One of the things i hadn't considered before is how much laziness can help to build modular code. The last section in the paper, about implementing the minimax algorithm, is a great example of this. The `evaluate` function is first naively defined as a simple chain of a couple of functions that iterate the tree of all possible game positions. Then a series of improvements are applied to it (e.g. pruning the tree to allow the algorithm to work on infinite trees, or ignoring branches that cannot yield favourable moves), but what's really nice is that thanks to lazy evaluation these improvements can be implemented as independent functions that are just "plugged in" the chain, without having to modify the original functions. For example, the original function that generates the whole game tree doesn't need to be changed to implement pruning.

I'd really recommend the paper to anyone who might be wondering "why all this fuss about functional programming?". It's not only very accessible, but also full of beautiful code examples solving very practical and concrete problems. I personally felt a bit sad having to "back" to the imperative programming world in my every-day job after reading it.

Feel free to share, vote, comment there too :) http://www.reddit.com/r/functionalprogramming/ A very healthy community, lots of interesting stuff in different programming languages.

  ;lazy-seq of Fibonacci numbers
  (defn fibo 
    []
    (map first (iterate (fn [[a b]] [b (+ a b)]) [1N 1N])))

I personally think that the following has much more impact on modern CS than the Hughes paper linked above.

http://www.erlang.org/download/armstrong_thesis_2003.pdf

This is focusing on the reality (operating system threading model, no shared memory across processes -in the Erlang world-, communicate only with message passing, etc.) and this yields to a much higher impact. If you look into Scala features you can find many that came from Erlang, or through Erlang (some of them originally from other languages).

SCP also gave a bigger kick to CS (even though it has very little to do with FP) and it seems that FP languages were adopting it faster (I might be wrong on that).

http://www.usingcsp.com/cspbook.pdf

Actually, it is quite hard for anyone who's not already versed in Lisp and equipped with some reasonable knowledge of basic FP constructs such as folds.

It's also important to look at the whole picture, and the author of the paper (and FP advocates in general) have this interesting tendency to completely ignore the opportunity cost of using FP and to dismiss the advantages of alternative approaches over FP.

Personally, I think laziness and immutability come at a very heavy price that explains why only the superficial aspects of FP (lambdas) have been adopted while the rest of FP remains the realm of research papers and conferences.

Are you referring to the disadvantages of using a non-mainstream style? That's not relevant here. We're comparing the styles themselves, not their popularity.

> Personally, I think laziness and immutability come at a very heavy price that explains why only the superficial aspects of FP (lambdas) have been adopted while the rest of FP remains the realm of research papers and conferences.

I have a much simpler explanation: first class procedures are compatible with imperative programming, while immutability is not. (And laziness needs immutability to be workable.)

People don't adopt FP because old habits die hard.

But immutability is not is not incompatible with imperative programming, otherwise people wouldn't be writing things like Guy Steele's "Lambda: the ultimate imperative" paper [1]. And of course, monads.

> People don't adopt FP because old habits die hard.

People don't adopt FP for the same reason they don't wear hair shirts; it is presented and marketed as an "eat your vegetables" affair.

[1] http://repository.readscheme.org/ftp/papers/ai-lab-pubs/AIM-...

You could de-sugar your way out of those (Turing completeness and all that), but then it wouldn't be imperative programming any more. You could isolate those things in a monad, but (i) the monadic part is not functional, and (ii) the rest of the program don't use those things. I stand by my incompatibility claim.

Your marketing argument is better, but I don't see any other way. No matter how you cut it, FP is big about not using some features, and what benefits we get from this restraint.

Now, you don't need to use imperative programming everywhere, and in a functional language you have the option to easily not fall into it (well, in Haskell, most other popular FPs are way less pure).

> No matter how you cut it, FP is big about not using some features, and what benefits we get from this restraint.

And that is really why FP will be niche (especially pure FP). Like very powerful static type systems that are really good at saying no...it adds to the resistance of writing code while claiming benefits further down the line. "Worse is better" wins out over and over again (why dynamic languages, imperative programming, OOP continue to be popular; we aren't Vulcans after all!).

[1] http://stackoverflow.com/questions/6622524/why-is-haskell-so...

