As a ‘hello world’ example for type definitions, I like to define a numeric type that can handle the mod p multiplicative group, where p is prime. This requires: · Implementing interface functions · Defining non-trivial implementations, where constructor must be private, etc. · Invoking an abstract superclass concrete instance method from within the subclass method definition The latter appears not to be possible in Haskell. Is this true? Here’s the basic code, but I punted on x^n. It looks like I’d have to paste in the entire original definition of ‘^’. data Modp a = Modp a a deriving (Eq, Show) mkModp p n | isPrime p = Modp p (n `mod` p) | otherwise = error $ show p ++ " is not a prime" instance Integral a => Num (Modp a) where (Modp q n) + (Modp p m) | p==q = Modp p $ (n+m) `mod` p | otherwise = error $ "unequal moduli" (Modp p n) * (Modp q m) | p==q = Modp p $ (n*m) `mod` p | otherwise = error $ "unequal moduli" negate (Modp p n) = Modp p (p-n) -- can't reuse base because ^ is impl. directly in prelude {- (Modp p x) ^ n | n <= p = (Modp p x) `baseExp` n | n1 == 0 = (Modp p x) | n > p = x ^ n1 where baseExp = ^ in Num n1 = n `mod` p -} instance Integral a => Fractional (Modp a) where recip (Modp p n) = (Modp p n)^(p-2) isPrime p = True -- stub _______________________________________________ Beginners mailing list [hidden email] http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners |
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From: [hidden email] <[hidden email]> Date: 3 January 2016 at 07:55:53 > As a ‘hello world’ example for type definitions, I like to define a numeric type that can > handle the mod p multiplicative group, where p is prime. This requires: > • Implementing interface functions […] I can’t help with the question you’re asking, but I have a minor nitpick: You want to have negate (Modp p 0) = Modp p 0, and not Modp p p as in your current implementation. – Harald _______________________________________________ Beginners mailing list [hidden email] http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners |
(^) is _not_ a method of Num, it is simply a function with a Num constraint. It will work on your new numbers as well as it would on any other that implements (*) correctly, you don't need to rewrite it. By the way, your functions are dangerously partial, it would seem useful to put the prime into the type so that you can't add or multiply different Mod p. Of course this demands a bit more knowledge of Haskell type system than is likely in a beginner, but if you're motivated, I encourage you to look at numbers in type (see GHC.TypeLits maybe).-- Le dim. 3 janv. 2016 à 14:07, Harald Hanche-Olsen <[hidden email]> a écrit : -----Original Message----- _______________________________________________ Beginners mailing list [hidden email] http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners |
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