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Is it worth using Monads in Perl ? and what the Monads are ?

by rootcho (Pilgrim)
on Jun 10, 2007 at 23:43 UTC ( [id://620386] : perlquestion . print w/replies, xml ) Need Help??

rootcho has asked for the wisdom of the Perl Monks concerning the following question:


I was reading lately some Haskell tutorials. The thing that come and come again was Monads :).
There is so many tutorials on Monads over the internet but almost none of them I think is describing the Monads well.
In most of the cases they explain just part of it..what I mean first most of them are Haskell oriented (nothing bad with that but, generally most of the ppl still learn Haskell or even don't want to learn Haskell at all, so it is of no bigger use for them), other tutorials underline the mechanics of Monads these are a litte better because most ppl coming from imperative background can relate things.
And finally there is those written from the perspective of other languages Perl,Python, Ruby, JS... the worst thing about them is that they will show you how to implement Maybe and/or State monads, which is good but ..:(
What all of them forget to explain why the hell you will want to use these monads in imperative languages !?
Is there any use at all and if yes when ?

So as I'm saynig there is no one good tutorial on the net for Monads. You have to read them all to combine the pieces to figure something at all.

The best tutorial IMHO is this one :

OK. I'm not trying to blame the authors of writing bad tutorials what I'm tring to say is that they always concentrate on a narrow view of either Monad mechanics or usage or examples or Haskell ;).

I will try to explain this to myself and to you (please be warned that I'm not totaly sure that I understand Monads myself ;) /so bear with me and don't blame me for being totally wrong/, what I'm trying is to provoke a discussion on the Monads mechanics, examples in Perl, when to use them, why to use them..etc..

Let start. From what I read the Monads in Haskell are used to bring ability to add control flow to the language (like the imperative languages). (Haskell is more like Math, rather than C-like lang where you describe the steps by step description how to solve a problem)

So if we have to translate this to Perl and similar lang. we should use Monads (design pattern :), some go nuts when they hear this) when we have to do "out-of-order" operations, which break the flow of the program. What are these things , IMO :

- Exceptions
- Debugging
- Logging
- State handling
- etc...fill in

We have one additional benefit to this and it is the ability to interfere to all this activities from outside of the normal-flow too, what I mean f.e. enabling/disabling debuging/logging or modifing the handling of them w/o changing our original program which is a good thing.

So what is the simplest way to implement Monads in Perl (for now w/o using objects). In general from my understaning it should be something like this (in its simplest possible form) : ("bind" is the focal point of the whole monad thing)
sub bind { my ($callback, @args) = @_; $callback->(@args); }
Then in our main program we do something like this :
bind(\&debug, "Entering xxx()"); ... bind(\&logit, "Username : $user logged in") ... and so on...
By itself bind() it is not that interesting. But now we can modify it to do millon other things we have not forseen when we wrote our program.
This is the point where I start loosing the grip with the monads. Normally in the examples instead of passing @args, they pack them in a container which would look more like this (if i'm not totaly wrong). :
sub bind { my $monad = shift;#self my $callback = shift; my @args = @_; my @res = $callback->(@args); $monad->pack_args(@res); return $monad } my $monad = new Monad; $monad->bind(\&debug, "Entering xxx()"); ... $monad->bind(\&logit, "Username : $user logged in") ... and so on...
I.e. our callback function will always get the arg as normal args not like monad. And then like result we will get the monad again and so on.. Still don't quite understand the purpose of all this (if i can do it simpler in the first case). Except that now I can modify the Monad-object to store much more state and info and of course that OO-way is more scalable.
(Yes they also mention they want to separate/decouple the things in a way so that Monad live in its own universe, so that your original program logic is not modified when you modify the Monad. I can see the benefit of this ) What I'm worried is that it now becomes much more hard to use, I mean alot more typing and of course it becomes slower.

And finally my last point, this seem alot to me like Aspect-design pattern ?!

So again excuse my total ignorance ;) and please explain and elaborate more on the topic.

Thanx for your attention.

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Re: Is it worth using Monads in Perl ? and what the Monads are ?
by BrowserUk (Patriarch) on Jun 11, 2007 at 07:02 UTC

    Disclaimer: This is a viewpoint of a 'failed', would be Haskell programmer, with all the jaundiced opinion that entails.

    Haskell needs Monads; Perl does not.

    One simple description of "pure functional code" is: Every function always gives the same output, for the same set of inputs; and has no side effects.

    Which sounds quite reasonable, and given a certain spin, very laudable, but here are a few (and just a very few), of the things that you can't do whilst remaining 'purely functional'*; things that most programmers in most programming languages take for granted.

    *...without Monads

    • You cannot read input--from a file, database or user or socket or another program via pipe, etc.

      The function you call to get the input would produce a different output for the same inputs.

    • You cannot read from a random number generator.

      Ditto. And the state of the PRNG (or other source) would be left in a different state to when you called it--that's a side-effect).

    • You cannot read the date or time; or the cpu usage; or free capacity of your harddrive, etc.


    • You cannot write output--to a file, or screen or database or socket or pipe etc.