My experience is the exact opposite: having a compiler that is good at saying no means I correct my errors earlier. With a dynamic typing, my errors are revealed later, and further from the root cause. So, static typing removes to the resistance of writing correct code. It speeds me up.

Static typing would indeed add to the resistance if it required you to jump through hoops. But it doesn't. Bad type systems have significant limitations, but the good ones have very few. Unless you go crazy with Smalltalk-like hot-plug live systems (and even then, see Yi and Xmonad), static typing is permissive enough.

> we aren't Vulcans after all!

I have two theories. The first is, some of us are Vulcans. And somehow, Vulcan brains function better with static typing and functional programming. In other words, Vulcans are better at "math", and put programming into the "math" bucket. Then there are humans, who see programming and mathematics as two quite separate disciplines, ran away from math, and function better with procedural programming and dynamic typing.

My second theory is that everyone could adapt to anything, if only they would bother to learn. Anyone can think like a Vulcan.

I currently lean towards the second theory, though frankly I'm not sure which theory is closest to reality.

I program in Haskell using the repl as well as any other languages that make it possible.

    def fibo():
        a, b = 1, 1
        while True:
            yield a
            a, b = b, a + b

What simplicity? That's even more complex to state than the traditional imperative solution, that's also closer to how mathematicians would write the equation.

- calculating the n-th element of the Fibonacci sequence - representing it correctly in code

The first one is (assuming the second is present, see code above):

(nth (fibo) 10)

It's only anecdotal, but I find pure, immutable code far easier to maintain in any language. To a first approximation, a functional interface == a testable interface.

I've joined several projects in their maintenance phase which had no tests, and introduced some as I went about debugging, adding features, etc. Since the code was often untestable, I'd make a few refactorings over and over again to allow testing, and these just-so-happen to tease apart the pure computation from the effects; in essence making the code more functional.

An obvious example is to turn implicit state into explicit parameters, eg.

    // BEFORE

    function foo(x, y) {
      b = x + y + a;
    }

    // AFTER

    function foo(x, y) {
      b = foo_pure(x, y, a);
    }

    function foo_pure(x, y, z) {
      return x + y + z;
    }

>What about programming in the large?

less code -> less code at large -> win

>What about efficiency of naive implementations?

like a stack overflow version of it the starters always come up with in Java? what exactly are you talking about?

>What about maintainability?

What does FP or any of this thread for that matter do with maintainability? You can write unmaintainable code in any language.

These are a very limited subset of what really matters in software engineering. (I would also remove the naive implementation part.)

that doesn't necessarily follow

Or did I misunderstood the meaning of "less code"?

It is neither disputable nor disputed, that pure functions are more modular than procedures: their result is independent from the order of their evaluation, and their data dependencies are explicit. That makes them easier to connect to one another.

It is neither disputable nor disputed, that first class functions enable more modularity than first-order functions alone. Just see `map`, `filter`, `fold`, which separate loop structure from loop body, in a way that would require special constructs or macros in first order languages.

It is neither disputable nor disputed, that in the absence of side effects, lazy evaluation is more modular than eager evaluation. Lazy evaluation lets you cleanly separate producers from consumers, by avoiding the full evaluation of what would otherwise be infinite data structures.

You may argue that the claims of increased productivity and correctness are extravagant, but you can not reasonably challenge the massive increase in modularity.

Some claims don't need "studies". Sometimes, a compelling argument is enough.

But there are definitions of at least the latter two which are substantially justified via an FP take on the world.

Really, though, I think FP does itself a disservice by claiming to be a "style" of computing much like OO. It's really just a back-to-the-basics take on what "is" computing and from it you can get a very well-behaved foundations of formal languages to build your CS (of whatever brand you like) atop. This has proven to be incredibly fruitful as a theory since, honestly, something like 1907.

From my experience with functional languages, they slack in that aspect.

I like Lisp's simplicity and I like the elegance in Haskell but the only Lisp I know that have a workflow that kinda matches my taste is Clojure, which reeks of java. I tried Haskell several times and I liked the language but I can't stand cabal.

That's why I believe in Go, the language isn't eye popping, but every aspect of the workflow makes me smile and think "that's how you do it".

