2• 9 years ago

This quote made me smile.. Thanks OP! Happy holidays!

Just in case all that wasn’t enough to convince you about the superiority of the functional gospel, take this threat: FP will displace OOP, so start thinking along our lines our you will eventually lose your job

discreteevent• 9 years ago

"The fact that the functions are collected into records and called methods is irrelevant. As a result, the typical object-oriented program makes far more use of higher-order values than many func- tional programs” - William Cook, On understanding data abstraction revisited.

OOP, especially with a focus on immutability, is not that far away from FP. It's not like, say physics where two domains can be conceptually quite different. OOP and FP are just two programming tools meaning that their variation is quite limited by the domain they are in.

quicksnap2• 9 years ago

Objects as a higher-order abstraction, as an encapsulation of data and methods, are all fine and dandy. When I think of OOP, however, I think of deep inheritance. I'm not a great fan of the latter.

platinumrad• 9 years ago

That unnecessary addendum made my eyes roll so hard they still haven't recovered eight hours later.

danidiaz• 9 years ago

One could also say that functional programming prefers expressions to statements —and treats functions as just another expression. When needed, statement-like things are constructed from expressions.

Equations in lambda calculus do seem to have a "preferred direction" specified by the evaluation rules, though referential transparency lets you go "in the other direction" in your head, when reasoning about your program.

Perhaps the programs ~ equations idea would apply even better to logic programming, or term rewriting?

ridiculous_fish• 9 years ago

Say we changed the problem to the geometric mean of non-negative numbers (instead of positive). This allows us to early-out if zero is encountered.

It's obvious how to change the imperative code: `if (x[i] == 0) return 0;` What would this optimization look like in APL or J?

efnx• 9 years ago

I haven’t used APL but it looks like it has list comprehensions, so a simple “x != 0,” would work there

avmich8• 9 years ago

Geometric mean is nth root of product of n numbers.

If you replace any of those numbers with 0, it will all collapse to 0 - perhaps not what you want. But it's not hard to write such a program:

      geometric_mean1 =: (+/ % #) &. (^."1) @: (0&>.)
      geometric_mean1 2 4 8
   4
      geometric_mean1 _2 4 8
   0

If you want to replace negative numbers with their positive counterparts, you may first replace a number with its absolute value:

      geometric_mean2 =: (+/ % #) &. (^."1) @: (>. -)
      geometric_mean2 _2 4 8
   4
      geometric_mean2 2 4 8
   4

Original geometric_mean probably meant to be

      geometric_mean =: (+/ % #) &. (^."1)

- note the copula (assignment symbol) and rank of first verb (^.) .

31reasons• 9 years ago

I think the main feature of Functional programming is not avoiding side effects but abstraction. You can compose different kinds of powerful abstractions and programmers are free to choose their "language" of abstractions, compared to "X Oriented" languages that forces programmer to think in certain terms and limits in ways you can create layers of abstractions.

Veedrac2• 9 years ago

It should be obvious that if a transformation is syntactically trivial, it can only solve trivial problems. If programming is not-math, it's not going to become math just because you change the surface syntax.

A mathematician's definition of a sorted list is different to a programmer's at least in part because a mathematician is interested in a sorted list and a programmer is interested in sorting a list. This difference is intrinsically invariant of the programming paradigm (though not of the context).

This issue isn't so much that this post didn't convince me that there is an underlying, semantically relevant sense in which the APL approach is more mathematical, but that it didn't even seem to notice that this was a thing that needed to be argued.

avmich8• 9 years ago

If programming is not-math

Programming is _always_ math; was it Dijkstra who said "programming is one of the hardest branches of applied mathematics"? It's also engineering - as in "engineers have to do some math occasionally, even if they don't realize that".

I often ask on the interviews to produce an expression returning sorted 3-element list using some simple primitives. I've found that with chosen primitives you still can model different approaches - and even though in all cases the result is an expression ("sorted list is..."), the structure of that expression can model imperative style ("first do this, then this...")

Veedrac2• 9 years ago

On one hand, yes. On the other, classifying whether programming is a math or not doesn't help you decide whether you should use APL, or much else for that matter.

twic• 9 years ago

“Well, that’s supposedly functional code, and it still doesn’t look like an equation” – I can hear you say

It does, we only need to change the syntax (semantics will stay the same), and the underlying mathematical structure will flourish before your eyes.

Hold on. Does this guy think "mathematical" just means "expressed as a string of symbols instead of words"?

wvlia510• 9 years ago

There is a J interpreter Android app which works like a charm. I enjoyed solving the Project Euler problem set in it. You might too: http://code.jsoftware.com/wiki/System/Installation

dahart2• 9 years ago

it’s usually defined by some of its features, such as: reification of functions, avoidance or banning of functions with side-effects, use of higher-order functions and so on. But, doesn’t that sound like a collection of random features? What’s the motivation behind them?

It's a bummer to pose that question as though there isn't an answer, when the answer is well known and very important.

The motivation of avoiding side effects is because we humans make more mistakes when there are side effects. Functional programming is about making a piece of code not depend on anything outside itself. When you do that, it's easier to get right, and harder to screw up the code. In a word, it's safer.

I’ll present you a view which, at least to me, makes that set of features seem coherent; and functional programming, like a deep and beautiful paradigm: Functional programming attempts to reduce programs to equations.

