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differential operation (Typing Question!)
by Jay Cox 11 Jan '02

11 Jan '02

|> Message: 1 |> From: "Zhe Fu" <fuzh(a)cs.orst.edu> |> To: <haskell-cafe(a)haskell.org> |> Subject: how to implement the differential operation with Haskell? |> Date: Wed, 9 Jan 2002 00:37:20 -0800 |> |> Is there any built-in functions in Haskell to implement diffential |> operation? Or can anyone give me some advices about how to implement |them |> with Haskell? Thanks. If you happen to be talking about symbolically differentiating expressions, I happen to be in the early stage of developing a extendible module to do such a thing right now! However I seem to have come across some typing problems. But to understand my problem I may need to try to summarize the details thereof I started out with a recursive datatype >data BasDif r = Ext (r (BasDif r)) | > Symbol Sym | Constant Rational | > Sum (BasDif r) (BasDif r) | > Prod (BasDif r) (BasDif r) | > Divide (BasDif r) (BasDif r) | > Negate (BasDif r) | D (BasDif r) Notice the Ext( r (BasDif r)). I use this to extend the datatype. I define a basic differentiating function "d" on all of these constructs except Ext. When d pattern matches (Ext x) it calls some instance of the diff class on x. diff on some function g(u) where u is an expression returns a pair (u,g') back to "d" so that "d" can complete the chain rule d(g(u))=g'(u)*d(u). (technically it returns a function g' which takes two arguments: a data constructor and a BasDif expression of some sort the current expected typing of diff (forgive me for not knowing proper vernacular) is given below. >class Diff x where > diff:: Sym -> x a -> (a, (x a1 -> r (BasDif r)) -> a1 -> BasDif r) Its rather complex but I'll admit I stole it from the ghci interpreter giving me the type of function which did conceptually what I wanted it to do. the types are below. Differentiate> :type diffTrig forall t a a1 r. t -> Trig a -> (a, (Trig a1 -> r (BasDif r)) -> a1 -> BasDif r) Differentiate> :type diffNe forall t a a1 r. t -> NumExp a -> (a, (NumExp a1 -> r (BasDif r)) -> a1 -> BasDif r) Before I expound upon why the type needs to be so complicated, let me tell you what I'm trying to do with these diff functions that follow. (In the following definitions, prod, sum_, negate_, are more or less helper functions which make some trivial simplifications as they make products, sums, and additive inverses) >data NumExp a = N Rational a >diffNe s (N i x) = > let j = i-1 > in if (j /= 0 ) > then (x,\f-> \v -> prod (Ext(f (N (i-1) v))) (Constant i)) > else (x,\_-> \_->Constant 1) > >instance Diff NumExp where > diff=diffNe >data Trig a = Sin a | Cos a | Tan a | Cot a| Sec a |Csc a deriving Show >diffTrig s (Sin x) = (x, \f -> Ext . f . Cos) >diffTrig s (Cos x) = (x, \f -> negate_ . Ext . f . Sin) ... more defs >instance Diff Trig where > diff = diffTrig With these definitions, I have enough to take derivatives of (BasDif Trig) expressions or (BasDif NumExp) expressions, but not both. Therefore I defined the above expressions (as complicated as they are) so that I could make a instance of diff by combining the two without copy/pasting code (and without explicitly calling diffTrig and diffNe) thus being able to differentiate expressions of BasDif TrigNumExp (and thus being able to differentiate expressions with + - * / sine,cosine,tangent,their reciprocals and any combination thereof with a rational exponent) >data TrigNumExp a= T (Trig a) | NE (NumExp