      The output medium would left in a different state--a side effect.

      The call could return a failure: the disk was full; the socket was closed; the database had been modified by another program.

    In essence, a purely functional program has to be completely self-contained at compile time. This is because the compiler has to be able to freely substitute the value of any given function wherever that function is used within the program. A purely functional program has no concept of sequence. They are defined in a declarative manner in terms of function definitions, whereby function A is defined in terms of some other function or functions (or itself), and a few constants. Once it is declared, its result (for any given set of inputs), is fixed forever. That means, in theory, the compiler can substitute its defined value at every point in the program where it is used, and in any order, and so reduce the program by substitution, until finally everything is reduced and the result is known.

    A constant program

    In other words, the results of every purely functional program is decidable by the compiler, and its result is known by the time the code is compiled. There is no need to actually run the program ever because the result will never vary--it is a constant!

    Besides, even if you did run it, the program could not output the result because that would have the side effect of changing the file, screen or wherever you output the result to. Ie. if you output the result twice--to say, the screen--the second time you output it, the output from the first time would still be on the screen meaning the result of doing it the second time would be different from the first. It would have had a side effect. And that's not purely functional.

    PFP? Purely Functional Programming or Pretty F..useless Programming*

    Read on; it's a joke :)

    Of course, that would make for a pretty useless programming language. For example, you could never write a purely functional compiler--that is, a compiler that is purely functional, rather than a compiler for a purely functional language--because you couldn't read the source code. So every program the compiler would ever compile would have to be embedded into the compiler. And you wouldn't be able to write out the compiled program, which would kind of negate the purpose of having it.

    Sequence in a program == procedural

    So, in order for a purely functional language to do anything useful, it has to incorporate some mechanism for performing IO. For getting data in and outputting results. And it has to introduce the concept of sequence. That is, it is necessary to read the data before you can perform the calculation upon that data; which in turn has to happen before you can output the results.

    But to do that, it becomes necessary to distinguish those functions that are purely functional--give the same results every time and have no side effects--from those that interact with the world outside of the program, and so are not: read() will produce a different result each time you call it; write() will have a permanent (side) effect upon the world each time you call it. It needs to distinguish them so that the compiler can know which functions can safely perform its reduction-by-substitution magic upon; and which it cannot.

    The mechanism chosen to distinguish the two is 'Monad'

    Ignoring the formal (and extremely obscure) mathematics behind this concept which I admit to not understanding at all and could never paraphrase, in simplistic terms a monad is a black box that represents (or contains) the world (or some small part of it), outside of a given, purely function program.

    And a monadic function is a function to which you must pass one of these monads as one of its parameters, and which returns (a different) monad as its only result. The output monad is the (constant and unchanging) result of applying that function to the input monad. If you call that same monadic function a second time, you will be passing a different monad as input; and recieve another, different, new monad as its result, And each time you run the program, the initial monad representing the outside world will be different--time will have passed; things will have changed--and when you call the monadic function, the input monad will again be different from any other time it has been called, so it will be free to return a different monad to every other time it has, or will be, called.

    And so the "same output for the same inputs" rule of functional programming has not been violated. And as every time you call, you pass a different monad in and a different monad out, any given monad only ever has one state, so there are no side effects. In this way, you have introduced the concept of sequence into a purely functional program, without violating the purely functional ethics(*).

    Every Perl program is a Monad (or maybe lives inside a Monad)

    In Haskell's terms, every function in a Perl program is monadic, carrying an implicit monad as an input parameter, and implicitly returning another as one of its return values. Passed into the 'main()' function at startup, and return (another) from whence it came--the OS? the world?--when the program terminates.

    As Perl does not subscribe to the purely functional ethic, it doesn't need the obscure, high maths concept of monads to 'excuse' its use of state, side-effects and the real world.

    Smoke and mirrors

    *Of course, some of you may, like me, consider this a diversionary tactic--so much smoke & mirrors--to obscure and defend from the charge that you cannot have a purely functional language and do anything useful.

    You may also consider that need to latch onto such an obscure and ethereal concept to explain the ethics of a programming language would simply go away if it was admitted that you cannot have a purely functional language. That, if you accept that some parts of any given program lend themselves to being coded in a (purely) functional style; whilst other parts do not, then you can use functional techniques where they are advantageous and not where they lead to clumsy or awkward coding (or their reliance on obscure and difficult to understand concepts).

    However, to a non-mathematician like me, the concept of imaginary numbers is difficult and obscure, but there is no denying their usefulness in allowing some things to be described and calculated, that would be very difficult, if not impossible, without them. And just as I have to accept the concept of imaginary numbers and the rules that define them; without trying to visualise what they look like :) So it may be that there are benefits to doing the same thing for monads. Just accept that they follow a set of rules and in doing so allow X, Y & Z that would be much harder if not impossible to do without them.

    The flaw

    The flaw that I see in most of the descriptions and treatise on monads I've seen, is that they fail to outline what X, Y & Z are.

