That said, there is a lot of Haskell I like, and despite billing myself upfront as a failed Haskell programmer, I still hold out hope of making progress in using it. Though I may need to transition to it through one or two other languages first.

And it is much harder to verify a proof than a program. You can run a program and subject its results to tests. Something you cannot easily do with formal mathematical notation. Of course, a big part of the desire for FP is the ability to have a compiler that takes standard mathematical notation and converts it to a running program. But then, you not only have to verify the notation, you also have to verify the compiler that does the conversion, and the results it produces, and the results that what it produces, produce.

Although I'm probably getting *really* OT, here's an excerpt I like from "The Way of Z: Practical Programming with Formal Methods" by Jonathan Jacky:

Many programmer believe that fomal specification are not useful. They believe that the program text -- the code itself -- can be the only really complete and unambifuous description of what a program does. This vew holds that a formal specification is nothing more that the program written over again in another language. It misinterprets Z to be some kind of very high-level programming language.

This example shows they are wrong. See for yourself; Here is the code in C.

int f(int a)
{
  int i, term, sum;
  
  term=1; sum=1;
  for (i=0; sum <= a; i++) {
       term=term+2;
       sum=sum+term;
  }
  return i;
}
[download]

The code couldn't be simpler. It is well structured and very brief -- in fact it looks trivial. But what does it do? Is seems to be adding up a series of number -- but why? And it returns the counter, rather than the sum -- is that a mistake? Try to answer before you turn the page.

And that's my problem with much of the hyperbole that surrounds and infuses FP.

This paper is saying that "we don't need to deal with errors, exceptions, dirty data etc.", or "need a language that is Turing complete" (elsewhere in the paper) except on "rare occasions", but that just doesn't make sense to me.

Show me the code.

For your test, I ran this:

#! perl -slw
use strict;

sub f {
    my $a = shift;
    my $term = 1;
    my $sum = 1;
    my $i;

    for( $i=0; $sum <= $a; $i++) {
        $term = $term + 2;
        $sum = $sum + $term;
#        print "i:$i term:$term sum:$sum";
    }
    return $i;
}

print "f($_) = ", f( $_ ) for -4 .. 36;
[download]

The terminating value for the test loop may indicate to you that I had a good idea of what it was doing before I ran it. I still haven't looked up the book. I'd term f as 'the integer root', but there is probably some proper term for that.

Now I'll turn the page...back.

So, not far wrong, but did I pass the test? I read on a few pages and it makes great play of how the Z axiomatic definition carries more information--such as the possible ranges of inputs and outputs from f()---but that ignores that the C definition could also have captured that information.

unsigned int f( unsigned int a ) {
  unsigned int i, term, sum;
  
  term=1; sum=1;
  for (i=0; sum <= a; i++) {
       term=term+2;
       sum=sum+term;
  }
  return i;
}
[download]

And actually, that carries more information. For one thing, on practical computer systems, variables are of finite size and can therefore only deal with finite ranges of values. It maybe mathematically convenient to reason about functions in terms of the infinite range of natural numbers, but in practice, that reasoning falls down because real hardware overflows, underflows and otherwise does not behave as mathematical theory would have it behave.

The Z definition won't tell you that for inputs above 2**31, (using the original C formulation on a 32-bit processor) that you are going to get bizarre outputs because the intermediate term sum will overflow.

In the Total FP paper, the author says:

RULE 1) All case analysis must be complete. So where a function is defined by pattern matching, every constructor of the argument type must be covered and in a set of guarded alternatives, the terminating ‘otherwise’ case must be present. In the same spirit any built in operations must be total. This will involve some non-standard decisions - for example we will have

0 / 0 = 0

Yeah, right! Good luck with that.

Now how hard do I have to think to come up with a scenario where the undetected, unreported, silent conversion of erroneous input into a mathematically convenient lie causes the reactor to go critical or the patient to receive a massive dose of something lethal? But the mathematicians are happy, so what the hey! Again, just a dramatisation.

Have you taken a look at Prolog?

Yes. I did a Prolog course at college back before the dawn of time. And more recently, about 10 years ago, I had to do some real work with an inferencing engine that used a dialect of Prolog. It does take a very different mindset. And the last time I frequently wrote short brute force C programs to verify the results I was getting from the inferencing engine. They usually ran longer, but they were much faster to produce and I had far more confidence in the results.