a) >instance Show a => Show (TrigNumExp a) where > showsPrec _ (T x) = shows x > showsPrec _ (NE x) = shows x > >diffTrigNumExp s (T x) = let (k,f)= diff s x in (k,\g->f (g .T)) >diffTrigNumExp s (NE x) = let (k,f)= diff s x in (k,\g->f (g .NE)) > >instance Diff TrigNumExp where > diff = diffTrigNumExp In this I have succeeded. THEN I tried to do the same for inverse trig functions. These are of a rather different nature. the derivative of inverse sine requires something to represent square roots of expressions, hence I use the constructor for NE expressions. >diffArcT s (ArcSin x) =(x,\f-> \y->Ext(f ( N (-1/2) > (sum_ (Constant 1) (negate_ (prod y y)))))) >diffArcT s _ = error "incomplete" the type of diffArcT is Differentiate> :type diffArcT forall t a r1 r. t -> ArcTrig a -> (a, (NumExp (BasDif r1) -> r (BasDif r)) -> BasDif r1 -> BasDif r) I suppose the error message I get when adding this function to the module is understandable given the class constraints.. ... Differentiate.v2.lhs:177: Couldn't match `ArcTrig a1' against `NumExp (BasDif r)' Expected type: Sym -> ArcTrig a -> (a, (ArcTrig a1 -> r1 (BasDif r1)) -> a1 -> BasDif r1) Inferred type: Sym -> ArcTrig a -> (a, (NumExp (BasDif r) -> r2 (BasDif r2)) -> BasDif r -> BasDif r2) In the definition of `diff': diffArcT ... but seems to me to be a reasonable relaxing of types for the class doesn't work either (in fact it produces errors for every instance of diff ... Old class >class Diff x where > diff:: Sym -> x a -> (a, (x a1 -> r (BasDif r)) -> a1 -> BasDif r) New class class Diff x where diff:: Sym -> x a -> (a, (x1 a1 -> r (BasDif r)) -> a1 -> BasDif r) New errors with new class Cannot unify the type-signature variable `x1' with the type `TrigNumExp' Expected type: Sym -> TrigNumExp a -> (a, (x1 a1 -> r (BasDif r)) -> a1 -> BasDif r) Inferred type: Sym -> TrigNumExp a -> (a, (TrigNumExp a11 -> r1 (BasDif r1)) -> a11 -> BasDif r1) In the definition of `diff': diffTrigNumExp Differentiate.v2.lhs:177: Cannot unify the type-signature variable `x1' with the type `NumExp' Expected type: Sym -> ArcTrig a -> (a, (x1 a1 -> r (BasDif r)) -> a1 -> BasDif r) Inferred type: Sym -> ArcTrig a -> (a, (NumExp (BasDif r1) -> r2 (BasDif r2)) -> BasDif r1 -> BasDif r2) ... etc. What I don't understand is WHY NumExp cannot be unified with x1. what I would personally would like to understand is if Haskell's Hindley-Miller type system can even deal with what I want to do (basically I want a type for diff such that the definition of diffArcT would be tolerable to the compiler.) I realize I am a bit over my head here so it might be concievable that just some pointer to a reference on how haskell deals with type resolution might help as well, or perhaps some general method for concieving of a general type for a member of a class, or perhaps some ideas to re-engineer this module. Anyway, I suppose this module might be of some interest to some people so I have put it in a temporary place so that some people may play with it. It doesnt have any functions for reading general expresssions yet, you could enter some funky multivariable expression and see what comes out. (I must warn you, if you happen to use the "d" function, it doesnt do much but the simplest simplifications. some of the less trivial simplifications have been commented out because they do not help the runtime. It is at (temporarely) http://home.flash.net/~flygal/Jay/Haskell/Differentiate/v0.1/Differentiate.… Have fun and thanks for any help Jay Cox

