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--></style></head><body lang=EN-US link=blue vlink="#954F72"><div class=WordSection1><p class=MsoNormal><span style='font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-family:"Courier New"'>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:<o:p></o:p></span></p><p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo1'><![if !supportLists]><span style='font-family:Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span style='font-family:"Courier New"'>Implementing interface functions<o:p></o:p></span></p><p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo1'><![if !supportLists]><span style='font-family:Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span style='font-family:"Courier New"'>Defining non-trivial implementations, where constructor must be private, etc.<o:p></o:p></span></p><p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo1'><![if !supportLists]><span style='font-family:Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span style='font-family:"Courier New"'>Invoking an abstract superclass concrete instance method from within the subclass method definition<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-family:"Courier New"'>The latter appears not to be possible in Haskell. Is this true?<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-family:"Courier New"'>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 ‘^’.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Courier New"'>data Modp a = Modp a a deriving (Eq, Show)<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-family:"Courier New"'>mkModp p n | isPrime p = Modp p (n `mod` p)<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Courier New"'> | otherwise = error $ show p ++ " is not a prime"<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-family:"Courier New"'>instance Integral a => Num (Modp a) where<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Courier New"'> (Modp q n) + (Modp p m) | p==q = Modp p $ (n+m) `mod` p<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Courier New"'> | otherwise = error $ "unequal moduli"<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Courier New"'> (Modp p n) * (Modp q m) | p==q = Modp p $ (n*m) `mod` p<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Courier New"'> | otherwise = error $ "unequal moduli"<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Courier New"'> negate (Modp p n) = Modp p (p-n)<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Courier New"'> -- can't reuse base because ^ is impl. directly in prelude<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Courier New"'>{- (Modp p x) ^ n | n <= p = (Modp p x) `baseExp` n<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Courier New"'> | n1 == 0 = (Modp p x)<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Courier New"'> | n > p = x ^ n1<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Courier New"'> where baseExp = ^ in Num<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Courier New"'> n1 = n `mod` p<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Courier New"'>-}<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Courier New"'>instance Integral a => Fractional (Modp a) where<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Courier New"'> recip (Modp p n) = (Modp p n)^(p-2)<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-family:"Courier New"'>isPrime p = True -- stub<o:p></o:p></span></p></div></body></html>