That being said, it's still fast enough for this example.

Also, Python solution along the same lines:

    import itertoolsdef
    def valueOf(*values, base=10):
        v = 0
        for v in itertools.accumulate(values, lambda a,b: a*base+b):
            pass
        return v
    def solve():
        for s,e,n,d,m,o,r,y in itertools.permutations(range(10), r=8):
            if valueOf(s,e,n,d) + valueOf(m,o,r,e) == valueOf(m,o,n,e,y):
                yield (s,e,n,d),(m,o,r,e),(m,o,n,e,y)

That's what I've noticed with Haskellers. They have a tendency to write really slow code and don't have a clear idea of the execution model behind what they write down.

A while ago I asked in #haskell for translations into Haskell of the following C++ code:

http://codepad.org/sQTXhqC2

This should be easy. The algorithm is right in front of you. There should not be a lot of thinking in transcribing an algorithm into Haskell. But most of them wrote down something with a fold which turned what is an O(m*n) algorithm in time and O(n) in space into something like O(m^n) in space and time. The only one who got close to the C++ implementation was one who used a lot of State monads.

Then, of course, there was someone who pointed me out to a radically different algorithm written in Haskell that I think is only O(n+m) in both space and time. I haven't been able to understand this other algorithm yet.

Certain highly stateful algorithms may be difficult to translate into Haskell, in the same way that certain highly structural or lazy algorithms may be difficult to translate to C++.

I'm curious if your time complexity analyses are accurate, given that you (admittedly) did not understand the faster algorithm. You could be getting tripped up by laziness.

In general, I've found that most production Haskell code is quite fast, in both big-O and absolute terms.

Of course, this isn’t unique to Haskellers. ;)

Granted, reasoning about performance in Haskell is still a relatively young art, and there aren’t many of us who are experienced with it.

http://en.wikipedia.org/wiki/Edit_distance and http://blog.notdot.net/2010/07/Damn-Cool-Algorithms-Levensht...

You can be sure if you read the generated Core and/or assembly code.

If you see any regressions, just post it to the ghc mailing list and it will probably be solved for you since it's much needed regression feedback/data.

That being said, I used to think that about Java as well - and then the whole substring thing happened.

https://wiki.haskell.org/Edit_distance

But that's not the point. The point is that Haskellers have a hard time translating an algorithm that's right in front of them and instead of writing down an O(m*n) algorithm they instinctively do O(m^n). This whole "many-worlds" approach of the original article is also leading to a very inefficient algorithm.

The abstractions Haskellers prefer lead them towards slow code.

    Haskellers have a hard time translating an algorithm that's right in front of them 

As of May 2015, nobody knows if lazy functional language can solve all problems with the same asymptotic time complexity as stateful languages.

[1] N. Pippenger, Pure Versus Impure Lisp.

[2] R. Bird, G. Jones, O. De Moor, More haste, less speed: lazy versus eager evaluation.

ST is clearly not pure in the sense that theory requires to make "can we implement this algorithm with the same complexity" an interesting question. It seems wrong to consider it part of "the unsafe stuff", however - it doesn't have the same kind of unenforced caveats as unsafePerformIO and unsafeCoerce and similar.

Separately, "the unsafe stuff" is still part of the language as used, and while it's certainly better practice to avoid it when you can, it's silly to exclude it when asking whether it's possible to do something - they are sometimes appropriate.

Are you suggesting to define purity by the inability to define O(1) mutable vector-like operations? That would be an interesting proposal. But I wonder if it captures the conceptual content of the informal concept of purity. Maybe a time complexity restriction should be provable from purity?

No, I mean ST. An entirely different monad: http://hackage.haskell.org/package/base-4.7.0.0/docs/Control...

"Are you suggesting to define purity by the inability to define O(1) mutable vector-like operations?"

"Define", no, as that certainly doesn't encompass the full scope of purity. I think mutability runs counter to most people's notion of purity, particularly when they say "Haskell isn't pure". Of course, we can fake mutability at a cost of O(log n), which is what makes the O(1) notable.

If you do think ST is "pure" then it's not an open question whether you can implement update-heavy array based algorithms in a pure language without algorithmic penalty - you clearly can.