    One possibility that seems to make sense to me, is that monads are a way of informing the (Haskell) compiler which functions it can perform its reduction through substitution processes on at compile time, and which it cannot. In this view, they are simply (or not so simply) a flag applied to each function definition saying: This function has side effects; it can only be reduced at run time.


    I have seen the argument that purely functional code is 'provable'. And therefore purely functional programs are more reliable than non-PFP. But there is an old & well-known saying that a chain is only as strong as its weakest link. And if a program requires input--and every useful program must, otherwise its result is a constant; indeed, the entire program would be a constant--then you cannot pre-prove it. You have to test it with a variety of inputs. And any non-trivial program will have far too many possible inputs to test exhaustively, so you will never be able to 'prove' any, non-trivial, useful program.

    The counter argument to that is: If you segregate the program into its purely functional, provable parts; and its monadic, non-provable parts, then you can reduce the number of possible errors, and therefore the risks, and therefore the amount of testing required. And that's a pretty good argument. Reduced risk and reduced testing are very laudable, real-world goals.

    However, in order to prove even the functional parts of the program, it becomes necessary to not only prove the algorithms they represent; but also that the code produced by the compiler, from the high level language descriptions of those algorithms; is also correct. That is, you have to prove that the code the compiler produces from the Haskell language source code descriptions you feed it, actually performs exactly what that description says it should.

    The rub

    And there's the rub. ......the Haskell language source code descriptions you feed it...". The compiler takes input. That input is infinitely variable. And we just got done saying that you cannot 'prove' a program that takes input; you can only test it.

    Chicken & egg

    So, it's a chicken and egg situation. If you had a provable implementation of a compiler that was built from provable descriptions of its algorithms, then you could use it to build (implement) programs from provable descriptions of provable algorithms.

    Until then, you will need to test programs--statistically. And as long that is true, there will never be a 100% guaranteed, bug-free program.

    A question

    So, the question becomes, are there (any) benefits of imposing this obscure view of procedural code--that's really all monads are (or perhaps; allow is a better term), that make the alienation and conceptual difficulties that their use introduces to the world of programming, worth it? Is provability of algorithm descriptions, without provability of the code that converts those descriptions into code, worth the costs?

    Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
    "Science is about questioning the status quo. Questioning authority".
    In the absence of evidence, opinion is indistinguishable from prejudice.
      It seems like your entire article would make a lot more sense if every instance of the word "monads" was replaced with "the IO monad". There are other monads, you know. Sequencing IO actions is probably the worst example of a monad, because it gives the least insight into how monads in general are put together and used. (In particular, the IO monad is primitive in Haskell by necessity, but it's the only monad like that.)

      It seems like an especially useless abstraction to be making if you only have that one example, and you're coming from an imperative background (like perl), which is quite a lot like working in the IO monad all the time.

      If you'd like to see other examples of monads and what they're good for, I highly recommend starting off with a look at Parsec, which is a library for parsing implemented in Haskell (and then reimplemented in a bunch of other languages). A simpler decent example is the list monad, which gives you what are essentially list comprehensions, or what computer scientists call nondeterministic computations.

      Also, having the monadic abstraction lets you write algorithms which are generic over a wide class of monads, and then apply those at specific monads for a variety of effects.

      Let me give a somewhat involved example, so you can hopefully get a sense for what I mean. A friend and I wrote an L-system fractal generator which was nondeterministic, in the sense that each rule gave a list of possible expansions for a symbol, and it enumerated all possible expansions of the L-system. For display on the screen however, we wanted to choose a random one. Generating the whole list was wasteful, so rather than do that, we replaced the lists of rules in the input to the algorithm with computations in a random-generation monad which would emit one of the results in the original list at random. Since the expansion algorithm itself was generic over monad, only the input to it had to change, and we had a randomised L-system generator.

      Similar changes to the input could be made to incorporate state transitions into the expansion of the L-systems (or even continuations, if you're crazy), all without changing the code that actually does the expansion.

      So what are monads really? They're embedded domain specific languages which have been constructed to conform to a particular basic structure so that various control structures and generic algorithms can be shared across those embedded languages. There are lots of good examples in Control.Monad. For instance, forM/mapM is essentially a for-each loop which works in any monad. This saves you the trouble of implementing a new for-each loop in every new EDSL you write.

      That is, when you're implementing your EDSL, if you just bother to implement return and bind, you immediately get a nice API of control structures for free. Implement mzero and mplus, and you get an instance of MonadPlus, which gives you a bunch more.

      By encouraging people to write and use EDSLs (which are essentially just really good APIs) you encourage people to write code which is closer to the domain, and hence easier to think about. I/O is a red-herring -- I/O is handled by a monad in Haskell not because it's absolutely necessary that it be handled by a monad, but because it's possible, and so you get all the basic control structures for I/O from that same monad library for free.

        It seems like your entire article would make a lot more sense if every instance of the word "monads" was replaced with "the IO monad". There are other monads, you know.

        Yes, I do know, but please think about where you are reading this and the target audience, as well as my admission to being a 'failed' Haskell programmer. You should not expect deep and authoritative discussion on Haskell in this environment :)

        It seems like an especially useless abstraction to be making if ... you're coming from an imperative background, which is ... like working in the IO monad all the time.