And by that I mean the no-versioning policy, web stuff built in to the language, and I just love the workspace structure[0].

It is transparent, no need to google to find out where external packages are installed if you want to fiddle with it's source, no worries about version hell, no worries about unicode.

I've read good things about racket in that aspect but I'm yet to try it.

[0]https://golang.org/doc/code.html

I worked at a startup whose Haskell backend was quite pleasant to work with and served them very well. This site itself is written in Arc, as you probably know, and Paul Graham has written several essays about the "productivity" he and his team achieved using Common Lisp.

People can work productively with software using all kinds of tools and languages. As you mention, a lot of it might come down to taste, likes and dislikes, habits, etc. Of course you're going to be more productive if you're familiar with your tools. So your experience with productivity isn't really an objective indicator for anyone else.

For me as a user Haskell(the platform) is inferior to, say, Go, simply because I can manage external packages that much easier. Thus if I needed to get something done I'd rather use Go, not because I think it's a better language than Haskell, but because of the pain in dealing with package versions, building, etc.

Basically what I'm saying is that you don't see that much adoption, and thus data to endorse the productivity claims because of the platforms and not because the languages per se are bad.

Pg said people don't use lisp because it looked weird and it's not popular[0] and I think it applies to functional languages in general. I don't think you can/should solve the former, but by having friendlier/better platforms you could start solving the latter.

http://www.paulgraham.com/iflisp.html[0]

Without version constraints it's much harder to even say "I can build this program" much less "I can fix this bug".

> that's unlikely to happen and as you have the packages as git repos you can just git reset it back to a commit when it was stable

You seem to be assuming you are the one who wrote the code. I'm more speaking in cases where someone you don't know and can't contact wrote the code. Have you ever had to reverse engineer a very large dependency chain? It is absolutely no fun :/

I agree that Go's workflow philosophy is great. I wish more languages adopted it. But that's the thing, it's easily mixed and matched. On the other hand, making something like Ruby genuinely type-theoretically typed, while an admirable and interesting goal, will probably never happen. Their worlds are just different.

I feel that we've given many years of attention to functional programming, and it's been disappointingly unfruitful in most areas of CS, such as computational complexity, cryptography, machine learning, or computer graphics. Most new ideas coming out of the FP camp are applicable only to FP itself, like monads. We've discussed that before: https://news.ycombinator.com/item?id=8563817

Part of the mismatch is that many interesting algorithms are impure and cannot be easily made pure. I'd like the "foundation" of CS to give a faithful mathematical description of what computers can and cannot do. Is that too much to ask?

But the bigger problem is that FP treats functions as black boxes, and that's just not enough to prove interesting results in most areas of CS. A better "foundation" would try to describe computational behavior and reason about it, instead of abstracting it away. I admit that's a very vague idea, but I'm not smart enough to make it concrete :-)

http://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis

> A better "foundation" would try to describe computational behavior and reason about it, instead of abstracting it away

A lot of interesting research does exactly this, and a lot of it has found its way into ML-family languages. The starting point (or "foundation") in every case is a typed lambda calculus. Machine models, like turing machines, are just annoying to reason about and not extensible in any meaningful way.

My point was that it's possible to systematically extend (or restrict) the lambda calculus and associated techniques. You can add effectful operations and give them semantics (e.g. as functions on stores), define a cost semantics and prove whatever you want while being completely formal.

Try extending RAMs with dynamic allocation, call stacks, or anything to make it more natural to write down a whole algorithm. Try proving something about the composition of RAM programs. I don't think you'll get very far.

There are many interesting algorithms that are usually analyzed in an imperative setting, like in-place quicksort, Knuth-Morris-Pratt, or Gaussian elimination. There doesn't seem to be any benefit to analyzing them in an FP setting, because it's not easier and doesn't yield new insights.

It seems to me that the FP approach only really shines on algorithms that are "naturally tree-like". For example, I'm a big fan of Okasaki's work on purely functional data structures, and of Blelloch's work-depth model. But let's not oversell FP techniques as the foundation of all algorithm work.

