January 2001 - Haskell-Cafe

Re: 'any' and 'all' compared with the rest of the Report
by Jan-Willem Maessen 26 Jan '01

26 Jan '01

Marko Schuetz <MarkoSchuetz(a)web.de> starts an explanation of bottom vs. error with an assumption which I think is dangerous: > Assuming we want > > \forall s : bottom \le s > > including s = error, then we should also have error \not\le > bottom. He uses this, and an argument based on currying, to show that strict functions ought to force their arguments left to right. This seems to me to be another instance of an age-old debate in programming language design/semantics: If we can in practice observe evaluation order, should we therefore specify that evaluation order? This is a debate that's raged for quite a while among users of imperative languages. Some languages (Scheme comes to mind) very clearly state that this behavior is left unspecified. Fortunately, for the Haskell programmer the debate is considerably simpler, as only the behavior of "wrong" programs is affected. I am more than willing to be a little ambiguous about the error behavior of programs, by considering "bottom" and "error" to be one and the same. As I noted in my last message, this allows some optimizations which would otherwise not be allowed. Here's the worker-wrapper optimization at work; I'll use explicit unboxing to make the evaluation clear. forever x = forever x -- throughout. addToForever :: Int -> Int addToForever b = forever () + b main = print (addToForever (error "Bottom is naughty!")) == -- expanding the definition of + addToForever b = case forever () of I# a# -> case b of I# b# -> a# +# b# == -- At this point strictness analysis reveals that addToForever -- is strict in its argument. As a result, we perform the worker- -- wrapper transformation: addToForever b = case b of I# b# -> addToForever_worker b# addToForever_worker b# = let b = I# b# in case forever () of I# a# -> case b of I# b# -> a# +# b# == -- The semantics have changed---b will now be evaluated before -- forever(). I've experimented with versions of Haskell where order of evaluation did matter. It was a giant albatross around our neck---there is simply no way to cleanly optimize programs in such a setting without doing things like termination analysis to justify the nice old transformations. If you rely on precise results from an analysis to enable transformation, you all-too-frequently miss obvious opportunities. For this reason I *very explicitly* chose not to make such distinctions in my work. In general, making too many semantic distinctions weakens the power of algebraic semantics. Two levels---bottom and everything else---seems about the limit of acceptable complexity. If you look at the work on free theorems you quickly discover that even having bottom in the language makes life a good deal more difficult, and really we'd like to have completely flat domains. I'd go as far as saying that it also gives us some prayer of explaining our algebraic semantics to the programmer. A complex algebra becomes too bulky to reason about when things act stragely. Bottom is making things hard enough. -Jan-Willem Maessen PS - Again, we don't try to recover from errors. This is where the comparison with IEEE arithmetic breaks down: NaNs are specifically designed so you can _test_ for them and take action. I'll also point out that infinities are _not_ exceptional values; they're semantically "at the same level" as regular floats---so the following comparison is a bit disingenuous: > If error \equiv bottom and you extend, say, Int with NaNs, how do you > implement arithmetic such that Infinity + Infinity \equiv Infinity and > Infinity/Infinity \equiv Invalid Operation?

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'any' and 'all' compared with the rest of the Report
by Jan-Willem Maessen 25 Jan '01

25 Jan '01

(Note, I've kept this on Haskell-cafe) Bjorn Lisper wrote (several messages back): > ... What I in turn would like to add is that specifications like > > any p = or . map p > > are on a higher level of abstraction ... > The first specification is, for instance, directly data parallel > which facilitates an implementation on a parallel machine or in hardware. As was pointed out in later discussion, the specification of "or" uses foldr and is thus not amenable to data parallelism. On which subject Jerzy Karczmarczuk <karczma(a)info.unicaen.fr> later noted: > On the other hand, having an even more generic logarithmic iterator > for associative operations seems to me a decent idea. In my master's thesis, "Eliminating Intermediate Lists in pH using Local Transformations", I proposed doing just that, and called the resulting operator "reduce" in line with Bird's list calculus. I then gave rules for performing deforestation so that sublists could be traversed in parallel. The compiler can choose from many possible definitions of reduce, including: reduce = foldr reduce f z = foldl (flip f) z reduce = divideAndConquer (most of the complexity of the analysis focuses on making this choice intelligently; the rest could be re-stated RULES-style just as the GHC folks have done with foldr/build.) We've been using this stuff for around 6-7 years now. Fundamentally, many associative operators have a "handedness" which we disregard at our peril. For example, defining "or" in terms of foldl as above is very nearly correct until handed an infinite list, but it performs really badly regardless of the input. Thus, we need a richer set of primitives (and a lot more complexity) if we really want to capture "what is most commonly a good idea" as opposed to "what is safe". For example, our deforestation pass handles "concat" as part of its internal representation, since no explicit definition using reduction is satisfactory: concat = foldr (++) [] -- least work, no parallelism concat = reduce (++) [] -- parallelizes well, but could pessimize -- the program For this reason, it's hard to use "reduce" directly in more than a handful of prelude functions. We use reduce a lot, but only after uglification of the prelude definitions to convince the compiler to "guess right" about the appropriate handedness. There is also the problem of error behavior; if we unfold an "or" eagerly to exploit its data parallelism we may uncover errors, even if it's finite: > or [True, error "This should never be evaluated"] True My current work includes [among other things] ways to eliminate this problem---that is, we may do a computation eagerly and defer or discard any errors. -Jan-Willem Maessen My Master's Thesis is at: ftp://csg-ftp.lcs.mit.edu/pub/papers/theses/maessen-sm.ps.gz A shorter version (with some refinements) is found in: ftp://csg-ftp.lcs.mit.edu/pub/papers/csgmemo/memo-370.ps.gz

