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  • Unsure of how to get the right evaluation order

    - by Matt Fenwick
    I'm not sure what the difference between these two pieces of code is (with respect to x), but the first one completes: $ foldr (\x y -> if x == 4 then x else x + y) 0 [1,2 .. ] 10 and the second one doesn't (at least in GHCi): $ foldr (\x (y, n) -> if x == 4 then (x, n) else (x + y, n + 1)) (0, 0) [1,2 .. ] ....... What am I doing wrong that prevents the second example from completing when it hits x == 4, as in the first one? I've tried adding bang-patterns to both the x and to the x == 4 (inside a let) but neither seems to make a difference.

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  • Use QuickCheck by generating primes

    - by Dan
    Background For fun, I'm trying to write a property for quick-check that can test the basic idea behind cryptography with RSA. Choose two distinct primes, p and q. Let N = p*q e is some number relatively prime to (p-1)(q-1) (in practice, e is usually 3 for fast encoding) d is the modular inverse of e modulo (p-1)(q-1) For all x such that 1 < x < N, it is always true that (x^e)^d = x modulo N In other words, x is the "message", raising it to the eth power mod N is the act of "encoding" the message, and raising the encoded message to the dth power mod N is the act of "decoding" it. (The property is also trivially true for x = 1, a case which is its own encryption) Code Here are the methods I have coded up so far: import Test.QuickCheck -- modular exponentiation modExp :: Integral a => a -> a -> a -> a modExp y z n = modExp' (y `mod` n) z `mod` n where modExp' y z | z == 0 = 1 | even z = modExp (y*y) (z `div` 2) n | odd z = (modExp (y*y) (z `div` 2) n) * y -- relatively prime rPrime :: Integral a => a -> a -> Bool rPrime a b = gcd a b == 1 -- multiplicative inverse (modular) mInverse :: Integral a => a -> a -> a mInverse 1 _ = 1 mInverse x y = (n * y + 1) `div` x where n = x - mInverse (y `mod` x) x -- just a quick way to test for primality n `divides` x = x `mod` n == 0 primes = 2:filter isPrime [3..] isPrime x = null . filter (`divides` x) $ takeWhile (\y -> y*y <= x) primes -- the property prop_rsa (p,q,x) = isPrime p && isPrime q && p /= q && x > 1 && x < n && rPrime e t ==> x == (x `powModN` e) `powModN` d where e = 3 n = p*q t = (p-1)*(q-1) d = mInverse e t a `powModN` b = modExp a b n (Thanks, google and random blog, for the implementation of modular multiplicative inverse) Question The problem should be obvious: there are way too many conditions on the property to make it at all usable. Trying to invoke quickCheck prop_rsa in ghci made my terminal hang. So I've poked around the QuickCheck manual a bit, and it says: Properties may take the form forAll <generator> $ \<pattern> -> <property> How do I make a <generator> for prime numbers? Or with the other constraints, so that quickCheck doesn't have to sift through a bunch of failed conditions? Any other general advice (especially regarding QuickCheck) is welcome.

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  • Binding type variables that only occur in assertions

    - by Giuseppe Maggiore
    Hi! I find it extremely difficult to describe my problem, so here goes nothing: I have a bunch of assertions on the type of a function. These assertions rely on a type variable that is not used for any parameter of the function, but is only used for internal bindings. Whenever I use this function it does not compile because, of course, the compiler has no information from which to guess what type to bind my type variable. Here is the code: {-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies, FlexibleInstances, UndecidableInstances, FlexibleContexts, EmptyDataDecls, ScopedTypeVariables, TypeOperators, TypeSynonymInstances #-} class C a a' where convert :: a -> a' class F a b where apply :: a -> b class S s a where select :: s -> a data CInt = CInt Int instance S (Int,String) Int where select (i,_) = i instance F Int CInt where apply = CInt f :: forall s a b . (S s a, F a b) => s -> b f s = let v = select s :: a y = apply v :: b in y x :: Int x = f (10,"Pippo") And here is the generated error: FunctorsProblems.hs:21:4: No instances for (F a Int, S (t, [Char]) a) arising from a use of `f' at FunctorsProblems.hs:21:4-17 Possible fix: add an instance declaration for (F a Int, S (t, [Char]) a) In the expression: f (10, "Pippo") In the definition of `x': x = f (10, "Pippo") Failed, modules loaded: none. Prelude>