        That was and is pretty much exactly my point. I'm aware that the bits I've elided make the statement much less definitive than I did, and within that lies the power of the monad abstraction, but that brings me back to my final question above, which can be paraphrased as: Do I, as a jobbing programmer need that power. It may be a endlessly fascinating subject for the academic/language designer, but does it really give the working stiff something that he does not already have in other languages.

        Isn't there a dichotomy between these sentances from your first and last paragraphs?

        • "(In particular, the IO monad is primitive in Haskell by necessity, but it's the only monad like that.)"
        • "I/O is handled by a monad in Haskell not because it's absolutely necessary that it be handled by a monad, but because it's possible,"

        From this point I'm going to have to resist the temptation to get drawn into arguing about the efficacy and effectiveness of Haskell (here). This is the wrong place, and I am not qualified. I've already allowed myself to over-extend my reach, and I'll probably regret doing so. But I'd be willing to continue and would relish the opportunity to learn) off-post via email, but not here.

        However, your arguments above remind me of a post I made some time ago. Please do not take offense. Nor think I am aiming the first line (or most of the rest of it) at you. And definitely ignore the context in which it was posted. But...there is one bit that I think is applicable, though even that isn't worded quite right for application in this context.

        ...and succeeded in re-creating your system using theirs, will you be in a position to counter their objections to your system, in their own terms.

        Only then will you have the ammunition with which to prove the veracity and accuracy of your system, in a way such that they can accept it.

        What I'm trying to get at here is that if you 'buy in' to the whole Haskell experience--from the efficacy of Hindley-Miller and functional programming, and purity up--then everything you say above, and all the deep discussions and treatise and papers in the Haskell world may (probably) make sense.

        But, if you are coming from a long and deeply imperative background as I am, and with respect, the vast majority of the worlds programmers are, then without the mathematical grounding to fully appreciate the full implications of HM, and the category theory underlying monads, it does seem like, as you put it above, " an especially useless abstraction".

        The problem with the rich and extensive set of information available on Haskell, and monads in particular, is that for the most part, it assumes a deep understanding of those underlying (and often obscure) mathematical concepts. It is often also somewhat pejorative and condescending ("... or what computer scientists call nondeterministic computations.") of those that do not come from that background.

        I'm not offended by that. It may well be true that I am either too old and set in my way, wrongly educated, or just too stupid, to ever make the journey of enlightenment required. Required to allow me get beyond the feelings of frustration when I encounter something (in Haskell) that seems clumsy, over-complicated or outright impossible, when I know that I could do that same thing in any of a dozen other languages in my sleep.

        You'll note (or rather I'm going to do it for you), that I never said that Haskell didn't need or benefit from monads. Indeed, I said the exact opposite. And when I asked "Are monads worth [the bother]", I was doing so from the perspective of someone who has written hundreds of programs and 10s or 100s of thousands of lines of code (guesstimate!), without ever once needing 'monads'.

        And to explain that monads are necessary "because they ensure referential integrity", isn't enough. Because I've written those same number of programs and lines of code without needing that either. And that's where the quote from my old post above comes in.

        Until I can understand how the provision of the same facilities Haskell has would benefit my programs in Perl (or C, or Java, or ...), then it's just not possible to see beyond the argument that Haskell only has those facilities because Haskell needs them.

        And Haskell only needs them because it makes certain (dogmatic) decisions about the need for purity, referential integrity, strong typing and provability. And all of those are just too easy to dismiss as unnecessary and/or non-beneficial.

        (I can see) There are several aspects of Haskell that are desirable, but as a language it is impossible to have those bits without taking all the rest, and the rest imposes such burdens upon the development and thought processes, that I have to question whether they are worth it.

        Don't misunderstand me. I know (for example) that proficient Haskellers tend to win against-the-clock programming competitions with unerring regularity, almost to the exclusion of all other languages. So i know that, in the right hands, Haskell very much challenges and often surpasses Perl at it's own game in the programmer productivity stakes. But, how many expert Haskellers are there?

        And how many of those programmers earning a living on a daily basis in other languages have the (maths theory) background and nouce to make the transition to using Haskell? And if they have to acquire a good understanding of category theory and type system theory and dog knows what else in order to see the benefits of the transition to using Haskell, how many of them are going to have the incentive to try?

        Until someone can explain its benefits to them in their own terms, the incentive to learn enough to understand the concepts in Haskell's terms, and those of functional programming purity, are minimal. Mostly just curiosity, which is easily 'cured' by work pressures, or condescension, or apparently self-describing, self-confirming 'belief' systems.

        Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
        "Science is about questioning the status quo. Questioning authority".
        In the absence of evidence, opinion is indistinguishable from prejudice.
        If you'd rather read that with proper spacing, see:
        Oops, all the spacing got squashed out of that. Oh well.
      Unfortunately, I/O is probably the worst example of a monad there is. The next worse example is the state monad. The "Maybe" monad is much better example, especially for beginners.