Looking over the PLDI paper, I get the impression that the key difference between ST and the usual State monad is (1) the ability to name state, and (2) the use of parametric polymorphism to prevent scope-extrusion of state.

Of course ML has scope-extrusion of state, and one of my questions/examples upthread was about the ability of Haskell's monadically controlled effects to implement such scope extrusion without 'tricks'.

All in all I feel that the notion of purity is controversial, insufficiently theorised, and that the community would benefit from a clearer understanding of the trade-offs involved in the different notions of purity

If you object to notions of purity, why did you bring it up in the first place?

The first place it was used in this thread was your citing a paper entitled "Pure versus Impure Lisp".

In that paper, it was used to mean prohibiting "set-car!" and "set-cdr!". ST provides the equivalent of "set-car!" and "set-cdr!", so in the presence of ST the result you were citing in the paper doesn't even apply to a strict version of Haskell.

Please just stop making claims about Haskell until you have some sense of what you're talking about (or at least add a caveat warning others that you might not).

The original discussion started because somebody complained that Haskell programmers often appear unable to transliterate imperative algorithms. I assume that this complaint was about transliteration into pure Haskell (whatever that may mean exactly). Clearly transliteration into full Haskell with actual mutability is possible. I mentioned Pippenger's article to bring to the debate the idea that the question whether such transliteration is always possible is an open research problem.

Ah, if you'd made that assumption explicit I would not have objected.

I don't see anywhere the querent suggesting that his translation demand invoked any notion of purity. If it did, then certainly he was asking a harder question than he presented, although even in that case a naive translation could have trivially produced an O(m n lg(n)) solution and O(m^n) should quite reasonably be considered failure.

I think the issue in the main is that relatively novice Haskell developers are likely to be the most eager to try and translate arbitrary code on demand in #haskell.

Anyway, I'm a bit unhappy about the requirement of full evaluation order independence, because even the purest of pure languages (e.g. the untyped lambda-calculus or PCF) don't have full evaluation order independence. I guess you mean evaluation order independence modulo termination?

My intuition is that pure means that all language expressions M can always be evaluated locally by just looking at the meaning of all subterms of M. In terms of Hoare logic (for total correctness) that would mean that the pre-condition speaks only about the termination of the free variables of M (sorry for being so terse, I think this can be made formal).

The notions of purity I was pointing at was any that entailed the restrictions in the paper you'd linked. There are restrictions of Haskell that are pure in those senses, but Haskell taken as a whole is not, even without invoking anything unsafe.

They're about what purity means!

The key difference between ST and the State monad is that the State monad is simply sugar for a function call of the form (s -> (a, s)), whereas ST allows for actual mutability. This is what changes the asymptotic complexity.

ST also does things to prevent references from leaking, and that's valuable and more useful in the context of ST, but that's irrelevant to our questions up-thread.

"Of course ML has scope-extrusion of state, and one of my questions/examples upthread was about the ability of Haskell's monadically controlled effects to implement such scope extrusion without 'tricks'."

That wasn't this thread.

I still think scope extrusion - without asking for it - would be a bug not a feature; particularly so in the case of a multithreaded, lazily evaluated language with inlining and CSE - where you really have little control over what gets executed when if you're ducking the features that guide what gets executed when.

This doesn't limit expressibility, because you do have the ability to ask for it, using those "tricks" that you keep excluding for no good reason. "How expressive is Haskell if it lacked those" is an interesting question, but not am immediately practical one, and you should be clear that that is the question you're asking.

Purity is more subtle. I don't think there's an agreed upon definition. [1] essentially ties purity to the equivalency of call-by-name, call-by-need and call-by-value evaluation orders (ignoring divergence and errors). I'm not totally sure that is the right definition.

[1] A. Sabry, What is a Purely Functional Language?

Anyway, Haskell is perfectly decent at implementing your algorithm, and imperative algoritms in general. He's a more-or-less direct translation

    http://lpaste.net/132519

In any case the author of the post in question, Bartosz Milewski, is an expert in C++ and not particularly an expert in Haskell, so your point seems misdirected.

I'm not a "C++ programmer". I'm just a programmer. I happened to have the algorithm written in C++, but I could quite easily have written it in pseudocode.

