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Re: Analyzing Efficiency
by Shawn P. Garbett 13 Aug '02

13 Aug '02

-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 On Tuesday 13 August 2002 01:37 pm, you wrote: > > I would like to compare the three in terms of reductions, memory > > usage, and overall big O complexity. > > I wouldn't use number of reductions as a guide if I was you. Number of reductions does make a difference in this case, because it's a simple test problem with three equivalent implementations (in the same compiler). Nothing to create confusion like a system call, well actually all three solutions must call a set of IO calls in the same order. So I think it would make a good baseline comparison. I do agree that it's not a good general measurement of efficiency, and really doesn't reflect the scalability of the solution either (whereas big O notation would). Thanks for the heads up though. The other tips and hints you gave me are exactly what I was looking for. No I just need a huge data set to pump into so it does a significant amount of garbage collection, and memory management... Shawn Garbett - -- You're in a maze of twisty little statements, all alike. Public Key available from http://www.garbett.org/public-key -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.0.7 (GNU/Linux) iD8DBQE9WVM5DtpPjAQxZ6ARAn2XAJ98Y4jNmnCocHzHEFpUM/vN3kTGmACfTnkf Vk3m8x1OYHGyckskR4DDKQo= =OWav -----END PGP SIGNATURE-----

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RE: Text in Haskell: a second proposal
by Simon Marlow 13 Aug '02

13 Aug '02

> At 2002-08-09 03:26, Simon Marlow wrote: > > >Why combine I/O and {en,de}coding? Firstly, efficiency. > > Hmm... surely the encoding functions can be defined efficiently? > > decodeISO88591 :: [Word8] -> [Char]; > encodeISO88591 :: [Char] -> [Word8]; -- uses low octet of > codepoint > > You could surely define them as native functions very efficiently, if > necessary. That depends what you mean by efficient: these functions represent an extra layer of intermediate list between the handle buffer and the final [Char], and furthermore they don't work with partial reads - the input has to be a lazy stream gotten from hGetContents. I don't want to be forced to use lazy I/O. > A monadic stream-transformer: > > decodeStreamUTF8 :: (Monad m) => m Word8 -> m Char; > > hGetChar h = decodeStreamUTF8 (hGetWord8 h); > > This works provided each Char corresponds to a contiguous block of > Word8s, with no state between them. I think that includes all the > standard character encoding schemes. This is better: it doesn't force you to use lazy I/O, and when specialised to the IO monad it might get decent performance. The problem is that in general I don't think you can assume the lack of state. For example: UTF-7 has a state which needs to be retained between characters, and UTF-16 and UTF-32 have an endianness state which can be changed by a special sequence at the beginning of the file. Some other encodings have states too. Cheers, Simon

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Fw: Modification of State Transformer
by Scott J. 12 Aug '02