The field that gave rise to FP has a lot to say about how we specify languages and their properties and how we prove things about programs in general. That includes languages with all kinds of effects: state, exceptions, concurrency, etc, and equally as imporant, mechanisms for abstraction and modularity. There's currently no other "foundation" for computation that lets us define these ideas formally.

In discussions of FP, the contributions of the field get reduced to "programming with functions".

Elsewhere mafribe mentions parallel processing... which is also clearly in another class.

Past that: all the correct systems I know were built using formal methods and a mix of functional languages and assembler to reduce the semantic gap.

All the highly productive programmers I know use either functional languages (or logical languages, same reasons) or else very assembler over very tight machine models--and the one using MMIX is an exception.

I think SML makes a good case to have won the modularity front, but there I don't feel as certain.

I am with you, I also think that functional languages the way to go and I almost exclusively using those, but I would not make this big of a jump.

(i) Higher-order functions: Yes, slam-dunk win. Essentially all new languages have them, Java and C++ retrofit them.

(ii) Lazy evaluation order by default: mostly dead. All new language use eager evaluation, even SPJ is sceptical that lazy evaluation should be the default. Scala has an interesting approach: eager by default, but you can switch to CBN (although not full laziness) if required. This hybrid form enables you to define control-operators easily, while keeping the simplicity and efficiency of eager evaluation. Exceptions are languages with dependent types that are really theorem provers (e.g. Agda).

(iii) Purity: dead. All new languages have side-effects. The widely used FP languages like Haskell, Ocaml and F# have side-effects. Exceptions are languages with dependent types for Curry-Howard-based theorem provers (e.g. Agda), because there is no convincing Curry-Howard correspondence using state.

(iv) Everything is function application: open. This may work reasonably well in purely sequential languages, but there are theoretical reasons to believe that message passing is not function application (while function application is a special case of message passing).

(v) Types. The answer on this one depends on whether one is a proponent of statically typed languages or not, clearly an unresolved question. For dynamically typed languages, the question is moot, so the rest of the discussion is irrelevant to those who think that static typing is a bad idea.

(vi) Types (1), type inference: Slam dunk winner. All new languages have inference or wish they could have it but don't know how to do it (Scala). There are probably some hard trade-offs between expressivity of types and efficient decidability of type inference (B Pierce termed Hindley-Milner a "sweet spot"), so we might have to tolerate some type annotation being required, e.g. in local or bidirectional inference.

(vii) Types (2), algebraic data types, pattern matching: winner. Most new languages have them in some form.

(viii) Types (3), monadic encapsulation of effects: open. Most new languages have not yet embraced this. Some conceptual problems not yet solved, e.g. destructors for state monads. There are also expressivity problems, e.g. not all effects can easily be expressed as monads, and composition of monads doesn't always work as desired. Moreover there are pragmatic questions about whether monadic encapsulation should be required or optional.

(ix) Types (4), higher-kinded types: open. Not all new languages have them, but HKTs are generally considered useful, but not super important, cf Rust's evolution. If monadic encapsulation of effects is used, then HKTs become highly desirable, cf the recent Scala fork.

   --------------------

As for me, I get a little tired of these pseudo-objective "debates" trying to decide which programming language is "better" by evaluating bullet lists, trends, and so on.

It seems pretty clear that different people can be very productive in different languages and using different techniques. Different projects and companies use different language; that's a plain fact.

For someone who's working with a happily functioning system written in, say, Haskell, it's a little weird to go on discussion forums and see people arguing over whether or not Haskell is a "productive" language.

In almost every HN thread about something related to Haskell, there'll be a few comment threads started by someone who claims that "functional programming doesn't work in the real world" or that "laziness is only good for research papers" or something like that. That's frankly flamebait by now, and I'm generally saddened by how much of the discourse about functional programming (on here, specifically) becomes this kind of groundless fight about whether or not it's possible to build real software with it.

Yes, of course Haskell, as a real-world thing instead of a perfect Platonic idea, has flaws, things that could be improved, problems one has to work around, and so on. That is inevitable and it is true for all programming systems ever!

It's always interesting to hear from people who have made good-faith efforts to use functional programming techniques and systems, and failed. Specific complaints, even feelings and vague opinions, are useful information—when they come from experience.