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Re: 'any' and 'all' compared with the rest of the Report
by Iavor Diatchki 23 Jan '01

23 Jan '01

hello i myself am not an experienced Haskell user, so please correct me if i am wrong. it is difficult in general to reason about the performance of lazy programs, so i don't think one can assume much. in particular i dont think 'any' and 'all' will perform in linear space. here is why i think so: take an example when 'any' is applied to some list (x:xs) and someone is actually interested in the result: any p (x:xs) 1. -> (or . map p) (x:xs) 2. -> or (map p (x:xs)) 3. -> foldr (||) False (map p (x:xs)) [at this stage we need to know what what kind of list is (map p (x:xs)) i.e. empty or a cons thing, so we need to do some evaluation] 4. -> foldr (||) False (p x : map p xs) 5. -> p x || (foldr (||) False (map p xs)) [at this stage we need to know what kind of thing is p x, i.e. True or False, so we need to evaluate p x] 6. -> if p x is True we are done (result True) 7. -> if p x is False the result is (foldr (||) False (map p xs)) and we go back to 3. note that p x has become garbage and so it doesnt really take up any space, so one really needs only enough space to process the list one element at a time. what causes problems is the need to create unnecessary cons cells (i.e. the evaluation after 3.). this is bad because it takes time. of course it only adds a constant so the complexity is the same but in practise programs run slower. this is where i would expect a good compiler to do some optimisation, i.e to remove the need for the intermediate list. i like the idea of programming at a higher level, as i believe it produces "better structured" programs. what i mean is that one manages to capture certain aspects of a program, which would be obscured if one always used explicit recursion. i think higher order functions like maps and folds really go a long way toward structuring functional programs. in a way this is simillar to using loops instead of explicit gotos in procedural programs. anyways these are my deep thought on the matter :) bye iavor On Tue, Jan 23, 2001 at 12:35:19PM -0600, Eric Shade wrote: ... > > Then I get to 'any' and 'all', whose specification requires linear > time and *linear* space when it should run in constant space. (By the > way, I checked and GHC does *not* use the Prelude definitions but > rather the obvious recursive ones, and most of its optimizations based > on "good consumers/producers" use meta-linguistic rewrite rules. So > without knowing the specific optimizations that a compiler provides, I > think it's safe to assume that the Prelude 'any' and 'all' *will* > require linear space.) ... -- +---------------------------------+---------------------------------------+ |Iavor S. Diatchki | email: diatchki(a)cse.ogi.edu | |Dept. of Computer Science | web: http://www.cse.ogi.edu/~diatchki | |Oregon Graduate Institute | tel: 5037481631 | +---------------------------------+---------------------------------------+

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Re: Specifications of 'any', 'all', 'findIndices'
by D. Tweed 23 Jan '01

23 Jan '01

On Tue, 23 Jan 2001, Mark Tullsen wrote: > Johannes Waldmann wrote: > > ... > > I'd rather write clear code, than worry about efficiency too early. > > Who said this, "premature optimization is the root of all evil". > > I've always attributed this to Donald Knuth: > > Premature optimization is the root of all evil in programming. In his paper on the errors of TeX (no proper ref but it's reprinted in his book on Literate Programming) he calls it Hoare's dictum (i.e. Tony Hoare) although the context suggests that this isn't an `official name'. Dunno if Hoare heard it from someone else though... ___cheers,_dave________________________________________________________ www.cs.bris.ac.uk/~tweed/pi.htm|tweed's law: however many computers email: tweed(a)cs.bris.ac.uk | you have, half your time is spent work tel: (0117) 954-5250 | waiting for compilations to finish.

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RE: {-# LINE 100 "Foo.hs #-} vs. # 100 "Foo.hs"
by Simon Marlow 19 Jan '01

19 Jan '01

> Indeed. Or do you want to tell me that you are going to > break one of my favourite programs? > > [ code deleted ] > # 111 "Foo.hs" Actually the cpp-style pragma is only recognised if the '#' is in the leftmost column and is followed by optional spaces and a digit. It's quite hard to write one of these in a legal Haskell program, but not impossible. Simon

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Re: A simple problem
by Tom Pledger 18 Jan '01

18 Jan '01

Ashley Yakeley writes: > At 2001-01-18 15:38, I wrote: > > >3 is not always an Integer. It's of type "(Num a) => a". > > Of course, it would be nice if 3 were an Integer, and Integer were a > subtype of Real. I haven't come across a language that does this, where > for instance 3.0 can be cast to Integer (because it is one) but 3.1 > cannot be. A cast in that direction - becoming more specific - would be nicely typed as: Real -> Maybe Integer or with the help of the fail and return methods: Monad m => Real -> m Integer