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Re: State Transformer
by Ketil Z Malde 11 Jan '02

11 Jan '02

Jorge Adriano <jadrian(a)mat.uc.pt> writes: > Anyway, I was coding some simple GA, and as you probably know I need to use > random values. The most elegant way I could think of was to generate some [...] > Monads! (right?) Well, I suppose so. Generally speaking. But, you might want to consider using the standard random generation routines from the (IO) top level of your program, and just split the random generator for each function that uses it. IOW, passing each function its own random generator, instead of worrying about returning the "rest" of a global random sequence. (I don't have any good example code, I'm afraid, but at leat have a look at the chapter on Random in the library report on http://haskell.org) -kzm -- If I haven't seen further, it is by standing in the footprints of giants

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how to implement the differential operation with Haskell?
by Zhe Fu 09 Jan '02

09 Jan '02

Is there any built-in functions in Haskell to implement diffential operation? Or can anyone give me some advices about how to implement them with Haskell? Thanks.

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State Transformer
by Jorge Adriano 07 Jan '02

07 Jan '02

Hi, I'm studying, among other things, Genetic Algorithms and Neural Networks and I decided I'd use haskell to code some simple GAs and NNs along with my study. Well, maybe it was not such a good idea after all, because I've been spending way more time learning more Haskell then GAs and NNs :( Anyway, I was coding some simple GA, and as you probably know I need to use random values. The most elegant way I could think of was to generate some infinite list of random values and pass them around as arguments to the functions that need those values. I called data which wraped this list Environment, and at first it seemed a nice way to solve the problem. Well, now I think it gets kind of weird because some functions will end up to have type something -> (otherthing, Environment), to update those lists... it's just ugly. Beside those lists I'd also like to control some statistics like the number of mutations, n. of crossovers, best fitness value in each generation, etc... I figured out that there should be a better way to do this then just chaging all the signatures and passing all this values around. Monads! (right?) Till then I had just read what I needed to be able to use the IO Monad. Seems to me like having a State Transformer monad its the best way to do it. Now I've read a great deal of Richard Birds Book chap 10 (Monads), as well as the "Monads for the Haskell Working Programmer"[1] by Theodore Norvell. I was going to try to make my own simple examples using a ST. A State Monad seemed something like would most probably be in some Standard Library, or at least in some GHC library. And it was (section 4.31.ST in the hslibs documentation) I wanted to use this ST, but then I noticed it was different from the one described in tutorial[1]. I was expecting the ST Monad ghc module to provide an apply function, analogue to the > applyST :: StateTrans s a -> s -> (s, a) > applyST (ST p) s = p s in the tutorial. I also expected to have general functions to access and change State. I can't implement them myself since the ST constructor is (obviously) not exported. But this ST module seems to work in a completely diferent way. >From what I can tell it is not suposed to be applyed to an initial state, instead it starts with an 'empty' state... State is controled with Referencies (mutable variables). Ok, now my problem, how do I use this? I can't really see how to change this referencies from within some function. (Got an example in the end to explain better waht I mean with that [Example1]) I'd also appreciate some coments on: Using a ST monad (good idea, bad?) Using the Ghc ST monad? Chromosomes defined as arrays? - either IArray or Diff array got to give it some more thought... (don't want Ints + bitwise operations right now...) Well, any other comments or hints that you think that might be usefully are welcome. I've already checked out the paper from the TAIGA project[2], it's not exactly done the way I'm thinking about doing it, but I got some usefull tips from there, like the use of a Monad to control statistics. One of my main problems so far as been *knowing what do I need to know*! I don't know anyone that codes in haskell, not having anyone to talk to and share ideas doesn't helps much either. Things get complicated where you (you - the guy that comes from the imperative paradigm) less expects it too... the space leaks, using monads to control state... if you still have not read about this stuff, IMO, it is easy to feel like you already know enough to do some solve some kind of problems when you actually don't. Any newbie to C or Pascal can make a few randoms here and there, and keep track of statistics... when you already spent some time with haskell you don't even question whether you already know enough to do something like *that*. Only when you start to work, and thing start to get messy, you begin to think that *maybe you need something you still don't know about*, and then you got to find out what it is... Documentation, I also feel like it could be more and better... the ST module in ghc for instance... would it be that hard to put at least some simple example there? No, just the type signatures... Well, this is just my opinion anyway. Thanks for your atention, and happy 2002 ;-) J.A. [Example1] How can I do this for instance, with the Ghc ST Monad: ------------------------------------------------------------------------ -- the State Trans defined as in the tutorial newtype StateTrans s a = ST( s -> (s, a) ) instance Monad (StateTrans s) where -- (>>=) :: StateTrans s a -> (a -> StateTrans s b) -> StateTrans s b (ST p) >>= k = ST( \s0 -> let (s1, a) = p s0 (ST q) = k a in q s1 ) -- return :: a -> StateTrans s a return a = ST( \s -> (s, a) ) applyST :: StateTrans s a -> s -> (s, a) applyST (ST p) s = p s -- just change the state putST :: (Char,Int) -> StateTrans (Char,Int) () putST (c',n') = ST(\(c,n)->((c',n'),())) -- get the state getST :: StateTrans (Char,Int) (Char,Int) getST = ST(\(x,y)-> ((x,y), (x,y))) testfunc :: StateTrans (Char,Int) Int testfunc = do foo bar (c,n)<-getST return n foo = do (c,n)<-getST putST ('a',n+1) bar = do (c,n)<-getST putST (c,n+2) tryTestFunc = applyST testfunc ('x',0) ------------------------------------------------------------------------ I is something like this? ---------------------------------------- stupidFunc runST ( do { initstate <- newSTRef ('x',0) -- and now what? }) ----------------------------------------- [1] http://www.engr.mun.ca/~theo/Misc/haskell_and_monads.htm [2] http://www.scms.rgu.ac.uk/staff/db/Taiga/ http://www.scms.rgu.ac.uk/staff/db/Taiga/APGA2000.ps.gz

