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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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  • Is there a good way to QuickCheck Happstack.State methods?

    - by Paul Kuliniewicz
    I have a set of Happstack.State MACID methods that I want to test using QuickCheck, but I'm having trouble figuring out the most elegant way to accomplish that. The problems I'm running into are: The only way to evaluate an Ev monad computation is in the IO monad via query or update. There's no way to create a purely in-memory MACID store; this is by design. Therefore, running things in the IO monad means there are temporary files to clean up after each test. There's no way to initialize a new MACID store except with the initialValue for the state; it can't be generated via Arbitrary unless I expose an access method that replaces the state wholesale. Working around all of the above means writing methods that only use features of MonadReader or MonadState (and running the test inside Reader or State instead of Ev. This means forgoing the use of getRandom or getEventClockTime and the like inside the method definitions. The only options I can see are: Run the methods in a throw-away on-disk MACID store, cleaning up after each test and settling for starting from initialValue each time. Write the methods to have most of the code run in a MonadReader or MonadState (which is more easily testable), and rely on a small amount of non-QuickCheck-able glue around it that calls getRandom or getEventClockTime as necessary. Is there a better solution that I'm overlooking?

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  • How are design-by-contract and property-based testing (QuickCheck) related?

    - by Todd Owen
    Is their only similarity the fact that they are not xUnit (or more precisely, not based on enumerating specific test cases), or is it deeper than that? Property-based testing (using QuickCheck, ScalaCheck, etc) seem well-suited to a functional programming style where side-effects are avoided. On the other hand, Design by Contract (as implemented in Eiffel) is more suited to OOP languages: you can express post-conditions about the effects of methods, not just their return values. But both of them involve testing assertions that are true in general (rather than assertions that should be true for a specific test case). And both can be tested using randomly generated inputs (with QuickCheck this is the only way, whereas with Eiffel I believe it is an optional feature of the AutoTest tool). Is there an umbrella term to encompass both approaches? Or am I imagining a relationship that doesn't really exist.

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  • F# in ASP.NET, mathematics and testing

    - by DigiMortal
    Starting from Visual Studio 2010 F# is full member of .NET Framework languages family. It is functional language with syntax specific to functional languages but I think it is time for us also notice and study functional languages. In this posting I will show you some examples about cool things other people have done using F#. F# and ASP.NET As I am ASP/ASP.NET MVP I am – of course – interested in how people use different languages and technologies with ASP.NET. C# MVP Tomáš Petrícek writes about developing ASP.NET MVC applications using F#. He also shows how to use LINQ To SQL in F# (using F# PowerPack) and provides sample solution and Visual Studio 2010 template for F# MVC web applications. You may also find interesting how you can create controllers in F#. Excellent work, Tomáš! Vladimir Matveev has interesting example about how to use F# and ApplicationHost class to process ASP.NET requests ouside of IIS. This is simple and very straight-forward example and I strongly suggest you to take a look at it. Very cool example is project Strom in Codeplex. Storm is web services testing tool that is fully written on F#. Take a look at this site because Codeplex offers also source code besides binaries. Math Functional languages are strong in fields like mathematics and physics. When I wrote my C# example about BigInteger class I found out that recursive version of Fibonacci algorithm in C# is not performing well. In same time I made same experiment on F# and in F# there were no performance problems with recursive version. You can find F# version of Fibonacci algorithm from Bob Palmer’s blog posting Fibonacci numbers in F#. Although golden spiral is useful for solving many problems I looked for some practical code example and found one. Kean Walmsley published in his Through the Interface blog very interesting posting Creating Fibonacci spirals in AutoCAD using F#. There are also other cool examples you may be interested in. Using numerical components by Extreme Optimization  it is possible to make some numerical integration (quadrature method) using F# (also C# example is available). fsharp.it introduces factorials calculation on F#. Robert Pickering has made very good work on programming The Game of Life in Silverlight and F# – I definitely suggest you to try out this example as it is very illustrative too. Who wants something more complex may take a look at Newton basin fractal example in F# by Jonathan Birge. Testing After some searching and surfing I found out that there is almost everything available for F# to write tests and test your F# code. FsCheck - FsCheck is a port of Haskell's QuickCheck. Important parts of the manual for using FsCheck is almost literally "adapted" from the QuickCheck manual and paper. Any errors and omissions are entirely my responsibility. FsTest - This project is designed to Language Oriented Programming constructs around unit testing and behavior testing in F#. The goal of this project is to create a Domain Specific Language for testing F# code in a way that makes sense for functional programming. FsUnit - FsUnit makes unit-testing with F# more enjoyable. It adds a special syntax to your favorite .NET testing framework. xUnit.NET - xUnit.net is a developer testing framework, built to support Test Driven Development, with a design goal of extreme simplicity and alignment with framework features. It is compatible with .NET Framework 2.0 and later, and offers several runners: console, GUI, MSBuild, and Visual Studio integration via TestDriven.net, CodeRush Test Runner and Resharper. It also offers test project integration for ASP.NET MVC. Getting started Well, as a first thing you need Visual Studio 2010. Then take a look at these resources: F# samples @ MSDN Microsoft F# Developer Center @ MSDN F# Language Reference @ MSDN F# blog F# forums Real World Functional Programming: With Examples in F# and C# (Amazon) Happy F#-ing! :)

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  • What are best practices for managing related Cabal packages?

    - by Norman Ramsey
    I'm working on a dataflow-based optimization library written in Haskell. It now seems likely that the library is going to have to be split into two pieces: A core piece with minimal build dependencies; call it hoopl-core. A full piece, call it hoopl, which may have extra dependencies on packages like a prettyprinter, QuickCheck, and so on. The idea is that the Glasgow Haskell Compiler will depend only on hoopl-core, so that it won't be too difficult to bootstrap the compiler. Other compilers will get the extra goodies in hoopl. Package hoopl will depend on hoopl-core. The Debian package tools can build multiple packages from a single source tree. Unfortunately Cabal has not yet reached that level of sophistication. But there must be other library or application designers out there who have similar issues (e.g., one package for a core library, another for a command-line interface, another for a GUI interface). What are current best practices for building and managing multiple related Haskell packages using Cabal?

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  • Yet another Haskell vs. Scala question

    - by Travis Brown
    I've been using Haskell for several months, and I love it—it's gradually become my tool of choice for everything from one-off file renaming scripts to larger XML processing programs. I'm definitely still a beginner, but I'm starting to feel comfortable with the language and the basics of the theory behind it. I'm a lowly graduate student in the humanities, so I'm not under a lot of institutional or administrative pressure to use specific tools for my work. It would be convenient for me in many ways, however, to switch to Scala (or Clojure). Most of the NLP and machine learning libraries that I work with on a daily basis (and that I've written in the past) are Java-based, and the primary project I'm working for uses a Java application server. I've been mostly disappointed by my initial interactions with Scala. Many aspects of the syntax (partial application, for example) still feel clunky to me compared to Haskell, and I miss libraries like Parsec and HXT and QuickCheck. I'm familiar with the advantages of the JVM platform, so practical questions like this one don't really help me. What I'm looking for is a motivational argument for moving to Scala. What does it do (that Haskell doesn't) that's really cool? What makes it fun or challenging or life-changing? Why should I get excited about writing it?

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