Anyway, that's my rant for today about the discourse on functional programming...

There is another dimension to language wars: discussing languages is part of language learning, part of becoming a master. After all, teaching/discussing is one of the most efficient learning tools, and having to defend one's language helps to clarify one's own thoughs, in parts by looking at it from other peoples perpectives.

Although even there, I'm hesitant. There's a sense in which the idea of the language as separate from its tooling is a judgment in itself, one that tends to divide the language community into camps already. For example, Smalltalk, Forth, and Common Lisp are radically "integrated" systems, in which the languages themselves can be redefined at runtime. There, it's in a way academic to talk about the formal grammar and semantics of the language in a "Platonic" sense.

But that might be a tangential point.

Probably I am uninterested in and somewhat averse to the kind of language discussion you're defining. I think that "language systems" operate in the world in complex ways, only a fraction of which are accessible through bullet-point-style comparisons of PL features.

And something about the interminability of "language wars," like the eternally recurring static-vs-dynamic skirmishes, fuels my aversion. I've heard so many pseudo-objective arguments for and against static typing, and these arguments have had so little cash value, that I've become skeptical of the whole mode of discussion.

So I'm much more interested to hear about, say, concrete successes or failures (or ongoing attempts) using static or dynamic typing (or laziness, or what have you) in concrete real-world settings.

Not as academic as you might think. We could analyse how easily a language makes such an integration possible. I'm not sure you could have a lispy environment in C, for instance.

Once you know what kind of ecosystem a language enables, you can compare those ecosystems. (As opposed to existing ecosystems, which are highly influenced by sheer popularity and historical accidents.)

To say "every language design has its own set of tradeoffs" implies that all languages are equal, but that's clearly not true; we can all think of languages that are worse than others. I'm not at all convinced that there isn't an overall best language out there (I don't think it's Haskell, FWIW).

I don't think that implication is there at all. It absolutely doesn't hold for strong notions of equality - strong equality of all languages should imply that they all share a single set of tradeoffs.

It also clearly doesn't hold for "equal suitability to any purpose", since something less suitable to the purpose may be traded off for something more suitable.

I think any general notion of "equality of quality" can probably be viewed as a special case of the above reasoning - we are picking a set of attributes, of benefits and drawbacks - but we've no guarantee that they all net out the same however we are measuring them.

PHP isn't a bad language if its tradeoffs work for you. But you would be hard pressed to see anything good today in BASIC from the 80s (like we might miss things if we all of a sudden were sent 1000 years back in time). There is no best PL, but there are new PL technologies that make programmer experiences better; using a language that doesn't include at least a few of those technologies is probably going to be a handicap (compared to your peers who are using them). Haskell is bit up the tech tree, but not incredibly so compared to other modern languages like Scala and even C#.

But this is just a way of thinking that makes me feel comfortable because I like to have a physical model. If someone else is happy with function application as being the fundamental building block then I have no problem with that. However you said that "there are theoretical reasons to believe that message passing is not function application (while function application is a special case of message passing)." I would be interested to get more background on this. Would you have any references for this? Thanks.

I don't remember off the top of who first showed that parallel computation has no 'good' encoding into functional computation (lambda-calculus). I'll try to dig out a reference and post it here if I find it.

But the upshot of all this is that message-passing is more fundamental than functions / function application.

[1] C. Hewitt, H. Baker, Actors and Continuous Functionals.

[2] C. Hewitt, Viewing Control Structures as Patterns of Passing Messages.

[3] R. Milner, Functions as Processes.

     x!<a> | y!<b> | x?(c).y?(d).P

Conversely, I don't think linear logic is a good typing system for pi-calculus for a variety of reasons: among them that linear logic does not track causality well, and because it doesn't take care of affine (at most once) interactions well.

(Also, to be clear and with reference to other threads we've conversed on here, I think of linear logic and pi calculus, even if they aren't well-corresponding, as fantastic, unavoidable examples of non-function-application style programming.)

I'm not sure what you're talking about here - could you elaborate?

