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  • What is wrong with this simple type definition? (Expecting one more argument to...)

    - by fluteflute
    basic.hs: areaCircle :: Floating -> Floating areaCircle r = pi * r * r Command: *Main> :l basic.hs [1 of 1] Compiling Main ( Sheet1.hs, interpreted ) Sheet1.hs:2:15: Expecting one more argument to `Floating' In the type signature for `areaCircle': areaCircle :: Floating -> Floating Failed, modules loaded: none. I see that areaCircle :: Floating a => a -> a loads as expected. Why is the above version not acceptable?

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  • Step by Step / Deep explain: The Power of (Co)Yoneda (preferably in scala) through Coroutines

    - by Mzk
    some background code /** FunctorStr: ? F[-]. (? A B. (A -> B) -> F[A] -> F[B]) */ trait FunctorStr[F[_]] { self => def map[A, B](f: A => B): F[A] => F[B] } trait Yoneda[F[_], A] { yo => def apply[B](f: A => B): F[B] def run: F[A] = yo(x => x) def map[B](f: A => B): Yoneda[F, B] = new Yoneda[F, B] { def apply[X](g: B => X) = yo(f andThen g) } } object Yoneda { implicit def yonedafunctor[F[_]]: FunctorStr[({ type l[x] = Yoneda[F, x] })#l] = new FunctorStr[({ type l[x] = Yoneda[F, x] })#l] { def map[A, B](f: A => B): Yoneda[F, A] => Yoneda[F, B] = _ map f } def apply[F[_]: FunctorStr, X](x: F[X]): Yoneda[F, X] = new Yoneda[F, X] { def apply[Y](f: X => Y) = Functor[F].map(f) apply x } } trait Coyoneda[F[_], A] { co => type I def fi: F[I] def k: I => A final def map[B](f: A => B): Coyoneda.Aux[F, B, I] = Coyoneda(fi)(f compose k) } object Coyoneda { type Aux[F[_], A, B] = Coyoneda[F, A] { type I = B } def apply[F[_], B, A](x: F[B])(f: B => A): Aux[F, A, B] = new Coyoneda[F, A] { type I = B val fi = x val k = f } implicit def coyonedaFunctor[F[_]]: FunctorStr[({ type l[x] = Coyoneda[F, x] })#l] = new CoyonedaFunctor[F] {} trait CoyonedaFunctor[F[_]] extends FunctorStr[({type l[x] = Coyoneda[F, x]})#l] { override def map[A, B](f: A => B): Coyoneda[F, A] => Coyoneda[F, B] = x => apply(x.fi)(f compose x.k) } def liftCoyoneda[T[_], A](x: T[A]): Coyoneda[T, A] = apply(x)(a => a) } Now I thought I understood yoneda and coyoneda a bit just from the types – i.e. that they quantify / abstract over map fixed in some type constructor F and some type a, to any type B returning F[B] or (Co)Yoneda[F, B]. Thus providing map fusion for free (? is this kind of like a cut rule for map ?). But I see that Coyoneda is a functor for any type constructor F regardless of F being a Functor, and that I don't fully grasp. Now I'm in a situation where I'm trying to define a Coroutine type, (I'm looking at https://www.fpcomplete.com/school/to-infinity-and-beyond/pick-of-the-week/coroutines-for-streaming/part-2-coroutines for the types to get started with) case class Coroutine[S[_], M[_], R](resume: M[CoroutineState[S, M, R]]) sealed trait CoroutineState[S[_], M[_], R] object CoroutineState { case class Run[S[_], M[_], R](x: S[Coroutine[S, M, R]]) extends CoroutineState[S, M, R] case class Done[R](x: R) extends CoroutineState[Nothing, Nothing, R] class CoroutineStateFunctor[S[_], M[_]](F: FunctorStr[S]) extends FunctorStr[({ type l[x] = CoroutineState[S, M, x]})#l] { override def map[A, B](f : A => B) : CoroutineState[S, M, A] => CoroutineState[S, M, B] = { ??? } } } and I think that if I understood Coyoneda better I could leverage it to make S & M type constructors functors way easy, plus I see Coyoneda potentially playing a role in defining recursion schemes as the functor requirement is pervasive. So how could I use coyoneda to make type constructors functors like for example coroutine state? or something like a Pause functor ?

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  • mapping list of different types implementing same function?