We also make more mistakes when we make things too abstract, remove specificity. Write code that is too concise, and you lose meaning, context, and readability.

The "functional python" is the best looking code in the article to my eyes. It explains what it does to the reader, semantically. The APL & J examples aren't very enticing to me. I'm curious about them, but I wouldn't want to work in a codebase where if you don't know what the name of the function means, you can't figure out what it does.

Making code mathier is good occasionally, when working on mathy problems, but generally I'd rather have words and const statements in my functional programs than a concise expression with single letter variables.

SwellJoe• 9 years ago

"The APL & J examples aren't very enticing to me. I'm curious about them, but I wouldn't want to work in a codebase where if you don't know what the name of the function means, you can't figure out what it does."

Is it possible that APL and J fail this test only because you (and I) don't know how to read APL or J? I think there are some languages that end up being difficult to read due to failings of the language, but I don't know enough to know if APL or J is among them.

Python is, perhaps, more readable than most languages, but I've seen people learning Python have a hard time with many of its choices, so we really have to consider whether we find some version of the code more readable only because we've read a lot more of that kind of code.

Most of the time "easy to use" just means "what I'm used to", and I don't think programming languages are an exception to that.

dahart2• 9 years ago

Is it possible that APL and J fail this test only because you (and I) don't know how to read APL or J?

Yes and no. :) Its a great point; familiarity and practice is a big part of comfort and productivity, absolutely.

I love playing code golf in Python. You can make Python very concise, and very unreadable. But I don't write professional code that way, and I definitely don't have a goal of making production code as concise as possible. Conciseness is good for very small projects, for the 5 minutes while I'm working in the code. Conciseness is awesome for Project Euler. Too concise, and when I come back to my own code days/weeks/months later, I can't understand it at all. Anyone who's coded for long enough on big projects will know the feeling of coming back to clean, well commented, semantically explicit code years after writing it, only to have no clue what it's doing or how it works.

I also know how to read math, and math (typically... almost always) has this very problem. The conciseness is good for proofs and multi-step algebra, you need it while deriving things and working with the math. Once you codify it into a process, the conciseness is a big obstacle to understanding and code safety. I make lots of mistakes with math because it's too abstract. The mistakes are usually easy to fix because it's only a line or two at a time, but it'd be unworkable and unreadable if I had many thousands of lines of math the same way I have with regular code.

skywhopper3• 9 years ago

This is an interesting post, and the code sample from APL got my attention. I have questions.

How do I learn/get/run APL or J? How do I even type the APL code given? What does the J code even mean?

As for the content...

"makes code super concise (less room for bugs)"

Unfortunately, while this sounds great, it does not logically follow. And while geometric mean is well-defined and understood, most functions I'm probably going to write in whichever language are going to be more complicated and less well-defined. So, how does APL/J/pure-functional help/make my non-trivial code more beautiful/concise/bug-free/provable?

wvlia510• 9 years ago

How to type APL characters

They are unicode characters. Type them the way you would type any unicode character. If you have not yet found a practical way of doing it, there are plugins for editors to help you type APL characters with no hassle.

How to learn APL?

There's a Dyalog APL manual which is quite clear, Google it. Also, you can use the GNU APL interpreter. I would recommend learning APL first, only by reading the Dyalog manual and writing programs with pencil an paper, then learn J in detail.

How do I learn J?

Jsoftware provides a free interpreter. They also have a sleek interpreter app for Android. I would recommend to download this app and go through the project Euler problem set. Jsoftware provides all the documentation you will need in their webpage

http://code.jsoftware.com/wiki/System/Installation

what good will J do for me?

The best would be to learn it and see it for yourself. Sadly, you find yourself in Paul Graham's Blob Paradox.I can't get you out.

avmich8• 9 years ago

> what good will J do for me?
The best would be to learn it and see it for yourself.

I've found the statement on the front page of jsoftware.com to be rather accurate:

"If you are interested in programming solutions to challenging data processing problems, then the time you invest in learning J will be well spent."

And "data processing problems" could be understood pretty widely. I've had a case when I first spent about 45 minutes producing a prototype (a program which would generate realistic plans for floor of an office building) using J, then converted that prototype in functionally equivalent (no embellishments) program in C# spending a couple of hours. Certainly working on a prototype took several failed attempts, yet it was still faster than doing the same in C# after the algorithm was already clear.

euske• 9 years ago

I kinda agree with the idea; functional programming turns your program into a series of tubes.

kortex2• 9 years ago

This is exactly it. I don't write 100% functional code, but when given a possibility of implementing functionality using state vs pure function, I aim for the pure function whenever possible.

dgreensp• 9 years ago

you might know that it’s usually defined by some of its features, such as: reification of functions, avoidance or banning of functions with side-effects, use of higher-order functions and so on

The "function" in "functional programming" and the "function" in "avoidance or banning of functions with side-effects" are two different words, by the way! FP is named after the math word, not the programming language word, which means different things in different languages but usually means a kind of subroutine. FP means programming in a style that emphasizes composition of mathematical functions, and in an imperative language this generally amounts to writing your subroutines in a certain way. It just so happens that many imperative languages call subroutines "functions."

d--b• 9 years ago

Declarative programming is the attempt of reducing programming to equations.

Functional programming is a way of organizing code as chains of functions...

oh-kumudo3• 9 years ago

The example is so simplistic and toy-like that it is not remotely convincing.

A different view on Functional Programming

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