12 Aug '02

----- Original Message ----- From: "Scott J." <jscott(a)planetinternet.be> To: "Shawn P. Garbett" <Shawn(a)Garbett.org> Sent: Monday, August 12, 2002 9:04 PM Subject: Re: Modification of State Transformer > I 'm sorry, > > What I meant was discussion about the state transformer ST s a itself. And > how it works. What does mean the second inner forall loop and so on. I can't > find explanations of this in the Haskell library. > > Regards > > Scott > ----- Original Message ----- > From: "Shawn P. Garbett" <Shawn(a)Garbett.org> > To: "Scott J." <jscott(a)planetinternet.be> > Cc: <haskell-cafe(a)haskell.org> > Sent: Monday, August 12, 2002 4:19 PM > Subject: Re: Modification of State Transformer > > > > -----BEGIN PGP SIGNED MESSAGE----- > > Hash: SHA1 > > > > On Sunday 11 August 2002 07:26 pm, Scott J. wrote: > > > Hi, > > > > > > I invite you then to explain what happens with every step. > > > > > > The use of "forall" is misleading and fast to be misunderstood: I > mention > > > here the inner forall's. > > > > > > Thx > > > > > > Scott > > > > This list is great. The implementation in the ST module solves the > > > > problem and I understand how it works. > > > > > > > > Shawn > > > > Given the level of detailed explanations to date, I don't see the point. > But > > I'll go ahead and do so anyway, by summarizing what I've learned from the > > previous posts. > > > > I had read the example in Bird'd book on state transformers. The > definition > > of state however was a fixed type in the examples. Wanting to extend the > > definition and make it more general I was trying to figure out how to > modify > > the type. > > > > Bird's definition was: > > newtype St a = MkSt (State -> (a,State)) > > type State = type > > > > I had attempted to extend the type as follows > > newtype St a s = MkSt (s -> (a,s)) > > > > This died in the compiler when declaring this type as an instance of > Monad: > > instance Monad St where > > return x = MkSt f where f s = (x,s) > > p >>= q = MkSt f where f s = apply(q x) s' > > where (x,s') = apply p s > > ghc returned the following (referencing the instance line): > > Couldn't match `*' against `* -> *' > > Expected kind: (* -> *) -> * > > Inferred kind: (* -> * -> *) -> * > > When checking kinds in `Monad St' > > In the instance declaration for `Monad St' > > > > When a type constructor has an argument it has a type of `* -> *'. > > When a type constructor has two arguments it has a type of `* -> * -> *'. > > This construction of the type can be extended to n arguments by having the > > number of `->' match the n arguments of type and the `*' be n+1. > > > > The class definition of Monad contains the following: > > class Monad m where > > return :: a -> m a > > (>>=) :: m a -> (a -> m b) -> m b > > > > > > So the class of St a s needs reduction from `* -> * -> *' to `* -> *' to > fit > > the single argument type constructor of the Monad class. By using (St a) > > which causes the type constructor to be of type `(* -> *) -> *'. Since > `(* -> > > *)' can be used as `*', by creation of another type. This because > equivalent > > to `* -> *'. > > > > The only thing left is reversing the order so that the result type is of > the > > correct form in the Monad usage. I.e, in my initial ordering the `return' > of > > the Monad would end up returning something of type `s' which is not > > particularly useful, since type `a' is the desired return type from the > > transformer. > > > > So the corrected version of State becomes: > > newtype St s a = MkSt (s -> (a, s)) > > > > instance Monad (St s) where > > ... > > > > Shawn Garbett > > - -- > > You're in a maze of twisty little statements, all alike. > > Public Key available from http://www.garbett.org/public-key > > -----BEGIN PGP SIGNATURE----- > > Version: GnuPG v1.0.7 (GNU/Linux) > > > > iD8DBQE9V8P4DtpPjAQxZ6ARAq0VAJ9toEiEm+d58vgbKEofzXBISyXrEACfasbc > > eaEg2zVi9y90vk+fXKGSrt0= > > =OrwN > > -----END PGP SIGNATURE----- > > _______________________________________________ > > Haskell-Cafe mailing list > > Haskell-Cafe(a)haskell.org > > http://www.haskell.org/mailman/listinfo/haskell-cafe > > >

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Re: Modification of State Transformer
by Jon Cast 12 Aug '02

12 Aug '02

"Shawn P. Garbett" <listman(a)garbett.org> wrote: > I'm trying to modify Richard Bird's state transformer. The example > in his book (_Introduction_to_Functional_Programming_using_Haskell_) > has State defined as a explicit type. > I.e. Here's the relevant snippet: > -- State transformer definition > newtype St a = MkSt (State -> (a, State)) > type State = Int > -- State transformer applied to state > apply :: St a -> State -> (a, State) > apply (MkSt f) s = f s > -- State monad > instance Monad St where > return x = MkSt f where f s = (x,s) > p >>= q = MkSt f where f s = apply (q x) s' > where (x, s') = apply p s > ----------------------------------------- > What I want is something like this, so that the state transformer > has a generic state type: Btw: This has already been done, in GHC: see the ST module in GHC's library <http://www.haskell.org/ghc/docs/latest/html/base/Control.Monad.ST.html>. To answer your specific question, though: > newtype St a s = MkSt (s -> (a, s)) These are in the wrong order (see below); you want: > newtype St s a = MkSt (s -> (a, s)) > apply :: St a s -> s -> (a, s) > apply (MkSt f) s = f s Again, s/St a s/St s a/. > instance Monad St where > return x = MkSt f where f s = (x,s) > p >>= q = MkSt f where f s = apply (q x) s' > where (x, s') = apply p s > ----------------------------------------------------------- > The trouble occurs on the instance line > Couldn't match `*' against `* -> *' > Expected kind: (* -> *) -> * > Inferred kind: (* -> * -> *) -> * > When checking kinds in `Monad St' > In the instance declaration for `Monad St' > Failed, modules loaded: none. Right. The problem here is that St is a type constructor with two arguments (i.e., of kind (* -> * -> *)), whereas Monad wants a type constructor with one argument (i.e., of kind (* -> *)). Hence the error. This is the same type of error you'd get if you tried to declare an instance for `Eq Tree', where `Tree' is a standard (polymorphic) BST. The way you solve that is to instantiate `Eq (Tree a)', and it's the same thing here: instantiate `Monad (St s)'. Of course, you need to switch the order of the arguments to St first (as done above), so Haskell knows `s' is a the state type, not the result type. HTH Jon Cast

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Re: Newbie question on "statefullness"
by Ashley Yakeley 12 Aug '02

12 Aug '02

At 2002-08-11 23:48, I wrote: >>I want to implement something like the C idea of: >>n += i >> >>So how does one doe this in Haskell? > > do { > val <- readIORef n; > writeIORef n (val + i); > }; Or even... modifyIORef n ((+) i); -- Ashley Yakeley, Seattle WA