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  • Asymptotic runtime of list-to-tree function

    - by Deestan
    I have a merge function which takes time O(log n) to combine two trees into one, and a listToTree function which converts an initial list of elements to singleton trees and repeatedly calls merge on each successive pair of trees until only one tree remains. Function signatures and relevant implementations are as follows: merge :: Tree a -> Tree a -> Tree a --// O(log n) where n is size of input trees singleton :: a -> Tree a --// O(1) empty :: Tree a --// O(1) listToTree :: [a] -> Tree a --// Supposedly O(n) listToTree = listToTreeR . (map singleton) listToTreeR :: [Tree a] -> Tree a listToTreeR [] = empty listToTreeR (x:[]) = x listToTreeR xs = listToTreeR (mergePairs xs) mergePairs :: [Tree a] -> [Tree a] mergePairs [] = [] mergePairs (x:[]) = [x] mergePairs (x:y:xs) = merge x y : mergePairs xs This is a slightly simplified version of exercise 3.3 in Purely Functional Data Structures by Chris Okasaki. According to the exercise, I shall now show that listToTree takes O(n) time. Which I can't. :-( There are trivially ceil(log n) recursive calls to listToTreeR, meaning ceil(log n) calls to mergePairs. The running time of mergePairs is dependent on the length of the list, and the sizes of the trees. The length of the list is 2^h-1, and the sizes of the trees are log(n/(2^h)), where h=log n is the first recursive step, and h=1 is the last recursive step. Each call to mergePairs thus takes time (2^h-1) * log(n/(2^h)) I'm having trouble taking this analysis any further. Can anyone give me a hint in the right direction?

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  • When should I use $ (and can it always be replaced with parentheses)?

    - by J Cooper
    From what I'm reading, $ is described as "applies a function to its arguments." However, it doesn't seem to work quite like (apply ...) in Lisp, because it's a binary operator, so really the only thing it looks like it does is help to avoid parentheses sometimes, like foo $ bar quux instead of foo (bar quux). Am I understanding it right? Is the latter form considered "bad style"?

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  • Why this Either-monad code does not type check?

    - by pf_miles
    instance Monad (Either a) where return = Left fail = Right Left x >>= f = f x Right x >>= _ = Right x this code frag in 'baby.hs' caused the horrible compilation error: Prelude> :l baby [1 of 1] Compiling Main ( baby.hs, interpreted ) baby.hs:2:18: Couldn't match expected type `a1' against inferred type `a' `a1' is a rigid type variable bound by the type signature for `return' at <no location info> `a' is a rigid type variable bound by the instance declaration at baby.hs:1:23 In the expression: Left In the definition of `return': return = Left In the instance declaration for `Monad (Either a)' baby.hs:3:16: Couldn't match expected type `[Char]' against inferred type `a1' `a1' is a rigid type variable bound by the type signature for `fail' at <no location info> Expected type: String Inferred type: a1 In the expression: Right In the definition of `fail': fail = Right baby.hs:4:26: Couldn't match expected type `a1' against inferred type `a' `a1' is a rigid type variable bound by the type signature for `>>=' at <no location info> `a' is a rigid type variable bound by the instance declaration at baby.hs:1:23 In the first argument of `f', namely `x' In the expression: f x In the definition of `>>=': Left x >>= f = f x baby.hs:5:31: Couldn't match expected type `b' against inferred type `a' `b' is a rigid type variable bound by the type signature for `>>=' at <no location info> `a' is a rigid type variable bound by the instance declaration at baby.hs:1:23 In the first argument of `Right', namely `x' In the expression: Right x In the definition of `>>=': Right x >>= _ = Right x Failed, modules loaded: none. why this happen? and how could I make this code compile ? thanks for any help~

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  • Complete Haskore example

    - by Bill
    Does anyone know of a complete Haskore example that will take a small example and output a MIDI file? I'm looking for a starting point to start using Haskore and Google isn't turning up much. Thanks!

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  • Is do-notation specific to "base:GHC.Base.Monad"?