      You might like the Clean language more, where I/O is done with unique types. And then, once you get tired of carrying this "world parameter", you might say to yourself, "Why don't we tuck this boilerplate away into a function, so that we don't have to mess with it all the time?" Bingo, there's the usefulness of monads.

      And to answer the OP's question, there is essentially no reasonable reason why anyone would use monads in Perl. Besides the fact that Perl's syntax makes it heavyweight and messy, its lack of static typing makes it hard to program in a functional manner.

        Unfortunately, I/O is probably the worst example of a monad there is. The next worse example is the state monad. The "Maybe" monad is much better example, especially for beginners.

        As I hope I demonstrated above, I understand what monads, and the IO Monad, are and do.

        The problem I have with monads, is not the name, or their obscure math derivation, or using them (much, though I admit I probably couldn't derive my own any time soon).

        The problem I have with them, is the need for, and the benefits of, having them at all.

        They are, emotionally, just a way of concealing the fact that Haskell programs contain code that has state, has side effects and is procedural. Technically, they are a way of indicating to the compiler which functions have no side-effects and can therefore be safely re-written at compile time; and which aren't. And that's makes them a really awkward way of setting a flag.

        It would be so much easier to simpler to have a keyword that could be placed at the top of a module or even half way down that says any definitions above this line are purely functional and anything below it is procedural code that has side effects. The 'monadic code' then just becomes normal procedural code that carries an implicit 'world state' from one step/statement to the next; it could be coded in a normal, procedural style with loops and state and side-effects; and without all that faffing around that monads introduce.

        No need to (badly) re-invent all the standard procedural constructs--like try/catch et al.

        At this point, I'm gonna stop, and ask you to email me (address on my home node) if you feel like continuing this, because this has become about me and Haskell (and Clean--which I do like more, though it lacks the community and available tutorial information that Haskell has. Eg. A search for lang:clean on google codesearch finds zero hits!), and has ceased to have any relevance to Perl. I'd enjoy the rebuttal :)

        Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
        "Science is about questioning the status quo. Questioning authority".
        In the absence of evidence, opinion is indistinguishable from prejudice.

      You may be interested to know that Haskell did not always use monads for I/O. This paper describes three alternative, purely functional methods for implementing I/O in Haskell that were used before monads:

      It is also important to note that monads not special things wired into the compiler. They are built using normal Haskell code and live in the standard libraries.

      It is quite possible to write real programs in Haskell without using any monads. Of course, you would probably just reinvent them without realizing it.

        On the Expressiveness of Purely Functional I/O Systems

        It's possibly a very interesting paper, but all I can find online are citations and references--which means it might as well be printed in a 9 point font on the Moon for all the accessability it has.

        It is also important to note that monads not special things wired into the compiler. They are built using normal Haskell code and live in the standard libraries.

        That sounds promising. Care to show an example of how to read from stdin and write to stdout without using a IO Monad? Or just perform an question and answer session interactively without them/it?

        It is quite possible to write real programs in Haskell without using any monads.

        Again, care to post an example that can be compiled with GHC v6.4?

        Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
        "Science is about questioning the status quo. Questioning authority".
        In the absence of evidence, opinion is indistinguishable from prejudice.
      If I am not wrong, FP-people say that absence of side effects simplify proofs of correctness (wrt specifications), not that proofs of programs with side effects are impossible.

      For a comparison of 4 methods of proving programs with side effects (FloydHoare logic, E. W. Dijkstra's Discipline of Programming, Cliff B. Jones' Vienna Development Method (VDM) and E. C. R. Hehner's Practical Theory of Programming) see:

      E.C.R.Hehner, What's wrong with formal programming methods? (PDF), Conference on Computing and Information, Ottawa, 1991 May (keynote address, invited); chapter in Advances in Computing and Information, Lecture Notes in Computer Science v.497, Springer, Berlin, 1991, p.2-23

        Wow! A rave from the grave.

        First off, thank you for the links. I've only browsed most of then so far, but they will make for interesting reading over time.

        If I am not wrong, FP-people say that absence of side effects simplify proofs of correctness (wrt specifications), not that proofs of programs with side effects are impossible.

        Maybe they do, but not in most papers I've read. When I read a formal proofs paper that deals with a real world problem rather than isolated, mathematically pure problems--like incrementing a number or multiplying two numbers together--then I (and other programmers), might to start to sit up and take notes.

        What do I mean by a real world problem? Let's start with something really trivial. Command line filter programs. Say wc and tee. Show me (and explain) a formal proof for one of these programs. How it will handle taking input from a local disk file; or a remote disk file; or via pipe from another program; or from the keyboard; and ditto for the sink; and still do its job.