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Re: Newbie question on "statefullness"
by Ashley Yakeley 12 Aug '02

12 Aug '02

At 2002-08-11 17:36, Alex Peake wrote: >I want to implement something like the C idea of: >n += i > >So how does one doe this in Haskell? do { val <- readIORef n; writeIORef n (val + i); }; -- Ashley Yakeley, Seattle WA

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Haskell-Cafe -- confirmation of subscription -- request 321501
by Cyril Baratoff 09 Aug '02

09 Aug '02

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Combining type constraints
by Andrew J Bromage 09 Aug '02

09 Aug '02

G'day all. I have a large number of functions all of which use the same set of type constraints, such as: > foo :: (Monad m, Ord t, Show t) => ... Ideally, I'd like to combine them into one typeclass. At the moment, I'm using the equivalent of: > class (Monad m, Ord t, Show t) => Constraints m t where { } > instance (Monad m, Ord t, Show t) => Constraints m t where { } > foo :: (Constraints m t) => ... This requires undecidable instances. Is there a way to do this that doesn't require non-98 features apart from multi-parameter type classes? If not, is there an argument for a language construction which supports this idiom, analogous to type synonyms, except for type classes? Cheers, Andrew Bromage

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Transformations of cyclic graphs [Was: Efficiency of list indices in definitions]
by oleg＠pobox.com 08 Aug '02