My best guess would be that by "state monads" you mean streaming libraries like pipes and conduit, where there have indeed been some interesting questions around finalization. Calling these "state monads" is surprising enough that I seek clarification, however. Regarding those libraries, I don't know the current status of that discussion (which mostly took place a couple years back) but I do know the libraries themselves are quite useful.

    def f x = 
       let i = ref 17 in
       while i > 0 { i := i-1 }
       return i 

    -- we need a primitive first
    while :: Monad m => m Bool -> m a -> m ()
    while conde bodye = do
      cond <- conde
      if cond then bodye else return ()

    -- then we can make a direct, verified pure translation
    f :: a -> Int
    f x = runST $ do
      i <- newSTRef 17
      while (readSTRef i >>= \ival -> return (ival > 0)) $ do
        modifySTRef i (\ival -> ival - 1)
      ival <- readSTRef i
      return ival

    while :: Monad m => m Bool -> m a -> m ()
    while conde bodye = do
      cond <- conde
      if cond then bodye >> while conde bodye else return ()

The one that probably most closely matches the semantics of the pseudo-code would be:

    let f0 x = unsafePerformIO $ do
        iRef <- newIORef 17
        whileM_ (fmap (>0) $ readIORef iRef) $ do
            modifyIORef iRef (\ i -> i - 1)

        readIORef iRef

    let f1 x = runST $ do
        iRef <- newSTRef 17
        whileM_ (fmap (>0) $ readSTRef iRef) $ do
            modifySTRef iRef (\ i -> i - 1)

        readSTRef iRef

    let f2 x = go 17
      where
        go i | i > 0 = go (i - 1)
             | otherwise = i

    let f3 x = execState countdown 17
      where
        countdown = whileM_ (>0) $ modify (\ i -> i - 1)

In your function, "while i > 0 { i := i - 1 }" is clearly not referentially transparent. Attempting to transliterate in a way that preserves this expression, it is unsurprising that we wind up with expressions that depend on state. The State monad is one way of encapsulating this. Note that f3 and f2 are actually very similar. The execState function doesn't do any deep voodoo - a value of type "State s a" is a thin wrapper around a function of type "s -> (a, s)"; execState simply extracts this function, applies it to a value, and returns the second part of the output.

The actual definitions are equivalent to these (albeit slightly more complicated to keep things DRY w/ transformers):

    newtype State s a = State (s -> (a, s))

    execState (State f) s = let (_, s') = f s in s'

More precisely, since the argument isn't used it's type is unconstrained, and the result could be any numeric type, so they all actually have type (Num b => a -> b), but that can be used anywhere you're expecting an Int -> Int.

Sure, literally translating imperative procedures into Haskell code often needs the State monad since imperative procedures gratuitously use state modifications that are logically unnecessary for their function.

But I'm not sure why any meaning should be ascribed to this beyond "translate function, not code".

    f x = g 17 x
        where g i x = if i > 0 then g (i - 1) x else i

The example is intended to point towards an expressivity gap of the monadic encapsulation approach to effects, in that one can't (as far as I'm aware -- I have not programmed in Haskell) hide state usage, even when this is extensionally OK.

It is an open research question to define type/effect systems that (a) enable programmers to hide such benign state usage, (b) preserve type inference for interesting typing systems (say F-omega which is the heart of Haskell's types), and (c) are pragmatically viable.

You absolutely can do exactly that. Even without cheating (unsafePerformIO and friends), usually.

Could you point me towards an explanation how the hiding of stateful expressions works in Haskell in general?

Let me clarify my question (a bit). Are you saying one of the following is true?

(1) You are saying for any program M that uses state (i.e. M's type mentions the state monad in an essential way) but in a pure way, i.e. M's stateful behaviour is not visible from the outside, there is a context C[.] (not involving tricks like UnsafeIO) such that C[M] has the same behaviour as M (as seen from the outside), and C[M] has (essentially) the same type as M, except that the state monad is gone?

(2) There is a 'nice' translation function f on programs such that for any program M that uses state in a pure way (same as (1)), f(M) has the same behaviour as M (as seen from the outside), and f(M) has (essentially) the same type as M, except that the state monad is gone?

A fruitful way to look at monads is to say a value of type M (where M is an instance of Monad) is a program in a language. State is a language for describing stateful computation. Reader is a language for describing parameterized computation. ST is a language for describing controlled, local mutation. IO is a language for describing arbitrary side effects.