    - by sisif
    I want to apply a function to every element in a list (map) but the elements may have different types but all implement the same function (here "putOut") like an interface. However I cannot create a list of this "interface" type (here "Outputable"). How do I map a list of different types implementing the same function? main :: IO () main = do map putOut lst putStrLn "end" where lst :: [Outputable] -- ERROR: Class "Outputable" used as a type lst = [(Out1 1),(Out2 1 2)] class Outputable a where putOut :: a -> IO () -- user defined: data Out1 = Out1 Int deriving (Show) data Out2 = Out2 Int deriving (Show) instance Outputable Out1 where putOut out1 = putStrLn $ show out1 instance Outputable Out2 where putOut out2 = putStrLn $ show out2 I cannot define it this way: data Out = Out1 Int | Out2 Int Int putOut Out1 = ... putOut Out2 = ... because this is a library and users should be able to extend Out with their own types

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  • Pattern matching for lambda expressions

    - by alphomega
    21 --Primitive recursion constructor 22 pr :: ([Int] -> Int) -> ([Int] -> Int) -> ([Int] -> Int) 23 pr f g = \xs 0 -> f xs 24 pr f g = \xs (y+1) -> g xs y ((pr f g) xs y) I want the function this function creates to act differently on different inputs, so that it can create a recursive function. As expected, the above code doesn't work. How do I do something like pattern matching, but for the function it creates? Thanks

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  • GADTs and Scrap your Boilerplate

    - by finnsson
    I'm writing a XML (de)serializer using Text.XML.Light and Scrap your Boilerplate (at http://github.com/finnsson/Text.XML.Generic) and so far I got working code for "normal" ADTs but I'm stuck at deserializing GADTs. I got the GADT data DataBox where DataBox :: (Show d, Eq d, Data d) => d -> DataBox and I'm trying to get this to compile instance Data DataBox where gfoldl k z (DataBox d) = z DataBox `k` d gunfold k z c = k (z DataBox) -- not OK toConstr (DataBox d) = toConstr d dataTypeOf (DataBox d) = dataTypeOf d but I can't figure out how to implement gunfold for DataBox. The error message is Text/XML/Generic.hs:274:23: Ambiguous type variable `b' in the constraints: `Eq b' arising from a use of `DataBox' at Text/XML/Generic.hs:274:23-29 `Show b' arising from a use of `DataBox' at Text/XML/Generic.hs:274:23-29 `Data b' arising from a use of `k' at Text/XML/Generic.hs:274:18-30 Probable fix: add a type signature that fixes these type variable(s) It's complaining about not being able to figure out the data type of b. I'm also trying to implement dataCast1 and dataCast2 but I think I can live without them (i.e. an incorrect implementation). I guess my questions are: Is it possible to combine GADTs with Scrap your Boilerplate? If so: how do you implement gunfold for a GADT?

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  • Why does s ++ t not lead to a stack overflow for large s?

    - by martingw
    I'm wondering why Prelude> head $ reverse $ [1..10000000] ++ [99] 99 does not lead to a stack overflow error. The ++ in the prelude seems straight forward and non-tail-recursive: (++) :: [a] -> [a] -> [a] (++) [] ys = ys (++) (x:xs) ys = x : xs ++ ys So just with this, it should run into a stack overflow, right? So I figure it probably has something to do with the ghc magic that follows the definition of ++: {-# RULES "++" [~1] forall xs ys. xs ++ ys = augment (\c n -> foldr c n xs) ys #-} Is that what helps avoiding the stack overflow? Could someone provide some hint for what's going on in this piece of code?

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  • Adding class constraints to typeclass instance

    - by BleuM937
    I'm trying to implement the Cantor Pairing Function, as an instance of a generic Pair typeclass, as so: module Pair (Pair, CantorPair) where -- Pair interface class Pair p where pi :: a -> a -> p a k :: p a -> a l :: p a -> a -- Wrapper for typing newtype CantorPair a = P { unP :: a } -- Assume two functions with signatures: cantorPair :: Integral a => a -> a -> CantorPair a cantorUnpair :: Integral a => CantorPair a -> (a, a) -- I need to somehow add an Integral a constraint to this instance, -- but I can't work out how to do it. instance Pair CantorPair where pi = cantorPair k = fst . cantorUnpair l = snd . cantorUnpair How can I add the appropriate Integral constraint to the instance? I have a vague feeling I might need to modify the Pair interface itself, but not sure how to go about this.

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  • Strange pattern matching with functions instancing Show

    - by Sean D
    So I'm writing a program which returns a procedure for some given arithmetic problem, so I wanted to instance a couple of functions to Show so that I can print the same expression I evaluate when I test. The trouble is that the given code matches (-) to the first line when it should fall to the second. {-# OPTIONS_GHC -XFlexibleInstances #-} instance Show (t -> t-> t) where show (+) = "plus" show (-) = "minus" main = print [(+),(-)] returns [plus,plus] Am I just committing a motal sin printing functions in the first place or is there some way I can get it to match properly? edit:I realise I am getting the following warning: Warning: Pattern match(es) are overlapped In the definition of `show': show - = ... I still don't know why it overlaps, or how to stop it.