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Re: A simple problem
by Ashley Yakeley 18 Jan '01

18 Jan '01

At 2001-01-18 15:57, William Lee Irwin III wrote: >class C a where > fun :: a -> Integer > >instance Integral a => C a where > fun = toInteger . succ Gives "syntax error in instance head (constructor expected)" at the 'instance' line in Hugs. Is there a option I need to turn on or something? -- Ashley Yakeley, Seattle WA

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Re: A simple problem
by William Lee Irwin III 18 Jan '01

18 Jan '01

Moving over to haskell-cafe... At 2001-01-18 05:16, Saswat Anand wrote: >> fun 3 --gives error in Hugs >> fun (3::Integer) -- OK >> >> I am a building an embedded language, so don't want user to cast. Is >> there a solution? On Thu, Jan 18, 2001 at 03:38:10PM -0800, Ashley Yakeley wrote: > 3 is not always an Integer. It's of type "(Num a) => a". > I couldn't find a way to say that every Num is a C. I didn't try to say every Num is C, but I found a way to make his example work: class C a where fun :: a -> Integer instance Integral a => C a where fun = toInteger . succ One has no trouble whatsoever with evaluating fun 3 with this instance defined instead of the original. I'm not sure as to the details, as I'm fuzzy on the typing derivations making heavy use of qualified types. Is this the monomorphism restriction biting us again? Cheers, Bill -- <nrut> how does one decide if something is undecidable? <Galois> carefully --

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Re: O'Haskell OOP Polymorphic Functions
by Ashley Yakeley 17 Jan '01

17 Jan '01

At 2001-01-17 16:07, Johan Nordlander wrote: >Ashley Yakeley wrote: >> >> OK, I've figured it out. In this O'Haskell statement, >> >> > struct Derived < Base = >> > value :: Int >> >> ...Derived is not, in fact, a subtype of Base. Derived and Base are >> disjoint types, but an implicit map of type "Derived -> Base" has been >> defined. >> >> -- >> Ashley Yakeley, Seattle WA > >Well, they are actually subtypes, as far as no implicit mapping needs to be >defined. But since Derived and Base also are two distinct type constructors, >the overloading system treats them as completely unrelated types (which is >fine, in general). All O'Haskell treats them as completely unrelated types. In fact, this O'Haskell... > struct Base = > b1 :: Int > b2 :: Char > > struct Derived < Base = > d1 :: Int ...is a kind of syntactic sugar for this Haskell... > data Base = Base (Int,Char) > dotb1 (Base (x,_)) = x > dotb2 (Base (_,x)) = x > > data Derived = Derived (Int,Char,Int) > dotd1 (Derived (_,_,x)) = x > > implicitMap (Derived (b1,b2,d1)) = Base (b1,b2) This seems to be stretching the concept of 'subtype'. Sorry if I sound so bitter and disappointed. I was hoping for a Haskell extended with real dynamic subtyping... -- Ashley Yakeley, Seattle WA

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Boolean Primes Map (continued)
by Shlomi Fish 17 Jan '01

17 Jan '01

Well, after some thought, I decided to try re-writing the boolean primes map program only using a list instead of an array. I came up with this program: primes :: Int -> [Int] primes how_much = (iterate 2 initial_map) where initial_map :: [Bool] initial_map = (map (\x -> True) [ 0 .. how_much]) iterate :: Int -> [Bool] -> [Int] iterate p (a:as) | p > mybound = process_map p (a:as) | a = p:(iterate (p+1) (mymark (p+1) step (2*p) as)) | (not a) = (iterate (p+1) as) where step :: Int step = if p == 2 then p else 2*p mymark :: Int -> Int -> Int -> [Bool] -> [Bool] mymark cur_pos step next_pos [] = [] mymark cur_pos step next_pos (a:as) = if (cur_pos == next_pos) then False:(mymark (cur_pos+1) step (cur_pos+step) as) else a:(mymark (cur_pos+1) step next_pos as) mybound :: Int mybound = ceiling(sqrt(fromIntegral(how_much))) process_map :: Int -> [Bool] -> [Int] process_map cur_pos [] = [] process_map cur_pos (a:as) | a = cur_pos:(process_map (cur_pos+1) as) | (not a) = (process_map (cur_pos+1) as) I don't know too much about Haskell yet, so it is possible this program can be further optimized using some Haskell built-ins. Now, this program can scale to 100,000 and beyond, as opposed to the array version which only got until 30,000 or 40,000. It's a pity Haskell doesn't handle arrays very well, but I guess every language has its faults. Regards, Shlomi Fish ---------------------------------------------------------------------- Shlomi Fish shlomif(a)vipe.technion.ac.il Home Page: http://t2.technion.ac.il/~shlomif/ Home E-mail: shlomif(a)techie.com The prefix "God Said" has the extraordinary logical property of converting any statement that follows it into a true one.

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