        But they never do that. Somehow, they manage to persuade someone, somewhere to pay them public money (it has to be public, because no one would fund this stuff privately), to write papers on how to "prove" a computer can successfully increment a number. And they come up with

        Let's try it on a trivial example. Informally, the specification is to increase the value of integer variable x . Formally, we face a problem: we are given no way to relate the final value of a variable to its initial value. We have to use a trick: introduce an extra variable, not part of the state space, to carry the relation. We write

        ∀X� {x = X} S {x > X}

        meaning: whatever x may have been equal to at the start, it is greater than that at the end. For S we might propose the assignment x:= x+1 . To prove it correct, we must use the assignment rule {substitute e for x in R } x:= e {R} In the example, this means

        {x+1 > X} x:= x+1 {x > X}

        The precondition is not what we want, so we now use the consequence rule (∀σ� A ⇒ P) ∧ {P} S {R} ∧ (∀σ� R ⇒ Z) ⇒ {A} S {Z} where σ (the state) stands for all variables. In the example, this means we must prove

        ∀x� (x = X) ⇒ (x+1 > X)

        which is now a simple theorem of ordinary logic. All that, just to prove the obvious!

        No shit Sherlock. All of that, to prove $i++? And that doesn't even handle the case where $i = 2147483648;. They'll undoubtedly determine that the outcome of incrementing that to be 2147483649, but the reality is, on 32-bit computers systems that it might be. Or it might be -1.

        But that formalism above won't consider the case of what happens when you increment a signed integer across its register size boundaries, because mathematicians live in a theoretical world of Real and Natural (who knows how many other obscure theoretically infinite, mathematically convenient) number domains, and none of them pay the slightest consideration to mundane realities like register sizes and word lengths.

        Now lets look at what they come up with for multiplying two numbers. This is the modern, advanced, abbreviated, compacted version. See the last linked paper above, page 9 for the unabridged nightmare:

        x' = x y�: s:= 0; s' = s + x y; x:= s

        s' = s + x y�: if y=0 then ok

        else if even(y) then (x:= x 2; y:= y/2; s' = s + x y)

        else (s:= s+x; x:= x 2; y:= (y–1)/2; s' = s + x y)

        I won't pretend to fully understand that, so I'll ask a few questions: Does it handle register overflow? How about one or both inputs being #NaN? Or either or both being one of the two flavours of infinity?

        I'm not mathematician, but take a closer look at the case above where if y=0 then ok. According to the paper, "ok is the identity relation and then later on "The empty (do nothing) program ok is the identity relation". Que? The way I read that, if the second (or one of?), the inputs to multiplying two numbers is zero, we do nothing! So-orry, but my schoolboy arithmetic tells me that anything times zero is zero--not throw your arms up in disgust and do nothing.

        Bad rhetoric

        I realise that the author is a much clever person than I am, but right from the start of this paper there are a bunch of things that just don't ring true.

        Formal programming methods allows us to prove that a computation does what its specification says it should do. More importantly, formal methods help us to write specifications, and to design programs so that their computations will provably satisfy a specification.

        This is analogous to the use of mathematics in all professional engineering: civil engineers must know and apply the theories of geometry and material stress; electrical engineers must know and apply electromagnetic theory.

        So why don't software engineers know and apply a theory of programming?

        I've broken that into three paragraphs. The first is the sales pitch. A broad-termed, theoretically desirable goal. A panacea. A magic bullet.

        The second paragraph is supporting argument.

        • Argumentum ad verecundiam

          in all professional engineering

          Most civil engineers to not use theories of geometry and material stress. They use tables.

          If this member is at this angle carrying this load, it will need to be--scan across for the angle, scan down for the load--this strong. And looking that up in the manufacturers tables for (say) steel girders or reinforced concrete lintels, including the statutory increment for safe working load for this type of construction, it will need to have this cross-sectional area. And that means part number xyz. Of course, for the most part these days, they'll feed their proposed design into a finite element analysis simulation, and increase the strength of the members until they eliminate any "hot spots".

          And an electrical engineer will rarely need to remember, let alone actually calculate any "electromagnetic theory" once he's left college. It's mostly just a case of picking the appropriately rated parts from the manufacturers catalog. Sure, someone somewhere had to design those parts, but I guarantee that not one single rating was arrived at through mathematical processes. The ratings are arrived at by testing--probably to destruction--and then applying a substantial "fudge factor" to indemnify the manufacturer against failures when close to the limits.

          As an example, there is a whole sub-culture of computer geeks that get their jollies by seeing how far the can push the clock rates of cpus beyond the manufacturers ratings.

        • Cum hoc ergo propter hoc.

          The paper postulates that because of the use of mathematics in all professional engineering, all programs should be written using the theories of mathematics. And all programmers should be mathematicians.

          Except, as I've shown above, the cum hoc is false, hence the ergo doesn't.

        To date, in all the sources I've read, mathematicians completely miss the point about engineering.

        Engineering is not about specifying products, from the ground up, in logically provable, theoretical terms. Engineering is about about assembling a collection of standard parts, to meet a set of requirements, in a timely fashion, for the lowest cost. And whilst some of those requirements will be measurable in ISO units: speed, weight, strength etc. Another bunch of requirements will be ethereal things like looks, feel, affects on the environment, impact on the view, life-time costs, built-in obsolescence, usability, desirability, etc.