Oh, sure, there are going to be some enthusiastic advocates of any language,

It's not "enthusiastic advocates" that disturb me.

• It's the claim that Haskell's purity allows provability of its programs which results in more reliable software.

  This claim is not restricted to appearing in fly-by-night blogs of enthusiastic advocates. I think this claim is bogus. I think I proved it was bogus using evidence from one of your favorite papers above.

• It's the claim that the absence of side effects increases provability (or "the ability to reason about") of Haskell programs.

  It may increase either or both, for those parts of Haskell programs that are purely functional, and for mathematicians and those that are used to thinking in that way.

  But, as I've alluded to elsewhere in the thread, Haskell programs--every useful Haskell program--does have side effects. It may deal with them better than many other FP languages, and possibly other non-FP languages, but they are still there.

  But is there any hard evidence that useful Haskell programs are more bug free than other languages?

• It's the claim that Haskell increases programmer productivity.

  It may do so, for expert Haskell programmers but if the World Programming Council banned all programming languages except pure lazy functional languages tomorrow, how productive would the worlds (1 million?) programmers be the day after? Or the week after? Or 1 year from now?

  How many of the worlds programmers would successfully make the transition from imperative to functional programming?

  Even when they had, they would still have to program in a world where data gets corrupted; where strings have to mutate into integers and reals; where disks fail; communications channels go away; where files are bigger than memory and have the wrong line endings; where DoS attacks abound; where input are accidentally supplied in inches instead of millimetres.

  Will their conversion to Haskell make them any more capable of dealing with these situations?

  Even within the field of Maths itself, most of the best math packages are still written in Fortran.

IMO Haskell should be downplaying the arguments about whether the rules underlying Monads are correct, or whether MonadPlus is better. And whether Lazy is a good or a bad thing.

I didn't get to go through the Xmonad stuff, but there doesn't appear, at first glance at the page you linked, to be any tutorial associated with it? I did say show me the code, but went on to say "But more importantly, show me how you arrived at it."

---

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.

"Too many [] have been sedated by an oppressive environment of political correctness and risk aversion."

• It's the claim...
• It's the claim...
• It's the claim...

How many of the worlds programmers would successfully make the transition from imperative to functional programming?

I'm still a little bit confused. Is someone trying to "convert" to the Haskell religion? Certainly I hope you don't think I am. Who cares how many people can transition from imperative to functional programming? Go with what works for you. I'm quite content that you at least tried something new, even if it didn't work out for you. In my previous postings, I was trying to get across the idea that there's no one-size-fits-all when it comes to programming languages. My personal experience has been that Haskell lets me write easier to understand programs with less fuss and fewer bugs. Other people have had similar experiences. YMMV.

for those parts of Haskell programs that are purely functional

Er, *All* Haskell programs are 100% referentially transparent and purely functional. You can substitute equals for equals anywhere and everywhere. Always. No Exceptions. Anyway, I also meant to link to the Q Lanugage in my previous post. Good luck and best wishes.

I dearly hope that you will come back and see this.

I cannot thankyou enough for the link to Backus. I understand why this is your favorite. I think it may well become one of mine. Actually I think it already is, and I haven't finished reading it yet.

What a refreshing change from most of the other papers I have been reading. Clear points, made with clear explanations and clear examples. Where he uses algebraic notation, each symbol is briefly described, in-situ.

By the time I finished section 11, I understood why I so want to like FP. Simplicity, brevity, clarity. Thankyou.

30 years on, his presentation style shows why the greats are.

---

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.

"Too many [] have been sedated by an oppressive environment of political correctness and risk aversion."

You're welcome. And if you really want to get into functional programming or Haskell, I still recommend getting a book, rather than slogging throught PDFs and online tutorials. And although I admire your persistance, I'll temper your expectations by stating that, while I personally like Haskell, it is only an incremental improvement. The language is nicer, but Perl still wins hand-down when it comes to libraries, finding people to do maintenance, etc. And Haskell does have its own warts (Laziness induced space leaks for instance). So while you may still want to pursue it for intellectual reasons, don't expect that functional programming will make you twice as much money or somesuch.