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RE: Compiler error using IO
by Ashley Yakeley 07 Jan '02

07 Jan '02

>| while :: IO Bool -> IO () -> IO () >| >| while test action = do res <- test >| if res then do action >| while test action >| else return () > >Haskell uses "layout" to reduce the need for parentheses. For your code to >parse, "if" should align with "res" vertically, as in: > > ... = do res <- test > if res ... The "layout" rules drive me nuts. You might prefer using parentheses and semicolons, as I do: -- (not tested) while :: IO Bool -> IO () -> IO (); while test action = do { res <- test; if res then do { action; while test action; } else return (); }; -- ...and then you can put the whitespace wherever you want. -- Ashley Yakeley, Seattle WA

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(no subject)
by Noriyuki Sugita 05 Jan '02

05 Jan '02

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Compiler error using IO
by Tom Bevan 03 Jan '02

03 Jan '02

When trying to right IO I continually run across this sort of compile error which I just don't understand. Any help would be very muich appreciated. Function: while :: IO Bool -> IO () -> IO () while test action = do res <- test if res then do action while test action else return () Error: io.hs: 112 lines, 2463 characters. Reading file "io.hs": Parsing ERROR io.hs:110 - Last generator in do {...} must be an expression Tom

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Intro to Functional Prog. by Bird, Section 2.5
by Shawn P. Garbett 02 Jan '02

02 Jan '02

I've been working on understanding Haskell using hugs98 and playing with some of the examples in Bird's book. In section 2.5, page 46 of the second edition, he gives an example of dependent types: But I get this error I've been unable to solve: ---------------------------------------------------------------------------------------------------------------- --Type checking --ERROR sec2-5.hs:8 - Type error in application --*** Expression : case' (Left' f,Right' g) --*** Term : (Left' f,Right' g) --*** Type : (Either' (d -> e) f,Either' g (h -> i)) --*** Does not match : (a -> b,c -> b) data Either' a b = Left' a | Right' b case' :: (a->g, b->g) -> Either' a b -> g case' (f, g) (Left' x) = f x case' (f, g) (Right' y) = g y plus' :: (a->b , g->d) -> Either' a g -> Either' b d plus' (f,g) = case' (Left' f, Right' g) ----------------------------------------------------------------------------- Please note that the version I've entered is correct by the errata published for this section.

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RE: haskell sockets
by Simon Marlow 02 Jan '02

02 Jan '02

> i want to write/read data to the soccerserver of the robocup. > the sample > code below works, but i want to have a handle for writing to > the server > instead of SocketPrim.sendTo. how can i do that ? SocketPrim.socketToHandle gives you back a Handle which you can use to read/write to/from using Haskell's normal IO operations. Note that you need to call SocketPrim.connect, even for a Datagram socket, to fix the endpoint for the socket. Cheers, Simon

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PHOTOS XXX GRATUITES !!!
by sandy000＠hotmail.com 29 Dec '01

29 Dec '01

1 0