08 Aug '02

[Moved to Haskell-Cafe] Hello! Cycles sure make it difficult to transform graphs in a pure non-strict language. Cycles in a source graph require us to devise a way to mark traversed nodes -- however we cannot mutate nodes and cannot even compare nodes with a generic ('derived') equality operator. Cycles in a destination graph require us to keep track of the already built nodes so we can complete a cycle. An obvious solution is to use a state monad and IORefs. There is also a monad-less solution, which is less obvious: we can't add a node to the dictionary of constructed nodes until we have built the node, then means we can't use the updated dictionary when building descendants -- which need the dictionary when linking back. The problem can be overcome however with a credit card transform (a.k.a. "buy now, pay later" transform). To avoid hitting the bottom, we just have to "pay" by the "due date". The will use as an example the NFA->DFA transformation considered earlier. Perhaps we should first attempt a few obvious optimizations of a NFA/DFA recognizer. It seems that performance matters. finAuAcceptStringQ startStates string = or [faStateAcceptStringQ s string | s <- startStates] where faStateAcceptStringQ (FaState _ acceptQ _) [] = acceptQ faStateAcceptStringQ (FaState _ _ trans) (a:as) | null followerStates = False | otherwise = or [ faStateAcceptStringQ s as | s <- followerStates ] where followerStates = if a > (length trans) - 1 then [] else trans!!a Computing (length trans) when determining the followerStates is inefficient: even if 'a' is zero, we still have to traverse the whole list 'trans'. If our alphabet is binary, perhaps its better to specialize the FaState correspondingly and write: -- Automata over a binary alphabet data (Ord l,Show l) => FaState l = FaState {label :: l, acceptQ :: Bool, trans0:: [FaState l], trans1:: [FaState l]} -- Then a finite automaton is merely a list of starting FaStates: type FinAu l = [FaState l] --So, for example, an automaton equivalent to the regular expression --0*(0(0+1)*)* could be defined as: dom18 = [one] where one = FaState 1 True [one,two] [] two = FaState 2 True [two,one] [one,two] The acceptance function can be written as finAuAcceptStringQ start_states str = foldr (\l seed -> acceptP l str || seed) False start_states where acceptP (FaState _ acceptQ _ _) [] = acceptQ acceptP (FaState _ _ t0 t1) (s:rest) = finAuAcceptStringQ (if s then t1 else t0) rest We have simplified the original expression, and manually deforested it. test1= finAuAcceptStringQ dom18 $ map (>0) [0,1,0,1] test2= finAuAcceptStringQ dom18 $ map (>0) [1,1,0,1] test3= finAuAcceptStringQ dom18 [True] test4= finAuAcceptStringQ dom18 [False] It would be great to be able to compare and print the nodes: instance (Ord l,Show l) => Eq (FaState l) where (FaState l1 _ _ _) == (FaState l2 _ _ _) = l1 == l2 but printing a node is already a slight problem. We need to keep track of the already printed nodes to avoid looping. -- a data class for an occurrence check class OCC occ where empty:: occ a seenp:: (Eq a) => a -> occ a -> Bool put:: a -> occ a -> occ a -- Currently, it's just a list. -- In the future, we can pull in something fancier from the Edison instance OCC [] where empty = [] seenp = elem put = (:) -- Depth-first, pre-order traversal of the graph, keeping track of -- already printed nodes instance (Ord l,Show l) => Show (FaState l) where show state = "{@" ++ showstates [state] (empty::[FaState l]) "@}" where -- showstates worklist seen_states suffix showstates [] states_seen suffix = suffix showstates (st:rest) states_seen suffix | st `seenp` states_seen = showstates rest states_seen suffix showstates (st@(FaState l accept t0 t1):rest) states_seen suffix = showstate st $ showstates (t0++t1++rest) (st `put` states_seen) suffix showstate (FaState l accept t0 t1) suffix = "{State " ++ (show l) ++ " " ++ (show accept) ++ " " ++ (show $ map label t0) ++ " " ++ (show $ map label t1) ++ "}" ++ suffix Now, "print dom18" prints as [{@{State 1 True [1,2] []}{State 2 True [2,1] [1,2]}@}] For the NFA->DFA conversion, we need to keep track of already built states. -- A dictionary of states class StateDict sd where emptyd :: sd (l,FaState l) locate :: (Eq l) => l -> sd (l,FaState l) -> Maybe (FaState l) putd :: (l,FaState l) -> sd (l,FaState l) -> sd (l,FaState l) -- if performance matters, we can use a fancier dictionary from the Edison instance StateDict [] where emptyd = [] locate = lookup putd = (:) -- [nfa_state] -> dictionary_of_seen_states -> ([dfa_state],updated_dictionary) -- [dfa_state] is a singleton list determinize_cc states converted_states = -- first, check the cache case dfa_label `locate` converted_states of Nothing -> build_state Just dfa_state -> ([dfa_state],converted_states) where -- [NFA_labels] -> DFA_labels det_labels = sort . nub . (map label) dfa_label = det_labels states -- find out NFA-followers for [nfa_state] upon ingestion of 0 and 1 (t0_followers,t1_followers) = foldr (\st (f0,f1) -> (trans0 st ++ f0, trans1 st ++ f1)) ([],[]) states acceptQ' = or (map acceptQ states) -- really build the dfa state and return ([dfa_state],updated_cache) build_state = let -- node, dfa_state is computed _below_ converted_states1 = (dfa_label,dfa_state) `putd` converted_states (t0', converted_states2) = (determinize_cc t0_followers converted_states1) (t1', converted_states3) = (determinize_cc t1_followers converted_states2) dfa_state = (FaState dfa_label acceptQ' t0' t1') in ([dfa_state],converted_states3) finAuDeterminize states = fst $ determinize_cc states [] At the heart of the credit card transform is the phrase converted_states1 = (dfa_label,dfa_state) `putd` converted_states we added to the dictionary of the computed states the state that we haven't built yet. Because (,) is non-strict in its arguments and `locate` is non-strict in its result, we can get away with a mere promise to "pay". We can print the DFA for dom18 to see what we've got: finAuDeterminize dom18 -- shows [{@{State [1] True [[1,2]] [[]] } {State [1,2] True [[1,2]] [[1,2]]} {State [] False [[]] [[]] }@}] which is a DFA (which happens to be minimal) recognizing (0+1)* - 1(0+1)* An example from the original message: dom19 = [one,two] where one = FaState 1 True [two] [] two = FaState 2 True [one] [one] finAuDeterminize dom19 -- shows [{@{State [1,2] True [[1,2]] [[1]] } {State [1] True [[2]] [[]] } {State [2] True [[1]] [[1]] } {State [] False [[]] [[]] }@}] which recognizes (0+1)* - (0+1)*11(0+1)*

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Modification of State Transformer
by Shawn P. Garbett 08 Aug '02

08 Aug '02

I'm trying to modify Richard Bird's state transformer. The example in his book (_Introduction_to_Functional_Programming_using_Haskell_) has State defined as a explicit type. I.e. Here's the relevant snippet: -- State transformer definition newtype St a = MkSt (State -> (a, State)) type State = Int -- State transformer applied to state apply :: St a -> State -> (a, State) apply (MkSt f) s = f s -- State monad instance Monad St where return x = MkSt f where f s = (x,s) p >>= q = MkSt f where f s = apply (q x) s' where (x, s') = apply p s ----------------------------------------- What I want is something like this, so that the state transformer has a generic state type: newtype St a s = MkSt (s -> (a, s)) apply :: St a s -> s -> (a, s) apply (MkSt f) s = f s instance Monad St where return x = MkSt f where f s = (x,s) p >>= q = MkSt f where f s = apply (q x) s' where (x, s') = apply p s ----------------------------------------------------------- The trouble occurs on the instance line Couldn't match `*' against `* -> *' Expected kind: (* -> *) -> * Inferred kind: (* -> * -> *) -> * When checking kinds in `Monad St' In the instance declaration for `Monad St' Failed, modules loaded: none.

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