        And the impact of those ethereal elements on the success of products becomes ever more important. Take the success of things like:

        • the mediocre technical capabilities of the iPhone:

          but boy does that interface ever make for good TV ads.

        • the heavy, slow and expensive Toyota Prius:

          it's not that much more fuel efficient than a modern say 1.2 litre VVT petrol engined four seater, and far less fuel efficient than a modern, common rail 1.4 diesel engined equivalent.

          The secret of its success? You cannot mistake a Prius for anything else. And there are no 200+ HP, 16-valve, turbo charged variants of it. So when you pull up along side the red carpet in it, amongst all the 40' long, gas-guzzling stretched limos, no one is in any doubt that "you care".

          Even if you did just fly half way around the world in your private jet to attend.

        Engineering is not theoretical

        Engineering is not about proving that the product complies with theories. It's about satisfying a few theoretically quantifiable requirements, and a whole bunch more unquantifiable ones. Read about the construction of the Millau Viaduct. A very small part of the effort involved the solving of well-known formulae ensuring the strength of the beams, cables and towers. A larger proportion was to do with the logistics of constructing those huge skinny towers in a "continuous pour", running the cables and manoeuvring the decks into position.

        But a far larger proportion of the effort was involved in minimising the impact of the construction on the environment; ensuring the aesthetics of the final construction; engendering national pride in the French psyche.

        Very few if any software projects have anything like these logistics and emotional criteria to deal with.

        Dark Ages

        In engineering terms, the software industry is currently, roughly equivalent to the 16th century cathedral building industry in terms of sophistication. Like them, we build each construction from scratch, individually, to fit its landscape. Each building block is carved to fit its individual neighbours. We build the infrastructure just as thick as we think it needs to be, and if it starts to fall down when we're half way up, we build it thicker.

        In metalworking terms, we may no longer need to start by extracting the raw metal from the ore, but we are still at the point of fettling pieces of standard stock to manufacture individual components.

        Software development has as much to do with "engineering" as does cookery. Indeed, cookery is now routinely done on a mass production, engineering scale, and software hasn't even come close to achieving that.

        I sit here at this computer with a dozen or more languages installed and, despite the theoretically provable, analysed and documented to death nature of a simple sort function, there are probably 2 or 3 dozen implementations of quicksort in the various libraries on my system. And they probably all have bugs.

        Until we start constructing programs from standard parts, the terms 'software' and 'engineering' do not belong in the same sentence. And I don't mean standard libraries of functions, or extended class hierarchies.

        The former come in huge great globs of disparate facilities all lumped together into single linkable, statically or dynamically, chunks. If I want to replace a single function, be it sort() or strcmp(), I have to replace everything else it's library contains also. And that means re-testing everything.

        And the latter is source code. The approximate equivalent of blueprints. To replace the implementation of a single class means rebuilding the program (and every program) that uses it. And that means re-testing everything from scratch.

        More craft than engineering

        Until OSs provide us with a catalog of standard parts, specified in high-level, generic terms, that we can replace individually, and assemble together, at runtime, into higher level sub-components; test in the abstract and then assemble those into higher level components still; software development will remain more craft than engineering.

        And formal methodologies will remain a theoretical pipe dream beloved of academics but largely ignored by the industry just as it has, as pointed out by the paper, ever since Hoare first proposed it in 1969.

        It took metalworking nearly two millenia to move from the bronze age to engineering. I doubt that software will take quite so long, but we are currently still somewhere in the Dark Ages and (IMO) Hehner's optimism: "I am optimistic that Kieburtz is right, that the use of formal design methods is just around the corner." is still wildly misplaced.

        Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
        "Science is about questioning the status quo. Questioning authority".
        In the absence of evidence, opinion is indistinguishable from prejudice.
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Re: Is it worth using Monads in Perl ? and what the Monads are ?
by chromatic (Archbishop) on Jun 11, 2007 at 00:27 UTC

    Monads could be useful if you wanted to write your program as purely as possible, but they're really a mathematical attempt to make Haskell a usable language. I've never needed them in Perl. The only time I would use them is if I were to build my own transactional system and I needed composable operations.

Re: Is it worth using Monads in Perl ? and what the Monads are ?
by Dominus (Parson) on Jun 12, 2007 at 10:59 UTC
    A couple of years ago I tried writing a monad tutorial in Perl. It went pretty well for a while, and I think I was able to explain what was interesting about them and how they might be useful. But the syntax was totally abominable. You couldn't actually use it.

    Even in Haskell, the syntax is pretty bad, but is saved by two things. First, Haskell's notation for constructing and composing functions is more terse than Perl's. And second, Haskell has special syntactic sugar (the "do" notation) for expressing monadic computations.

    Anyway, I think it would be worth doing, if it could be expressed readably, but I was not able to figure out a way to do that.

    This is the best explanation of monads that I have ever read. I hope you enjoy it.

      ++for the link. I've seen similar descriptions of monads as wrappers elsewhere but the nice thing about that article is that it gives an example of a purpose for wanting to wrap things. And it gives a nice analogy with a familiar concept--tainting--that bring that purpose home in a nice familiar way.