    - by yairchu
    The idea that the standard Monad class is flawed and that it should actually extend Functor or Pointed is floating around. I'm not necessarily claiming that it is the right thing to do, but suppose that one was trying to do it: import Prelude hiding (Monad(..)) class Functor m => Monad m where return :: a -> m a join :: m (m a) -> m a join = (>>= id) (>>=) :: m a -> (a -> m b) -> m b a >>= t = join (fmap t a) (>>) :: m a -> m b -> m b a >> b = a >>= const b So far so good, but then when trying to use do-notation: whileM :: Monad m => m Bool -> m () whileM iteration = do done <- iteration if done then return () else whileM iteration The compiler complains: Could not deduce (base:GHC.Base.Monad m) from the context (Monad m) Question: Does do-notation work only for base:GHC.Base.Monad? Is there a way to make it work with an alternative Monad class? Extra context: What I really want to do is replace base:Control.Arrow.Arrow with a "generalized" Arrow class: {-# LANGUAGE TypeFamilies #-} class Category a => Arrow a where type Pair a :: * -> * -> * arr :: (b -> c) -> a b c first :: a b c -> a (Pair a b d) (Pair a c d) second :: a b c -> a (Pair a d b) (Pair a d c) (***) :: a b c -> a b' c' -> a (Pair a b b') (Pair a c c') (&&&) :: a b c -> a b c' -> a b (Pair a c c') And then use the Arrow's proc-notation with my Arrow class, but that fails like in the example above of do-notation and Monad. I'll use mostly Either as my pair type constructor and not the (,) type constructor as with the current Arrow class. This might allow to make the code of my toy RTS game (cabal install DefendTheKind) much prettier.

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  • Better exception for non-exhaustive patterns in case

    - by toofarsideways
    Is there a way to get GHCi to produce better exception messages when it finds at runtime that a call has produced value that does not match the function's pattern matching? It currently gives the line numbers of the function which produced the non-exhaustive pattern match which though helpful at times does require a round of debugging which at times I feel is doing the same set of things over and over. So before I tried to put together a solution I wanted to see if something else exists. An exception message that in addition to giving the line numbers shows what kind of call it attempted to make? Is this even possible?

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  • Nested parsers in happy / infinite loop?

    - by McManiaC
    I'm trying to write a parser for a simple markup language with happy. Currently, I'm having some issues with infinit loops and nested elements. My markup language basicly consists of two elements, one for "normal" text and one for bold/emphasized text. data Markup = MarkupText String | MarkupEmph [Markup] For example, a text like Foo *bar* should get parsed as [MarkupText "Foo ", MarkupEmph [MarkupText "bar"]]. Lexing of that example works fine, but the parsing it results in an infinite loop - and I can't see why. This is my current approach: -- The main parser: Parsing a list of "Markup" Markups :: { [Markup] } : Markups Markup { $1 ++ [$2] } | Markup { [$1] } -- One single markup element Markup :: { Markup } : '*' Markups1 '*' { MarkupEmph $2 } | Markup1 { $1 } -- The nested list inside *..* Markups1 :: { [Markup] } : Markups1 Markup1 { $1 ++ [$2] } | Markup1 { [$1] } -- Markup which is always available: Markup1 :: { Markup } : String { MarkupText $1 } What's wrong with that approach? How could the be resolved? Update: Sorry. Lexing wasn't working as expected. The infinit loop was inside the lexer. Sorry. :) Update 2: On request, I'm using this as lexer: lexer :: String -> [Token] lexer [] = [] lexer str@(c:cs) | c == '*' = TokenSymbol "*" : lexer cs -- ...more rules... | otherwise = TokenString val : lexer rest where (val, rest) = span isValidChar str isValidChar = (/= '*') The infinit recursion occured because I had lexer str instead of lexer cs in that first rule for '*'. Didn't see it because my actual code was a bit more complex. :)

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  • Weird cabal error: "inappropriate type"

    - by Bill
    ~ % cabal install --reinstall time Resolving dependencies... [1 of 1] Compiling Main ( /var/folders/0D/0D3du+YyGzuRETgUJZ5m8U+++TI/-Tmp-/time-1.2.0.251774/time-1.2.0.2/Setup.hs, /var/folders/0D/0D3du+YyGzuRETgUJZ5m8U+++TI/-Tmp-/time-1.2.0.251774/time-1.2.0.2/dist/setup/Main.o ) Linking /var/folders/0D/0D3du+YyGzuRETgUJZ5m8U+++TI/-Tmp-/time-1.2.0.251774/time-1.2.0.2/dist/setup/setup ... Configuring time-1.2.0.2... setup: dist/setup-config51799.tmp: inappropriate type cabal: Error: some packages failed to install: time-1.2.0.2 failed during the configure step. The exception was: ExitFailure 1 ~ % Has anyone seen this before?