Most of these have pure interpreters, with the most generic typically called runM (so, runState, runReader, &c). The only place cheating comes in is unsafePerformIO - interpreting IO is the job of the runtime, which does it in a more controlled way relative to the rest of your program.

The type of the return value of an interpreter, of course, doesn't tell you what kind of program you ran - it just tells you the result.

For 1, to get from a value of type "State s a" to a value of type a, you simply call evalState and supply an initial state of type s.

For 2, you could look at the structure of the program and unwrap all (State s a) values to have type (s -> (a, s)), updating the various functions used to operate on (State s a) values to match.

In either case, you would not see State in the resulting type signature. In case 2, you would still need to provide an initial value of type s - you can't do much interesting with a function but apply it.

Note that the function in 2 is more theoretical than practical. You could in principle write it with Template Haskell, but since it doesn't change the behavior and you can just do 1 to change the type the same way there isn't reason to.

I still wonder how this would work with scope extrusion of references. Consider this little Ocaml program

    let ( impure, pure ) =
      let i = ref 0 in
      let impure x = ( i := !i + 1; x + !i ) in
      let pure x = (
        i := !i + 1;
        let res = !i + x in
        i := !i - 1;
        res - !i ) in
      ( impure, pure );;

Is it possible to do the same in Haskell? By "the same" I mean giving "pure" the type int -> int, despite using hidden state that is used elsewhere?

Something with a similar form that would be more realistic to ask for would be a cache for a pure-but-expensive function and some IO operations to inspect/manipulate that cache. I believe you would need a call to unsafePerformIO, but that could be a reasonable thing to do.

I don't think (iv) is open at all. The fact that you can encode everything as function passing is an interesting trick, but it's merely one of several (you can, e.g., also encode everything categorically or via supercombinators and graph reduction, which turns out to be more practical for lazy languages). Function application is just one really well understood semantic foundation.

I find (v) far more subtle than you make it out to be. The standard static/dynamic types divide is silly because both sides are talking about different things. The static side wins completely because honestly, taken at face value, they don't claim that much. All languages are typed, some have interesting type theories, some compilers reject programs which are syntactically OK but violate the type theory.

(viii) is interesting. In my mind, you've conflated this with what most people would call purity---however, monads are merely an implementation of effect typing/purity. Others exist and are experimented with. Also, composition of monads always works as desired... there's no strange edge-case to it. It's merely that they don't compose like functions in a simple way. When you examine what they would entail you learn that they ought not to as well.

(ix) HKTs are sort of a gateway drug to type-level computation. It's remarkable how many languages just more or less let their type-level language wither and die. I'm not claiming that HKTs are a slam dunk victory, but I would be willing to bet that the evolution of languages will lead us to (a) having them universally in the next two decades and (b) wondering why everyone was so hung up on HKTs---I mean, I suppose I can understand singletons, but HKTs? Really?

     monads are merely an implementation of effect typing/purity. 

As to HKTs, I agree, languages should have them. I was just pointing out the state of the art, post Haskell.

A more interesting dividing line are things like computation effect typing in languages like Bauer and Pretnar's "Eff" or McBride's "Frank".

http://www.eff-lang.org/

http://homepages.inf.ed.ac.uk/slindley/papers/frankly-draft-...

But yes, if you consider other "practical, modern" languages, many retain impurity.

First, approaches like Eff take pure functional computation as a basis and layer effects like call/cc or concurrency on top of that. I think it's better to go the other way and take concurrency, or, if you want to start sequential, a lambda-calculus with jumps a la call/cc or lambda-mu, as a basis see pure functional computation as a restriction of the base calculus.

Second, it's unclear that effects should be reflected in types for reasoning. That road leads to complicated typing systems without type inferences (see also dependent types). I think the following alternative is more appealing: stick with lightweight types (think Hindley-Milner), and leave reasoning to an external calculus (variants of Hoare logic).

I also really worry that external proofs will ultimately be neglected in practice. I suppose this is again a "UX of Types" thing, but I'm something of a believer that anything that you do not literally demand of the programmer will eventually be sacrificed.