I got about 6 responses in 20 minutes. Four of those were O(m^n). Yes, I think this is quite indicative that Haskellers have a hard time writing performant code.

For details, look at the first code block in the "The Client Side" section, here: http://bartoszmilewski.com/2015/05/18/using-monads-in-c-to-s...

However, this doesn't mean we have to punt the easy cases just because there are hard cases.

That no one seems to have produced (or pointed at) an asymptotically better solution in any language, I think that's some small evidence that there isn't such a solution and substantially more evidence that it's not easy to find.

Although I don't know how one would go about proving or disproving if this is asymptotically better or just a (substantial) constant-factor speedup.

I had initially skimmed the article, and assumed he was already handling uniqueness. With the correct definition of StateL, the solution presented is equivalent to what you describe here, but apparently that definition is deferred to a future article.

The idea would be that, for StateL, for_each would pick one value and pass that value to the lambda, interpreting the result in a context where the sel only sees the remaining values in the list.

Nope. It looks like it at first glance, but it isn't.

Look at what happens when n == b/C:

    b^(b/C) / (b!/(b - b/C)!) ==
    b^(b/C) / (b!/(b*(C-1)/C)!) ==
    e^(log(b^(b/C)) + log((b/C)!) - log((b*(C-1)/C)!)) ~=
    e^(b/C log(b) + [b*(C-1)/C] log (b*(C-1)/C) - [b*(C-1)/C] - b log b + b) ==
    e^((b+b (-1+C) log((-1+C)/C))/C) == 
    e^(b/C* (1+(C-1)log((C-1)/C)))

However, note that (1+(C-1)log((C-1)/C)) / C is greater than zero for all C > 1, as 1+(C-1)log((C-1)/C) > 0 for all C > 1. As such, this diverges for all C > 1.

In any case, I make the assertion that the algorithm proposed in the article is in fact O(b!/(b-n)!), with the intended definition of StateL.

Edit: edited.

  import numpy as np

  def valueOf(*v):
    return sum( v * np.power(10,range(len(v)))[::-1] )

  > valueOf( 2,3,4 )  # => 234

To put it simply, I don't see an improvement with that version.

And Python 3 has some improvements w.r.t. wildcard arguments.

But it's still relatively verbose, due to Python's whole "join-only-takes-strings" thing:

    def valueOf(*values, base=10):
        return int("".join(map(str, values)), base=10)

    import itertools as it
    a =  'dog'
    b =  'food'
    c = 'tasty'
    letters = sorted(set(a+b+c))
    for combo in it.permutations('0123456789', len(letters)):
        mapping = dict(zip(letters, combo))
        if len(c) > max(len(a), len(b)) and mapping[c[0]] is '0':
            continue
        f = lambda string: int(''.join(map(mapping.get, string)))
        n1, n2, n3 = map(f, [a, b, c])
        if n1 + n2 == n3:
            print( mapping )
            print( n1, n2, n3 )
            break

Why would you write an algorithm in C++ if the runtime will be bad?

ETA since he mentions the implementation is a translation of this Haskell implementation: http://blog.jle.im/entry/unique-sample-drawing-searches-with... presumably the uniqueness is done by updating the list of remaining possibilities for selection each time a new value is selected.

    from functools import reduce
    def valueOf(*values, base=10):
        return reduce(lambda x,y: x*base+y, values)

That being said, that's much cleaner. Thanks!

I'll also note that int() returns 0.

"In computer science, functional programming is a programming paradigm—a style of building the structure and elements of computer programs—that treats computation as the evaluation of mathematical functions and avoids changing-state and mutable data." -- https://en.wikipedia.org/wiki/Functional_programming

So the answer to the question "Who said you can't have state in functional programming?" is: "Every introduction to functional programming ever."

This is why people hate Haskell and make fun of Haskellers. In their quest to appear more clever than the rest of us, they engage in utterly disingenous rhetoric. Which is too bad, because I'm pretty sure they are actually more clever than the rest of us--certainly more clever than me--and don't need this nonsense.

Haskell is an amazingly cool language, and I've talked to people at meetups who are using it for interesting things, and learning a bit of it myself has been an interesting and educational challenge. But getting around to learning it took five years longer than it should have because I was so put off by the rhetorical nonsense the language community engages in.

5 years?