      In turn, that has crystallised, for me, various feelings and intuitions about the process that I couldn't quite get a handle on before. And that leads to another analogy that allows me to express those intuitions, and relate them to Perl in a nice way.

      It all stems from one sentence in the linked article:

      But we've already said that we don't want to allow people to unwrap these things.

      Perl already has a taint-mode. When enabled, it will taint 'at risk data' and ensure that whilst you can pass it around, you cannot use it in any way that would constitute a risk. And if you copy that tainted data, or amalgamate it with some other non-tainted data, the results are also tainted to ensure you cannot use those for at risk operations. And it does all this without requiring monads. It could probably be successfully argued that implementing tainting for Perl would have been much easier had it's source code (C) had a monad-like concept. But that's history, and perl exists and has tainting.

      But there is one (huge) difference between the way it is implemented in perl, and the way it could be implemented using monads. Perl allows you/me/the programmer, to unwrap tainted data. It doesn't impose the language designers will upon me that tainted data must always and forever remain tainted--which in Haskell's terms is anything and everything that isn't hard-coded in the source file. And that is huge in it's implications for the ease of programming every further manipulation the program will perform upon that data.

      The analogy

      In certain high security buildings--airports, courts, government buildings, even private firms--visitors, including potential employees, customers and the like, are 'tagged' (a visitor badge), and 'wrapped' (a security guard, secretary or other escort) when they come on site. And they (should) remain so tagged and wrapped throughout the duration of their visit.

      But, when a visitor makes the transition to becoming an employee, they loose the tagging and wrapping. Okay, they may trade one tag for another, but they cease to be escorted. And the process that facilitates that unwrapping is a (more or less thorough depending) vetting procedure. It is simply impractical to have every employee be escorted (by whom?) throughout their working day. So after vetting--to what ever level is commensurate with their position--they are trusted.

      And that's what Perl does also. It allows me--as the user of the language, the writer of the application and the best arbiter of what constitutes 'safe data' for my application and what risk I will accept; to 'vet' the data and declare it to no longer be tainted. From that point on, I can treat that data in exactly the same way as I do any values that I embedded in my application, using all of the standard language constructs the language provides.

      I don't need to have a duplicate set of control structures--fmap as well as map, forM as well as for, and so on. And I certainly don't need to have to have a mechanism for re-using those extraordinary (and duplicated) control structure for every type of data.

      In effect, Haskell's need for all external data to remain wrapped for the rest of its working existence, is like requiring all your employees to continue to be escorted throughout their working days.

      Haskell's need for these extraordinary control structures arises solely from the language designers decision that Haskell users (programmers) cannot be trusted to decide for themselves, when their data is safe to be manipulated using the standard language facilities.

      They could have taken a different route(*). Then could have taken the decision to provided primitives that would validate in-bound data (bytes--all external data coming into a program is at the base level bytes strings), to be of some intrinsic type, or some compound type(*). From that point on, that validated data would be manipulable using the standard language facilities. The manipulations may still have had to be performed within sections of the code marked as being effectful and/or sequenced (the IO monad), but the need for many of the other facilities 'provided' by other monads would disappear.

      *This is exactly what several other functional languages (eg.ML) have done...but then the language is no longer 'pure'.

      There is probably some deeply meaningful reason embedded within the Hindley-Miller type system why it is impossible to trust a programmer to decide when external data is safe(ly typed), but that only makes me question the need for HM typing--not the efficacy of trusting the programmer to make his own decisions regarding the (type) safety of his data.

      Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
      "Science is about questioning the status quo. Questioning authority".
      In the absence of evidence, opinion is indistinguishable from prejudice.
        I'm looking really hard for any kind of analogy or figure of speech here, but I don't see it. As is, I can't see much sense in this comment. In case it was unclear, Haskell doesn't have a taint mode feature. This blog entry was about someone building one. They could have provided a way to unwrap the data, but they chose not to. Most monads do provide an unwrap operation; it's often called something like "runBlah".

        So you don't like this person's specific choice for your intended purposes, and that's fine. It's quite expected, in fact, since it was just a friggin' example! If I told you I don't like Perl because Larry imposes his will on me that I use regular expressions for parsing XML, you'd probably tell me I'm an idiot, and rightfully so. This is the same thing.

        If you don't want this monad (which you probably don't) you could write your own. If you don't like the monad, you could write some other kind of type operator besides a monad. Indeed, using a monad for tainted form data in a CGI doesn't seem like such a great idea. How about:

        newtype Taint a = Taint { untaint :: a }
        instance Functor (Taint a) where ...

        The point is that it's a free world, and the language provides you with the tools to build this stuff on your own. No one has to implement taint mode for you.

      thanx that definitely helped to clear the clouds abit ;)
      This thread is mentioned in yegge's blog Here
Re: Is it worth using Monads in Perl ? and what the Monads are ?
by zentara (Archbishop) on Jun 11, 2007 at 12:30 UTC
    Perl has gonads, not monads. (Sorry couldn't resist :-) )

    I'm not really a human, but I play one on earth. Cogito ergo sum a bum