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  • How to redirect within a monad in Yesod?

    - by Squazic
    I'm currently using the fb package to write a Yesod app that takes data from Facebook. In my Handler, I've managed to get the first step of the authentication to work, but I need to redirect to the url that getUserAccessTokenStep1 returns, which I've defined as fbRedirUrl. I'm having trouble with all the monad wrapping and type checking to make sure I can redirect to this url. getAccessTokenR :: Handler RepHtml getAccessTokenR = do withManager $ \manager -> do FB.runFacebookT creds manager $ do fbRedirUrl <- FB.getUserAccessTokenStep1 redirUrl [] liftIO $ print fbRedirUrl

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  • Kernighan & Ritchie word count example program in a functional language

    - by Frank
    I have been reading a little bit about functional programming on the web lately and I think I got a basic idea about the concepts behind it. I'm curious how everyday programming problems which involve some kind of state are solved in a pure functional programing language. For example: how would the word count program from the book 'The C programming Language' be implemented in a pure functional language? Any contributions are welcome as long as the solution is in a pure functional style. Here's the word count C code from the book: #include <stdio.h> #define IN 1 /* inside a word */ #define OUT 0 /* outside a word */ /* count lines, words, and characters in input */ main() { int c, nl, nw, nc, state; state = OUT; nl = nw = nc = 0; while ((c = getchar()) != EOF) { ++nc; if (c == '\n') ++nl; if (c == ' ' || c == '\n' || c = '\t') state = OUT; else if (state == OUT) { state = IN; ++nw; } } printf("%d %d %d\n", nl, nw, nc); }

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  • Are monads Writer m and Either e categorically dual?

    - by sdcvvc
    I noticed there is a dual relation between Writer m and Either e monads. If m is a monoid, then unit :: () -> m join :: (m,m) -> m can be used to form a monad: return is composition: a -> ((),a) -> (m,a) join is composition: (m,(m,a)) -> ((m,m),a) -> (m,a) The dual of () is Void (empty type), the dual of product is coproduct. Every type e can be given "comonoid" structure: unit :: Void -> e join :: Either e e -> e in the obvious way. Now, return is composition: a -> Either Void a -> Either e a join is composition: Either e (Either e a) -> Either (Either e e) a -> Either e a and this is the Either e monad. The arrows follow exactly the same pattern. Question: Is it possible to write a single generic code that will be able to perform both as Either e and as Writer m depending on the monoid given?

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  • Applying a function to an arbitrarily long list of arguments

    - by alphomega
    I want to create a function apply that takes a function with an arbitrary amount of arguments as well as a list of integers, and returns the result of the function (Where each integer in the list is an argument in order. I was thinking something like: apply :: ([Int] -> Int) -> [Int] -> Int apply f x:xs = apply (f x) xs apply f [] = f But I know this won't work because the type signature is wrong - the function doesn't take a list of ints, it just takes some amount of int arguments. Additionally, when I get to the base case the f argument to apply should actually be an integer, violating the type signature anyway. Does anyone know how to deal with this sort of problem?

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  • Safe and polymorphic toEnum

    - by jetxee
    I'd like to write a safe version of toEnum: safeToEnum :: (Enum t, Bounded t) => Int -> Maybe t A naive implementation: safeToEnum :: (Enum t, Bounded t) => Int -> Maybe t safeToEnum i = if (i >= fromEnum (minBound :: t)) && (i <= fromEnum (maxBound :: t)) then Just . toEnum $ i else Nothing main = do print $ (safeToEnum 1 :: Maybe Bool) print $ (safeToEnum 2 :: Maybe Bool) And it doesn't work: safeToEnum.hs:3:21: Could not deduce (Bounded t1) from the context () arising from a use of `minBound' at safeToEnum.hs:3:21-28 Possible fix: add (Bounded t1) to the context of an expression type signature In the first argument of `fromEnum', namely `(minBound :: t)' In the second argument of `(>=)', namely `fromEnum (minBound :: t)' In the first argument of `(&&)', namely `(i >= fromEnum (minBound :: t))' safeToEnum.hs:3:56: Could not deduce (Bounded t1) from the context () arising from a use of `maxBound' at safeToEnum.hs:3:56-63 Possible fix: add (Bounded t1) to the context of an expression type signature In the first argument of `fromEnum', namely `(maxBound :: t)' In the second argument of `(<=)', namely `fromEnum (maxBound :: t)' In the second argument of `(&&)', namely `(i <= fromEnum (maxBound :: t))' As well as I understand the message, the compiler does not recognize that minBound and maxBound should produce exactly the same type as in the result type of safeToEnum inspite of the explicit type declaration (:: t). Any idea how to fix it?