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  • breadth-first traversal of directory tree is not lazy

    - by user855443
    I try to traverse the diretory tree. A naive depth-first traversal seems not to produce the data in a lazy fashion and runs out of memory. I next tried a breadth first approach, which shows the same problem - it uses all the memory available and then crashes. the code i have is: getFilePathBreadtFirst :: FilePath -> IO [FilePath] getFilePathBreadtFirst fp = do fileinfo <- getInfo fp res :: [FilePath] <- if isReadableDirectory fileinfo then do children <- getChildren fp lower <- mapM getFilePathBreadtFirst children return (children ++ concat lower) return (children ++ concat () else return [fp] -- should only return the files? return res getChildren :: FilePath -> IO [FilePath] getChildren path = do names <- getUsefulContents path let namesfull = map (path </>) names return namesfull testBF fn = do -- crashes for /home/frank, does not go to swap fps <- getFilePathBreadtFirst fn putStrLn $ unlines fps I think all the code is either linear or tail recursive, and I would expect that the listing of filenames starts immediately, but in fact it does not. Where is the error in my code and my thinking? where have I lost lazy evaluation?

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  • Are comonads a good fit for modeling the Wumpus world?

    - by Tim Stewart
    I'm trying to find some practical applications of a comonad and I thought I'd try to see if I could represent the classical Wumpus world as a comonad. I'd like to use this code to allow the Wumpus to move left and right through the world and clean up dirty tiles and avoid pits. It seems that the only comonad function that's useful is extract (to get the current tile) and that moving around and cleaning tiles would not use be able to make use of extend or duplicate. I'm not sure comonads are a good fit but I've seen a talk (Dominic Orchard: A Notation for Comonads) where comonads were used to model a cursor in a two-dimensional matrix. If a comonad is a good way of representing the Wumpus world, could you please show where my code is wrong? If it's wrong, could you please suggest a simple application of comonads? module Wumpus where -- Incomplete model of a world inhabited by a Wumpus who likes a nice -- tidy world but does not like falling in pits. import Control.Comonad -- The Wumpus world is made up of tiles that can be in one of three -- states. data Tile = Clean | Dirty | Pit deriving (Show, Eq) -- The Wumpus world is a one dimensional array partitioned into three -- values: the tiles to the left of the Wumpus, the tile occupied by -- the Wumpus, and the tiles to the right of the Wumpus. data World a = World [a] a [a] deriving (Show, Eq) -- Applies a function to every tile in the world instance Functor World where fmap f (World as b cs) = World (fmap f as) (f b) (fmap f cs) -- The Wumpus world is a Comonad instance Comonad World where -- get the part of the world the Wumpus currently occupies extract (World _ b _) = b -- not sure what this means in the Wumpus world. This type checks -- but does not make sense to me. extend f w@(World as b cs) = World (map world as) (f w) (map world cs) where world v = f (World [] v []) -- returns a world in which the Wumpus has either 1) moved one tile to -- the left or 2) stayed in the same place if the Wumpus could not move -- to the left. moveLeft :: World a -> World a moveLeft w@(World [] _ _) = w moveLeft (World as b cs) = World (init as) (last as) (b:cs) -- returns a world in which the Wumpus has either 1) moved one tile to -- the right or 2) stayed in the same place if the Wumpus could not move -- to the right. moveRight :: World a -> World a moveRight w@(World _ _ []) = w moveRight (World as b cs) = World (as ++ [b]) (head cs) (tail cs) initWorld = World [Dirty, Clean, Dirty] Dirty [Clean, Dirty, Pit] -- cleans the current tile cleanTile :: Tile -> Tile cleanTile Dirty = Clean cleanTile t = t Thanks!

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  • understanding syb boilerplate elimination

    - by Pradeep
    In the example given in http://web.archive.org/web/20080622204226/http://www.cs.vu.nl/boilerplate/ -- Increase salary by percentage increase :: Float -> Company -> Company increase k = everywhere (mkT (incS k)) -- "interesting" code for increase incS :: Float -> Salary -> Salary incS k (S s) = S (s * (1+k)) how come increase function compiles without binding anything for the first Company mentioned in its type signature. Is it something like assigning to a partial function? Why is it done like that?

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  • What is considered bleeding edge in programming these days?