     I find (v) far more subtle than you make it out to be.

So, I guess I just tire of it. If you're making a language today you can either take advantage of information known statically or not. I think there's a relative burst in activity here as some of the more genuinely useful forms of static analysis have become recently more popularized and I personally feel it's silly to not use this information... but it's just a choice, not a religious war.

    Purity is growing more and more day by day.

PS what is the "normal" definition of purity?

"Purity" is a tricky technical concept that can be defined, but rather than do so explicitly I'd rather note that it necessarily requires the asserter to take a stance on what "observable" means. Haskell is clearly impure in that its laziness is implemented using mutation "behind the scenes", but it is also taken to have an "observable" semantics where such mutation is invisible and IO is merely an interesting value. This gives it purity [0] according to that degree of observability.

I think I'm having difficulty parsing your interpretation of purity because you're moving smoothly between analytic and synthetic judgements of the notion. Agda, as an example, is a system which has a synthetic notion of purity as the "language" is thought to not contain terms which represent effects. Haskell plays a trick where it has, essentially, two sets of semantics. The first shares this property (modulo non-termination, see [0]) and is where most "programming" occurs---here we use monads as a system for constructing terms of the second semantics, IO. The second, IO, semantics are vastly impure.

To the degree that this trick is "purity in a language" then purity is becoming a very popular idea. Haskell uses its type system to provide synthetic distinction between the two choices of semantics, but if you use a language lacking that discipline then you can merely call this "isolation of side effecting code" and then nobody will disagree with you.

If you don't want to call this "purity", and maybe you don't, then I feel you're in the minority though you aren't without an island to stand on.

Frankly, both are sort of an overloading of the term, though.

[0] Actually, it gets a lot trickier. It's well known that non-termination is an effect and it's a little slippery to define Haskell's notion of "observability" so as to no longer observe non-termination. I mean "slippery" here to say that it takes some technical finesse and that it tends to go against people's intuition a bit more harshly than the rest.

     I don't think (iv) is open at all ... Function application is just one really well understood semantic foundation.

Regarding lazyness by default, although you are right, I would say the lazy modifier found in Scala/ML derivatives/C#/D and the use of sequences/ranges kind of help half way there.

Consider this Scala program

     object Main extends {

       def tryit [ T ] ( block : => T ) : Unit = {
         println ( "----- Running 1st block -----" )
         block
         println ( "----- Running 2nd block -----" )
         block
         println ( "--------- Finished ----------" ) }

       def main ( args : Array [ String ] ) {
         var i = -1
         tryit ( { i += 1; println ( s"i = $i" ) } ) }

     }

You don't consider Haskell to be pure? A big win of using monads for side effects was to keep purity right?

Sense (1): The return value of f can only depend on x, and not y (or anything else)

    x   = ...
    y   = ...
    ret = f x

What Haskell contributes (in a concrete implementation, the ideas go back to Moggi's theory) is the monadic encapsulation of effects, which I treat as a separate point under (viii). Monadic encapsulation of effects is not absence of effects. It's a reflection of effects at the type level.

http://research.microsoft.com/en-us/um/people/simonpj/papers...

hello :: IO () hello = putStrLn "Hello World"

`hello` is a "pure" value of type IO (). putStrLn a "pure" function of type -> IO ()

IO () is a value like any other "pure" value, like [Int].

The statement

   puts ("hello");

The C equivalent of

    putStrLn "hello"

    void putsHello(void) {
        puts("hello");
    }

https://news.ycombinator.com/item?id=9085403

Haskell IO is severely misunderstood.

Or are you talking about divergent side-effects like bottom and exceptions?

That said, I was talking about effects in general, including non-termination, exceptions, concurrency ...

If you want to verify your programs (and in 99.9% of programs you probably don't as you get it sufficiently correct by more lightweight techniques such as testing and code-reviews), then purity is fine, since you have to track effects explicitly anyway to prove non-trivial results, and doing this in a pure functional way or say with auxiliary variables in a Hoare-logic are kind-of/sort-of notational variants.

> We conclude that since modularity is the key to successful programming, functional programming offers important advantages for software development

The conclusion section is more elaborate, but I don't see anything there that warrants the label "extravagant".