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  • problem with Double and Rational Number

    - by altair211
    Hi, I am writing a function in which I need to read a string contains floating point number and turn it back to Rational. But When I do toRational (read input :: Double), it will not turn for eg: 0.9 into 9 % 10 as expected, but instead 81..... % 9007... Thx

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  • Using MonadPlus in FRP.Reactive.FieldTrip

    - by ony
    I'm studying FRP at this moment through FieldTrip adaptor. And hit the problem with strange way of frames scheduling and integration. So now I'm trying to build own marker Event for aligning Behaviour stepping. So... flipflop :: Behavior String flipflop = stepper "none" (xflip 2) where xflip t0 = do t <- withTimeE_ (atTime t0) return "flip" `mplus` xflop (t+3) xflop t0 = do t <- withTimeE_ (atTime t0) return "flop" `mplus` xflip (t+2) txtGeom = ((uscale2 (0.5::Float) *%) . utext . show <$>) main = anim2 (txtGeom . pure flipflop) Questions is: Why this example leads to memory leak? Is there safe way to build sequence of events where each next one is scheduled depending on previous?

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  • Existentials 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 existentials. I got the existential data type 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 existentials with Scrap your Boilerplate? If so: how do you implement gunfold for an existential data type?

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  • How do I use multiple where clauses in GHCi?

    - by T.R.
    I'm playing around with GHCi for the first time, and I'm having some trouble writing multi-line functions. My code is as follows: Prelude> :{ Prelude| let diffSquares lst = abs $ squareOfSums lst - sumOfSquares lst Prelude| where Prelude| squareOfSums lst = (fst (sumsAndSquares lst))^2 Prelude| sumOfSquares lst = snd (sumsAndSquares lst) Prelude| sumsAndSquares = foldl (\(sms,sqrs) x -> (sms+x,sqrs+x^2)) (0,0) Prelude| :} It gives the following error: <interactive>:1:142: parse error on input `=' Could someone kindly point me in the direction of what I'm missing?

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  • Program to find the result of primitive recursive functions

    - by alphomega
    I'm writing a program to solve the result of primitive recursive functions: 1 --Basic functions------------------------------ 2 3 --Zero function 4 z :: Int -> Int 5 z = \_ -> 0 6 7 --Successor function 8 s :: Int -> Int 9 s = \x -> (x + 1) 10 11 --Identity/Projection function generator 12 idnm :: Int -> Int -> ([Int] -> Int) 13 idnm n m = \(x:xs) -> ((x:xs) !! (m-1)) 14 15 --Constructors-------------------------------- 16 17 --Composition constructor 18 cn :: ([Int] -> Int) -> [([Int] -> Int)] -> ([Int] -> Int) 19 cn f [] = \(x:xs) -> f 20 cn f (g:gs) = \(x:xs) -> (cn (f (g (x:xs))) gs) these functions and constructors are defined here: http://en.wikipedia.org/wiki/Primitive_recursive_function The issue is with my attempt to create the compositon constructor, cn. When it gets to the base case, f is no longer a partial application, but a result of the function. Yet the function expects a function as the first argument. How can I deal with this problem? Thanks.

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  • Which is your favorite "hidden gem" package on Hackage?

    - by finnsson
    There are a lot of packages on Hackage, some well known (such as HUnit) and some less known (such as AspectAG). I'm wondering which package you think is a hidden gem that deserves more users. Maybe a useful data structure, helpers for monads, networking, test, ...? Which is your favorite "hidden gem" package on Hackage?

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  • What is being passed in?

    - by Delirium tremens
    In the code: oneChar :: Char -> Doc oneChar c = case lookup c simpleEscapes of Just r -> text r Nothing | mustEscape c -> hexEscape c | otherwise -> char c where mustEscape c = c < ' ' || c == '\x7f' || c > '\xff' simpleEscapes :: [(Char, String)] simpleEscapes = zipWith ch "\b\n\f\r\t\\\"/" "bnfrt\\\"/" where ch a b = (a, ['\\',b]) r isn't being passed to oneChar. Where does r come from?

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