    - by iestyn
    What is "bleeding edge" these days? has it all been done before us, and we are just discovering new ways of implementing mathematical constructs within programming? Functional Programming seems to be making inroads in all areas, but is this just marketing to create interest in a programming arena where it appears that the state of the art has climaxed too soon. have the sales men got hold of the script, and selling ideas that can be sold, dumbing down the future? I see very old ideas making their way into the market place....what are the truly new things that should be considered fresh and new in 2010 onwards, and not some 1960-1980 idea being refocused.

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  • Collecting IO outputs into list

    - by sisif
    how can i do multiple calls to SDL.pollEvent :: IO Event until the output is SDL.NoEvent and collect all the results into a list? in imperative terms something like this: events = [] event = SDL.pollEvent; while( event != SDL.NoEvent ) events.add( event ) event = SDL.pollEvent

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  • Strange type-related error

    - by vsb
    I wrote following program: isPrime x = and [x `mod` i /= 0 | i <- [2 .. truncate (sqrt x)]] primes = filter isPrime [1 .. ] it should construct list of prime numbers. But I got this error: [1 of 1] Compiling Main ( 7/main.hs, interpreted ) 7/main.hs:3:16: Ambiguous type variable `a' in the constraints: `Floating a' arising from a use of `isPrime' at 7/main.hs:3:16-22 `RealFrac a' arising from a use of `isPrime' at 7/main.hs:3:16-22 `Integral a' arising from a use of `isPrime' at 7/main.hs:3:16-22 Possible cause: the monomorphism restriction applied to the following: primes :: [a] (bound at 7/main.hs:3:0) Probable fix: give these definition(s) an explicit type signature or use -XNoMonomorphismRestriction Failed, modules loaded: none. If I specify signature for isPrime function explicitly: isPrime :: Integer -> Bool isPrime x = and [x `mod` i /= 0 | i <- [2 .. truncate (sqrt x)]] I can't even compile isPrime function: [1 of 1] Compiling Main ( 7/main.hs, interpreted ) 7/main.hs:2:45: No instance for (RealFrac Integer) arising from a use of `truncate' at 7/main.hs:2:45-61 Possible fix: add an instance declaration for (RealFrac Integer) In the expression: truncate (sqrt x) In the expression: [2 .. truncate (sqrt x)] In a stmt of a list comprehension: i <- [2 .. truncate (sqrt x)] 7/main.hs:2:55: No instance for (Floating Integer) arising from a use of `sqrt' at 7/main.hs:2:55-60 Possible fix: add an instance declaration for (Floating Integer) In the first argument of `truncate', namely `(sqrt x)' In the expression: truncate (sqrt x) In the expression: [2 .. truncate (sqrt x)] Failed, modules loaded: none. Can you help me understand, why am I getting these errors?

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  • Applying a function that may fail to all values in a list

    - by Egwor
    I want to apply a function f to a list of values, however function f might randomly fail (it is in effect making a call out to a service in the cloud). I thought I'd want to use something like map, but I want to apply the function to all elements in the list and afterwards, I want to know which ones failed and which were successful. Currently I am wrapping the response objects of the function f with an error pair which I could then effectively unzip afterwards i.e. something like g : (a->b) -> a -> [ b, errorBoolean] f : a-> b and then to run the code ... map g (xs) Is there a better way to do this? The other alternative approach was to iterate over the values in the array and then return a pair of arrays, one which listed the successful values and one which listed the failures. To me, this seems to be something that ought to be fairly common. Alternatively I could return some special value. What's the best practice in dealing with this??

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  • Nested Lambdas in wxHaskell Library

    - by kunkelwe
    I've been trying to figure out how I can make staticText elements resize to fit their contents with wxHaskell. From what I can tell, this is the default behavior in wxWidgets, but the wxHaskell wrapper specifically disables this behavior. However, the library code that creates new elements has me very confused. Can anyone provide an explanation for what this code does? staticText :: Window a -> [Prop (StaticText ())] -> IO (StaticText ()) staticText parent props = feed2 props 0 $ initialWindow $ \id rect -> initialText $ \txt -> \props flags -> do t <- staticTextCreate parent id txt rect flags {- (wxALIGN_LEFT + wxST_NO_AUTORESIZE) -} set t props return t I know that feed2 x y f = f x y, and that the type signature of initialWindow is initialWindow :: (Id -> Rect -> [Prop (Window w)] -> Style -> a) -> [Prop (Window w)] -> Style -> a and the signature of initialText is initialText :: Textual w => (String -> [Prop w] -> a) -> [Prop w] -> a but I just can't wrap my head around all the lambdas.

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